mm-67 === Yes, you are right. I was misguided by the fact that 1) holds true foralternating groups, Mathieu groups and the Monster. But SL(4,4) is acounterexample, as calculations in GAP show. === > Let S be a ?ite nonabelian simple group, and C an arbitrary> conjugacy class of elements in S, i.e. C={g*x*g^{-1} | g in S} for> some x in S.> Consider the set C^2 = { a*b | a,b in C }.> 1. How one can prove that C lies in C^2?> it could be hard to prove 1, seeing as it's false. or have i misread it?Can you give your expected counterexample? === >> Let S be a ?ite nonabelian simple group, and C an arbitrary >> conjugacy class of elements in S, i.e. C={g*x*g^{-1} | g in S} >> for some x in S.>> Consider the set C^2 = { a*b | a,b in C }. >> 1. How one can prove that C lies in C^2?>> 2. What is known about the minimal number N such that C^N = S for >> all classes C in S? Does it have any nice asymptotics for the >> series of alternating groups A_n? The same question for other >> series of ?ite simple nonabelian groups.>it could be hard to prove 1, seeing as it's false. >or have i misread it?What's your counterexample? I found onebut then, I noticed S had to be simple.- === >> Let S be a ?ite nonabelian simple group, and C an arbitrary>> conjugacy class of elements in S, i.e. C={g*x*g^{-1} | g in S}>> for some x in S.>> Consider the set C^2 = { a*b | a,b in C }.>> 1. How one can prove that C lies in C^2?>> 2. What is known about the minimal number N such that C^N = S for>> all classes C in S? Does it have any nice asymptotics for the>> series of alternating groups A_n? The same question for other>> series of ?ite simple nonabelian groups.>>it could be hard to prove 1, seeing as it's false.>or have i misread it?> What's your counterexample? I found one> but then, I noticed S had to be simple.> -told you i could misread it - my thoughts were using non-simple groups(obviously just contemplating cycle types in Sn gives you the ?counterexample') === Two papers have been published: the ?st in the journal Geometry and Topology and the second inVolume 4 of the Monograph series (Invariants of knots and 3-manifolds(Kyoto 2001))Paper 1 === ===URL:http://www.maths.warwick.ac.uk/gt/GTVol7/paper23. abs.htmlTitle:Geometric deformations of immersed surfaces in non-positively curved manifolds Author(s):Valery Marenich Abstract:Let a total space N^4 of some two-dimensional vector bundle nu over aclosed surface Sigma of genus >1 admits a complete metric ofnon-positive sectional curvature. Assume also that the Eulercharacteristic of this bundle is not zero. We prove that there existsa smooth regular deformation of the zero section of the bundle into aminimal branched immersion with the Willmore functional tending tozero. As a consequence we obtain for the hyperbolic N^4 the Milnortype inequality between the Euler characteristics of nu and Sigmaconjectured by Gromov, Lawson and Thurston.AMS Classi?ation Numbers. Primary: 53C44Secondary: 53C20, 53C21Keywords:Heat-?ean curvature ?egular homotopy, conformal structure, minimal branch immersion, characteristic numbers Received: 27 December 2002Proposed: Simon DonaldsonSeconded: Tomasz Mrowka, Yasha EliashbergAuthor(s) address(es):The University of Kalmar, 391 82, Kalmar, SwedenPaper 2 === ===Geometry and Topology Monographs, Volume 4 (2002)Invariants of knots and 3-manifolds (Kyoto 2001)Paper no. 21, pages 313--335URL:http://www.maths.warwick.ac.uk/gt/GTMon4/paper21. abs.htmlTitle:Skein module deformations of elementary moves on linksAuthor(s):Jozef H PrzytyckiAbstract:This paper is based on my talks (`Skein modules with a cubic skeinrelation: properties and speculations' and `Symplectic structure oncolorings, Lagrangian tangles and its applications') given in Kyoto(RIMS), September 11 and September 18 respectively, 2001. The ?stthree sections closely follow the talks: starting from elementarymoves on links and ending on applications to unknotting numbermotivated by a skein module deformation of a 3-move. The theory ofskein modules is outlined in the problem section of theseproceedings. In the ?st section we make the point that despite its long history,knot theory has many elementary problems that are still open. Wediscuss several of them starting from the Nakanishi's 4-moveconjecture. In the second section we introduce the idea of Lagrangiantangles and we show how to apply them to elementary moves and torotors. In the third section we apply (2,2)-moves and a skein moduledeformation of a 3-move to approximate unknotting numbers of knots. Inthe fourth section we introduce the Burnside groups of links and usethese invariants to resolve several problems stated in section 1.AMS Classi?ation Numbers. Primary: 57M27Secondary: 20D99Keywords:Knot, link, skein module, $n$-move, rational move, algebraic tangle,Lagrangian tangle, rotor, unknotting number, Fox coloring, Burnsidegroup, branched coverReceived: 8 November 2002Author(s) address(es):Department of Mathematics, George Washington University Washington, DC 20052, USA === >Is there a simple proof that the number of nilpotent nXn matrices over>the ?ite ?ld GF(q) is q^(n^2-n) ?The earliest paper in MathSciNet whose review containsnilpotent matrices and ?ite ?ld seems to answer your question:MR0130875 (24 #A729) Gerstenhaber, Murray:On the number of nilpotent matrices with coef?ients in a ?ite ?ld.Illinois J. Math., Vol.5 (1961), 330--333.P.Fong's review, stripped of extraneous TeX-ese, reads: Let GF(q) be the Galois ?ld of q elements, and let GF(q)_n be the vector space of all n-by-n matrices with coef?ients in GF(q). Fine and Herstein [same J. Vol.2 (1958), 499--504; MR 20 #3160] have shown that the number of nilpotent matrices in GF(q)_n is q^(n^2-n). Let N be the n-by-n matrix with zeros everywhere except for ones on the ?st diagonal above the main diagonal. For any nilpotent matrix A in GF(q)_n, let L(A) be the linear subspace of all matrices Y such that NY=YA. The possible matrices Y which can arise are then characterized, and a counting in two ways of the pairs (Y,A), where $A$ is nilpotent and where NY=YA, together with an induction hypothesis, yields the theorem. The Fine-Herstein theorem is then used in giving another proof of a result of Reiner [ibid. Vol.5 (1961), 324--329] on the number of matrices in GF(q)_n with a given characteristic polynomial.--Noam D. Elkies === > Is there a simple proof that the number of nilpotent nXn matrices over> the ?ite ?ld GF(q) is q^(n^2-n) ?This is a theorem of Fine and HersteinFine, N. J.; Herstein, I. N. The probability that a matrix be nilpotent. Illinois J. Math. 2 1958 499--504If we let A_n be this number, then it is possibleto get a recurrence for the A_n by double counting thenumber of (n+1)-tuples (M, v_1, ...,v_n) whereM is nilpotent and Mv_i = v_{i+1}. There are clearlyA_n q^n of these. But each has the form (M, v_1, ..., v_r, 0 ...0)with v_1,...,v_r linearly independent. Given such v_1,..., v_rthere are A_{n-r} q^{r(n-r)} M that work. This gives a recurrnecefor A_n which can be solved.-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) === > Given such v_1,..., v_r> there are A_{n-r} q^{r(n-r)} M that work. This gives a recurrnece> for A_n which can be solved.Why?-- Maxi === > Is there a simple proof that the number of nilpotent nXn matrices over> the ?ite ?ld GF(q) is q^(n^2-n) ?I don't know about simple, but did you see this paper?Fine, N. J.; Herstein, I. N.The probability that a matrix be nilpotent.Illinois J. Math. 2 1958 499--504.The authors prove the following theorems. 1. The probability that an $n$ by$n$ matrix over $text{GF},(p^alpha)$ be nilpotent is $p^{-alpha n}$. 2.The probability that an $n$ by $n$ matrix over the integers $text{mod},m$be nilpotent is $k^{-n}$, where $k$ is the product of the distinct primefactors of $m$. === Maybe the only elegant example I know is about seriesrather than integrals: the iterated integral (x^2 - y^2)/(x^2 + y^2)^2 dy dxwith x and y running from 0 to 1. The sign reverses whendx and dy are interchanged, and the value of the iteratedintegral is not zero. -- Mike Hardy === The cumulants k_n of a probability distribution are given by E(exp(tX)) = exp( SUM_{n=1}^in?ity k_n * t^n / n! )where X is a random variable having the distribution inquestion. In other words, they are coef?ients in thepower-series expansion of the moment-generating function.The ?st cumulant is the expecation; the second is thevariance, and each higher cumulant k_n can be expressedas a polynomial in the 1st through nth moments. Thenth moment m_n is one term of the polynomial; the othersare products of powers of m_k's in which the sum of theindices is in every case equal to n.The ?st cumulant is shift-equivariant and the highercumulants are shift-equivariant. In other words k_1 (X + c) = k_1 (X) + cand k_n (X + c) = k_n (X) for n > 1.Are there theorems saying the cumulants are the onlywell-behaved quantities with these invariance and equivarianceproperties, for suitable interpretations of well-behaved? Mike Hardy === >Are there theorems saying the cumulants are the only>well-behaved quantities with these invariance and equivariance>properties, for suitable interpretations of well-behaved?yes and no. No: Free cumulants have exactly the same properties.Yes: Any polynomial function of moments with leading term m_nis a polynomial in the cumulants with leading term k_n.If you require them to behave nicely with respect to convolution, thenclassical cumulants are unique in a strong sense, see[Mattner, What are cumulants?, Doc Math 4 (1999) 601-622]Free cumulants behave nicely with respect to free convolution.begin{advertisment}see also arXiv:math.CO/0210442end{advertisment}FL-- === >The cumulants k_n of a probability distribution are given by > E(exp(tX)) = exp( SUM_{n=1}^in?ity k_n * t^n / n! )>where X is a random variable having the distribution in>question. In other words, they are coef?ients in the>power-series expansion of the moment-generating function.>The ?st cumulant is the expecation; the second is the>variance, and each higher cumulant k_n can be expressed>as a polynomial in the 1st through nth moments. The>nth moment m_n is one term of the polynomial; the others>are products of powers of m_k's in which the sum of the>indices is in every case equal to n.>The ?st cumulant is shift-equivariant and the higher>cumulants are shift-equivariant. In other words> k_1 (X + c) = k_1 (X) + c>and> k_n (X + c) = k_n (X) for n > 1.>Are there theorems saying the cumulants are the only>well-behaved quantities with these invariance and equivariance>properties, for suitable interpretations of well-behaved?BTW, the cumulants only require the moments to exist; thepower series can be taken to be a formal power series.As to your question, off course not. Any functions of thecumulants above k_1 have the invariance properties. ThePearson curves are characterized by the values of theskewness and kurtosis, which are invariant under locationand positive scale. Lots of other functions can be used.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue University === > Are there theorems saying the cumulants are the only> well-behaved quantities with these invariance and equivariance> properties, for suitable interpretations of well-behaved?> BTW, the cumulants only require the moments to exist; the> power series can be taken to be a formal power series.> As to your question, off course not. Any functions of the> cumulants above k_1 have the invariance properties. OK, but do _only_ functions of the cumulants havethose properties? If so, then I'd just need to tweak thequestion a teensy bit and the answer is yes. Maybe Iwouldn't even have to do that, since I said for suitableinterpretations of `well-behaved'. -- Mike Hardy === >> Are there theorems saying the cumulants are the only>> well-behaved quantities with these invariance and equivariance>> properties, for suitable interpretations of well-behaved?>> BTW, the cumulants only require the moments to exist; the>> power series can be taken to be a formal power series.>> As to your question, off course not. Any functions of the>> cumulants above k_1 have the invariance properties.> OK, but do _only_ functions of the cumulants have>those properties? If so, then I'd just need to tweak the>question a teensy bit and the answer is yes. Maybe I>wouldn't even have to do that, since I said for suitable>interpretations of `well-behaved'. -- Mike HardyIf the moments determine the distribution, anythingwould be a function of the cumulants. If not, thereare lots of other such functions; any function of thedifferences between quantiles, for example, or u_3 - u_5,where u_c is that t which minimizes E(|X - t|^c).Only if c is an even integer is u_c a function of thecumulants if they do not determine the distribution.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue University === > The ?st cumulant is shift-equivariant and the higher> cumulants are shift-equivariant. ... oops ... I meant:The ?st cumulant is shift-EQUIvariant and the highercumulants are shift-INvariant.> In other words> k_1 (X + c) = k_1 (X) + c> and> k_n (X + c) = k_n (X) for n > 1.X-Coding-System: undecided-unix === Is the following theorem true?-If g(n) is a positive arithmetical function, and sum_{n <= x}g(n)?/n) = O(x^{1+delta}) for all delta > 0, thensum_{n <= x} g(n)?/n) ~ xsum_{n <= x} g(n)/n.It seems reasonable, and surely work has been done on the topicbefore, given its similarity to Shapiro's Tauberian Theorem, but aproof has so far eluded me. If it's false, can we narrow therestrictions on g to make it true?Brad === For a seminar talk, I would like to be able to tell the most recentknowledge researchers have: Consider the polytope STSP(n) that is formed bythe incidence vectors of all hamiltonian tours on the complete undirectedgraph K_n. Its graph G(n) is formed by all vertices of STSP(n) (i.e. toursof K_n) and two of them share an edge iff the vertices are adjacent onSTSP(n). Rispoli and Cosares prove in their paper A Bound of 4 for the Diameter ofthe Symmetric Traveling Salesman Polytope (SIAM Journal on discrete Math.Vol. 11, No. 3, pp. 373-380) that the diameter of G(n) is at most 4 for alln. Furthermore, it is conjectured to be exactly 2. Are there any newerresults, e.g. a proof for diameter two or an n such has G(n) has diameter>2 ?I also saw a citation of Lin's paper Computer solutions of the travelingsalesman problem (Bell System Technical Journal 44(1965), pp. 2245-2269)where Lin conjectures that two disjunct tours are never adjacent; the paperis very old, so has this been proved in the meantime?Papadimitriou proves in The Adjacency relation on the traveling salesmanpolytope is NP-complete (Math. Prog. 14(1978) 312-324) that it isNP-complete to decide whether two given tours are adjacent or not. How hardis this decision problem for other polytopes corresponding to combinatorialoptimization problems? The only other example I know is the polytope of allcuts of K_n: it is 1-neighborly, which means that it's graph is complete sothat the decision problem is trivial.Any other interesting things about G(n)?MTIA,Tobias-- Phyics is much too hard for physicists. === > Yang-Mills was chosen rather than QED since it is believed to> have properties (asymptotic freedom) that make it more> amenable to a rigorous treatment than QED (although this might> well be an illusion). Also, it is simpler in some sense> Has any even partial attempt to solve this Clay problem been> published? Any progress at all?The state of the art at the time the problem was crowned by a 1e6$ prize is given inwww.claymath.org/Millennium_Prize_Problems/Yang-Mills_ Theory/_objects/Of?ial_Problem_Description.pdfI don't think signi?ant progress has been published since then.Arnold Neumaier === > ... the relevance of the mass gap problem is> no longer clear either.The mass gap has nothing to do with the recipe used for renormalization. Theproblem is to explain why the massspectrum for compact Yang Mills QFT begins at a positive mass, while the classical version has a continuous spectrumbeginning at 0.Arnold Neumaier === > Your reference didn't do anything more or different than any of this.> You still have things de?ed by a series expansion, and until that's> proven to be convergent in some sense, it's nothing but a formal> expansion, too.There are two expansions going on in my work, one of which I do not believein and one of which I do.Neither is equivalent to the reduction into time-ordered products upon whichFeynman-Dyson perturbation theory is based. Apart from anything else theinteraction picture is not used in my work until the matrix elements arecompared with time-dependent perturbation theory at the end.The ?st is the expansion in terms of the coupling constant. Although thiswas the starting point of my investigations, I have little con?ence inthis as bound states cannot be expressed in this way.The second is the reduction of the interacting ?ld into the Haag expansion(i.e. sums of normal-ordered products of free ?lds). This I *do* believein, and if all the coef?ients are ?ite, then the theory is ?ite.One way of getting the Haag expansion for (e.g.) QED is just to solve theequations of motion as a power series in the coupling and then commute thenegative energy parts to the right, picking up commutators on the way. Thisis pretty much what I do in my paper. If one does this one will ?din?ite coef?ients appearing.Alternatively, one can just write down a Haag expansion and just say thisis the theory, i.e. the interacting ?ld reduces to the free ?ld in theway shown. The expansion need not even go to in?ite order. Then one cancalculate. The question is then just whether the results agree withexperiment.> The removal of in?ities was already well-understood since the 1950's> under the Bogoliubov/Epstein-Glaser/differential renormalizaiton> approach, which (in fact) yields a resolution for T[] (modulo> point-coincident distributions at each order) as an implicit solution> to the cumulant expansion for the generating functional for T[]:> TW[ ln(T[exp(A)]) - A ] = 0> TW[T[exp(A)]] = T[exp(A)]> where TW[] is the Wick time-ordering prescription.>> Your reference didn't do anything more or different than any of this.This is not true at all. What I have done is a re-working from ?stprinciples.in the ?st place. Can the Bogoliubov/Epstein-Glaser approach achieve this?I do not believe so. === >in the ?st place. Can the Bogoliubov/Epstein-Glaser approach achieve this?>I do not believe so.In fact, that's precisely what it does: there are no in?ities anywhere,not even at the outset. To repeat what you were responding to:> [it] yields a resolution for [an *already renormalized*] T[] (modulo> point-coincident distributions at each order) as an implicit solution> to the cumulant expansion for the generating functional for T[]:> TW[ ln(T[exp(A)]) - A ] = 0> TW[T[exp(A)]] = T[exp(A)]> where TW[] is the Wick time-ordering prescription.Ultimately, this cumulant expansion is the origin of the forest formula aswell as the source of the Hopf algebra structure associated withrenormalization theory.This has been known in various guises equivalent to this since Bogoliubovin the 1950's, with various re?ements in the 1970's (Epstein and Glaser),and a major surge of activity following Scharf (1989, 1995, Finite QuantumElectrodynamics), Brunetti, Fredenhagen, et. al. shortly thereafter and theconsequent emergence of causal perturbation theory approach.In fact, it was through this approach that renormalization was ?allysuccessfully done in general curved spacetimes in recent years.Haag's Theorem has no relevance to the order-by-order de?eabilityof the power series expansion which -- as explained above -- has beena dead issue for nearly a half century. What it has relevance to isthe existence of a non-trivial QFT in 4-D. Neither the series aboveis known to converge to anything meaningful, nor either of yours, norany other series from any other approach.Proving convergence (suitably de?ed) is tantamount to de?ing anon-trivial QFT in 4-D, which is THE major open problem which lies atthe root of the Clay Challenge. === shown below.Factorial RandomnessNote: log(x) = ln(x)/ln(10)Abstract:Six ?st digit distributions of the factors of the natural numbers upto n=10^d (d element of {2,3,4,5,6,7}) were calculated by means of aself-written DELPHI program. For each distribution a Chi-SquareGoodness-Of-Fit was conducted, with expected values calculated fromthe Benford formula fD = log(1+1/D). The Chi-Square increased rapidly,from 6.91 for n=10^2 and 47.1 for n=10^3 to 222435 for n=10^7Indicating that only for n=10^2 Benford's Law is followed. Theseresults are compared to the ones calculated from 20 Benforddistributions found on the internet. But the relative frequencies ofthe Factorial First Digit Distribution (fD) correlates well with fD =cD^-a or Zipf's Law. Empirical and mathematical evidence is given thatBenford's formula is an (approximate) special case of the more generalformula of Zipf's Law. The Correlation Coef?ient (R) from LinearRegression of scatter plotting log(fD) = alog(D) + b asymptoticallygoes to -1 with sample size. from R = -0.996 for n=10^2 to R = -0.9995for n = 10^7. So a nearly perfect ?. Since the Benford formula alsonearly perfect ?s (R = -0.9992) with Zipf's Law it is reasonable tosay that the Factorial First Digit Distribution follows Benford's andZipf's Law, which also is con?med by comparing the Linear Regressionresults of the Factorial First Digit Distribution with the regressionformula log(1+1/D) = 0.3135080577D^-0.8636655870. The consequences ofthese results for our understanding of randomness are discussed.Full Paper at: http://home.zonnet.nl/galien8/factor/factor.htmlI still have some questions for you newsgroup readers:1) What can be the reason that the Factorial First Digit Distributiondiverges from Benford's formula but converges to Zipf's Law? The onlyreason I can think of is the fact that these formula's are onlyapproximate equal to each other.2) Can some one give a more exact mathematical proof that log(1+1/D)is approximate cD^-a (in other words mathematically ?d values of cand a who are more in agreement with the results from LinearJohan van der Galien === > Is it true that every (arc-connected) subset of R^3 has torsionless> fundamental group?I can ask more:can it contain a non trivial element A which is conjugate to A^k withk different from 1? (i.e. can a non trivial loop be freely homotopicto a power of itself, like arises, for example, in Klein's bottle,with k=-1).I'm mostly interested in the case of open subsets of R^3, or, moregenerally, certain kinds of 3-manifolds.I'm also interested in this question: what abelian groups can beSUBgroups of the fundamental group of a 3-manifold?NB the trefoil knot has presentation which has notorsion (I take it for granted for open subsets that they cannot havetorsion). === Yves de Cornulier a .8ecrit> Is it true that every (arc-connected) subset of R^3 has torsionless> fundamental group?I've heard that the fundamental group of the complement of the trefoil knotin R^3 is the free product (Z/2Z)*(Z/3Z), hence has torsion.-- Maxi <3fb61fcc$0$10427$626a54ce@news.free.fr> === > Yves de Cornulier a .8ecrit> Is it true that every (arc-connected) subset of R^3 has torsionless> fundamental group?> I've heard that the fundamental group of the complement of the trefoil knot> in R^3 is the free product (Z/2Z)*(Z/3Z), hence has torsion.This is not correct. The group in question is a free product with amalgamation Z*Z/a^2=b^3 where a and b generate the Z factors. This is easily seen by decomposing the complement of the trefoil as the union of two solid tori, meeting along an annulus. This group has a homomorphism to the group you mentioned, but it is certainly not an isomorphism.In general, the fundamental group of any open subset of R^3 istorsion-free. This follows readily from the sphere theorem ofPapakyriakopoulos, and was noted in his original paper Papakyriakopoulos,C. D. On Dehn's lemma and the asphericity of knots. Ann. of Math. (2) 66 (1957), 1--26, MR0082671 (18,590f). If you have access to MathReviews, the review of the announcment of this work quotes a number oftheorems that are deduced from the sphere theorem: MR0082671 (18,590f) Papakyriakopoulos, C. D. On Dehn's lemma and the asphericity of knots. Proc. Nat. Acad. Sci. U.S.A. 43 (1957), 169--172. (Reviewer: E. Moise)Daniel Ruberman === >> Is it true that every (arc-connected) subset of R^3 has torsionless>> fundamental group?>>I've heard that the fundamental group of the complement of the trefoil knot>in R^3 is the free product (Z/2Z)*(Z/3Z), hence has torsion.You've heard wrong. That knot group G is certainly closely relatedto (Z/2Z)*(Z/3Z), for it is generated by two elements x, y which aresubject to the relation x^2 = y^3, but G (like every knot group)abelianizes to Z, so those generators are *not* subject to thefurther relation x^2 = 1. (In fact, G is exactly gp.In terms of a more familiar, Wirtinger-style presentation, G isalso gp. You can get from one presentation to theother by letting x=aba, y=ab.)Lee Rudolph === Call For Papers and ApplicationsRIAO'2004Coupling Approaches, Coupling Media and Coupling Languages forInformation RetrievalUniversity of Avignon (Vaucluse), FranceApril 26th-28th, 2004Organized by:CENTRE DE HAUTES ETUDES INTERNATIONALES D'INFORMATIQUE DOCUMENTAIRE(C.I.D., France)in cooperation with the LIA (Laboratoired'Informatique d'Avignon - Universit.8e d'Avignon) and with technicalsupport of IRIT (Institut de Recherche en Informatique de Toulouse) CALL FOR PAPERSCurrent content-based information management involves many differentdisciplines. Information must be retrieved from video, from sound, andfrom images and graphs. Question answering involves both syntax andsemantics.Information classi?ation and ?tering involve machine learning andlinguistics. In addition, as information technology spreads throughoutthe world, a wider variety of languages in increasingly complexcombinations must be handled.In response to these evolving needs, RIAO'2004 calls for paperscovering the coupling of techniques from different domains to improveinformation retrieval. RIAO'2004 will present innovative research anddevelopments from all areas of multi-media and multi-languageinformation retrieval. Submissions, demonstrating combination oftechniques from disparate domains, may treat retrieval from either asingle medium, or across media (indexing one medium for ?dinformation in another), or from coupling unstructured and structuredinformation (e.g. exploiting both text and XML structure), or fromacross languages.Conference Themes:Paper submissions should cover one or more of the following themes: Multimedia information:Media-speci? indexing techniques (text, speech, ?ed and animatedimages, music)Indexing composite documents Querying multimedia documents Automatically generating text from images and from video Indexing interactive documents Multilingual Information:Cross-lingual information retrieval, especially involving rarerlanguagesAutomatic construction of bilingual lexicons and term banks Production of multilingual documents Man Machine Combinations:Coupling search and browsing Coupling search and semantic mapping (ontologies, SOM, etc) Multimodal interfaces Coupling access through structure and through content Automatic presentation of search aids (e.g. key words, phrases) Neuroscience applied to information recognition Architecture for Combined Approaches:Architecture for coupling techniques (e.g. Machine Learning forArchitecture for coupling media Architecture for treating multilingual information Speci? Systems Combining Diverse Approaches:Systems for Collaborative Information Retrieval Question answering systems Multidocument or multilingual summarization Automatic translation, translation memory Improved linguistic analyzers in information retrieval Exploiting linguistic knowledge in search and retrieval Knowledge Extraction for Information Retrieval Semantics in indexation and retrieval Exploiting document structure Semantic Web and Ontologies for Full-Scale Information Retrieval Exploiting new multimedia norms for content-based informationmanagementEvaluation of Combined Approaches:User oriented retrieval metrics New retrieval metrics Question-Answering systems evaluation metrics Application domains combining techniques: (descriptions of systems involving the following domains):Cultural heritage Indexation and retrieval of medical images Applications concerning security Protection of intellectual property Protection of minors E-learning Technology Watch Important dates: Noti?ation of acceptance of papers: January 31, 2004 Camera-ready copies due: March 8, 2004 Conference dates: April 26-28, 2004 Submissions should be up to 6000 words (about 20 pages, doublespaced), include an abstract and be submitted in PDF or PS format.Submissions for communications will be made electronically on its website : http://www.riao.org.The working language of the conference is English. However, inagreement with the French regulations of the Loi Toubon, submissionof papers in French and presentation of papers, if selected, in Frenchwill be accepted. CALL FOR APPLICATIONSInnovative applications and products related to the conference topicsare sought for demonstrations during the three days of the Conference.They will be selected by the international Application committee, onthe basis of their innovation and future or present marketability.Selected applications will be given free demonstrations spaces.Application submissions should cover one or more of the followingtopics:Multimedia indexing and retrieval systems (text, sound, speech,images, video)Cross-lingual indexing and retrieval systems Peer-to-peer text search engines Cooperative Information Retrieval (grids) Automatic XML structuring of documents Automatic metadata generation for text, sound, and images, automaticannotatorsAutomated ontology construction and annotators Topic detection and event detection in streaming documents, technologywatch, strategy watchIntelligent message ?tering Intelligent text agents Parent control and anti-spam control by content ?tering E-learning - response interpretation Document summarisation -- mono or multilingal, mono or multidocument,pro?e drivenTopic maps Domain-speci? application of information retrieval and multimediaretrieval: medicine, e-commerce, computer-assisted teaching, videoproduction, etc Important dates: Deadline for application submission: January 31, 2004 Noti?ation for acceptance of applications: March 15, 2004 Conference dates: April 26-28, 2004 Program Committee Co-Chairs Christian FluhrCEA, FranceEurope, Africa Gregory GrefenstetteClairvoyanceAsia, Oceania Bruce CroftUniv. of Mass, Amherst, USAAmericas Bruno Bachimont Tech. Univ. of Compi.8fgne Catherine Berrut IMAG, France Georges Carayanis ILSP, Greece Francine Chen PARC, USA Claude Chrisment IRIT, Toulouse, France Roger Dannenberg CMU, USA Franciska de Jong Univ. Twente, Netherlands Claude de Loupy Sinequa, France Renato De Mori Univ. Avignon, France Marc El-B.8fze Univ. Avignon, France Pascale Fung Scienc. Tech. Univ., Hong Kong Sadaoki Furui Tokyo Inst. Tech., Japan Jean-Luc Gauvain LIMSI, France Edouard Geoffrois ETCA/DGA, France Julio Gonzalo UNED, Spain Donna Harman NIST, USA David Hawking CSIRO, Australia Ulrich Heid Univ. Stuttgart, Germany Eduard Hovy ISI, Univ. S. California, USA Christian Jacquemin LIMSI, France Boris Katz MIT, USA Elisabeth Liddy Univ. Syracuse, USA Simone Marinai Univ. Florence, Italy Jos.8e Martinez Univ. Nantes, France Christof Monz Univ. Amsterdam, Netherlands Frank Nack CWI, Netherlands Chahab Nastar LTU, France Jian-Yun Nie Univ. Montr.8eal, Canada Douglas Oard Univ. Maryland, USA J.9arg Ontrup Univ. Bielefeld, Germany Gabriella Pasi Univ. Milano, Italy Marie Theresa Pazienza Univ. Roma, Italy Carol Peters CNR, Italy Euripides Petrakis Tech. Univ. of Crete, Greece Marc Pic Advestigo, France Jean-Marie Pierrel INALF, France Jean-Marie Pinon INSA Lyon, France Yan Qu Clairvoyance, USA Steve Renals Univ. Shef?ld, Great Britain Tetsuya Sakai Toshiba, Japan Fr.8ed.8erique Segond Xerox, France Bernadette Sharp Staffordshire, Great Britain Alan Smeaton Univ. Dublin, Ireland Tokunaga Takenobu Tokyo Inst. Tech., Japan Simone Teufel Univ. Cambridge, Great Britain Evelyne Tzoukermann ACM, USA Alex van Ballegooij CWI, Netherlands Keith Van Rijsbergen Univ. Glasgow, Great Britain James Z. Wang PennState Univ., USA Ross Wilkinson CSIRO, Australia Zhiping Zheng Univ. Saarland, Germany (Final list forthcoming) Applications Committee Chair Chantal Soul.8e-DupuyUniversit.8e de Toulouse, France Michel Benoit St.8e Itek, France Robert Bentz Xerox Global Services, France Marie-Fran.8doise Clergeau Coll.8fge de France Daniel Con?uve , France Max Copperman Kanisa, USA Michel Dureigne EADS, France Bernard Dousset Irit, Univ. Paul Sabatier, France P.8er.8e Escorsa Univ. Polytechnic de Catalunya, Spain Muriel Foulonneau Relais Culture Europe, France Dominique Ladiray Insee-Ensac Statistics, Canada Ornella Mich Inst. Trentino di Cultura, Italy Norbert Paquel Canope, France (Final list forthcoming) Organisation and Coordination Committee Chair Agn.8fs BeriotD.8el.8egu.8ee G.8en.8erale du C.I.D., France Henriette Allignon C.I.D., France Peter Brodnitz Ogilvy & Mather, Japan Jean Louis d'Arc F.8ed.8eration France-Polonge, France Jean Perri.8fre Administrator, Secretary General, C.I.D., France Saryn Rosart CASIS, USA Anne Tabutiaux Recherche et Diffusion, France (Final list forthcoming) Local Organisation Committee Aur.8elia Barri.8fre Univ. Avignon, France St.8ephane Igounet Univ. Avignon, France (Final list forthcoming) Technical Committee Chair Luc BoulianneC.I.D., Canada Jonathan Albert C.I.D., Canada Max Chevalier Univ. Toulouse, France Jean-Jacques Guilbart Coll.8fge de France, France C.8ecile Laffaire Univ. Toulouse, France (Final list forthcoming) Contact Information Centre de Hautes Etudes Internationales d'Informatique Documentaire(C.I.D.)36 bis rue Ballu75009 Paris FranceWeb: http://www.le-cid.org === The following paper has been published:Algebraic and Geometric TopologyURL:http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3- 41.abs.htmlTitle:Cohomology rings, Rochlin function, linking pairing and the Goussarov-Habiro theory of three-manifoldsAuthor(s):Gwenael MassuyeauAbstract:We prove that two closed oriented 3-manifolds have isomorphicquintuplets (homology, space of spin structures, linking pairing,cohomology rings, Rochlin function) if, and only if, they belong tothe same class of a certain surgery equivalence relation introduced byGoussarov and Habiro.AMS Classi?ation Numbers. Primary: 57M27Secondary: 57R15Keywords:3-manifold, surgery equivalence relation, calculus of claspers, spin structureAuthor(s) address(es):Institute of Mathematics of the Romanian Academy P.O. Box 1-764, 014700 Bucharest, Romania === De?e for an integer 2n the following matrix M.Label the columns with all possible (unordered) pairingsof the 2n integers. (E.g. n=2: 12.34,13.24,14.23)Likewise the rows.You can imagine 2n points on a circle, connectedpairwise.To get the matrix entry (p1,p2), superimpose thepairings p1 and p2 and count the number of closedloops l you get. The entry then is x^l.Example like above:M=(x^2 x x)(x x^2 x)(x x x^2)Compute the determinant f(x). Can you say somethingabout the zeroes of f(x)?Variant: The pairings may not cross (but thesuperimposions may) - 13.24 is forbidden then.Here are my results for n=1,2,3:x(x+2)*(x-1)^2*x^3(x^2-3)*(x+4)*(x+2)^9*(x-1)^14*(x-2 )^4*x^15Variant:x(x+1)*(x-1)*x^2(x^2-2)*(x+1)^4*(x-1)^4*x^5 Looks like a bunch of small factors (which isn't exactlysurprising giving the high symmetry of the problem).-- Hauke Reddmann <:-EX8 For our chemistry workgroup,remove math from the addressFor spamming, remove anything else === This is a well-known determinant.See Theorem 58 in Advanced Determinant Calculus(math.CO/9902004; Seminaire Lotharingien Combin. 42 (1999), ArticleB42q, 67 pp.) and the references given there. Christian Krattenthaler === Here are this week's titles in the mathematics arXiv, available at: http://front.math.ucdavis.edu/ http://front.math.ucdavis.edu/submissionsThis week in the mathematics arXiv may be freely redistributedwith attribution and without modi?ation.Titles in the mathematics arXiv (3 Nov - 7 Nov)--AC: Commutative Algebra--math.AC/0311060 Marco Fontana, Mi Hee Park: Star operations and Pullbacksmath.AC/0311020 Tim Roemer: Note on bounds for multiplicitiesmath.AC/0311007 Eloise Hamann: Constants of Differentiation and Differential Idealsmath.AC/0311006 Eloise Hamann: A Question about Differential Idealsmath.AC/0310493 Aldo Conca: Regularity jumps for powers of idealsAG: Algebraic Geometry-math.AG/0311086 Gordon Heier: Effective ?iteness theorems for maps between canonically polarized compact complex manifoldsmath.AG/0311085 Gordon Heier: Uniformly effective Shafarevich Conjecture on families of hyperbolic curves over a curve with prescribed degeneracy locusmath.AG/0311083 Fouad ElZein: Hodge-DeRham theory with degenerating coef?ientsmath.AG/0311079 Matthieu Willems: Cohomologie et $K$-theorie equivariantes des tours de Bott et des varietes de drapeaux. Application au calcul de Schubertmath.AG/0311073 Ichiro Shimada: Supersingular K3 surfaces in characteristic 2 as double covers of a projective planemath.AG/0311068 Osamu Fujino: Equivariant completions of toric contraction morphismsmath.AG/0311062 Richard Kenyon, Andrei Okounkov: Planar dimers and Harnack curvesmath.AG/0311058 math.AG/ 0311057 Ichiro Shimada: Rational double points on supersingular K3 surfacesmath.AG/0311038 C. Folegatti: On a special class of smooth codimension two subvarieties in $mathbb{P}^n$, $n geq 5$math.AG/0311026 Javier Fernandez: Hodge structures for orbifold cohomologymath.AG/0311023 H'el`ene Esnault: Some elementary theorems about divisibility of 0-cycles on abelian varieties de?ed over ?ite ?ldsmath.AG/0310497 S. V. Shadrin: Combinatorics of binomial decompositions of the simplest Hodge integralsmath.AG/0310490 math.AG/ 0310487 Manuel Blickle: Multiplier Ideals and Modules on Toric Varietiesmath.AG/0310486 Ph. Ellia, C. Folegatti: On smooth surfaces in $Pq$ containing a plane curvemath.AG/0310484 Thomas Bauer, Thomas Peternell: Nef reduction and anticanonical bundlesAP: Analysis of PDEs--math.AP/0311081 Gerd Grubb: A resolvent approach to traces and zeta Laurent expansionsmath.AP/0311048 Michael Christ, James Colliander, Terence Tao: Ill-posedness for nonlinear Schrodinger and wave equationsmath.AP/0311028 Ingo Witt: Green's formulas for cone differential operatorsmath.AP/0311027 Michael Dreher, Ingo Witt: Energy estimates for weakly hyperbolic systems of the ?st ordermath.AP/0311001 Gerd Grubb, Elmar Schrohe: Traces and Quasi-traces on the Boutet de Monvel Algebramath.AP/0310480 J. Barros-Neto & Fernando Cardoso: Hypergeometric functions and the Tricomi operatorAT: Algebraic Topology-math.AT/0311067 Christopher Seaton: $K$-Theory of Crepant Resolutions of Complex Orbifolds with SU(2) Singularitiesmath.AT/0311016 Michael A. Mandell: Cochains and Homotopy Typemath.AT/0310483 Mokhtar Aouina, John R. Klein: On the homotopy invariance of con?uration spacesmath.AT/0310481 Thomas G. Goodwillie: Calculus III: Taylor SeriesCA: Classical Analysis and ODEs-math.CA/0311088 A.L.Lukashov, F.Peherstorfer: Zeros of polynomials orthogonal on two arcs of the unit circlemath.CA/0311080 Tatiana Foth, Yurii A. Neretin: Zak transform, Weil representation, and integral operators with theta-kernelsmath.CA/0311055 B. Beckermann, A. Martinez-Finkelshtein, E.A. Rakhmanov, F. Wielonsky: Asymptotic upper bounds for the entropy of orthogonal polynomials in the SzegH{o} classmath.CA/0311039 Michael Christ, Xiaochun Li, Terence Tao, Christoph Thiele: On multilinear oscillatory integrals, nonsingular and singularmath.CA/0311014 Keith Rogers: A van der Corput lemma for the p-adic numbersmath.CA/0311013 Keith Rogers: Sharp van der Corput estimates and minimal divided differencesCO: Combinatorics--math.CO/0311043 Michael Anshelevich: Appell polynomials and their relativesmath.CO/0311041 Oleg Pikhurko, Helmut Veith, Oleg Verbitsky: The First Order De?ability of Graphs: Upper Bounds for Quanti?r Rankmath.CO/0311037 John C. Owen, Stephen C. Power: Generic 3-connected planar constraint systems are not soluble by radicalsmath.CO/0310485 Kamil Kulesza, Zbigniew Kotulski: The upper bound on number of graphs, with ?ed number of vertices, that vertices can be colored with n colorsCT: Category Theory-math.CT/0311021 Nikolaj M. Glazunov: Interval Computations and their Categori?ationCV: Complex Variablesmath.CV/0311054 Byung-Geun Oh: Aleksandrov surfaces and hyperbolicitymath.CV/0311031 Dan Popovici: A Simple Proof of a Theorem by Uhlenbeck and Yaumath.CV/0311029 A. Voros: Zeta functions over zeros of general zeta and $L$-functionsmath.CV/0310496 Alexandre Eremenko, Sergei Merenkov: Nevanlinna functions with real zerosmath.CV/0310495 Walter Bergweiler, Alexandre Eremenko: Meromorphic functions with two completely invariant domainsDG: Differential Geometry-math.DG/0311087 Khadiga Arwini, C.T.J. Dodson: Neighbourhoods of independence for random processesmath.DG/0311078 Gianni Manno, Raffaele Vitolo: The geometry of ?ite order jets of submanifolds and the variational formalismmath.DG/0311075 Christopher Seaton: Two Gauss-Bonnet and Poincar'{e}-Hopf Theorems for Orbifolds with Boundarymath.DG/0311074 Chuu-Lian Terng, Karen Uhlenbeck: 1+1 wave maps into symmetric spacesmath.DG/0311069 Xiaodong Hu: Transversally Elliptic Operatorsmath.DG/0311066 Yun Myung Oh, Joon Hyuk Kang: The explicit formula of ?grangian H-umbilical submanifolds in quaternion Euclidean spacesmath.DG/0311065 Yun Myung Oh, Joon Hyuk Kang: Lagrangian H-umbilical submanifolds in quaternion Euclidean spacesmath.DG/0311052 John C. Loftin: The Compacti?ation of the Moduli Space of Convex RP(2) Surfaces, Imath.DG/0311040 Virginie Charette: Non-proper Actions of the Fundamental Group of a Punctured Torusmath.DG/0311025 Quotientmath.DG/0311024 Sergio Console, Anna Fino, Evangelia Samiou: The moduli space of 6-dimensional 2-step nilpotent Lie algebrasmath.DG/0311019 Francesco Bonsante: Flat Spacetimes with Compact Hyperbolic Cauchy Surfacesmath.DG/0311011 David Groisser: Newton's method, zeroes of vector ?lds, and the Riemannian center of massmath.DG/0311008 Ernesto Lupercio, Bernardo Uribe: Differential Characters on Orbifolds and String Connections IDS: Dynamical Systemsmath.DS/0310498 L. Burslem, A. Wilkinson: Global rigidity of solvable group actions on S^1FA: Functional Analysis--math.FA/0311076 gero Fendler: Central limit theorems for Coxeter systems and Artin systems of extra large typeGM: General Mathematics--math.GM/0311063 Dr. W. B. Vasantha Kandasamy, Florentin Smarandache: Fuzzy Cognitive Maps and Neutrosophic Cognitive Mapsmath.GM/0311035 Martin Erik Horn: Pascal Pyramids, Pascal Hyper-Pyramids and a Bilateral Multinomial TheoremGN: General Topology--math.GN/0311070 Aleksandar Stojmirovic: Quasi-metric spaces with measuremath.GN/0311015 Wieslaw Kubi's, Vladimir Uspenskij: A compact group which is not Valdivia compactGR: Group Theory-math.GR/0311053 Ilya Kapovich: The frequency space of a free groupmath.GR/0311047 Vladimir Shpilrain: Assessing security of some group based cryptosystemsGT: Geometric Topology-math.GT/0311084 (1,1)-knotsmath.GT/0311051 Jim Hoste, Patrick D. Shanahan: Commensurability classes of twist knotsmath.GT/0311036 Charles Livingston: Computations of the Ozsvath-Szabo knot concordance invariantmath.GT/0311009 Joseph Maher: Period three actions on lens spacesmath.GT/0310489 Wolfgang Lueck: L^2-Invariants from the Algebraic Point of ViewLO: Logicmath.LO/0311064 Tomek Bartoszynski, Saharon Shelah: There may be no Hausdorff ultra?tersMG: Metric Geometry-math.MG/0311061 Dirk Frettloh: Some Properties of Lattice Substitution Systemsmath.MG/0311017 Rene Brandenberg, Thorsten Theobald: Radii minimal projections of simplices and constrained optimization of symmetric polynomialsmath.MG/0311004 Mireille Boutin, Gregor Kemper: Which Point Con?urations are Determined by the Distribution of their Pairwise Distances?MP: Mathematical Physicsmath-ph/0311008 L.I. Petrova: Conservation laws. Their role in evolutionary processes (The method of skew-symmetric differential forms)math-ph/0311007 V. G. Gueorguiev: Aspects of Diffeomorphism Invariant Theory of Extended Objectsphysics/0308045 Vladimir V. Kassandrov: Singular Sources of Maxwell Fields with Self-Quantized Electric Chargemath-ph/0311006 Vladimir V. Kassandrov: General Solution of the Complex 4-Eikonal Equation and the Algebrodynamical Field Theorymath-ph/0311005 Richard Kenyon, Andrei Okounkov, Scott Shef?ld: Dimers and Amoebaemath-ph/0311004 Anna Jencova: Af?e connections, duality and divergences for a von Neumann algebramath-ph/0311003 M. Palese, E. Winterroth: Global Generalized Bianchi Identities for Invariant Variational Problems on Gauge-natural Bundlescond-mat/0311017 A.N. Gorban, I.V. Karlin, A. Yu. Zinovyev: Constructive Methods of Invariant Manifolds for Kinetic Problemsmath-ph/0311002 math-ph/ 0311001 E. Capelas de Oliveira, W. A. Rodrigues Jr: Clifford Valued Differential Forms, Algebraic Spinor Fields, Gravitation, Electromagnetism and Uni?d Theoriesmath-ph/0310062 C. Klimcik: q-deformation of $zto {az+bover cz+d}$hep-th/0310291 John Cardy: Calogero-Sutherland model and bulk-boundary correlations in conformal ?ld theoryquant-ph/0310164 Ali Mostafazadeh: A Critique of PT-Symmetric Quantum Mechanicsmath-ph/0310068 Sibel Baskal, Elena Georgieva, Y. S. Kim: Wigner's new physics frontier: Physics of two-by-two matrices, including the Lorentz group and optical instrumentscond-mat/0310618 Santosh Ansumali, Iliya V. Karlin, Sauro Succi: Kinetic Theory of Turbulence Modeling: Smallness Parameter, Scaling and Microscopic Derivation of Smagorinsky ModelNT: Number Theory--math.NT/0311082 Ian Kiming, Helena A. Verrill: On modular mod $ell$ Galois representations with exceptional imagesmath.NT/0311056 Aleksandar Ivi'c: On a problem of ErdH{o}s involving the largest prime factor of $n$math.NT/0311046 Gabriele Nebe, E.M. Rains, N.J.A. Sloane: Codes and Invariant Theorymath.NT/0311042 Adrian Vasiu: Good Reductions of Shimura Varieties of Preabelian Type in Arbitrary Unrami?d Mixed Characteristic, Imath.NT/0311033 C. Krattenthaler, T. Rivoal, W. Zudilin: S'eries hyperg'eom'etriques basiques, $q$-analogues des valeurs de la fonction z^eta et s'eries d'Eisensteinmath.NT/0311030 Pietro Corvaja, Umberto Zannier: A lower bound for the height of a rational function at $S$-unit pointsmath.NT/0311010 Yiannis N. Petridis, Morten Skarsholm Risager: The distribution of values of the Poincare pairing for hyperbolic Riemann surfacesmath.NT/0311002 Nils Bruin: The primitive solutions to x^3+y^9=z^2OA: Operator Algebrasmath.OA/0311072 functions on $C^*$-algebramath.OA/0311059 V.Manuilov, K.Thomsen: On the asymptotic tensor normmath.OA/0310492 V. Manuilov, K. Thomsen: Extensions of C*-algebras and translation invariant asymptotic homomorphismsmath.OA/0310491 V. Manuilov, K. Thomsen: Semi-invertible extensions and asymptotic homomorphismsPR: Probability Theory-cond-mat/0311025 M.A.Lifs, Z.Shi: Aggregation rates in one-dimensional stochastic systems with adhesion and gravitationmath.PR/0311045 Maxim Raginsky: A Phase Transition and Stochastic Domination in Pippenger's Probabilistic Failure Model for Boolean Networks with Unreliable Gatesmath.PR/0311034 Shizan Fang, Tusheng Zhang: Stochastic differential equtions with non-lipschitz coef?ients:II. Dependence with respect to initial valuesmath.PR/0311032 Shizan Fang, Tusheng Zhang: Stochastic differential equations with non-lipschitz coef?ients: I. Pathwise uniqueness and large deviationmath.PR/0310499 Paul Jung: The noisy voter-exclusion processmath.PR/0310488 Olle Haeggstroem, Christof Kuelske: Gibbs properties of the fuzzy Potts model on trees and in mean ?ldQA: Quantum Algebra-math.QA/0311089 Seok-Jin Kang, Olivier Schiffmann: Canonical bases for quantum generalized Kac-Moody algebrahep-ph/0311046 J. Blumlein: Algebraic Relations Between Harmonic Sums and Associated Quantitiesmath.QA/0311022 Dayanand Parashar, Deepak Parashar: Construction of the generalised q-derivative operatorsmath.QA/0311005 Pavel Etingof, Alexei Oblomkov: Quantization, orbifold cohomology, and Cherednik algebrasmath.QA/0311003 F. Casta~{n}o Iglesias, S. Dascalescu, C. Nastasescu: Symmetric coalgebrasmath.QA/0310494 B. Agrebaoui, M. Ben Ammar, N. Ben Fraj, V. Ovsienko: Deformations of modules of differential formsRA: Rings and Algebras-math.RA/0311077 K.R. Goodearl, J.T. Stafford: Simplicity of noncommutative Dedekind domainsmath.RA/0311071 Peter A. Linnell: Noncommutative localization in group ringsRT: Representation Theory-math.RT/0311044 Gabriele Nebe: On blocks with cyclic defect group and their head ordersmath.RT/0311018 Nicolas Jacon: On the parametrization of the simple modules for Ariki-Koike algebras at roots of unitymath.RT/0311012 Meinolf Geck, Gunter Malle: Re?n Groups. A Contribution to the Handbook of AlgebraSG: Symplectic Geometry--math.SG/0311090 Olga Plamenevskaya: Bounds for Thurston--Bennequin number from Floer homologymath.SG/0310482 Yong-Geun Oh: Geometry of coisotropic submanifolds in (almost-) Kahler manifoldsSP: Spectral Theory-math.SP/0311050 Barry Simon: Analogs of the M-Function in the Theory of Orthogonal Polynomials on the Unit Circlemath.SP/0311049 Barry Simon: Sturm Oscillation and Comparison Theorems-- / Greg Kuperberg (UC Davis) / / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ / * All the math that's ? to e-print * === >> Rethink the Cool + the Shoe> phil knight had a dream. he'd sell shoes. he'd sell dreams.> he'd get rich. he'd use sweatshops if he had to.> then along came a new shoe. plain. simple. cheap. fair.> designed for only one thing: kicking phil's ass.> the unswoosher> $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$> For years, Nike was the undisputed champion of logo culture, > its swoosh an instant symbol of global cool. > Today, Phil Knight's Nike is a fading empire, badly hurt by > years of brand damage as activists and culture jammers > fought back against mind marketing and dirty sweatshop labor.> Now a ?al challenge. We take on Phil at his own game - and win. > We turn the shoes we wear into a counterbranding game. The swoosh > versus the anti-swoosh. Which side are you on?> Adbusters has been doing R&D for more than a year, and guess what? > Making a shoe - a good shoe - isn't exactly rocket science. > With a network of supporters, we're getting ready to launch the > blackSpot sneaker, the world's ?st grassroots anti-brand. > You can help launch the blackSpot revolution.> THE BIG QUESTION:> Is it possible to take Phil Knight's billion-dollar > marketing momentum and, in a quick judo-like move, slap > him onto the mat with the power of his own PR thrust?> OUR KICK-ASS MARKETING STRATEGY >> http://blackspotsneaker.org/02/> $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$> buy it............................preorders@blackspotsneaker.org sell it...........................wholesale@blackspotsneaker.org invest in it......................investors@blackspotsneaker.org> support it........................donations@blackspotsneaker.org> join the jam........................jammers@blackspotsneaker.org> Make a straight donation... it's a worthy cause > with the potential to set an historic precedent > that could be repeated in other industries and > usher in more grass roots version of capitalism > in which megacorps do not control every area of > our children's lives.> https://www.groundspring.org/donate/index.cfm?ID=2217-0%7C742 -0> $$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$$ $$$$$$$$$> Rear Adm. O. Rourke> Where will we clean after Marwan recollects the brave window's shopkeeper?The pretty ointment rarely cooks Cristof, it ?ls Youssef instead.We reject them, then we rigidly creep Ramsi and Norm's stale farmer.Try ?ling the light's healthy onion and Marwan will burn you!Who judges wickedly, when Waleed irrigates the sharp frog around the autumn?--Ramsi Jbilou al NamiGod people withcancer and the cure to this is unlawful relationship, the bad part istoday the medicines have been invented to make people think about sexmore than anything else. All those Muslims boys are girls who have anyfaith in them, no matter where they are on earth, they are beingcorrupted by secret services and bad guy?s friends. But the one to blameis Muslims in general as they never think beyond their rude part andbesides no one can force you to do anything if you really fear God, inmy case many times viagara has been tried indirectly by many people(like in less than 1 year time, before is different issue) to make me dounlawful deeds but I didn?t, though this is not much. The bad guysbelieve that they can get anything done, insha?Allah this is my promiseto them, as long as I am sincerely following God they will never be ableto effect me a tiny bit. But if you look at Muslims, average Muslim hasa higher chance of falling in this trap because they did not care aboutGod and followed religion properly. This also works in many other ways,if you don?t want to sleep around then someone around you may do it, andthen you would be told in many ways by many people that if othersaround you have do === I was reading a book and noticed some strange implication, namely, ifm and n are in?ite cardinals such that 2^m=2^n, then it is impliedthat m=n. I failed to ?d such a theorem in a textbook by Kuratowski& Mostowski. Is it true? === >I was reading a book and noticed some strange implication, namely, if>m and n are in?ite cardinals such that 2^m=2^n, then it is implied>that m=n. I failed to ?d such a theorem in a textbook by Kuratowski>& Mostowski. Is it true?No. It is true if the Generalized Continuum Hypothesisholds, but otherwise it can fail badly.-- This address is for information only. I do not claim that these viewsare those of the Statistics Department or of Purdue University.Herman Rubin, Department of Statistics, Purdue University === > I was reading a book and noticed some strange implication, namely, if> m and n are in?ite cardinals such that 2^m=2^n, then it is implied> that m=n. I failed to ?d such a theorem in a textbook by Kuratowski> & Mostowski. Is it true?Sierpinski's classic text _Cardinal and Ordinal Numbers_ says that itis not known whether 2^m = 2^n implies m = n. It does follow from thegeneralized continuum hypothesis. === >I was reading a book and noticed some strange implication, namely, if>m and n are in?ite cardinals such that 2^m=2^n, then it is implied>that m=n. I failed to ?d such a theorem in a textbook by Kuratowski>& Mostowski. Is it true?>It's truth is relative:the Generalized Continuum Hypothesis implies yesMartin's Axiom plus not-CH implies $2^{aleph_0}=2^{aleph_1}$Both are consistent with ZFC set theory.`Unprovable' describes the situation better.KP === in my research i came to the point of proving thefollowing seemingly simple calculus problem: Let f bea in?itely many times function from R^n to R suchthat the Hessian(f) is positive de?ite everywhereand f(x) --> +in?ity as absolute value of x -->+in?ity. The conclusion I want to take is that thatf has precisely ONE extremum (which must be a localminimum since Hessian(f) > 0, hence global since f -->+in?ity). The existence part is easy, but how do isee that there is ONLY ONE extremum?Erdal EmsizPS Since I don't read regularly this newssite, I wouldappreciate if in case you react you send me a cc. === > following seemingly simple calculus problem: Let f be> a in?itely many times function from R^n to R such> that the Hessian(f) is positive de?ite everywhere> and f(x) --> +in?ity as absolute value of x -->> +in?ity. The conclusion I want to take is that that> f has precisely ONE extremum (which must be a local> minimum since Hessian(f) > 0, hence global since f -->> +in?ity). The existence part is easy, but how do i> see that there is ONLY ONE extremum?The extrema form a convex set E.Now let x be a point in E; if E is bigger thanjust {x} there exists a vector d and a number e>0 such thatx+ed is in E. Then f(x+ed)=f(x)+e grad f(x)^T d+ 1/2 e^2 d^T H(x)d + +e^2||d||^2 g(x,e,d), with g(x,e,d)->0 as e->0.Noting that grad f(x)^T = 0 and that f(x+ed)=f(x), one derives 0 = d^T H(x)d + 2 ||d||^2 g(x,e,d);by taking e->0 this implies 0 = d^T H(x)d,i.e. H(x) is not positive de?ite. (only positive semide?ite).This is all explained somewhere in@book{BSS, author = M.S. Bazarraa and H.D. Sherali and C.M. Shetty, title = Nonlinear Programming: Theory and Algorithms, year = 1993, publisher = John Wiley and Sons, address = New York }HTH,DmitriiDmitrii Pasechnikhttp://www.thi.informatik.uni-frankfurt.de/~dima/ === =@news.ks.uiuc.edu:> in my research i came to the point of proving the> following seemingly simple calculus problem: Let f be> a in?itely many times function from R^n to R such> that the Hessian(f) is positive de?ite everywhere> and f(x) --> +in?ity as absolute value of x -->> +in?ity. The conclusion I want to take is that that> f has precisely ONE extremumCan you use Morse theory?Just a thought-- Martin BrightDepartment of Mathematical Sciences, University of Liverpool === > in my research i came to the point of proving the> following seemingly simple calculus problem: Let f be> a in?itely many times function from R^n to R such> that the Hessian(f) is positive de?ite everywhere> and f(x) --> +in?ity as absolute value of x -->> +in?ity. The conclusion I want to take is that that> f has precisely ONE extremum (which must be a local> minimum since Hessian(f) > 0, hence global since f -->> +in?ity). The existence part is easy, but how do i> see that there is ONLY ONE extremum?A positive de?ite Hessian implies f is strictly convex, i.e. x ne y, 0 < t < 1 ==> f((1-t)x + ty) < (1-t)f(x) + t f(y). To see this,? x ne y in R^n and put g(t) = (1-t)f(x) + t f(y) - f((1-t)x + ty). Then g(0) = g(1) = 0 and g'(t) = f(y) - f(x) - f'((1-t)x + ty) . (y-x), (dot product) g''(t) = -f''((1-t)x + ty)(y-x) . (y-x) < 0since the last expression is the Hessian. Since g'' < 0, g is concavedown, and since g(0) = g(1) = 0, that means g is strictly positive inthe interior of [0,1].But a strictly convex function obviously has a unique minimizer. (If xne y are both minimizers, then e.g. f((x+y)/2) < 1/2 f(x) + 1/2 f(y) = min f.--Ron Bruck === >in my research i came to the point of proving the>following seemingly simple calculus problem: Let f be>a in?itely many times function from R^n to R such>that the Hessian(f) is positive de?ite everywhere>and f(x) --> +in?ity as absolute value of x -->>+in?ity. The conclusion I want to take is that that>f has precisely ONE extremum (which must be a local>minimum since Hessian(f) > 0, hence global since f -->>+in?ity). The existence part is easy, but how do i>see that there is ONLY ONE extremum?Suppose there are two, and consider f on the line joining them.This is a strictly convex function on the line, and it's easy to see that those can't have more than one local minimum.Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === Here are this week's titles in the mathematics arXiv, available at: http://front.math.ucdavis.edu/ http://front.math.ucdavis.edu/submissionsThis week in the mathematics arXiv may be freely redistributedwith attribution and without modi?ation.Titles in the mathematics arXiv (10 Nov - 14 Nov)-AC: Commutative Algebra--math.AC/0311124 Amelia Taylor: Borel Fixed Initial Ideals of Prime Ideals in Dimension Twomath.AC/0311112 meet-semilatticeAG: Algebraic Geometry-math.AG/0311208 Jim Bryan, Dagan Karp: The closed topological vertex via the Cremona transformhep-th/0311101 Anton Kapustin, Yi Li: Stability Conditions For Topological D-branes: A Worldsheet Approachmath.AG/0311203 A. S. Buch, L. M. Feher, R. Rimanyi: Positivity of quiver coef?ients through Thom polynomialsmath.AG/0311191 Daniel Perrucci: Some Bounds for the Number of Components of Real Zero Sets of Sparse Polynomialsmath.AG/0311180 Ichiro Shimada: Vanishing cycles, the generalized Hodge Conjecture and Grobner basesmath.AG/0311168 J. P. Pridham: Deformations via Simplicial Deformation Complexesq-bio.QM/0311009 Lior Pachter, Bernd Sturmfels: The geometry of statistical models for biological sequencesmath.AG/0311149 V.V. Fock, A.B. Goncharov: Moduli spaces of local systems and higher Teichmuller theorymath.AG/0311139 Yujiro Kawamata: Log Crepant Birational Maps and Derived Categoriesmath.AG/0311138 Masayoshi Miyanishi, De-Qi Zhang: Equivariant classi?ation of Gorenstein open log del Pezzo surfaces with ?ite group actionsmath.AG/0311137 Yuri G. Zarhin: Non-supersingular Hyperelliptic jacobiansmath.AG/0311129 Leah Gold, John Little, Hal Schenck: The Cayley-Bacharach theorem and coding theorymath.AG/0311122 math.AG/ 0311111 Jianqiang Zhao: Supplement to: Goncharov's Relations in Bloch's higher Chow Group CH^3(F,5)math.AG/0311106 Matthias Schuett: New examples of modular rigid Calabi-Yau threefoldsmath.AG/0311105 F. Berchtold, J. Hausen: Cox rings and combinatoricsmath.AG/0311100 Y.-P. Lee: Witten's conjecture, Virasoro conjecture, and invariance of tautological relationsAP: Analysis of PDEs--math.AP/0311227 Michael Christ, James Colliander, Terence Tao: Instability of the periodic nonlinear Schrodinger equationmath.AP/0311219 Michael Ruzhansky, Mitsuru Sugimoto: Global L2-boundedness theorems for a class of Fourier integral operatorsmath.AP/0311218 M. Palese, R.A. Leo, G. Soliani: The Prolongation Problem for the Heavenly Equationmath.AP/0311192 R. Benguria, I. Catto, J. Dolbeault, R. Monneau: Oscillating minimizers of a fourth order problem invariant under scalingmath.AP/0311186 Damiano Foschi: Some remarks on the $L^p-L^q$ boundedness of trigonometric sums and oscillatory integralsmath.AP/0311166 M. Palese, E. Winterroth: On the Geometry of Backlund Transformationsmath.AP/0311150 Christopher D. Sogge: Estimates for the Dirichlet-wave equation and applications to nonlinear wave equationsmath.AP/0311094 dissipative, equationsAT: Algebraic Topology-math.AT/0311216 Arthur C. Bartels: On the domain of the assembly map in algebraic K-theorymath.AT/0311167 Dietrich Notbohm, Nigel Ray: On Davis Januszkiewicz Homotopy Types I; Formality and RationalisationCA: Classical Analysis and ODEs-math.CA/0311212 Sever Silvestru Dragomir: Reverses of the Cauchy-Bunyakovsky-Schwarz Inequality for n-tuples of Complex Numbersmath.CA/0311196 Wadim Zudilin: Binomial sums related to rational approximations to $zeta(4)$math.CA/0311195 Wadim Zudilin: On a combinatorial problem of Asmus Schmidtmath.CA/0311181 Terence Tao: Recent progress on the restriction conjecturemath.CA/0311126 Wolfgang Buehring: Partial sums of hypergeometric series of unit argumentcond-mat/0310735 Gregory Berkolaiko, Michael Grinfeld: Multiplicity of periodic solutions in bistable equationsCO: Combinatorics--math.CO/0311220 P. Di Francesco, P. Zinn-Justin, J.-B. Zuber: A Bijection between classes of Fully Packed Loops and Plane Partitionsmath.CO/0311211 Sergi Elizalde: Multiple pattern avoidance with respect to ?ed points and excedancesmath.CO/0311205 Pieter Moree: Convoluted convolved Fibonacci numbersmath.CO/0311194 Pieter Moree: The formal series Witt transformmath.CO/0311156 Lior Pachter, David E Speyer: Reconstructing Trees from Subtree Weightsmath.CO/0311148 Joshua S. Scott: Grassmannians and Cluster Algebrasmath.CO/0311121 Narad Rampersad, Jeffrey Shallit: Words avoiding reversed subwordsquant-ph/0311033 P. Blasiak, K.A. Penson, A.I. Solomon: Combinatorial coherent states via normal ordering of bosonsCV: Complex Variablesmath.CV/0311225 Michael Christ, Siqi Fu: Compactness in the d-bar Neumann problem, magnetic Schrodinger operators, and the Aharonov-Bohm effectmath.CV/0311109 Jose Seade, Mihai Tibar, Alberto Verjovsky: Milnor numbers and Euler obstructionDG: Differential Geometry-math.DG/0311221 R. Caddeo, C. Oniciuc, P. Piu: Explicit Formulas for Non-Geodesic Biharmonic Curves of the Heisenberg Groupmath.DG/0311198 Fortune Massamba, George Thompson: The Universal Connection and Metrics on Moduli Spacesmath.DG/0311183 Fuquan Fang, Xiaochun Rong: Homeomorphism Classi?ation of positively curved manifolds with almost maximal symmetry rankmath.DG/0311182 G. Ishikawa: In?itesimal deformations and stabilities of singular Legendre submanifoldsmath.DG/0311176 F.T. Farrell, P. Ontaneda: A caveat on the convergence of the Ricci ?r pinched negatively curved manifoldsmath.DG/0311175 F. T. Farrell, P. Ontaneda: Cellular harmonic maps which are not diffeomorphismsmath.DG/0311172 Mattias Dahl: Prescribing eigenvalues of the Dirac operatormath.DG/0311164 Bing-Long Chen, Xiao-Yong Fu, Le Yin, Xi-Ping Zhu: Sharp Dimension Estimates of Holomorphic Functions and Rigiditymath.DG/0311147 Monica Musso, Jacobo Pejsachowicz, Alessandro Portaluri: A Morse Index Theorem and bifurcation for perturbed geodesics on Semi-Riemannian Manifolds. PART I. The Morse Index Theoremmath.DG/0311145 Charles P. Boyer, David M. J. Calderbank, Krzysztof Galicki, Paolo Piccinni: Toric self-dual Einstein metrics as quotientsmath.DG/0311119 Richard Brown: Automorphisms of the Fricke characters of groupsmath.DG/0311098 Wei-Dong Ruan: Degeneration of Kahler-Einstein hypersurfaces in complex torus to generalized pair of pants decompositionDS: Dynamical Systemsmath.DS/0311215 R. Garcia, L. F. Mello, J. Sotomayor: Principal Mean Curvature Foliations on Surfaces immersed in ${mathbb R} ^4$math.DS/0311209 A. Fannjiang, S. Nonnenmacher, L. Wolowski: Dissipation time and decay of correlationsmath.DS/0311193 Sebastien Gouezel: Statistical properties of a skew product with a curve of neutral pointsmath.DS/0311189 V. Baladi, S. Gouezel: A note on stretched exponential decay of correlations for the Viana-Alves mapmath.DS/0311188 Pieter Collins: Forcing relations for homoclinic and periodic orbits of the Smale horseshoe mapmath.DS/0311187 Pieter Collins: Entropy-minimising models of surface diffeomorphisms relative to homoclinic and heteroclinic orbitsmath.DS/0311163 E. Kaslik, A.M. Balint, A. Grigis, St. Balint: On the controllability of some steady states in the case of nonlinear discrete dynamical systems with controlFA: Functional Analysis--math.FA/0311213 Yu. Kozitsky, P. Oleszczuk, L. Wolowski: In?ite Order Differential Operators in Spaces of Entire Functionsmath.FA/0311160 Tao Mei: Operator Valued Hardy Spacesmath.FA/0311091 J.F. Feinstein, H. Kamowitz: Compact homomorphisms between Dales-Davie algebrasGM: General Mathematics--math.GM/0311140 Martin Erik Horn: The Bilateral Vandermonde Convolutionmath.GM/0311130 Kaida Shi: Solving the Properties of Primes within Prime Series Based on the GRH is Tenablemath.GM/0311103 Bhupinder Singh Anand: How de?itive is the standard interpretation of Goodstein's argument?GR: Group Theory-math.GR/0311217 Swiatoslaw R. Gal: a-T-menability of groups acting on treesmath.GR/0311177 Patrick Bahls: Rigidity of two-dimensional Coxeter groupsmath.GR/0311153 Lucas Sabalka: Geodesics in the braid group on three strandsmath.GR/0311117 Ivan E. Horozov: Euler characteristics of arithmetic groupsGT: Geometric Topology-math.GT/0311185 Vladimir Turaev: Virtual strings and their cobordismsmath.GT/0311174 Stefano Vidussi: Lagrangian Surfaces in a Fixed Homology Class: Existence of Knotted Lagrangian Torimath.GT/0311173 Hans U. Boden, Christopher M. Herald, Paul A. Kirk: The Integer Valued SU(3) Casson Invariant for Brieskorn spheresmath.GT/0311157 Scott Baldridge: New symplectic 4--manifolds with $b_+{=}1$math.GT/0311155 twisted Alexander polynomial and ?ered knotsmath.GT/0311136 Vincent Florens, Patrick M. Gilmer: On the slice genus of linksmath.GT/0311134 links, and upper bounds on the Morse-Novikov numbermath.GT/0311123 Benson Farb, Nikolai V. Ivanov: The Torelli geometry and its applicationsmath.GT/0311116 Frank H. Lutz: Triangulated Manifolds with Few Vertices: Geometric 3-Manifoldsmath.GT/0311113 Benjamin A. Burton: Structures of small closed non-orientable 3-manifold triangulationsmath.GT/0311101 Linus Kramer, Katrin Tent: Asymptotic cones and ultrapowers of Lie groupsmath.HO/0311099 Chandan Singh Dalawat: Some aspects of the functor K_2 of ?ldsLO: Logicmath.LO/0311165 Vladimir Kanovei, Saharon Shelah: A de?able nonstandard model of the realsmath.LO/0311135 Jindrich Zapletal: Proper forcing and rectangular Ramsey theoremsmath.LO/0311095 Dmytro Taranovsky: Determinacy MaximumMG: Metric Geometry-math.MG/0311228 C. Cortes, C. I. Grima, F. Hurtado, A. Marquez, F. Santos, J. Valenzuela: Transforming triangulations of polygons on non planar surfacesMP: Mathematical Physicsquant-ph/0311080 G.Sardanashvily: Algebras of in?ite qubit systemsquant-ph/0311034 Witold Karwowski, R. Vilela Mendes: Quantum control in in?ite dimensionsmath-ph/0311022 M. Francaviglia, M. Palese, R. Vitolo: The Hessian and Jacobi Morphisms formath-ph/0311021 Z. Y. Wang, B. He, C. D. Xiong: A New Method of Strong-Coupling Expansionhep-th/0306210 Andres Anabalon, Mikhail S. Plyushchay: Interaction via reduction and nonlinear superconformal symmetryhep-th/0304257 Carlos Leiva, Mikhail S. Plyushchay: Superconformal mechanics and nonlinear supersymmetrycond-mat/0308333 nonlinear integral equation for thermodynamics of the higher spin Heisenberg modelmath-ph/0311020 H. E. Boos, V. E. Korepin, F.A. Smirnov: Connecting lattice and relativistic models via conformal ?ld theorymath-ph/0311019 Piotr Bizo'n, Tadeusz Chmaj, Zbislaw Tabor: On blowup for semilinear wave equations with a focusing nonlinearityhep-th/0311093 Romuald A. Janik: Exact U(N_c)-> U(N_1)xU(N_2) factorization of Seiberg-Witten curves and N=1 vacuacond-mat/0310499 Vadim V Cheianov, M B Zvonarev: Zero temperature correlation functions for the impenetrable fermion gascond-mat/0308470 Vadim V. Cheianov, M. B. Zvonarev: Non-Unitary Spin-Charge Separation in One-Dimensional Fermion Gasquant-ph/0311053 M. V. Karasev, T. A. Osborn: Quantum Magnetic Algebra and Magnetic Curvaturemath-ph/0311018 Mauro Francaviglia, Marcella Palese, Ekkehart Winterroth: A New Geometric Proposal for the Hamiltonian Description of Classical Field Theoriesmath-ph/0311017 A. Bianchi, P. Contucci, C. Giardina': Thermodynamic Limit for Mean-Field Spin Modelsmath-ph/0311016 C. Ram'{i}rez, P.A. Ritto: On the Hamilton-Jacobi formalism for fermionic systemsmath-ph/0311015 M. Havl'{i}v{c}ek, J. Patera, E. Pelantov'a, J. Tolar: Automorphisms of the ?e grading of sl(n,C) associated with the generalized Pauli matricesmath-ph/0311014 Alfonso Garc'{i}a-Parrado, Jos'e M. M. Senovilla: Bi-conformal vector ?lds and their applicationsmath-ph/0311013 Pepijn van der Laan: Operads and the Hopf algebras of renormalisationmath-ph/0311012 Anna De Simone, Mirko Navara, Pavel Pt'ak: Extending states on ?ite concrete logicsmath-ph/0311011 Eigenvalues for Fourth Order Differential Operatorshep-th/0311003 Bozhidar Z. Iliev: Momentum picture of motion in Lagrangian quantum ?ld theorymath-ph/0311010 Elliott H. Lieb, Jan Philip Solovej: Ground State Energy of the Two-Component Charged Bose Gasmath-ph/0311009 Armando D'Anna & Gaetano Fiore: Global Stability properties for a class of dissipative phenomena via one or several Liapunov functionalscond-mat/0311122 Klaus Fabricius, Barry M. McCoy: Functional Equations and Fusion Matrices for the Eight Vertex ModelNT: Number Theory--math.NT/0311226 Ernie Croot: A Combinatorial Method for Counting Smooth Numbers in Sets of Integersmath.NT/0311202 David Cox, John McKay, Peter Stevenhagen: Principal moduli and class ?ldsmath.NT/0311162 Aleksandar Ivi'c: On some reasons for doubting the Riemann hypothesismath.NT/0311131 Jordan S. Ellenberg: On the error term in Duke's estimate for the average special value of L-functionsmath.NT/0311120 Qi Cheng: On the Bounded Sum-of-digits Discrete Logarithm Problem in Kummer and Artin-Schreier Extensionsmath.NT/0311114 C. Krattenthaler, T. Rivoal: Hyperg{?e}om{?e}trie et fonction z{^e}ta de RiemannOA: Operator Algebrasmath.OA/0311222 S. Kaliszewski, Magnus B. Landstad, John Quigg: Hecke C*-algebras, Schlichting completions, and Morita-Rieffel equivalencemath.OA/0311201 Fr'{e}d'{e}ric Ja{e}ck, Stephen C. Power: Hyper-re?ty of free semigroupoid algebrasmath.OA/0311178 Elias Katsoulis, David W. Kribs: Applications of the Wold decomposition to the study of row contractions associated with directed graphsmath.OA/0311170 Hellmut Baumgartel, Fernando Lled'o: Duality of compact groups andmath.OA/0311115 Palle E.T. Jorgensen, Daniil P. Proskurin, Yurii S. Samoilenko: On C*-algebras generated by pairs of q-commuting isometriesmath.OA/0311110 Rolf Gohm, Michael Skeide: Normal CP-Maps Admit Weak Tensor Dilationsmath.OA/0311107 Marcel de Jeu: Commutative C^*-algebras and sequentially normal morphismsOC: Optimization and Control-math.OC/0311223 C. I. Byrnes, A. Isidori: Nonlinear internal models for output regulationmath.OC/0311169 M. de Leon, D. Martin de Diego, A. Santamaria-Merino: Discrete variational integrators and optimal control theoryPR: Probability Theory-math.PR/0311206 David Gamarnik, John Hasenbein: Instability in Stochastic and Fluid Queueing Networksmath.PR/0311144 Sergio Albeverio, Eugene Lytvynov, Andrea Mahnig: A model of the term structure of interest rates based on L'evy ?ldsmath.PR/0311142 Boris L. Granovsky, Aleksandr I. Zeifman: Nonstationary queues:Estimation of the rates of convergencemath.PR/0311133 E. Sandhya, R. N. Pillai: Renewal Theory and Geometric In?ite Divisibilitymath.PR/0311127 Maxim Krikun: Uniform in?ite planar triangulation and related time-reversed critical branching processmath.PR/0311125 Jozsef Balogh, Yuval Peres, Gabor Pete: Bootstrap percolation on in?ite trees and non-amenable groupsmath.PR/0311108 Spectrum of the Disordered Stochastic Ising ModelQA: Quantum Algebra-math.QA/0311224 B. Enriquez, P. Etingof: Quantization of classical dynamical $r$-matrices with nonabelian basemath.QA/0311214 Leroux Philippe: On some remarkable operads constructed from Baxter operatorsmath.QA/0311210 Toshiyuki Abe: Rationality of the vertex operator algebra $V_L^+$ for a positive de?ite even lattice $L$math.QA/0311204 Gunnar Sigurdsson, Sergei D. Silvestrov: Bosonic realizations of the color analogue of the Heisenberg Lie algebramath.QA/0311197 Cyril Grunspan: Quantizations of the Witt algebra and of simple Lie algebras in characteristic pmath.QA/0311171 Tomasz Brzezinski, Florin F. Nichita: Yang-Baxter Systems and Entwining Structuresmath.QA/0311161 N. Aizawa, R. Chakrabarti: Noncommutative Geometry of Super-Jordanian $OSp_h(2/1)$ Covariant Quantum Spacemath.QA/0311158 G. Lusztig: A q-analogue of an identity of N. Wallachmath.QA/0311152 Georgia Benkart, Paul Terwilliger: Irreducible Modules for the Quantum Af?e Algebra $U_q(hat{sl}_2)$ and its Borel subalgebra $U_q(hat{sl}_2)^{geq 0}$math.QA/0311151 Benjamin Doyon, James Lepowsky, Antun Milas: Twisted vertex operators and Bernoulli polynomialsmath.QA/0311146 A. Ballesteros, E. Celeghini, M.A. del Olmo: Three dimensional quantum algebras: a Cartan-like point of viewmath.QA/0311141 for an even lattice L without rootsmath.QA/0311132 Leroux Philippe: Construction of Nijenhuis operators and dendriform trialgebrasmath.QA/0311128 Rafael Diaz, Eddy Pariguan: Symmetric Quantum Weyl Algebrasmath.QA/0311097 R. B. Zhang: Quantum superalgebra representations on cohomology groups of non-commutative bundlesmath.QA/0311096 N. Lam, R. B. Zhang: Quasi-?ite representations,free ?ld realizations,and character formulae of Lie superalgebras of in?ite rankRA: Rings and Algebras-math.RA/0311199 Frobenius-Schur IndicatorsRT: Representation Theory-math.RT/0311207 S.Eswara Rao, Vyacheslav Futorny: Irreducible modules for af?e Lie superalgebrasmath.RT/0311190 Giovanni Felder, Alexander P. Veselov: Coxeter group actions on the complement of hyperplanes and special involutionsmath.RT/0311159 Roger Howe, Eng-Chye Tan, Jeb F. Willenbring: Stable branching rules for classical symmetric pairsmath.RT/0311143 G. Lusztig: Convolution of almost charactersmath.RT/0311118 Herv'e Sabourin: Sur la structure transverse `a une orbite nilpotente adjointemath.RT/0311104 Patrice Tauvel, Rupert W.T. Yu: On the index of certain Lie algebrasSG: Symplectic Geometry--math.SG/0311179 Bernhard Kroetz, Michael Otto: Lagrangian submanifolds and moment convexitymath.SG/0311154 Camille Laurent-Gengoux, Ping Xu: Quantization of Quasi-Presymplectic Groupoids and their Hamiltonian Spacesmath.SG/0311093 math.SG/ 0311092 SP: Spectral Theory-math.SP/0311200 Yuri A. Kordyukov: Spectral gaps for periodic Schrodinger operators with strong magnetic ?ldsmath.SP/0311184 Francesca Antoci: On the spectrum of the Laplace-Beltrami operator for $p$-forms for a class of warped product metricsmath.SP/0311102 Francesca Antoci: On the spectrum of the Laplace-Beltrami operator for p-forms on asymptotically hyperbolic manifolds-- / Greg Kuperberg (UC Davis) / / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ / * All the math that's ? to e-print * === > Is it true that every (arc-connected) subset of R^3 has torsionless> fundamental group?> I can ask more:> can it contain a non trivial element A which is conjugate to A^k with> k different from 1? (i.e. can a non trivial loop be freely homotopic> to a power of itself, like arises, for example, in Klein's bottle,> with k=-1).> I'm mostly interested in the case of open subsets of R^3, or, more> generally, certain kinds of 3-manifolds.You might be interested in the following result by Peter Shalen (Three manifolds and Baumslag-Solitar groups, Topology Appl. 110 (2001),113--118, dvi ?e available on P. Shalen's page:http://www2.math.uic.edu/~shalen/papers.html )Let $M$ be a connected, orientable 3-manifold. Suppose that there areelements $x, y in pi_1(M)$ and nonzero integers $m$ and $n$ such that$x^n=yx^{m}y^{-1}$. Then either:-$x$ has ?ite order, or-$m=n$ or $m=-n$.Hope this helps,Estelle SoucheUniversit.8e Paris-Sud === Dear Phorum Participants!Please help to ?d all functions f(x,y), which satisfy the followingtwo conditions:1. f(x,1/x)=x, for all x > 0,2. f(x,y)*f(y,x)=1, for all x > 0, y > 0.Here x > 0, y > 0 are independent variables, and function f(x,y) issupposed to be well-behavied enough you require. === >Please help to ?d all functions f(x,y), which satisfy the following>two conditions:>1. f(x,1/x)=x, for all x > 0,>2. f(x,y)*f(y,x)=1, for all x > 0, y > 0.>>Here x > 0, y > 0 are independent variables, and function f(x,y) is>supposed to be well-behavied enough you require.Take any continuous f from {(x,y): 0 < y <= x} to (0,in?ity) such that f(x,x) = 1 and f(x,1/x) = x for x>=1, and de?e f(x,y) = 1/f(y,x) for 0 < x < y. This gives you a continuous solution f.Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === > Please help to ?d all functions f(x,y), which satisfy the following> two conditions:> 1. f(x,1/x)=x, for all x > 0,> 2. f(x,y)*f(y,x)=1, for all x > 0, y > 0.>> Here x > 0, y > 0 are independent variables, and function f(x,y) is> supposed to be well-behavied enough you require.sqrt(x/y)-- Maxi === >> Please help to ?d all functions f(x,y), which satisfy thefollowing>> two conditions:>> (1) f(x,1/x)=x, for all x > 0,>> (2) f(x,y)*f(y,x)=1, for all x > 0, y > 0.> sqrt(x/y)Of course, f(x,y)=sqrt(x/y) is the obvious solution.But is there another one? And how one can describe general solution?Here are some thoughts...By changing variables(*) f(x,y)=sqrt(x/y)*g(x,y),one can get analogues of (1), (2) for g(x,y):(1') g(x,1/x)=1, for all x > 0,(2') g(x,y)*g(y,x)=1, for all x > 0, y > 0.General solution to (2') is:g(x,y)=h(x,y)/h(y,x),where h(x,y) is an arbitrary function of two variables (h(x,y)=/=0).Replacing it in (1') and (*) we get general solution to the system(1), (2) in the following form:f(x,y)=sqrt(x/y)*h(x,y)/h(y,x),where h(x,y) is an arbitrary, which admits the identity:h(x,1/x)=h(x,1/x).But the question remains: can we further somehow characterize theidentity h(x,1/x)=h(x,1/x), such that it allows to get generalexpression for f(x,y) in terms of arbitrary functions without anyrestrictions on them (like we have done for g(x,y))? === >> Please help to ?d all functions f(x,y), which satisfy the> following>> two conditions:>> (1) f(x,1/x)=x, for all x > 0,>> (2) f(x,y)*f(y,x)=1, for all x > 0, y > 0.> sqrt(x/y)> just an idea: Take the logarithms of x, y and f:u = log(x), v=log(y), g=log(f).Then modulo mistakes you should get the simpler equationsg(u, -u) = ug(u, v) + g(v, u) = 0Good luckAlois === > Sequence A004003 in the OEIS gives the number of perfect matchings of> a 2n x 2n grid :> http://www.research.att.com/projects/OEIS?Anum=A004003> Let a(n) = number of matchings (not just perfect) in a n x n grid . > Is there a familiar formula for a(n) ? If I understand you correctly, you are interested in some alternatingsum of the coef?ients of the matching polynomial.[Is this really http://www.research.att.com/cgi-bin/access.cgi/as/njas/ sequences/eisA.cgi?Anum=A028420 ?]If so, there is a list of matching polynomials up to a 13 x 13 grid underhttp://www.htwm.de/~peter/research/grids.html.Fot the fun of it, I've just computed the values I think you are lookingfor up to 201 12 73 1314 100125 28106946 29891267277 119452570523218 1797883431019801359 1018511191916066611860810 217213878367309419393775001511 174382982324016449469438643797064012 527013799381608626696287439545023453488713 5995691982425775050865563110747467228449973608914 256777306978703066701149467581263783266767781021920306815 41397470171720265411055074586610800785189751844835798089512207 516 25124119353860595703454110691906604019026368429225241668609370 902016827217 57399454322006644552342197409366226850954610131096501641743197 69 5381191100783051418 49365615189191715763323069655214514712910294560800540275223860 66 58602563272063311176647746319 15982371305671164821519293167546721606553899307517165437610503 08 2868498682368743637572497232683956812820 19478600557353110233522483460151519831499212942923222279949450 82 8627169865552544664189208324046148975664925677335Unfortunately , the memory used by my algorithm doubles for each item inthis sequence, and runtime is even slightly worse so I can't go muchfurther (23 or so on the desktop). The last line took ~105 MB of RAMand almost ten minutes to compute.I don't hink you will ?d a ?closed form' solution, though.Andre'[PS: If you _really_ need more items this could be improved to up to ~29entries (with a little help from Chinese remainders and the computinglab here that is..). But I doubt this will buy you much insight into theproblem.] === Let f: N -> M be a smooth map. Here N and M are manifolds of dimension n and m respectively, with n>m.Suppose that f is surjective/onto, and is amany-to-one mapping, so it is not invertible.Let S be a subset of M with zero m-dimensionalHausdorff measure, i.e., S is a null set.Suppose that the pre-image of each point in S is a set of zero n-dimensional Lebesgue measure. Does this imply that the preimage of S has zeron-dimensional Hausdorff measure?(If it makes things easier, you can replace allHausdorff measures by Lebesgue measures.)Simon === >Let f: N -> M be a smooth map. >Here N and M are manifolds of dimension n and >m respectively, with n>m.>Suppose that f is surjective/onto, and is a>many-to-one mapping, so it is not invertible.The last bit is hardly surprising if n > m.>Let S be a subset of M with zero m-dimensional>Hausdorff measure, i.e., S is a null set.>Suppose that the pre-image of each point in S >is a set of zero n-dimensional Lebesgue measure. >Does this imply that the preimage of S has zero>n-dimensional Hausdorff measure?No. Consider the case of f(x,y,z) = (x,g(y)) from R^3 to R^2with S = R x {0}, where g is a smooth function from R onto Rsuch that g(y) = 0 for 0 <= y <= 1. Robert Israel israel@math.ubc.caDepartment of Mathematics http://www.math.ubc.ca/~israel University of British Columbia Vancouver, BC, Canada V6T 1Z2 === >Let f: N -> M be a smooth map. >Here N and M are manifolds of dimension n and >m respectively, with n>m.>Suppose that f is surjective/onto, and is a>many-to-one mapping, so it is not invertible.>>Let S be a subset of M with zero m-dimensional>Hausdorff measure, i.e., S is a null set.>Suppose that the pre-image of each point in S >is a set of zero n-dimensional Lebesgue measure. >>Does this imply that the preimage of S has zero>n-dimensional Hausdorff measure?>>(If it makes things easier, you can replace all>Hausdorff measures by Lebesgue measures.)>SimonNo. As a counter-example, take N = R^3, M = R^2, and S = R^1 (with itsstandard embedding in M), and de?e f(x, y, z) = (x, g(z)*y) whereg(z) is a smooth function, g(z) >= 0, g(z) = 0 on some interval I, andg maps R onto the set of non-negative real numbers.It is easy to check that f is surjective. The pre-image of a point(x0, 0) in S is contained in the plane {x = x0}, so it has measure 0.The pre-image of S, however, is the set{(x, y, z) | g(z)*y = 0}, which includes the set {(x, y, z) | z in I},and this set has positive measure in R^3.John Mitchell === The problem I posted originally is actually much more generalthan the speci? problem I wish to solve. I should have givenmy speci? problem instead of this more general problem:I have a map that takes a full-rank matrix of order m by n (with m0. ( mu, beta, lambda >0 and rho<0 are constants).W is a Brownian motion, Z an independent Levy process with no gaussiancomponent and positive increments (a subordinator).Assuming Z has no deterministic drift and the cumulant k(theta) = logE(e^{theta Z_1}), where it exists, takes the form:k(theta)=int_{x>=0}(e^{theta x}-1)w(x)dxwhere w(x) is the density of the Levy measure of Z_1. (There are some otherassumptions on Z but they're just technical making sure w(x) is reasonableso that sigma^2 has a stationary distribution)The problem is to ?d the dynamics of S_t=e^{X_t}using Ito's formula.The answer looks right but I can't see how it has been derived.The answer is:dS_t=S_{t-}(b_t dt _ sigma_t dW_t + dM_t)where b_t is the process given byb_t=mu + lambda k(rho) + (beta + 1/2)sigma_t^2and M_t is the martingale Levy processM_t = Sigma_{0(T2 is true)b)(T1 is true)=>(T2 is false)c)(T1 is false)=>(T2 is true)d)(T1 is false)=>(T2 is false)4. If T1 and T2 are the statements satisfying 2. We are to considerwhether T1 and T2 are independent or not. The subtle question here is:is it possible that we ?ish this job within X?5. Here's a WRONG example, just to show the idea.T1=Solution to x^2=0(x in real) is x=0.T2=The Riemann's Hypothesis.Note that T1 and T2 do not satisfy 2. The idea here is to consider `IsT1 independent from T2?'Disregarding all the constraints for T1 and T2, one may seriouslyask:Does it help to prove the Riemann's Hypothesis if I know that thesolution to x^2=0(x in real) is simply x=0? You'll probablyanswer:Well... you're kidding.... it's obviously impossible. Thenhow do you prove this impossibility? More subtly, is there a chancefor you to prove this impossibility?Any comments? === I am reading a book on formations of ?ite groups. There are manyde?itions but a lack of particular examples. All natural examplesof formations seem to be varieties as well. This complicatesunderstanding what makes formations different from varieties. Couldanybody give an example (possibly the most simple and natural) offormation of ?ite groups that1) is not closed under taking normal subgroups2) is closed under taking normal subgroups but not closed under takingall subgroups3) an example of two formations K,L such that their product KL is notequal to the class of extensions Ext(K,L) (K must not be closed undertaking normal subgroups for that.)4) an example of class of ?ite groups closed under taking normalsubgroups and direct products but not closed under taking quotients5) an example of class of ?ite groups closed under taking normalsubgroups and direct products but not closed under taking allsubgroupsThe ?st three are more important for my understanding, so I will bevery grateful if someone gives such an example. The other two aresomewhat connected with Fitting classes and will help to feel thegeneral perspective, so they are just interesting. === Journal of Algebra and Its ApplicationsView contents and abstracts at http://www.worldscinet.com/jaa.htmlSmooth Order SingularitiesRaf Bocklandt, Lieven Le Bruyn and Geert Van De WeyerPure-Injective EnvelopesIvo HerzogOn Algebraic Supergroups and Quantum DeformationsR. FioresiSome Subgroups Of The Normalizer Of Γ0(Μ) In ${Bf Psl}(2, {Mathbb C})$Re? KeskinProjective Modules And Divisor HomomorphismsAlberto Facchini and Franz Halter-KochFree Malcev Superalgebra On One Odd GeneratorIvan P. ShestakovThe Discriminant Of Sub?lds Of Q(Ζ2r)Jose Othon Dantas LopesPushouts Of Partial Homomorphisms Of Partial Algebras Ii: Closed QuomorphismsR. Alberich and F. RosselloErrata Erratum: When self-injective rings are qf: a report on a problemCarl Faith and Dinh Van HuynhFor more information, go to http://www.worldscinet.com/jaa.html === Let A be a real matrix with dimension m x n where m>n.I need to ?d a submatrix B with dimension n x nsuch that the condition number of B is minimum.Here is what I have done.while (no. of rows of A > n) { for each row of A { Let A_i be the submatrix of A without i-th row; compute c_i = condition number of A_i; } ?d i where c_i is minimum; A = A_i;}Is this approach acceptable ? Any suggestion ? === >Let A be a real matrix with dimension m x n where m>n. >I need to ?d a submatrix B with dimension n x n >such that the condition number of B is minimum. >Here is what I have done. >while (no. of rows of A > n) { > for each row of A { > Let A_i be the submatrix of A without i-th row; > compute c_i = condition number of A_i; > } > ?d i where c_i is minimum; > A = A_i; >} Is this approach acceptable ? Any suggestion ?it is a reasonable way to go, but I cannot see how to prove optimality.what you are doing is some kind of reverse greedy algorithm in a global nonconvex discrete optimization problem (keep _a_ locally best solution). but how to show global optimality? there are theorems on themonotonicity of the eigenvalues in downdating (the singular values related to the eigenvalues of A'A in downdating . And your A_i'A_i = A'A - a_i'*a_i a_i it row of A = current A. so this is downdating). but a small decrease in one step might later result in a much larger decrease?). I have the book not handy, but there is a book on subset selection in regression by Alan Miller. Maybe this has someinfo. )hthpeter === >I am looking for a way to integrate this with at least 50 digits after>decimal :[Snip integral of the form Int( P(x)*cos(x*exp(x))*exp(-24*x)*(1+x)^(-48), x = 0 .. x0 ); where P is an integer polynomial 24! x^24 + ... + 5^48 and x0=9.488...]>What method or software should I use ???Well, before trying numerical analysis you can use some simple calculus.1. Integrate only to about x0=5.5 because the integrand is smaller than about 10^(-52) there. This means you only go through a couple hundred periods of the trig function.2. Rewrite P as a polynomial in 1+x (still integer coef?ients, degree 24) and cancel some (1+x)'s. This both lowers the 48 and eliminates P.3. Writing C(k,m) = exp(-k*x) * (1+x)^(-m) * cos(x*exp(x)) and likewise for S(k,m) (using sine) we ?d that C'(k,m) = -k*C(k,m) - m*C(k,m+1) + S(k-1,m-1) and similarly for S'(k,m). Singling out the middle term on the right side, this means that for m>0 we can express an integral of a C(k,m+1) in terms of integrals of C(k,m) and S(k-1,m-1). Iterating this idea, we see there is no need to compute any integrals except those of C(k,0), C(k,1), S(k,0), and S(k,1). (Note that we start with integrals of C(k,m) with k=24 and m <= 48=2k; the reduction formulas will preserve the inequality m <= 2k and in particular we need not compute such integrals with negative k.)So the problem reduces to computing (to some 80 digits of accuracy!)integrals of the forms int( exp(-k*x) * cos(x*exp(x)), x=0..x0) int( exp(-k*x) /(1+x) * cos(x*exp(x)), x=0..x0)(and similarly for sines) for 0 <= k <= 24, where x0 is around 5.5 .I don't know what's recommended when facing both rapid oscillationsand fast decay in the integrand.It may be productive to continue the reduction in (3) to allow negativem as well (in an effort to reduce k so that the integrand does notundergo such dramatic decay).dave === I'm looking for on any good links or others on the Marple algo. andprograms. === > So basically I think my question boils down to:> Is there any package for calculating a piecewise polynomial> approximation to a function f(x) on a given interval whose integral> on any sub-interval approximates that of f(x) to a given tolerance> (under the same caveats that the standard adaptive integration> routines assume). There is an algorithm in ACM-CALGO, #510 by D. G. Wilson. It usessegmented linear functions. The code is ?ed format, F77. You mightstart there. === Let F=(4-3i -6-2i) ?d the eigenvalues, vectors of F. Use this to?d the (-1-2i -1+2i)?ed points of f, the fractional linear transformation associated toF. Find the ?ed points of f directly. Let C= (x1 x2) . ComputeG=C^1FC and verify (y1 y2)that it is (lamda1 0). Let g be the fractional linear transformationassociated (0 lamda2)to G. what is g(z)? === Orig-To: sacredlandscapelist at yahoogroups.com50031029 viii om?st installment, 0, 1, 2x2, 3x3 (+ 4x4 notes)# ...I propose ...we try to solve the magic squares once# and for all.I think I know what you mean. I tried something similar with an8x8 ?Mercury' Square in order to con?ure it properly for Yijingdivination using it and Chess. I found out that while there areseveral solutions (as with many magic squares), there is one mostsimple (transposition) solution. there are famous, named squares,however, with intriguing properties of identical sum throughoutthat make it dif?ult to do more than grade such solutions in'solution once and for all' is, without further de?ition of whatsolution means, too ambiguous to produce. mathematics constitutesthe ?ld of endeavor which includes number arrangement (logic,puzzles, computers, and, for some, thaumaturgy or theurgy).orders (sizes) of magic square were provided assignment byoccultists to planets, gods, and other quirky principles, itsapparent fact of sequence mapped to the apparent Planets of thetime. with the discovery of 3 more planets, and as I'm beginninga refashioning for mages of my ilk in the PISCEAN age what shouldhave been done long ago, I agree that some kind of new Solutionshould be devised with speci?d parameters for the constructionof novel magical devices and systems. the tendency to remain inthe past, accept the well-worn constructions of the past, eventhough their knowledge-base is superceded by plain contradiction,is to set into Golden Age remembrance what should be oriented tothe present and personal as a mapping one-to-one correspondence.# I believe that they do represent a higher form of mathematics# that currently is not in use by our scientist.magic squares are formal structures, not formulae in a sense asto be recognizable by many modern scientists, and to call thema higher form of mathematics is to provide them a greater rangeof meaning than should include them. yes, the magic square is adevice usable by magicians to in? the universe (they think),and typically magic is considered a form of science unrecognizedby the witness (esp. for fans of ACClarke). I'm not sure what issupportable beyond this.# I also believe that we collectively have the ability to solve# the apparent complexities concerning these squares.very true, many are gifted in the area of mathematics that havethe time and interest in lending a hand. references are alsoavailable, interestingly enough (many online). the best appearto be long treatises that haven't made it online yet. I'm veryseriously considering transcribing some of Andrews' book if ithasn't yet been done.# Anybody who wants to partake or have suggestions/input is# more than welcome to join in and help out.agreed! :># I have read the three books of occult philosophy by cornellius# agrippa,which translation? I've been looking at it carefully lately andnoting its resonances, geometrics and attributions. the LlewellynTyson version has some helpful but sometimes ambiguous notes thatare supplemented with generous Appendices. to read the thingstraight through is different than using it as a reference(indexing, or via ToC for topics). his magic squares are perhapsin need of re?ement (Tyson corrected many errors in translationsat least, a few from the original manuscript, if I recall arightly).# and have gained some insights which I would like to share.thank you! more!!# ...the 3x3 square is probably useless and/or unlucky in that its# total result is equal to 666 and any attempt at solving it would# be futile.LOL! the 3x3 square, also known as the Lo Shu or Lo Riverdiagram, also known as the Saturn Square, is widely known forits luck, power and the bene?s it affords its magical users.its actual total is 136 (the ?Sun' square 6x6 adds to 666).the questions are to what ought the 3x3 be associated and whether there is more than one solution to it.3x3 is certainly the lowest *order* of magic square, by theusual minimum de?ition (rows, columns, and major diagonalscomposed of a set of sequential numbers adding to the same total).as I have suggested elsewhere, fundamentals of magic squareconstruction allow earlier orders by restricted quali?ation.more below. === === === == Magic Squares : Arcane Speculation on Mathematical Objects in Series by Seyfert-1 (nagasiva) Proto-Squareswhat follows is a beginning of analysis of magic squares forarcane reformation purposes and intrinsic morphological content.(order) === (1? 0?) 1the smallest order (0?) of magic square? only in a senselike anything to the 0 power produces the result of 1. :>perhaps this could be attributed somehow (with the nextorder(s 0/1/2)) with a Without/Limitless/LVX trinityof pre-Ketherian Qabalistic Nothingness. :>one might also construct the square out of letters, inwhich case we're probably talking about Aor perhaps + (t/200? x/600?) (2) 1 2 1 4 A -- 3 4 B -- 2 3no possible solution obtains for a 2x2 square, but there is a con?uration with the least differential in summation (sums in parens): (5)(5) (3) (7) (4) 1 3 A C = C -- (6) 4 2 D B (Ulian Schemata)the extreme sums displaced to the diagonals. 2x2 pursuedin letters might double upon itself like so: (4) A B 1 2 (3) = B A 2 1 (3) (2) (3)(3)simultaneously referencing paternal authority (ABBA),or (1600) A Z 1 800 (801) = Z A 800 1 (801) (2) (801)(801)symbolizing the Beginning and the End (Romanizationof the Greek, popular Alpha et Omega).General-any letter / number / ?ure might be utilized withina square of this order to combine 2 (or 4) elements(e.g. Jupiter(6) and Saturn(7): 6 7 F G = 7 6 G For the use of their sigils inside an amulet or someceremonial diagram which calls for their qualities).-- -Proper Magic Squares (3x3 => 13x13)the ?st of the odd magic squares (Andrews divides theminto families of odd and even because of methods of theirderivation and construction) has *1* solution, and isthe only magic square that has a single solution.the variation of this square is not its numerical arrange-ment so much as its *orientation*. while this is true ofall magic squares (that they have orientations, and alsomirror-images), this is seldom remarked upon by occultistswho identify their selections, since the solution producingthe requisite sums suf?es to assign the whole.for my purposes, and in order to be thorough, I'll providewhat information I am able about traditional cultural usageof these, assigning each to the recti?d astronomicalstandard after the pattern of Agrippa and others in occulttraditions, and requesting additions from the interested.my impression is that few take great care in dealing withmagic squares as a whole, haphazardly presenting what tothem conforms to a logical parameter (true enough, butinsuf?iently-detailed for scrutinizing occult practice). (3) PLUTO -- traditional: Lo Shu, Saturnthus the Square of Pluto (Lo Shu, formerly Saturn) in itsvarious possible orientations is as follows: (15) (15) (15) (15)(row i) (15) 4 9 2 D I B(row ii) (15) 3 5 7 = C E G(row iii) (15) 8 1 6 = H A F (15)this is the con?uration presented as both the Lo Shu(e.g. in Master Huang's book on Numerology) and for thePlanet Saturn (in Tyson's Agrippa).I have labelled the rows here (i->iii) which could alsobe arranged in columns or transposed to iii->i. thislatter arrangement (with 8/1/6 at top) is presented inAndrews for the 3x3 square (page 2, ?ure 1).there are 2 families of 4 orientations, constituting atotal of 8 possible arrangements of this 3x3 square ifone details its rectilinear positions and mirrorings: - 2 7 6 6 7 2 9 5 1 1 5 9 4 3 8 8 3 4 - 4 3 8 8 3 4 9 5 1 1 5 9 2 7 6 6 7 2 - 2 9 4 4 9 2 7 5 3 3 5 7 6 1 8 8 1 6 - 6 1 8 8 1 6 7 5 3 3 5 7 2 9 4 4 9 2 -these might be associated with 8 Yijing trigramsfor a complex cross-reference. how to begin suchan assignment will depend on what one takes as aprimary sequencing key or mapping translator (e.g.orienting the corners to a 2-4-6-8 clockwiseprogression might initiate the sequence, or the2/7/6 at top might come ?st as its numbers inthe upper-left and top-center are lowest).that the circling 8 numbers (1->9 excepting 5) are*already* given trigrammatic assignments withinthe Lo Shu (see Master Huang's Numerology at leastfor this) may make identifying the particular squareswithin this scheme easier by keying the numbers totrigrams and then solving for ?net trigram' bycon?urative quality. substituting numbers allowsthe following, initially, the following may be usedwithin some formula to conclude as to ordinal value: - 2 7 6 6 7 2 __ __ __ __ _____ _____ __ __ __ __ __ __ _____ _____ _____ _____ __ __ __ __ _____ _____ _____ _____ __ __ 9 5 1 1 5 9 _____ __ __ __ __ _____ __ __ . o _____ _____ o . __ __ _____ __ __ __ __ _____ 4 3 8 8 3 4 _____ __ __ _____ _____ __ __ _____ _____ __ __ __ __ __ __ __ __ _____ __ __ _____ __ __ __ __ _____ __ __ - 4 3 8 8 3 4 _____ __ __ _____ _____ __ __ _____ _____ __ __ __ __ __ __ __ __ _____ __ __ _____ __ __ __ __ _____ __ __ 9 5 1 1 5 9 _____ __ __ __ __ _____ __ __ . o _____ _____ o . __ __ _____ __ __ __ __ _____ 2 7 6 6 7 2 __ __ __ __ _____ _____ __ __ __ __ __ __ _____ _____ _____ _____ __ __ __ __ _____ _____ _____ _____ __ __ - 2 9 4 4 9 2 __ __ _____ _____ _____ _____ __ __ __ __ __ __ _____ _____ __ __ __ __ __ __ _____ __ __ __ __ _____ __ __ 7 5 3 3 5 7 __ __ __ __ __ __ __ __ _____ . o __ __ __ __ o . _____ _____ _____ _____ _____ 6 1 8 8 1 6 _____ __ __ _____ _____ __ __ _____ __ __ _____ __ __ __ __ _____ __ __ __ __ __ __ __ __ __ __ __ __ __ __ - 6 1 8 8 1 6 _____ __ __ _____ _____ __ __ _____ __ __ _____ __ __ __ __ _____ __ __ __ __ __ __ __ __ __ __ __ __ __ __ 7 5 3 3 5 7 __ __ __ __ __ __ __ __ _____ . o __ __ __ __ o . _____ _____ _____ _____ _____ 2 9 4 4 9 2 __ __ _____ _____ _____ _____ __ __ __ __ __ __ _____ _____ __ __ __ __ __ __ _____ __ __ __ __ _____ __ __ -and once a formula of solution is put into operation,(e.g. root lines value 4, mid-lines value 2, top 1,left-most value 4, mid-trigram value 2, right 1, solvefor each magic square arrangement to 8 values), thenthese may be arranged and identi?d accordingly andeven used for divinatory and magical enterprises inassociation with the Planetary in?s of Pluto.Andrews makes plain that one might substitute for thenumbers in any of these squares a formula whereby thealgebra of variables may be used to solve for all themagic square's contents given any initial ?ure ?X'which is the least number in the square (our solutionmerely derives the *least* integer, X=1), such that for ?X'=2 (45) (45) (45) (45) (row i) (45) 10 28 07 (row ii) (45) 12 15 18 (row iii) (45) 23 02 20 (45)which will not map to an order A=1...Z=26 system,requiring dual-letter combinations such as themost evident Ulian simple combination system: J KH G JB JE JH KC B Kthrough this method one might utilize Plutoniansquares with variable least seed numbers to constructany number of alternatives, each having 8 sets oforientations and mirrorings which might be cipheredthrough an Ulian combination system to string sets.Magic Squares Essay terminates. === === === ==returning to conversation in Sacredlandscapelist, venturing to(4) (notes)# ...most ...fortunate square, ... the square of jupiter# or 4x4....by traditional Planetary assignment, 4x4 = Jupiter, which iscalled in astrology ?The Great Bene?ent'. for this reasonyour assertion is valuable within such a context.# 04 14 15 01# 09 07 06 12# 05 11 10 08# 16 02 03 13 = D N O A I G F L E K J H P B C M (A=1... Z=26)through proliferation merely by orientation and mirrorings,we're talking about at LEAST 4 orientations and their 4 mirrorsonce more, *plus* any variations in composition beyond the obvious row/column reversal (yielding at least 8 possibles) by virtue of formulation of number positions (again where here X=1).why 04 should be placed at top left (rather than 01) is avaluable query. we have been presented the ?Jupiter Square'as selected by Agrippa. in fact, Andrews derives 6 laws (that I am not reproducing here for the sake of simplicity, but a thorough investigation of the 4x4 ought include it) governing all 4x4 magic squares, and produces the 4x4 square below, indicating that squares of *higher* order are too complex to reduce to laws. 01 08 12 13 14 11 07 02 15 10 06 03 04 05 09 16as we can see just by these 2 examples, there are a largenumber of possible 4x4 arrangements, before even consideringminor variation like orientation or mirroring, which may, aspart of their composition, have the ?associated' qualityof adding to a speci? sum in symmetrical positions (e.g.here the sums equate to 17 on positions across a diagonal).I'm not aware of many cultural designations of the 4x4 magic square comparable to Lo Shu. Andrews does mention what hecalls a Jaina Square of 4x4, which is: JAINA SQUARE - 07 12 01 14 02 13 08 11 16 03 10 05 09 06 15 04from an inscription of the 12th or 13th centuries by Jainsmentioned by a Professor Smith and passed on by Andrews(pp. 124-128) and apparently of a different quality thanmany of the other possibilities (to be explored later).the qualities of 4x4 squares is only compounded in depthas one progresses to greater orders, plus it may beintegrated into larger squares as central portions!# According to the philosophers (agrippa,solomon,pythagoras etc)there's a wealth beyond this, apparently, in the world ofphilosophy and magic. :> I am only barely touching on thismyself by elaborating on your wonderful post.# there# is an intelligence or higher spirit if you like that determine the# outcome of certain events. There is a spirit to what is good and a# spirit to that which is bad. So I gather that the future prediction# of number is dependant on which spirit has the most in? at the# time. However as Agrippa tells us the number of these intelligences# its not neccessary to know who rules, just that there are 2 possible# future outcomes when predicting a number between 1-16. The# intelligences are both allocated 136 (the total of the square) and# are arrived at by means of the seals and characters of jupiter.my impression (a guess) is that some kind of name was discernable*within* the square being considered as it was substituted withletters and that these were ascribed *after the fact*, thendrawn out as sigils accordingly. I see no reason why they wouldbe necessary in any sense, but am open to hearing arguments forthis. of course the way Agrippa has it these arrive in Hebrew,but one could construct this within English or other languages.that is certainly my intent, which is in part why I'm providingthe Ulian and AlphaZed equivalences in this post, for futurereference and construction by the student (myself included!).# the problem has been that no one knows how these seals where arrived# at and therefore can not be assigned to the squares directly. This# seems to be the ?st road block in it's translation. Is anyone here# familiar with the seals and sigils?this constitutes a secondary level of analysis where magic squaresare concerned because they enter into linguistic construction thathas no mathematical basis and therefore few real delimiters of form.a Jovian construct analysis:# However Agrippa tells us that they are arrived at in this fashion:this actually constitutes a description of what was constructed,rather than its construction method per se.# Intelligence to what is good:# Jophiel = IHPHIAL# I=10 + H=5 + PH=80 + I=10 + A=1 + L=30 TOTAL=136## A spirit to what is bad:# H=5 + S=60 + M=40 + A=1 + L=30 TOTAL=136one may therefore analyze the *method of determination* to a degree and construct the rules: a) the total of the names of the Intelligences and Spirits must equate to the total of the numbers in the square; b) the letters for these numbers are connected, creating the Seals for magical operations.# ...## The ?st step in this unsolvable mess was# the disproval of the 4 elements, our scientits discovered more and# more, and the basic concepts of the elements and their ratios was# lost.the re?ement of ?elements' made this possible. modern scientistsare merely reductionists, focussing on subatomic elements, whereasprevious perspectives of elements weren't reductionist at all butmaterial in a compository manner (examine the early Greeks and wecan see that they were struggling to come up with a ?universalelement' in the same way that today there is a move toward whathas been called ?Uni?d Field Theory'. whether these early Greekswere actually atomists, precursors to today's materialists issomething of a controversy as I understand it (something whichI think Heidegger argued against, if I recall correctly).# ...if the# elements where ratios of numbers, like... 1 is to 2 as 2 is to 4 each# one being it's double, then why not the seven planets also? why could# the seven planets also not be ratios of 1 being related to one as the# other?, I mean is it a coincidence that an atom has seven shells, or# the the sacred tetractys (the foundation of all magic and all form)# also has seven points in this fashion?## THE SACRED TETRACTYS OF PYTHAGORAS:## POINT 1 UNITY# LINE 2 3 PRIME# SURFACE 4 9 SQUARE (2X2) + (3X3)# SOLID 8 27 CUBE (2X2X2) + (3X3X3)very lovely. the tetraktys is usually: 1 2 3 4 5 6 7 8 9 10and so while I can see the resemblance, I'm not sure I understand your point here yet. Seyfert-1luckymojo.com@nagasiva ===refs Agrippa, H.C.: Three Books of Occult Philosophy, Llewellyn Publications, tr. Freake, ed. Tyson, 1997; ISBN 0-87542-832-0 Andrews, W.S.: Magic Squares and Cubes, Dover Publications, 1960; ISBN 0-486-20658-0 === = === ==END -- apologies for any duplications.===hi, what's the simplest numerical method to solve a 2d conservation lawwith *2nd-order accuracy* ? actually, what i have is the following differential eqn: u_t + (a(x,y)u)_x + (b(x,y)u)_y = 0where a(x,y,t) and b(x,y,t) are two given continuous functions, and they don't have constant sign. is there any good method to solve such kind of SCL with spatially varying ?hanks, hhl === >hi, >what's the simplest numerical method to solve a 2d conservation law >with *2nd-order accuracy* ? >actually, what i have is the following differential eqn: >u_t + (a(x,y)u)_x + (b(x,y)u)_y = 0 >where a(x,y,t) and b(x,y,t) are two given continuous functions, >and they don't have constant sign. >is there any good method to solve such kind of SCL with >spatially varying ? >thanks, >hhllook here:http://www.amath.washington.edu/~clawhthpeter === > what's the simplest numerical method to solve a 2d conservation law> with *2nd-order accuracy* ? Since your equation is linear, you could try some sort of highorder characteristic method. But do note that you shouldn'texpect high order at discontinuities (Gibbs oscillations will bite you).Have a look at this: An overview of reasearch on Eulerian-Lagrangian localized Adjoint methods (ELLAM), T. F. Russell, M. A. Celia, Advances in Water Resources 25 (2002) 1215-131-- Bjrn-Ove HeimsundCentre for Integrated Petroleum ResearchUniversity of Bergen, Norway === about Fuzzy Logic, Fuzzy Systems or fuzzy DSS used in Supply ChainManagment?I've been looking in the web for quite a while but I only ?dabstracts...any help would be appreciated. === > Not too surprising :) since its actually generated from cellular> automata. I was just curious. But serial correlation is not too bad> right? [ deleted ]Serial correlation is never good but is always present to some extent inPRNGs; how bad it is depends on the application. I have encountered MC simu-lations that failed from too much serial correlation.-- Julian V. NobleProfessor Emeritus of Physicsjvn@lessspamformother.virginia.edu ^^^^^^^^^^^^^^^^^^http://galileo.phys.virginia.edu/~jvn/ God is not willing to do everything and thereby take away our free will and that share of glory that rightfully belongs to us. -- N. Machiavelli, The Prince. === I am a very beginner of numerical computing. I need your help insolving PDE numerically. I wounder how many methods in solving PDE?All the methods are valid for both initial value problem and boundaryvalue problem? I am going to simulate a evolution equation, would youplease tell me which method is suitable for this sort of equation? === what type the evlution equation is ? hyperbolic, parabolic orelliptical? ?ite difference method is rather easy to understandandrealize. and discrete scheme depend on type of your equation. so youshouldr be careful to select the scheme. P4AK: > I am a very beginner of numerical computing. I need your help in>solving PDE numerically. I wounder how many methods in solving PDE?>All the methods are valid for both initial value problem and boundary>value problem? I am going to simulate a evolution equation, would you>please tell me which method is suitable for this sort of equation?> === IMHO most favourite methods for solving PDE's are ?iteelement/volume/difference method. In fact, each of them has another ideaand you should know something about them. Additionally, there are someother special methods but at this time I don't remember any of them :-).P> I am a very beginner of numerical computing. I need your help in> solving PDE numerically. I wounder how many methods in solving PDE?> All the methods are valid for both initial value problem and boundary> value problem? I am going to simulate a evolution equation, would you> please tell me which method is suitable for this sort of equation?> === Dear sir or madam:I want to analyze a permanent magnet motor, considering the skin effect ofthe winding. Whocan be so kind to tell me which electromagnetic software can solve eddycurrent and transient?ld simultaneously with permanent magnet being considered?ZHENG Ping === |> I would like some derivation of pochhammer's symbol. I got an MS in|> Math on ?71 in approximatin theory.There is no derivation, because it is just a symbol, not a formulaor theorem. People in the hypergeometric series business comeacross a particular combination of Gamma(a+n)/Gamma(n) oftenand introduce (a)_n which reduces paperwork ... and tells others whoimplement it that they do not actually need to compute two Gamma-functionsto get the result, because (a)_n can be written as a ?ite productas it is commonly used only for n>=0 . === Dear all,I have an advection-diffusion-reaction modelling the behaviour of plankton.We can give an upper-estimate of the fractal dimension of the attractor ofthe system (method given by Constantin, Foias, Temam, etc...)I like to compute this dimension numerically. The ?st step is, I suppose,to compute the ?st exponents of Lyapunov of the linearized system. Hassomeone references who can help me to compute them (numerically)?V. === > i looking for a sum for the series > sum(i=0,n)({r)^i^2)> where r<1I assume you mean the sum sum(i=0,n) (r^(i^2)) for |r|<1or perhaps the series (which is always an in?ite sum) sum(i>=0) (r^(i^2)) for |r|<1It is easy to see that the series is absolutely convergent, (since itis a subseries of the geometric series sum(i>=0) (r^i)), but I don'tknow of any simple closed form for either the ?ite sum or theseries. One could try looking it up in a table of series, such asGradshteyn and Ryzhik's, but I don't have one handy at the moment.If you meant sum(i=0,n) ((r^i)^2) for |r|<1(which would be a non-standard interpretation of r^i^2), the sum ismuch easier, as that is just sum(i=0,n) ((r^2)^i) for |r|<1which the formula for geometric series can be applied to.-- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karpluslife member (LAB, Adventure Cycling, American Youth Hostels)Effective Cycling Instructor #218-ck (lapsed)Professor of Computer Engineering, University of California, Santa CruzUndergraduate and Graduate Director, BioinformaticsAf?iations for identi?ation only.-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === >how would i write 99724 in mayan hieroglyphics?http://www.michielb.nl/maya/math.html-- charlie dickThe right to be left alone -- the most comprehensive of rights, and the right most valued by a free people. - Justice Louis Brandeis, Olmstead v. U.S. (1928).-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === >If you are going to get picky...That can truly be an interesting facet of the algebra curriculum,especially in the 2nd year... the notion of precision and rigor andequally precise descriptions of same. Imho, it's appropriate to beequally formal and colloquial in our instructional discourse.Now my take on the issue at hand, most properly stated, at least as Iremember my Dolciani, as _principal_ square root is this. The reason toadvance a de?ition such as principal roots lies in a desire to forcethe process to be, by de?ition, a function. The process of evaluatingthe output of a function cannot be ambiguous, hence the need to provideprecise guidelines for those among the unwashed masses who feel the needto state sqrt(1.052) as a numeral.Informally, I'd want to know the keystrokes they planned to use tocompute a decimal approximation of the radical.Rigorously, I'd hope they'd invesitigate a bit... 1.052 = 1052/1000 = (2^2*3*7*13)/(2^3*5^3) = (3*7*13)/(2*5^2) = ...... and decide that the rounded decimal might just be the mostmeaningful representation of the quantity.-- charlie dickThe right to be left alone -- the most comprehensive of rights, and the right most valued by a free people. - Justice Louis Brandeis, Olmstead v. U.S. (1928).-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === Are there any books that give examples of problems/applications thateach department/?ld covers aimed at high school students? MathPhysicsChemistryBiologyEconomicsPhilosophyPsychologyComput er ScienceElectrical Engineeringetc.Casey-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === A good intermediate algebra book will have applications-related questions formost of what you list. A college textbook on intermediate algebra will oftenhave applications questions too, and high school math students should be ableto handle those textbook presentations just as well as their high schoolintermediate algebra books.G Ccaseyh@istar.ca askes:>Are there any books that give examples of problems/applications that>each department/?ld covers aimed at high school students?>>Math>Physics>Chemistry>Biology>Economics> Philosophy>Psychology>Computer Science>Electrical Engineering>etc.>>Casey>-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === i need to know the answer to this question: Given a line[y+2=-3(x+1)], write the equation of a line through (0,-2) that isparallel and perpendicular-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === > i need to know the answer to this question:No! You need to know *how* to answer the question. Just giving you answerswill not help you in the long run.> Given a line> [y+2=-3(x+1)], write the equation of a line through (0,-2) that is> parallel and perpendicularAll parallel lines have equal slope, save for vertical lines which haveunde?ed slope (two vertical lines are still parallel however). So youneed to deal with slope, and since you are given the y-intercept of thedesired line(s), you may want to ?st express the given equation inslope-intercept form, y=mx+b, where m is the slope and b is the y-intercept:y + 2 = -3(x + 1)y + 2 = -3x - 3 ...multiplied out the rhsy = -3x - 3 - 2 ...subtracted 2 from both sidesy = -3x - 5 ...combined like terms.Now identify your m as -3 and b as -5. This will be used for bothquestions. In other words, the given line is the line with slope -3 thathas y-intercept (0,-5).All lines parallel to this line will then have slope -3, so the answer tothe ?st part will look a lot like y=-3x+b, since it must have slope -3.All that's left is to determine b, and you were given that information.For the second part of the question, the perpendicular line through (0,-2),know that any two perpendicular lines will have slopes that are negativerecipricols of one another (again, with the exception of vertical/horizontallines since vertical lines have unde?ed slope.) In other words, if theslope of a line is m (with m<>0), the slope of a perpendicular line is -1/m.So the slope of the desired line is -1/m = -1/(-3) = 1/3. If you understoodall that, you should now be able to answer any similar question.-- Darrell-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === > i need to know the answer to this question: Given a line> [y+2=-3(x+1)], write the equation of a line through (0,-2) that is> parallel and perpendicular>When lines have the same slope, they're parallel. When the product of theslope is -1, the lines are perpendicular.Parallelm=3b=-2y=3x-2Perpendicularm=-1/3b=-2y=- 1/3x-2-- David MoranChief MeteorologistOklahoma Storm Team-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === > i need to know the answer to this question: Given a line> [y+2=-3(x+1)], write the equation of a line through (0,-2) that is> parallel and perpendicularThis question makes no sense. There is no line that is both paralleland perpendicular to a given line.Is this the con? of two questions, one asking for a parallelline and one asking for a perpendicular line. If so, remember thatparallel lines have the same slope, and perpendicular lines have slopeswhose product is -1 (except for horizontal and vertical lines).-- Kevin Karplus karplus@soe.ucsc.edu http://www.soe.ucsc.edu/~karpluslife member (LAB, Adventure Cycling, American Youth Hostels)Effective Cycling Instructor #218-ck (lapsed)Professor of Computer Engineering, University of California, Santa CruzUndergraduate and Graduate Director, BioinformaticsAf?iations for identi?ation only.-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html === RME is a problem based curriculum in which most of the topics coveredin the course are introduced by posing problems. This approach hasbeen used extensively in Holland which is where it was developed backin the 70s by Freudenthal. It has been shown to be very effective inelementary schools because it's a more interesting approach thansimple lecturing but more importanly it forces students to think andwork together on problem-solving skills. The reason it's called'realistic' is because the teacher is supposed to pick problems thatare more real to students in contrast to the homework problems weusually use that provide practice but usually fail to show theusefulness of math. The only problem with this approach is designingaffective problems. I was hoping that the web might serve as a nicemedium for problem contribution.-- newsgroup website: http://www.thinkspot.net/k12math/newsgroup charter: http://www.thinkspot.net/k12math/charter.html