mm-26 I point out that it is really difficult to find an account about the>geometry of Lie groups endowed with a left-invariant metric; the onlyI guess it depends on what you're interested in, but the fact that left-invariant metrics on a Lie group are the sameas inner products on its Lie algebra make a bunch of questions easy to answer - like the one you originally asked.V. I. Arnold's Mathematical Methods for Classical Mechanics talks about geodesics on a Lie group equipped with a left-invariant metric. This is important in physics, since a rigid rotating body traces out geodesics in SO(3) with respect to the left-invariant metric determined by the body's inertia tensor. Euler's equation for an incompressible fluid with no viscosity is also geodesic motion with respect to a left-invariant metric,but with the Lie group replaced by the infinite-dimensional group of all volume-preserving transformations of space. Arnold talks about how the rapid divergence of geodesics in this case begins to explain why it's hard to predict the weather! There were two meetings at AIM and MSRI in December, intended todiscuss aspects of Perelman's arguments. We invited Perelman to come speak, but he declined the invitation. It seems thatthe first paper is essentially correct, but many details are missing,and some mistakes had to be fixed. Several groups of mathematicianshave gone over this paper in some detail, and there are notesavailable on the web about the paper. The first week at AIM consistedof experts speaking about various aspects of Perelman's first paper,with the goal of disseminating his work to mathematician's interestedin the subject. The second week at MSRI was a larger seminar, withtalks aimed at a broader audience of mathematicians. The crux of the matter at this point is Perelman's second paper.Several mathematicians have attempted to read the paper, and no one israising any objections, but I don't think anyone has read it indetail, or filled in all the missing details. The argument is quitedelicate, and requires an intimate understanding of the techniques from Perelman's first paper. To finish the geometrization conjecture, Perelman claims to haveproved a collapsing result which he never published. It seems thatShioya and Yamaguchi have a preprint which claims to prove this result(or enough of it). They talked at the conferences. A third paper of Perelman would imply the Poincare conjecture, withoutusing the collapsing argument, in conjunction with his first twopapers. Again, the argument is difficult and maybe somewhat sketchy,but seems quite plausible. Colding and Minicozzi have a preprint witha slightly different approach. It may seem like it is taking quite a while for mathematicians toabsorb Perelman's arguments. But his arguments use techniques fromsomewhat different fields, so that not many mathematicians are expertson the different areas. I understand some aspects of his proof, and ifit is correct, it makes certain testable predictions (about volumes ofhyperbolic 3-manifolds). Nathan Dunfield did some computations tocheck these estimates, and found no contradictions. See http://www.math.lsa.umich.edu/research/ricciflow/ perelman.htmlhttp://www.aimath.org/WWN/geometrization/http:// www2.math.uic.edu/~agol/blog/blog.htmlfor more details on the subject. > ... I understand some aspects of [Perleman's] proof, and if it is> correct, it makes certain testable predictions (about volumes of> hyperbolic 3-manifolds). Nathan Dunfield did some computations to> check these estimates, and found no contradictions. Are these described in your blog at Pinching estimates for volumeentropy, or is it something else?Peace, Dylan According to Korean Media (Weekly Newsmaker)......1. Professor Yang-gon Kim (55) has said : my paper has been rejected by two US Journals (Perhaps SCI) andby another SCI Journal of China...So2.He has described Mathematical Society asConservative3. Two Anonymous Korean Mathematicians have said It is exaggerated... He doesn't understand basic concept of P/NP4. Preprint (mathpreprints.com)is the last version of paper.If JAADS(?) publishes paper, though, then it is just the preprint ofmathpreprints.com (Nothing to be changed).......** My Opinion : What's going on ????(http://news.naver.com/news_read.php?oldid= him) >3. Two Anonymous Korean Mathematicians have said >It is exaggerated... >He doesn't understand basic concept of P/NP[...]>** My Opinion : What's going on ????If you want to try to read the paper and understand something of whatis going on, my recommendation is this. Don't be frightened by the Lietheory (P-B-W theorem, Casimir operator, etc.). Turn directly to the lasttwo pages of the paper, where the alleged member of NPP is described,and it is argued firstly that it is in NP, and secondly that it is notin P. Naturally, these arguments appeal to earlier portions of the paper,with all the scary Lie theory. However, it is fairly clear where thehigh-powered Lie theory is appealed to: It is used to define a certainsystem of linear equations, whose coefficients are nondeterministic(i.e., their values can range over a certain set), to show that the set ofvalues of the nondeterministic coefficients is small enough to allow thesystem to be solved by a nondeterministic polynomial-time Turing machine,and to show that the solution of the system depends on the values chosenfor the nondeterministic coefficients. (Nondeterministic coefficientsis my term, not the authors', but if you look at their paper, you willsee what I am referring to.) The authors are obviously experts in Lietheory, so I am willing to grant all the above without needing to checktheir arguments in detail.However, to conclude that solving the system is not in P, one needsmore than this; in fact, here is the whole crux of the P = NP problem.Yet on this point, the authors are cryptic, saying only something to theeffect that for the problem to be in P, it has to depend only on thedeterministic parts of the system, not on the nondeterministic parts(which they call random). No appeal seems to be made at this point tothe heavy machinery earlier in the paper, even though this is exactlywhere you would expect heavy machinery to be needed. So either theauthors misunderstand what is really needed to show that a problem isnot in P, or they are somehow appealing to some heavy machinery at thispoint but in an obscure and cryptic manner. Not being completely surewhich is the case, even though I have some knowledge of Lie theory andcan follow at least the general outline of the earlier portions of thepaper, I cannot make a definitive judgment, but I bet that this is whatthe evaluators you mentioned found to be the sticking point.-- Tim Chow tchow-at-alum-dot-mit-dot-eduThe range of our projectiles---even ... the artillery---however great, willnever exceed four of those miles of which as many thousand separate us fromthe center of the earth. ---Galileo, Dialogues Concerning Two New Sciences Well;Let u,f,g be a continuous and increasing functions defined on theinterval [0,1),such that u(0)=0,f(0)=1,g(0)=1. def; A(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n), {k,0,n-1}] B(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n)*g(k/n), {k,0,n-1}] C(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n)*(g(k/n)^2), {k,0,n-1}] PROBLEM: Is |B(n)-A(n)|<=|C(n)-A(n)| & |C(n)-B(n)|<=|C(n)-A(n)| for infinitely many n's ??? (especially for u(t)=t ) LooonyTunes@yahoo.com says...> Let me try to pose the problem, I am trying to solve.I have a matrix, A (for simplicity let us assume it is a 2 X 2 matrix), that> is supposed to be symmetric and positive definite. There is a differential> equation the numerical solution of which gives me A at a current instant, in> the form Adot = f(x,p)..where x and p are the states of this dynamical> system and f is a nonlinear function in x, p. Since A has only three unique> parameters for this case, I actually obtain, theta_dot = g(x,p), where theta> A(t) thereby enforcing symmetry..... To enforce positive definiteness, I> need to do the following,theta(1) > 0, theta(2) > 0 and -sqrt(theta(1)*theta(2)) < theta(3) <> sqrt(theta(1)*theta(2))...Then by using some sort of a projection algorithm, I could enforce positive> definiteness in this way, however, this doesnt scale well for higher> dimensioned matrices.I was wondering if people were aware of literature that does something like> this...Any references would be greatly appreciated.L Tunes> An idea which may or may not be useful:The easiest way to check for positive semi-definiteness is to attempt to do Cholesky factorisation and see if it works (no negative numbers in the square-roots). Hence you can ensure positive semi-definiteness by adding to the diagonal elements so that you never get negative numbers in the square-roots when doing the Cholesky factorisation. This is very easy to implement algorithmically. Loony Tunes have a matrix, A (for simplicity let us assume it is a 2 X 2 matrix), that> is supposed to be symmetric and positive definite. There is a differential> equation the numerical solution of which gives me A at a current instant, in> the form Adot = f(x,p)..where x and p are the states of this dynamical> system and f is a nonlinear function in x, p. Since A has only three unique> parameters for this case, I actually obtain, theta_dot = g(x,p), where theta> A(t) thereby enforcing symmetry..... To enforce positive definiteness, I> need to do the following,theta(1) > 0, theta(2) > 0 and -sqrt(theta(1)*theta(2)) < theta(3) <> sqrt(theta(1)*theta(2))...Then by using some sort of a projection algorithm, I could enforce positive> definiteness in this way, however, this doesnt scale well for higher> dimensioned matrices.I was wondering if people were aware of literature that does something like> this...Any references would be greatly appreciated.Is it perhaps possible to take a sqrt of the initial value (Cholesky...? ) andto reformulate the DGL as a DGL for the sqrt?hthKlausL Tunes : One apparent way of avoiding the paradoxes of naive set theory is to: turn set-defining characteristic functions into partial functions from: sets to the three-valued logic {T,F,bot}. This three-valued logic: extends classical logic in the obvious way with: and(T,bot)=or(F,bot)=bot, and(F,x)=F, or(T,x)=T, not(bot)=bot, so that: every truth function has a fixed point.Very much Lukasiewicz' trivalent logic, then. That is good, and it allowseasy extension to polyvalent logics.: Obviously the law of excluded middle does not hold: or(a,not(a)) only: implies that a is T or bot. This gives the logic a constructive: character.Constructivism has been one of the driving reasons behind the introductionof alternate logics. Removing the constraint of excluded middlegeneralises one into the realm of Heyting algebras, where constructivetheories roam, while allowing the avoidance of the antinomies found in theBoolean.: In my formulation, I identify each set with its characteristic: function from sets to {T,F,bot}. Thus given s:set, the membership of: an element x can be tested with s(x). In the general case, this is a: partial function, returning bot for some values. I call such sets: partial sets, and sets whose characteristic function is in {T,F}: total sets. Every set of ZF and NF is a total set, with this theory: admitting a strictly larger class of sets than either.In some ways, this is the structure of a topoi, or at least a functor from atopoi category to something similar. Is the approach meant to be categorial(which, by the way, is a good thing in my eyes -- I'm just curious)? Then,your partial classification appears to mainly distinguish the topoi of setsfrom some of the many other topoi.: Russell's set R={s:set|not(s(s))} is then a partial set. All ZF sets: are elements of R, while some elements of NF are not elements of R,: while some new sets such as R itself are of undecidable membership.:: I've translated the ZF axioms to this set theory, rephrasing them in: terms of characteristic functions and new for-all and there-exists: logic operators performing logical conjunction and disjunctions across: all elements of a characteristic functions. Everything appears to be: sound and avoids known paradoxes.The categorial study of paradox is becoming a large field these days, and itappears you may be repeating some of the work already done (which can besoooo frustrating sometimes!). I don't mean to assume any level of study,but perhaps I might suggest that, if you haven't, you should check out someonline I can suggest.: With the new axioms, it is easy to construct a bijection from the: universal set to its power set. Cantor's proof that |P(x)|>|x| for: all non-empty sets x proceeds by constructing C={a:x|not(P(x)(a)} and: using the law of excluded middle to derive a contradiction on its: membership in P(x). This goes away for lack of excluded middle,: leaving C a partial set which appears not to be constructively: contradictory.:: The one worrying aspect of this approach is that it identifies sets: with characteristic functions from sets to logic values:: Set=Set->{T,F,bot}. I have only been able to develop an intuition of: such sets in a purely constructive way, by writing down a finite list: of possibly self-referential equations defining sets, and convincing: myself that a unique solution exists. This is much in the style of: NF's axiom that every (possibly cyclic) graph corresponds to a set,: but I allow unlimited comprehension.:: Are there any known problems with this approach to set theory? Any: pointers to research on the topic?No known problems that I am aware of. In fact, it seems to me to be one ofthe more successful modern approaches for classifying paradox. However, ifI could make one suggestion, it would be to not restrict yourself to yourtrivalent logic. Any Heyting algebra is possible, and expands your researchinto the much more fruitful world that all topoi present. In fact, becauseof natural distinctions that present themselves between propositions thattake on the middle value, trivalent theories are often looked at only assummarisations of a more natural infinitely valent theory. Good resourcesfor this can be found in intuitionist discussions, but it is more general.Also, may I ask why you posted to comp.lang.functional? This intrigues mebecause some of my own research has been around the evaluation of the lambdacalculus and proof / evaluation theory in the context of non standardlogics, but I do not see this approach explicitly stated in your message.Good luck with your researche!-- -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-galathaea: prankster, fablist, magician, liar >> If T is bunch of topologies that assure A, then sup T assures A.>> if (aj,a) in A, a in U some subbase set of sup T, then>> some tau in T with U in tau; aj -> a in tau>> aj eventually in U>> now use theorem>> aj -> a iff for all subbase sets U containing a, aj eventually in U>> Thus there's a largest topology for S assuring A.>> The sup of all topologies for S that assure A.>> Sup here is the 'largest' ( I think coarsest) topology whose open sets>> contain all the open sets of the set T? Assuming T is a set of course.> T_a subset T_b iff T_a coarser T_b iff T_a smaller T_b> T_b contains T_a iff T_b finer T_a iff T_b larger T_aThe sup of T contains all the open sets of / T = Union TA topology is a subset of P(S)> A collection of topologies for a set S is a subset of P(P(S)).> This is adequate bound to assure a collection of topologies is a set.But, while the existence of this larger topology is not i doubt, you might wantto impose some uniqueness or minimality condition on it. The key for me is that you talk about 'a larger'topology. >> f is a point in the space, how is a point continuous?> For example if f in R^R, the functions from R into R, the> the point f in the function space R^R can be continuous.> Such as f(x) = x for all x in R, viz f = { (x,x) | x in R }> But that wasn't what you were talking about. You just gave sometopological space with some topologies. Now it is a function space?>> Now the topology for S coinducted by all f in A, is>> the largest topology making all f in A continuous.>> largest? wouldn't that always just be the discrete topology? I'm taking>> largest to mean 'with the most open sets'. Oughtn't we to be using finest>> and coarsest?> The largest topology for any set is the discrete topology. When you> require a property of a topology, then the largest topology with that> property likely won't be the discrete topology.I like larger and smaller, you may use finer or coarser if you like.The larger or smaller semantics are dodgy cos, intuitively, a large numberof sets in the topology's base, means 'the open sets can be smaller'. Example, discrete is the finest which is your largest. yet the smallestset, the single point, is open.Anyway, the point I tried to get across, not very well, is that you needto say more than just there is a larger topology, as this is triviallytrue, but that there is some kind of 'smallest larger' topology. Anyway, where are you going with this? Download beta 1 - www.master-graph.com/mgraph20b1.exe (only 477KB).All who will help me to improve this program will get a freeregistration key.You can do the following:-find bugs-feedback about you impression by the program-advice me to change or add some new features-translate it to the other language (seewww.master-graph.com/instructions/interface.html)Feel free to contact with me - 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 modification.Titles in the mathematics arXiv (1 Commutative Algebra-----------------------math.AC/0401031 Shokrollah Salarian, Sean Sather-Wagstaff, Siamak Yassemi: Characterizing local rings via homological dimensions and regular sequencesmath.AC/0312513 Leila Khatami, Siamak Yassemi: Gorenstein injective dimension, Bass formula and Gorenstein ringsAG: Algebraic Geometry----------------------math.AG/0401079 Thierry Zell: Quantitative study of semi-Pfaffian setsmath.AG/0401074 Evgenia Soprunova: Zeros of systems of exponential sums and trigonometric polynomialsmath.AG/0401065 R. Pandharipande: Convex rationally connected varietiesmath.AG/0401064 Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen: Representations of surface groups in the general linear groupmath.AG/0401027 Euisung Park: On Syzygies of ruled varieties over a curvemath.AG/0401026 Sijong Kwak, Euisung Park: Some effects of property $N_p$ on the higher normality and defining equations of nonlinearly normal varietiesmath.AG/0401024 Stefan Wewers: Stable reduction of three point coversmath.AG/0401009 A. I. Bondal, M. Larsen, V. A. Lunts: Grothendieck ring of pretriangulated categoriesmath.AG/0401002 R. Bezrukavnikov, D. Kaledin: McKay equivalence for symplectic resolutions of singularitiesmath.AG/0312530 Grigory Mikhalkin: Enumerative tropical algebraic geometrymath.AG/0312520 Misha Verbitsky: Subvarieties in non-compact hyperkaehler manifoldsmath.AG/0312518 L. Chiantini, C. Ciliberto: On the classification of defective threefoldsmath.AG/0312515 Keiji Oguiso: Automorphism groups of generic hyperkahler manifolds - a note inspired by Curtis T. McMullenmath.AG/0312514 Nicolae Manolache: Cohen-Macaulay Nilpotent SchemesAP: Analysis of PDEs--------------------math.AP/0401078 Andreas Wannebo: Polynomial capacities, Poincare' type inequalities and Spectral synthesis in Sobolev spacemath.AP/0401061 Mohamed Ben Ayed, Khalil El Mehdi: On a Biharmonic Equation Involving Nearly Critical Exponentmath.AP/0401054 Kevin Zumbrun: Planar stability critera for viscous shock waves of systems with real viscositymath.AP/0401019 Nicolas Burq, Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh: Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical DecayAT: Algebraic Topology----------------------math.AT/0401075 Riccardo Longoni, Paolo Salvatore: Configuration spaces are not homotopy invariantmath.AT/0401052 Kevin P. Knudson: Representations of braid groups via conjugation actions on congruence subgroupsmath.AT/0401035 H. A. Dye, Louis H. Kauffman: Minimal Surface Representations of Virtual Knots and Linksmath.AT/0401033 Philippe Gaucher: S-homotopy as an analogue of homotopy of spacesmath.AT/0401007 Martin Markl: Transferring $A_infty$ (strongly homotopy associative) structuresmath.AT/0312531 A K Bousfield: Cosimplicial resolutions and homotopy spectral sequences in model categoriesCA: Classical Analysis and ODEs-------------------------------math.CA/0401015 Jenny Harrison: Cartan's Magic Formula and Soap Film Structuresmath.CA/0312526 Yuan Xu: Almost everywhere convergence of orthogonal expansions of several variablesmath.CA/0312525 Yuan Xu: Weighted Approximation of functions on the unit sphereCO: Combinatorics-----------------math.CO/0401067 Mireille Bousquet-Melou: Walks in the quarter plane: Kreweras' algebraic modelmath.CO/0401057 Zhi-Wei Sun, Ke-Jian Wu: An extension of a curious binomial identitymath.CO/0401045 Guangyue Han, Joachim Rosenthal: Unitary Space Time Constellation Analysis: An Upper Bound for the Diversitymath.CO/0401037 Brian Mazur: On Lattice Barycentric Tetrahedramath.CO/0401032 Michel Lassalle: A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomialsmath.CO/0401030 arcs in Desarguesian planes. IImath.CO/0401016 David Pask, John Quigg, Iain Raeburn: Fundamental groupoids of k-graphsmath.CO/0401012 Alexander Berkovich, Frank G. Garvan: On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5math.CO/0401006 Anders Bjorner, Michelle L. Wachs: Geometrically constructed bases for homology of partition lattices of types A, B and Dmath.CO/0401001 Pierre Leroux: Enumerative problems inspired by Mayer's theory of cluster integralsmath.CO/0312516 Anders Bjorner, Volkmar Welker: Segre and Rees products of posets, with ring-theoretic applicationsquant-ph/0312202 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela, A. I. Solomon:CV: Complex Variables---------------------math.CV/0401046 Dan Coman, Vincent Guedj: Invariant currents and dynamical Lelong numbersDG: Differential Geometry-------------------------math.DG/0401040 Zolfira Zakirova: Metrics of 6-dimensional h-spaces of the [3(21)], [(32)1], [(321)] typesmath.DG/0401034 S.A. Merkulov: PROP profile of Poisson geometrymath.DG/0401029 math.DG/0401020 Ruy Tojeiro: Isothermic submanifolds of Euclidean spacemath.DG/0312529 D.H. Phong, Jacob Sturm: The Futaki invariant and the Mabuchi energy of a complete intersectionmath.DG/0312528 D.H. Phong, Jacob Sturm: On asymptotics for the Mabuchi energy functionalmath.DG/0312524 Yvette Kosmann-Schwarzbach: Derived bracketsmath.DG/0312519 Arthur E. Fischer: An Introduction to Conformal Ricci FlowDS: Dynamical Systems---------------------math.DS/0401049 Oleg S. Kozlovski: Axiom A maps are dense in the space of unimodal maps in the $C^k$ topologymath.DS/0401044 Xavier Buff, Arnaud Cheritat: The Brjuno function continuously estimates the size of quadratic Siegel disksmath.DS/0401022 Frederic Laurent-Polz: Relative periodic orbits in point vortex systemsFA: Functional Analysis-----------------------math.FA/0312522 S. A. Argyros, J. Lopez-Abad, S. Todorcevic: A class of Banach spaces with few non strictly singular operatorsGM: General Mathematics-----------------------math.GM/0401039 L. I. Petrova: Invariant and evolutionary properties of the skew-symmetric differential formsGR: Group Theory----------------math.GR/0401059 Francois Dahmani: Parabolic groups acting on one-dimensional compact spacesmath.GR/0401050 Yann Ollivier: Growth exponent of generic groupsmath.GR/0401048 Yann Ollivier: Cogrowth and spectral gap of generic groupsmath.GR/0401042 Christophe Champetier, Vincent Guirardel: Limit groups as limits of free groups: compactifying the set of free groupsGT: Geometric Topology----------------------math.GT/0401068 Toshie Takata: The colored Jones polynomial and the A-polynomial for twist knotsmath.GT/0401056 Samuel Lelievre, Pascal Hubert: Square-tiled surfaces in H(2)math.GT/0401051 Thomas A. Gittings: Minimum Braids: A Complete Invariant of Knots and Linksmath.GT/0401047 Wolfgang Lueck: Equivariant Cohomological Chern Charactersmath.GT/0401003 Juan Souto: Hyperbolic cone-manifolds with large cone-anglesmath.GT/0312527 Jozef H Przytycki: Skein module deformations of elementary moves on linksmath.GT/0312523 Stefan Bauer: Refined Seiberg-Witten invariants------------------------math.HO/0401066 Wim van Dam: Summary of Delsarte's Nombre de Solutions des Equations Polynomials sur un Corps Finimath.HO/0401043 Michael J. Caola: A prime prime primerKT: K-Theory and Homology-------------------------math.KT/0401062 Grigory Garkusha: Systems of Diagram Categories and K-theory IMG: Metric Geometry-------------------math.MG/0401060 L.E. Bazylevych, M.M. Zarichnyi: On convex bodies of constant widthmath.MG/0401010 Matilde Lalin: Mahler measure and volumes in hyperbolic spacemath.MG/0401005 Boris A. Springborn: A unique representation of polyhedral typesmath.MG/0401004 Mathieu Dutour: Adjacency method for extreme Delaunay polytopesMP: Mathematical Physics------------------------quant-ph/0401021 Alexander Stotland, Andrei A. Pomeransky, Eitan Bachmat, Doron Cohen: The information entropy of quantum mechanical statesmath-ph/0401017 M. Dimassi, J.-C. Guillot, J. Ralston: On Effective Hamiltonians for Adiabatic Perturbations of Magnetic Schrodinger Operatorsmath-ph/0401016 Elliott H. Lieb, Michael Loss: A Note on Polarization Vectors in Quantum Electrodynamicshep-th/0312323 Stefano Bellucci, Armen Nersessian, Armen Yeranyan: Quantum Mechanics Model on Kahler conifoldgr-qc/0401010 R. Milson, A. Coley, V. Pravda, A. Pravdova: Alignment and algebraically special tensors in Lorentzian geometrymath-ph/0401015 Piers Kennedy, Richard L. Hall, Norman Dombey: Phase shifts and resonances in the Dirac equationmath-ph/0401014 Ayse H. Bilge, Sahin Kocak, Selman Uguz: Canonical bases for real representations of Clifford algebrasmath-ph/0401013 A. Alonso Izquierdo, J.C. Bueno Sanchez, M.A. Gonzalez Leon, M. de la Torre Mayado: Kink manifolds in a three-component scalar field theorymath-ph/0401012 Sebastian Bauer, Markus Kunze: The Darwin Approximation of the Relativistic Vlasov-Maxwell Systemmath-ph/0401011 P.J. Forrester, N.E. Frankel: Applications and generalizations of Fisher-Hartwig asymptoticsmath-ph/0401010 Thierry Bodineau, Roberto H. Schonmann, Senya Shlosman: 3D crystal: how flat its flat facets are?math-ph/0401009 M. Lorente: Creation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variablesmath-ph/0401008 M. Tidriri: Hydrodynamic limit of a B.G.K. like model on domains with boundaries and analysis of kinetic boundary conditions for scalar multidimensional conservation lawsmath-ph/0401007 Fabien Besnard: Number Operator Algebras and generalizations of supersymmetrycond-mat/0401026 Jesper Lykke Jacobsen, Jesus Salas, Alan D. Sokal: Spanning forests and the q-state Potts model in the limit q to 0cond-mat/0311658 Andras Suto: Normal and generalized Bose condensation in traps: One dimensional examplesquant-ph/0312199 Elena R. Loubenets: General framework for the probabilistic description of experimentsmath-ph/0401006 Jean-Marie Normand: Calculation of some determinants using the s-shifted factorialmath-ph/0401005 Yves Brihaye: On linear operators with an invariant subspace of functionsmath-ph/0401004 Elliott H. Lieb: Quantum Mechanics, The Stability of Matter and Quantum Electrodynamicsmath-ph/0401003 Harald Grosse, Edwin Langmann, Cornelius Paufler: Exact solution of a 1D many-body system with momentum dependent interactionsmath-ph/0401002 Richard Shurtleff: A Derivation of Vector and Momentum Matricesmath-ph/0401001 Y. M. Park: Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebrasmath-ph/0312074 Avinash Khare, Uday Sukhatme: Generalized Landen Transformation Formulas for Jacobi Elliptic Functionshep-th/0307108 of Q-operators and Schroedinger equationNT: Number Theory-----------------math.NT/0401014 Joshua Holden: Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete Logarithmmath.NT/0401013 Joshua Holden, Pieter Moree: Some Heuristics and Results for Small Cycles of the Discrete Logarithmmath.NT/0401008 Darren Glass & Rachel Pries: Hyperelliptic Curves with Given $a$-numbermath.NT/0312521 Joel Bellaiche: Sur la compatibilite entre les correspondances de Langlands locale et globale pour U(3). (On the compatibility between local and global Langlands correspondances for U(3))OA: Operator Algebras---------------------quant-ph/0401026 Christopher King, Mary Beth Ruskai: Comments on multiplicativity of maximal p-norms when p = 2math.OA/0401018 S. Kaliszewski, John Quigg: Mansfield's imprimitivity theorem for full crossed productsmath.OA/0401017 David Pask, John Quigg, Iain Raeburn: Coverings of k-graphsmath.OA/0312512 Victor G. Kac, Roberto Longo, Feng Xu: Solitons in Affine and Permutation OrbifoldsOC: Optimization and Control----------------------------math.OC/0401063 Jong-Shi Pang, Sven Leyffer: On the Global Minimization of the Value-at-RiskPR: Probability Theory----------------------math.PR/0401076 Jonas Gustavsson: Gaussian fluctuations of eigenvalues in the GUEmath.PR/0401073 Remco van der Hofstad, Gordon Slade: Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $mathbb{Z}^n$math.PR/0401072 Remco van der Hofstad, Gordon Slade: Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $Z^n$: the first three termsmath.PR/0401071 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: III. The phase transition for the $n$-cubemath.PR/0401070 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: II. The lace expansion and the triangle conditionmath.PR/0401069 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: I. The scaling window under the triangle conditionmath.PR/0401058 Filteringmath.PR/0401053 Marton Balazs: Multiple shocks in a zero range type modelmath.PR/0401041 Endre Cs'aki, Mikl'os Cs{o}rgH{o}, Zdzis{l}aw Rychlik, Josef Steinebach: On Vervaat and Vervaat-error type processes for partial sums and renewalsmath.PR/0401028 Benedicte Haas, Gregory Miermont: The genealogy of self-similar fragmentations with negative index as a continuum random treemath.PR/0401011 definite functions on semigroupsmath.PR/0312511 Harry Kesten, Vladas Sidoravicius: A shape theorem for the spread of an infectionmath.PR/0312510 Kosto V. Mitov, Anthony G. Pakes, George P. Yanev: Extremes of geometric variables with applications to branching processesQA: Quantum Algebra-------------------math.QA/0401055 Quantum Group B_{q,lambda}(A_2^(2))math.QA/0401038 Wee Liang Gan, Victor Ginzburg: Deformed preprojective algebras and symplectic reflection algebras for wreath productshep-th/0401022 I.V. Gorbunov, S.L. Lyakhovich, A.A. Sharapov: Wick Quantization of Cotangent Bundles over Riemannian Manifoldsmath.QA/0401036 Andrew Francis, Lenny Jones: On bases of centres of Iwahori-Hecke algebras of the symmetric groupmath.QA/0401025 Derek Bodin, Alice Fialowski, Michael Penkava: Classification and versal deformations of L_infinity algebras on a 2|1-dimensional spacemath.QA/0401023 Drazen Adamovic: A construction of admissible $A_1^{(1)}$-modules of level $-{4/3}$gr-qc/0312126 S. Majid, E. Raineri: Moduli of quantum Riemannian geometries on <= 4 pointshep-th/0311151 R. Coquereaux: The A2 Ocneanu quantum groupoidRT: Representation Theory-------------------------math.RT/0401077 Bernard Leclerc: A Littlewood-Richardson rule for evaluation representations of quantum affine sl(n)math.RT/0312517 Patrick Delorme, Eric Opdam: The Schwartz algebra of an affine Hecke algebraSG: Symplectic Geometry-----------------------math.SG/0401021 Denis Auroux, Ivan Smith: Lefschetz pencils, branched covers and symplectic invariants-- / Greg Kuperberg (UC Davis) / / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ / * All the math that's fit to e-print *979 >I point out that it is really difficult to find an account about the>geometry of Lie groups endowed with a left-invariant metric; the onlyI guess it depends on what you're interested in, but the fact that left-invariant metrics on a Lie group are the sameas inner products on its Lie algebra make a bunch of questions easy to answer - like the one you originally asked.V. I. Arnold's Mathematical Methods for Classical Mechanics talks about geodesics on a Lie group equipped with a left-invariant metric. This is important in physics, since a rigid rotating body traces out geodesics in SO(3) with respect to the left-invariant metric determined by the body's inertia tensor. Euler's equation for an incompressible fluid with no viscosity is also geodesic motion with respect to a left-invariant metric,but with the Lie group replaced by the infinite-dimensional group of all volume-preserving transformations of space. Arnold talks about how the rapid divergence of geodesics in this case begins to explain why it's hard to predict the weather! There were two meetings at AIM and MSRI in December, intended todiscuss aspects of Perelman's arguments. We invited Perelman to come speak, but he declined the invitation. It seems thatthe first paper is essentially correct, but many details are missing,and some mistakes had to be fixed. Several groups of mathematicianshave gone over this paper in some detail, and there are notesavailable on the web about the paper. The first week at AIM consistedof experts speaking about various aspects of Perelman's first paper,with the goal of disseminating his work to mathematician's interestedin the subject. The second week at MSRI was a larger seminar, withtalks aimed at a broader audience of mathematicians. The crux of the matter at this point is Perelman's second paper.Several mathematicians have attempted to read the paper, and no one israising any objections, but I don't think anyone has read it indetail, or filled in all the missing details. The argument is quitedelicate, and requires an intimate understanding of the techniques from Perelman's first paper. To finish the geometrization conjecture, Perelman claims to haveproved a collapsing result which he never published. It seems thatShioya and Yamaguchi have a preprint which claims to prove this result(or enough of it). They talked at the conferences. A third paper of Perelman would imply the Poincare conjecture, withoutusing the collapsing argument, in conjunction with his first twopapers. Again, the argument is difficult and maybe somewhat sketchy,but seems quite plausible. Colding and Minicozzi have a preprint witha slightly different approach. It may seem like it is taking quite a while for mathematicians toabsorb Perelman's arguments. But his arguments use techniques fromsomewhat different fields, so that not many mathematicians are expertson the different areas. I understand some aspects of his proof, and ifit is correct, it makes certain testable predictions (about volumes ofhyperbolic 3-manifolds). Nathan Dunfield did some computations tocheck these estimates, and found no contradictions. See http://www.math.lsa.umich.edu/research/ricciflow/ perelman.htmlhttp://www.aimath.org/WWN/geometrization/http:// www2.math.uic.edu/~agol/blog/blog.htmlfor more details on the subject. > ... I understand some aspects of [Perleman's] proof, and if it is> correct, it makes certain testable predictions (about volumes of> hyperbolic 3-manifolds). Nathan Dunfield did some computations to> check these estimates, and found no contradictions. Are these described in your blog at Pinching estimates for volumeentropy, or is it something else?Peace, Dylan According to Korean Media (Weekly Newsmaker)......1. Professor Yang-gon Kim (55) has said : my paper has been rejected by two US Journals (Perhaps SCI) andby another SCI Journal of China...So2.He has described Mathematical Society asConservative3. Two Anonymous Korean Mathematicians have said It is exaggerated... He doesn't understand basic concept of P/NP4. Preprint (mathpreprints.com)is the last version of paper.If JAADS(?) publishes paper, though, then it is just the preprint ofmathpreprints.com (Nothing to be changed).......** My Opinion : What's going on ????(http://news.naver.com/news_read.php?oldid= him) >3. Two Anonymous Korean Mathematicians have said >It is exaggerated... >He doesn't understand basic concept of P/NP[...]>** My Opinion : What's going on ????If you want to try to read the paper and understand something of whatis going on, my recommendation is this. Don't be frightened by the Lietheory (P-B-W theorem, Casimir operator, etc.). Turn directly to the lasttwo pages of the paper, where the alleged member of NPP is described,and it is argued firstly that it is in NP, and secondly that it is notin P. Naturally, these arguments appeal to earlier portions of the paper,with all the scary Lie theory. However, it is fairly clear where thehigh-powered Lie theory is appealed to: It is used to define a certainsystem of linear equations, whose coefficients are nondeterministic(i.e., their values can range over a certain set), to show that the set ofvalues of the nondeterministic coefficients is small enough to allow thesystem to be solved by a nondeterministic polynomial-time Turing machine,and to show that the solution of the system depends on the values chosenfor the nondeterministic coefficients. (Nondeterministic coefficientsis my term, not the authors', but if you look at their paper, you willsee what I am referring to.) The authors are obviously experts in Lietheory, so I am willing to grant all the above without needing to checktheir arguments in detail.However, to conclude that solving the system is not in P, one needsmore than this; in fact, here is the whole crux of the P = NP problem.Yet on this point, the authors are cryptic, saying only something to theeffect that for the problem to be in P, it has to depend only on thedeterministic parts of the system, not on the nondeterministic parts(which they call random). No appeal seems to be made at this point tothe heavy machinery earlier in the paper, even though this is exactlywhere you would expect heavy machinery to be needed. So either theauthors misunderstand what is really needed to show that a problem isnot in P, or they are somehow appealing to some heavy machinery at thispoint but in an obscure and cryptic manner. Not being completely surewhich is the case, even though I have some knowledge of Lie theory andcan follow at least the general outline of the earlier portions of thepaper, I cannot make a definitive judgment, but I bet that this is whatthe evaluators you mentioned found to be the sticking point.-- Tim Chow tchow-at-alum-dot-mit-dot-eduThe range of our projectiles---even ... the artillery---however great, willnever exceed four of those miles of which as many thousand separate us fromthe center of the earth. ---Galileo, Dialogues Concerning Two New Sciences Well;Let u,f,g be a continuous and increasing functions defined on theinterval [0,1),such that u(0)=0,f(0)=1,g(0)=1. def; A(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n), {k,0,n-1}] B(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n)*g(k/n), {k,0,n-1}] C(n):=Sum[exp(2*Pi*u(k/n)*i)*f(k/n)*(g(k/n)^2), {k,0,n-1}] PROBLEM: Is |B(n)-A(n)|<=|C(n)-A(n)| & |C(n)-B(n)|<=|C(n)-A(n)| for infinitely many n's ??? (especially for u(t)=t ) LooonyTunes@yahoo.com says...> Let me try to pose the problem, I am trying to solve.I have a matrix, A (for simplicity let us assume it is a 2 X 2 matrix), that> is supposed to be symmetric and positive definite. There is a differential> equation the numerical solution of which gives me A at a current instant, in> the form Adot = f(x,p)..where x and p are the states of this dynamical> system and f is a nonlinear function in x, p. Since A has only three unique> parameters for this case, I actually obtain, theta_dot = g(x,p), where theta> A(t) thereby enforcing symmetry..... To enforce positive definiteness, I> need to do the following,theta(1) > 0, theta(2) > 0 and -sqrt(theta(1)*theta(2)) < theta(3) <> sqrt(theta(1)*theta(2))...Then by using some sort of a projection algorithm, I could enforce positive> definiteness in this way, however, this doesnt scale well for higher> dimensioned matrices.I was wondering if people were aware of literature that does something like> this...Any references would be greatly appreciated.L Tunes> An idea which may or may not be useful:The easiest way to check for positive semi-definiteness is to attempt to do Cholesky factorisation and see if it works (no negative numbers in the square-roots). Hence you can ensure positive semi-definiteness by adding to the diagonal elements so that you never get negative numbers in the square-roots when doing the Cholesky factorisation. This is very easy to implement algorithmically. Loony Tunes have a matrix, A (for simplicity let us assume it is a 2 X 2 matrix), that> is supposed to be symmetric and positive definite. There is a differential> equation the numerical solution of which gives me A at a current instant, in> the form Adot = f(x,p)..where x and p are the states of this dynamical> system and f is a nonlinear function in x, p. Since A has only three unique> parameters for this case, I actually obtain, theta_dot = g(x,p), where theta> A(t) thereby enforcing symmetry..... To enforce positive definiteness, I> need to do the following,theta(1) > 0, theta(2) > 0 and -sqrt(theta(1)*theta(2)) < theta(3) <> sqrt(theta(1)*theta(2))...Then by using some sort of a projection algorithm, I could enforce positive> definiteness in this way, however, this doesnt scale well for higher> dimensioned matrices.I was wondering if people were aware of literature that does something like> this...Any references would be greatly appreciated.Is it perhaps possible to take a sqrt of the initial value (Cholesky...? ) andto reformulate the DGL as a DGL for the sqrt?hthKlausL Tunes : One apparent way of avoiding the paradoxes of naive set theory is to: turn set-defining characteristic functions into partial functions from: sets to the three-valued logic {T,F,bot}. This three-valued logic: extends classical logic in the obvious way with: and(T,bot)=or(F,bot)=bot, and(F,x)=F, or(T,x)=T, not(bot)=bot, so that: every truth function has a fixed point.Very much Lukasiewicz' trivalent logic, then. That is good, and it allowseasy extension to polyvalent logics.: Obviously the law of excluded middle does not hold: or(a,not(a)) only: implies that a is T or bot. This gives the logic a constructive: character.Constructivism has been one of the driving reasons behind the introductionof alternate logics. Removing the constraint of excluded middlegeneralises one into the realm of Heyting algebras, where constructivetheories roam, while allowing the avoidance of the antinomies found in theBoolean.: In my formulation, I identify each set with its characteristic: function from sets to {T,F,bot}. Thus given s:set, the membership of: an element x can be tested with s(x). In the general case, this is a: partial function, returning bot for some values. I call such sets: partial sets, and sets whose characteristic function is in {T,F}: total sets. Every set of ZF and NF is a total set, with this theory: admitting a strictly larger class of sets than either.In some ways, this is the structure of a topoi, or at least a functor from atopoi category to something similar. Is the approach meant to be categorial(which, by the way, is a good thing in my eyes -- I'm just curious)? Then,your partial classification appears to mainly distinguish the topoi of setsfrom some of the many other topoi.: Russell's set R={s:set|not(s(s))} is then a partial set. All ZF sets: are elements of R, while some elements of NF are not elements of R,: while some new sets such as R itself are of undecidable membership.:: I've translated the ZF axioms to this set theory, rephrasing them in: terms of characteristic functions and new for-all and there-exists: logic operators performing logical conjunction and disjunctions across: all elements of a characteristic functions. Everything appears to be: sound and avoids known paradoxes.The categorial study of paradox is becoming a large field these days, and itappears you may be repeating some of the work already done (which can besoooo frustrating sometimes!). I don't mean to assume any level of study,but perhaps I might suggest that, if you haven't, you should check out someonline I can suggest.: With the new axioms, it is easy to construct a bijection from the: universal set to its power set. Cantor's proof that |P(x)|>|x| for: all non-empty sets x proceeds by constructing C={a:x|not(P(x)(a)} and: using the law of excluded middle to derive a contradiction on its: membership in P(x). This goes away for lack of excluded middle,: leaving C a partial set which appears not to be constructively: contradictory.:: The one worrying aspect of this approach is that it identifies sets: with characteristic functions from sets to logic values:: Set=Set->{T,F,bot}. I have only been able to develop an intuition of: such sets in a purely constructive way, by writing down a finite list: of possibly self-referential equations defining sets, and convincing: myself that a unique solution exists. This is much in the style of: NF's axiom that every (possibly cyclic) graph corresponds to a set,: but I allow unlimited comprehension.:: Are there any known problems with this approach to set theory? Any: pointers to research on the topic?No known problems that I am aware of. In fact, it seems to me to be one ofthe more successful modern approaches for classifying paradox. However, ifI could make one suggestion, it would be to not restrict yourself to yourtrivalent logic. Any Heyting algebra is possible, and expands your researchinto the much more fruitful world that all topoi present. In fact, becauseof natural distinctions that present themselves between propositions thattake on the middle value, trivalent theories are often looked at only assummarisations of a more natural infinitely valent theory. Good resourcesfor this can be found in intuitionist discussions, but it is more general.Also, may I ask why you posted to comp.lang.functional? This intrigues mebecause some of my own research has been around the evaluation of the lambdacalculus and proof / evaluation theory in the context of non standardlogics, but I do not see this approach explicitly stated in your message.Good luck with your researche!-- -=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-galathaea: prankster, fablist, magician, liar >> If T is bunch of topologies that assure A, then sup T assures A.>> if (aj,a) in A, a in U some subbase set of sup T, then>> some tau in T with U in tau; aj -> a in tau>> aj eventually in U>> now use theorem>> aj -> a iff for all subbase sets U containing a, aj eventually in U>> Thus there's a largest topology for S assuring A.>> The sup of all topologies for S that assure A.>> Sup here is the 'largest' ( I think coarsest) topology whose open sets>> contain all the open sets of the set T? Assuming T is a set of course.> T_a subset T_b iff T_a coarser T_b iff T_a smaller T_b> T_b contains T_a iff T_b finer T_a iff T_b larger T_aThe sup of T contains all the open sets of / T = Union TA topology is a subset of P(S)> A collection of topologies for a set S is a subset of P(P(S)).> This is adequate bound to assure a collection of topologies is a set.But, while the existence of this larger topology is not i doubt, you might wantto impose some uniqueness or minimality condition on it. The key for me is that you talk about 'a larger'topology. >> f is a point in the space, how is a point continuous?> For example if f in R^R, the functions from R into R, the> the point f in the function space R^R can be continuous.> Such as f(x) = x for all x in R, viz f = { (x,x) | x in R }> But that wasn't what you were talking about. You just gave sometopological space with some topologies. Now it is a function space?>> Now the topology for S coinducted by all f in A, is>> the largest topology making all f in A continuous.>> largest? wouldn't that always just be the discrete topology? I'm taking>> largest to mean 'with the most open sets'. Oughtn't we to be using finest>> and coarsest?> The largest topology for any set is the discrete topology. When you> require a property of a topology, then the largest topology with that> property likely won't be the discrete topology.I like larger and smaller, you may use finer or coarser if you like.The larger or smaller semantics are dodgy cos, intuitively, a large numberof sets in the topology's base, means 'the open sets can be smaller'. Example, discrete is the finest which is your largest. yet the smallestset, the single point, is open.Anyway, the point I tried to get across, not very well, is that you needto say more than just there is a larger topology, as this is triviallytrue, but that there is some kind of 'smallest larger' topology. Anyway, where are you going with this? Download beta 1 - www.master-graph.com/mgraph20b1.exe (only 477KB).All who will help me to improve this program will get a freeregistration key.You can do the following:-find bugs-feedback about you impression by the program-advice me to change or add some new features-translate it to the other language (seewww.master-graph.com/instructions/interface.html)Feel free to contact with me - 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 modification.Titles in the mathematics arXiv (1 Commutative Algebra-----------------------math.AC/0401031 Shokrollah Salarian, Sean Sather-Wagstaff, Siamak Yassemi: Characterizing local rings via homological dimensions and regular sequencesmath.AC/0312513 Leila Khatami, Siamak Yassemi: Gorenstein injective dimension, Bass formula and Gorenstein ringsAG: Algebraic Geometry----------------------math.AG/0401079 Thierry Zell: Quantitative study of semi-Pfaffian setsmath.AG/0401074 Evgenia Soprunova: Zeros of systems of exponential sums and trigonometric polynomialsmath.AG/0401065 R. Pandharipande: Convex rationally connected varietiesmath.AG/0401064 Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen: Representations of surface groups in the general linear groupmath.AG/0401027 Euisung Park: On Syzygies of ruled varieties over a curvemath.AG/0401026 Sijong Kwak, Euisung Park: Some effects of property $N_p$ on the higher normality and defining equations of nonlinearly normal varietiesmath.AG/0401024 Stefan Wewers: Stable reduction of three point coversmath.AG/0401009 A. I. Bondal, M. Larsen, V. A. Lunts: Grothendieck ring of pretriangulated categoriesmath.AG/0401002 R. Bezrukavnikov, D. Kaledin: McKay equivalence for symplectic resolutions of singularitiesmath.AG/0312530 Grigory Mikhalkin: Enumerative tropical algebraic geometrymath.AG/0312520 Misha Verbitsky: Subvarieties in non-compact hyperkaehler manifoldsmath.AG/0312518 L. Chiantini, C. Ciliberto: On the classification of defective threefoldsmath.AG/0312515 Keiji Oguiso: Automorphism groups of generic hyperkahler manifolds - a note inspired by Curtis T. McMullenmath.AG/0312514 Nicolae Manolache: Cohen-Macaulay Nilpotent SchemesAP: Analysis of PDEs--------------------math.AP/0401078 Andreas Wannebo: Polynomial capacities, Poincare' type inequalities and Spectral synthesis in Sobolev spacemath.AP/0401061 Mohamed Ben Ayed, Khalil El Mehdi: On a Biharmonic Equation Involving Nearly Critical Exponentmath.AP/0401054 Kevin Zumbrun: Planar stability critera for viscous shock waves of systems with real viscositymath.AP/0401019 Nicolas Burq, Fabrice Planchon, John G. Stalker, A. Shadi Tahvildar-Zadeh: Strichartz estimates for the Wave and Schrodinger Equations with Potentials of Critical DecayAT: Algebraic Topology----------------------math.AT/0401075 Riccardo Longoni, Paolo Salvatore: Configuration spaces are not homotopy invariantmath.AT/0401052 Kevin P. Knudson: Representations of braid groups via conjugation actions on congruence subgroupsmath.AT/0401035 H. A. Dye, Louis H. Kauffman: Minimal Surface Representations of Virtual Knots and Linksmath.AT/0401033 Philippe Gaucher: S-homotopy as an analogue of homotopy of spacesmath.AT/0401007 Martin Markl: Transferring $A_infty$ (strongly homotopy associative) structuresmath.AT/0312531 A K Bousfield: Cosimplicial resolutions and homotopy spectral sequences in model categoriesCA: Classical Analysis and ODEs-------------------------------math.CA/0401015 Jenny Harrison: Cartan's Magic Formula and Soap Film Structuresmath.CA/0312526 Yuan Xu: Almost everywhere convergence of orthogonal expansions of several variablesmath.CA/0312525 Yuan Xu: Weighted Approximation of functions on the unit sphereCO: Combinatorics-----------------math.CO/0401067 Mireille Bousquet-Melou: Walks in the quarter plane: Kreweras' algebraic modelmath.CO/0401057 Zhi-Wei Sun, Ke-Jian Wu: An extension of a curious binomial identitymath.CO/0401045 Guangyue Han, Joachim Rosenthal: Unitary Space Time Constellation Analysis: An Upper Bound for the Diversitymath.CO/0401037 Brian Mazur: On Lattice Barycentric Tetrahedramath.CO/0401032 Michel Lassalle: A short proof of generalized Jacobi-Trudi expansions for Macdonald polynomialsmath.CO/0401030 arcs in Desarguesian planes. IImath.CO/0401016 David Pask, John Quigg, Iain Raeburn: Fundamental groupoids of k-graphsmath.CO/0401012 Alexander Berkovich, Frank G. Garvan: On the Andrews-Stanley Refinement of Ramanujan's Partition Congruence Modulo 5math.CO/0401006 Anders Bjorner, Michelle L. Wachs: Geometrically constructed bases for homology of partition lattices of types A, B and Dmath.CO/0401001 Pierre Leroux: Enumerative problems inspired by Mayer's theory of cluster integralsmath.CO/0312516 Anders Bjorner, Volkmar Welker: Segre and Rees products of posets, with ring-theoretic applicationsquant-ph/0312202 K. A. Penson, P. Blasiak, G. Duchamp, A. Horzela, A. I. Solomon:CV: Complex Variables---------------------math.CV/0401046 Dan Coman, Vincent Guedj: Invariant currents and dynamical Lelong numbersDG: Differential Geometry-------------------------math.DG/0401040 Zolfira Zakirova: Metrics of 6-dimensional h-spaces of the [3(21)], [(32)1], [(321)] typesmath.DG/0401034 S.A. Merkulov: PROP profile of Poisson geometrymath.DG/0401029 math.DG/0401020 Ruy Tojeiro: Isothermic submanifolds of Euclidean spacemath.DG/0312529 D.H. Phong, Jacob Sturm: The Futaki invariant and the Mabuchi energy of a complete intersectionmath.DG/0312528 D.H. Phong, Jacob Sturm: On asymptotics for the Mabuchi energy functionalmath.DG/0312524 Yvette Kosmann-Schwarzbach: Derived bracketsmath.DG/0312519 Arthur E. Fischer: An Introduction to Conformal Ricci FlowDS: Dynamical Systems---------------------math.DS/0401049 Oleg S. Kozlovski: Axiom A maps are dense in the space of unimodal maps in the $C^k$ topologymath.DS/0401044 Xavier Buff, Arnaud Cheritat: The Brjuno function continuously estimates the size of quadratic Siegel disksmath.DS/0401022 Frederic Laurent-Polz: Relative periodic orbits in point vortex systemsFA: Functional Analysis-----------------------math.FA/0312522 S. A. Argyros, J. Lopez-Abad, S. Todorcevic: A class of Banach spaces with few non strictly singular operatorsGM: General Mathematics-----------------------math.GM/0401039 L. I. Petrova: Invariant and evolutionary properties of the skew-symmetric differential formsGR: Group Theory----------------math.GR/0401059 Francois Dahmani: Parabolic groups acting on one-dimensional compact spacesmath.GR/0401050 Yann Ollivier: Growth exponent of generic groupsmath.GR/0401048 Yann Ollivier: Cogrowth and spectral gap of generic groupsmath.GR/0401042 Christophe Champetier, Vincent Guirardel: Limit groups as limits of free groups: compactifying the set of free groupsGT: Geometric Topology----------------------math.GT/0401068 Toshie Takata: The colored Jones polynomial and the A-polynomial for twist knotsmath.GT/0401056 Samuel Lelievre, Pascal Hubert: Square-tiled surfaces in H(2)math.GT/0401051 Thomas A. Gittings: Minimum Braids: A Complete Invariant of Knots and Linksmath.GT/0401047 Wolfgang Lueck: Equivariant Cohomological Chern Charactersmath.GT/0401003 Juan Souto: Hyperbolic cone-manifolds with large cone-anglesmath.GT/0312527 Jozef H Przytycki: Skein module deformations of elementary moves on linksmath.GT/0312523 Stefan Bauer: Refined Seiberg-Witten invariants------------------------math.HO/0401066 Wim van Dam: Summary of Delsarte's Nombre de Solutions des Equations Polynomials sur un Corps Finimath.HO/0401043 Michael J. Caola: A prime prime primerKT: K-Theory and Homology-------------------------math.KT/0401062 Grigory Garkusha: Systems of Diagram Categories and K-theory IMG: Metric Geometry-------------------math.MG/0401060 L.E. Bazylevych, M.M. Zarichnyi: On convex bodies of constant widthmath.MG/0401010 Matilde Lalin: Mahler measure and volumes in hyperbolic spacemath.MG/0401005 Boris A. Springborn: A unique representation of polyhedral typesmath.MG/0401004 Mathieu Dutour: Adjacency method for extreme Delaunay polytopesMP: Mathematical Physics------------------------quant-ph/0401021 Alexander Stotland, Andrei A. Pomeransky, Eitan Bachmat, Doron Cohen: The information entropy of quantum mechanical statesmath-ph/0401017 M. Dimassi, J.-C. Guillot, J. Ralston: On Effective Hamiltonians for Adiabatic Perturbations of Magnetic Schrodinger Operatorsmath-ph/0401016 Elliott H. Lieb, Michael Loss: A Note on Polarization Vectors in Quantum Electrodynamicshep-th/0312323 Stefano Bellucci, Armen Nersessian, Armen Yeranyan: Quantum Mechanics Model on Kahler conifoldgr-qc/0401010 R. Milson, A. Coley, V. Pravda, A. Pravdova: Alignment and algebraically special tensors in Lorentzian geometrymath-ph/0401015 Piers Kennedy, Richard L. Hall, Norman Dombey: Phase shifts and resonances in the Dirac equationmath-ph/0401014 Ayse H. Bilge, Sahin Kocak, Selman Uguz: Canonical bases for real representations of Clifford algebrasmath-ph/0401013 A. Alonso Izquierdo, J.C. Bueno Sanchez, M.A. Gonzalez Leon, M. de la Torre Mayado: Kink manifolds in a three-component scalar field theorymath-ph/0401012 Sebastian Bauer, Markus Kunze: The Darwin Approximation of the Relativistic Vlasov-Maxwell Systemmath-ph/0401011 P.J. Forrester, N.E. Frankel: Applications and generalizations of Fisher-Hartwig asymptoticsmath-ph/0401010 Thierry Bodineau, Roberto H. Schonmann, Senya Shlosman: 3D crystal: how flat its flat facets are?math-ph/0401009 M. Lorente: Creation and Annihilation Operators for Orthogonal Polynomials of Continuous and Discrete Variablesmath-ph/0401008 M. Tidriri: Hydrodynamic limit of a B.G.K. like model on domains with boundaries and analysis of kinetic boundary conditions for scalar multidimensional conservation lawsmath-ph/0401007 Fabien Besnard: Number Operator Algebras and generalizations of supersymmetrycond-mat/0401026 Jesper Lykke Jacobsen, Jesus Salas, Alan D. Sokal: Spanning forests and the q-state Potts model in the limit q to 0cond-mat/0311658 Andras Suto: Normal and generalized Bose condensation in traps: One dimensional examplesquant-ph/0312199 Elena R. Loubenets: General framework for the probabilistic description of experimentsmath-ph/0401006 Jean-Marie Normand: Calculation of some determinants using the s-shifted factorialmath-ph/0401005 Yves Brihaye: On linear operators with an invariant subspace of functionsmath-ph/0401004 Elliott H. Lieb: Quantum Mechanics, The Stability of Matter and Quantum Electrodynamicsmath-ph/0401003 Harald Grosse, Edwin Langmann, Cornelius Paufler: Exact solution of a 1D many-body system with momentum dependent interactionsmath-ph/0401002 Richard Shurtleff: A Derivation of Vector and Momentum Matricesmath-ph/0401001 Y. M. Park: Remarks on the Structure of Dirichlet Forms on Standard Forms of von Neumann Algebrasmath-ph/0312074 Avinash Khare, Uday Sukhatme: Generalized Landen Transformation Formulas for Jacobi Elliptic Functionshep-th/0307108 of Q-operators and Schroedinger equationNT: Number Theory-----------------math.NT/0401014 Joshua Holden: Distribution of the Error in Estimated Numbers of Fixed Points of the Discrete Logarithmmath.NT/0401013 Joshua Holden, Pieter Moree: Some Heuristics and Results for Small Cycles of the Discrete Logarithmmath.NT/0401008 Darren Glass & Rachel Pries: Hyperelliptic Curves with Given $a$-numbermath.NT/0312521 Joel Bellaiche: Sur la compatibilite entre les correspondances de Langlands locale et globale pour U(3). (On the compatibility between local and global Langlands correspondances for U(3))OA: Operator Algebras---------------------quant-ph/0401026 Christopher King, Mary Beth Ruskai: Comments on multiplicativity of maximal p-norms when p = 2math.OA/0401018 S. Kaliszewski, John Quigg: Mansfield's imprimitivity theorem for full crossed productsmath.OA/0401017 David Pask, John Quigg, Iain Raeburn: Coverings of k-graphsmath.OA/0312512 Victor G. Kac, Roberto Longo, Feng Xu: Solitons in Affine and Permutation OrbifoldsOC: Optimization and Control----------------------------math.OC/0401063 Jong-Shi Pang, Sven Leyffer: On the Global Minimization of the Value-at-RiskPR: Probability Theory----------------------math.PR/0401076 Jonas Gustavsson: Gaussian fluctuations of eigenvalues in the GUEmath.PR/0401073 Remco van der Hofstad, Gordon Slade: Asymptotic expansions in $n^{-1}$ for percolation critical values on the $n$-cube and $mathbb{Z}^n$math.PR/0401072 Remco van der Hofstad, Gordon Slade: Expansion in $n^{-1}$ for percolation critical values on the $n$-cube and $Z^n$: the first three termsmath.PR/0401071 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: III. The phase transition for the $n$-cubemath.PR/0401070 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: II. The lace expansion and the triangle conditionmath.PR/0401069 Christian Borgs, Jennifer T. Chayes, Remco van der Hofstad, Gordon Slade, Joel Spencer: Random subgraphs of finite graphs: I. The scaling window under the triangle conditionmath.PR/0401058 Filteringmath.PR/0401053 Marton Balazs: Multiple shocks in a zero range type modelmath.PR/0401041 Endre Cs'aki, Mikl'os Cs{o}rgH{o}, Zdzis{l}aw Rychlik, Josef Steinebach: On Vervaat and Vervaat-error type processes for partial sums and renewalsmath.PR/0401028 Benedicte Haas, Gregory Miermont: The genealogy of self-similar fragmentations with negative index as a continuum random treemath.PR/0401011 definite functions on semigroupsmath.PR/0312511 Harry Kesten, Vladas Sidoravicius: A shape theorem for the spread of an infectionmath.PR/0312510 Kosto V. Mitov, Anthony G. Pakes, George P. Yanev: Extremes of geometric variables with applications to branching processesQA: Quantum Algebra-------------------math.QA/0401055 Quantum Group B_{q,lambda}(A_2^(2))math.QA/0401038 Wee Liang Gan, Victor Ginzburg: Deformed preprojective algebras and symplectic reflection algebras for wreath productshep-th/0401022 I.V. Gorbunov, S.L. Lyakhovich, A.A. Sharapov: Wick Quantization of Cotangent Bundles over Riemannian Manifoldsmath.QA/0401036 Andrew Francis, Lenny Jones: On bases of centres of Iwahori-Hecke algebras of the symmetric groupmath.QA/0401025 Derek Bodin, Alice Fialowski, Michael Penkava: Classification and versal deformations of L_infinity algebras on a 2|1-dimensional spacemath.QA/0401023 Drazen Adamovic: A construction of admissible $A_1^{(1)}$-modules of level $-{4/3}$gr-qc/0312126 S. Majid, E. Raineri: Moduli of quantum Riemannian geometries on <= 4 pointshep-th/0311151 R. Coquereaux: The A2 Ocneanu quantum groupoidRT: Representation Theory-------------------------math.RT/0401077 Bernard Leclerc: A Littlewood-Richardson rule for evaluation representations of quantum affine sl(n)math.RT/0312517 Patrick Delorme, Eric Opdam: The Schwartz algebra of an affine Hecke algebraSG: Symplectic Geometry-----------------------math.SG/0401021 Denis Auroux, Ivan Smith: Lefschetz pencils, branched covers and symplectic invariants / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/