mm-437 === Subject: : Infering amplitude from power spectral densityAny help much appreciated on two points:1. I am using the spctrm function (chpt 13.4 nummerical recipes inC++) function to produce a power spectral density plot and amsurprised that when an ideal square wave of amplitude +/- 1 is inputthen the amplitudes of the harmonics are not at 1, 1/3, 1/5, 1/7 etcmust at much lower values2. How can I infer the amplitude of the input signal from the PSD.Russ=== === Subject: : Re: Keeping quaternion normalized> If you use a penalty term, you can use any high-performance> automatic integrator from the shelf, while if you rescale after> each step you need 1. to write your own code, and 2. are limited> to single-step (Runge-Kutta type) methods.OK, convinced!-- === === Subject: : Re: Tributary Area Algorithm>[Note F'up2 reduction to one group --- should have been done by OP!]> Not sure what this first comment means...Then you should re-learn about the ancient rules of Usenet... It'sgenerally considered a bad idea to cross-post the same question toseveral newsgroups. If it's necessary to do that, netiquette requiresto set a followup-to that redirects the ensuing discussion to asingle group from that cross-posted collection. You didn't do that inor original posting, so I did it in my reply. And again this time.> Assume that you have an underground room with open spaces and solid> pillars (much like a checker board) and assume that there is one solid> pillar in the center, with 8 other solid pillars around the center> pillar. All around the solid pillars is a void space, i.e. air. I> would like to find a polyline (a group of connected points) that> define an area around the center pillar. The points used to define> the closed polyline are obtained by determining the closest distance> between the edge of the center pillar and the edge of an outer pillar> and then locating the point half way between the two pillars.So in the setup you describe, this region will always be a polygon of8 vertices. One serious problem I see is that you don't have much ofa guarantee that none of the pillars intersects that polygon. AndI'm pretty sure you don't want that to happen.Seems like the real definition of that region you want to determinewould be the Voronoi zone of the central pillar, i.e. the set of allpoints closer to the central pillar than to any of the others. Ingeneral, the boundary of this set will not even be a polygon, letalone one restricted to only 8 vertices. Determining that will be alot more work than finding those 8 mid-points.-- === === Subject: : Re: Tributary Area Algorithm> 4) I need to find the closed polyline that surrounds the YYY area and> is half-way between the YYY area and each of the xxx defined areas.> The area defined by the half-way polyline defines a stress area that> the YYY solid area must support.> Any suggestions on the how to do this generically for the case of> irregular shaped solid YYY and xxx polylines?A reasonable approximation to what you want (assuming I understood youproperly) can be computed by sampling points along the perimeter of eachpolygon, computing the voronoi (nearest neighbor) diagram for the set ofpoints, finding the cells in the voronoi diagram that correspond to thethat, copied below. It highlights the region surrounding the firstpolygon in red. You would still need to determine the polyline boundaryof corresponding to these cells, but that shouldn't be too hard. (e.g.from the set of cells corresponding to polygon 1, determine all edges thatare owned by only one cell. Those lie on the boundary. Then order theedges so that they form a line.)There may well be probably a more efficient computational geometry methodfor solving your problem, but this may suit well enough for your needs?hope that helps,Rick% here are the polygons. The first one is the center one. You can% enter as many as you like. The code assumes they don't overlap.plg{1} = [0 0; 1 0; 1 1; 0 1; -0.4 0.3];plg{2} = [ 2.1659 3.1696; 1.7604 3.1462; 1.8710 2.2807;2.4055 2.1404; 2.8111 3.0292;];plg{3} = [2.3134 0.9240; 2.1843 0.2456; 2.6636 -0.2456;2.9585 0.4094;];plg{4} = [0.1567 -1.8129; 0.7834 -1.3684; 1.1521 -3.0760;0.3226 -2.9123; -0.3410 -2.3743];plg{5} = [-1.6866 -1.2047; -0.9493 -1.1813; -1.4101 -2.2339];plg{6} = [-2.2581 0.9942; -1.1705 0.9240; -1.1152 -0.2924;-1.9447 -0.2456];plg{7} = [-0.5991 2.4912; -0.7650 1.6257; -1.3917 1.3918;-1.5945 2.0468];% this is the discretization parameter. Turn it up to use more points on% the polygonsptsperunit=30;% run the routinetributary(plg,ptsperunit);% tributary function starts here% plg is a cell array of polygons. Each polygon is defined by an n x 2matrix% the first polygon plg{1} is the polygon for which the nearest neighbor% cell is computed.% ptsperunit is the number of points per unit distance that are placed% around each polygon. These points are used to compute the voronoi% diagram. Higher ptsperunit => finer discretization, so (hopefully)% better results.% v are the vertices of the voronoi diagram% c are the cells of the voronoi diagram% nc is the number of cells that correspond correspond the plg{1}.function [v,c,nc]=tributary(plg,ptsperunit)xy=[];for i=1:length(plg), plgpts{i} = ptsonpolygon(plg{i},ptsperunit); xy = [xy; plgpts{i}];endnc = length(plgpts{1});plotplg(plgpts);[v,c] = voronoin(xy);hold on;for i=1:nc, plot(v([c{i} c{i}(1)],1),v([c{i} c{i}(1)],2),'r')endhold off% takes a polygon defined by n x 2 matrix polyg, and samples points along% the perimeter with density ptsperunit. Return k x 2 array, where k is% determined (approximately) by length of perimeter * ptsperunitfunction [xy]=ptsonpolygon(polyg,ptsperunit)pgf = [polyg; polyg(1,:)];xy=[];for i=1:size(polyg,1), d=norm(pgf(i+1,:)-pgf(i,:)); n=ceil(d*ptsperunit); if (n<1) n=1; end xtemp = linspace(pgf(i,1),pgf(i+1,1),n+1); ytemp = linspace(pgf(i,2),pgf(i+1,2),n+1); xy = [xy; xtemp(1:n)' ytemp(1:n)'];end% Plot the polygonsfunction plotplg(plg)hold onplot([plg{1}(:,1)' plg{1}(1,1)],[plg{1}(:,2)' plg{1}(1,2)],'bx');for i=2:length(plg); plot([plg{i}(:,1)' plg{i}(1,1)],[plg{i}(:,2)' plg{i}(1,2)],'kx');endhold off=== === Subject: : Re: About Fortran complie and build> I used Compag Visual Fortran to compile some soucefilem. But it was> interupted by the error and gave the follow cue:***************> --------------------Configuration: mod_common - Win32> Debug--------------------> Linking...> dfor.lib(DFORMAIN.OBJ) : error LNK2001: unresolved external symbol> _MAIN__> Debug/mod_common.exe : fatal error LNK1120: 1 unresolved externals> Error executing link.exe.> mod_common.exe - 2 error(s), 0 warning(s)***************> I donnt know why?First, you probably want to post this question on comp.lang.fortran.Second, there is not enough information here to help.reason for the compiler complaining about there being no MAIN).=== === Subject: : Computationally cheap sin/acos approximationsCan anyone suggest *fast* approximations to sin and acos?I'm currently using a fiddled Taylor series for sin. Worst-case erroris around 0.00038, and it requires 8 multiples and 4 adds.My acos uses 5 multiples, 5 adds and a square-root, and has aworst-case error of around 0.00087 radians. It's a weighted sum of a1, X and root(1-x^2).Can anyone suggest more accurate approaches? These need to run on avideogame console with a pretty weak CPU, so they can't be much moreexpensive than the ones I'm using. Very roughly speaking, multiply andadd have a cost of 1, and square-roots and divides have a cost of 3.Any advice or pointers in the right direction would be muchappreciated.=== === Subject: : Re: Computationally cheap sin/acos approximations> Can anyone suggest *fast* approximations to sin and acos?> I'm currently using a fiddled Taylor series for sin. Worst-case error> is around 0.00038, and it requires 8 multiples and 4 adds.> My acos uses 5 multiples, 5 adds and a square-root, and has a> worst-case error of around 0.00087 radians. It's a weighted sum of a> 1, X and root(1-x^2).> Can anyone suggest more accurate approaches? These need to run on a> videogame console with a pretty weak CPU, so they can't be much more> expensive than the ones I'm using. Very roughly speaking, multiply and> add have a cost of 1, and square-roots and divides have a cost of 3.Over what domains should the approximations work? How about [0, pi/2]for sin(x) and [0, 1] for acos(x)?Also, just to make sure, am I right to think that you wish to minimize themaximum of |absolute error|, rather than |relative error|?=== === Subject: : Re: Computationally cheap sin/acos approximations>Can anyone suggest *fast* approximations to sin and acos?> Over what domains should the approximations work? How about [0, pi/2]> for sin(x) and [0, 1] for acos(x)?> Also, just to make sure, am I right to think that you wish to minimize the> maximum of |absolute error|, rather than |relative error|?Phew! I was using the range [-pi,pi] for sin(x), but I just recalculated bycoefficients for [0,pi/2] and the error dropped to 0.00001, which isdefinitely good enough.Acos is still a problem though...domain [0,1] is fine, and yes, I am lookingto minimise |absolute error|.Cheers=== === Subject: : Re: Computationally cheap sin/acos approximations >Can anyone suggest *fast* approximations to sin and acos? >I'm currently using a fiddled Taylor series for sin. Worst-case error >is around 0.00038, and it requires 8 multiples and 4 adds. >My acos uses 5 multiples, 5 adds and a square-root, and has a >worst-case error of around 0.00087 radians. It's a weighted sum of a >1, X and root(1-x^2). >Can anyone suggest more accurate approaches? These need to run on a >videogame console with a pretty weak CPU, so they can't be much more >expensive than the ones I'm using. Very roughly speaking, multiply and >add have a cost of 1, and square-roots and divides have a cost of 3. >Any advice or pointers in the right direction would be much >appreciated.or sin you could use the development in a chebyshev_seriesClenshaw has published a long paper of this. This is also possible for acos, but that series converges much slower (althoughmuch better than the taylor series) the book of Hart et al Computer approximations contains lots of approximationsfor many functions, sin and acos being special casesZbl 0174.20402 Hart, J.F.; Cheney, E.W.; Lawson, C.L.; Maehly, H.J.; Mesztenyi, C.K.; Rice, J.R.; Tha cher, H.G.jun.; Witzgall, C.Computer approximations (English)hthpeter === === Subject: : Re: Computationally cheap sin/acos approximations> Can anyone suggest *fast* approximations to sin and acos?> I'm currently using a fiddled Taylor series for sin. Worst-case error> is around 0.00038, and it requires 8 multiples and 4 adds.> My acos uses 5 multiples, 5 adds and a square-root, and has a> worst-case error of around 0.00087 radians. It's a weighted sum of a> 1, X and root(1-x^2).> Can anyone suggest more accurate approaches? These need to run on a> videogame console with a pretty weak CPU, so they can't be much more> expensive than the ones I'm using. Very roughly speaking, multiply and> add have a cost of 1, and square-roots and divides have a cost of 3.> Any advice or pointers in the right direction would be much> appreciated.Table lookup. Use logical arithmetic to handle the decisionsrather than IF ... ELSE ... ENDIF . Optimize with assembler.That's all I can suggest from my experience. There are no miracles.-- ^^^^^^^^^^^^^^^^^^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.=== === Subject: : Re: Computationally cheap sin/acos approximationsI was initailly doing this and getting satisfactory results, butunfortunately the cost of memory accesses was much too high. The machine inquestion is the Playstation2 which has a pathetically small data-cache (8KbL1, no L2), and *huge* penalties for cache-misses. It's not the mostforgiving machine in the world to work on...> Table lookup. Use logical arithmetic to handle the decisions> rather than IF ... ELSE ... ENDIF . Optimize with assembler.> That's all I can suggest from my experience. There are no miracles.> -- > Julian V. Noble> Professor Emeritus of Physics> jvn@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.=== === Subject: : Re: Averaging quaternions> Does anyone know if it is possible to take an average of regularly> sampled quaternions to get a mean orientation (i.e. a mean rotation> matrix)? I seem to recall there being a trick involved but beyond> re-normalizing the resuling (averaged) quaternion, I cannot remember> what it is.> Cheers,> Hi , It might help a lot to explain a little more about what you mean byregularly sampled and averaging. Do you mean that you have time samples of quaternions over time? In otherwords, you have q(t1), q(t2), q(t3), etc., where t1, t2, t3, etc. are evenlyspaced time points (not that even spacing is all that important). Is each sample a valid quaternion? By averaging, what do you really want? SLERP (as suggested by OUP) is generally used to interpolate between two(valid) quaternions. The result is always a valid quaternion. SLERP is infact valid for any two unit vectors of equal dimension (not justquaternions). So, you can use SLERP to find the quaternion at the midpointof your time interval and call that an average. My guess is that you need something more complex - try Googling onaveraging quaternions.=== === Subject: : Re: Averaging quaternions>Does anyone know if it is possible to take an average of regularly>sampled quaternions to get a mean orientation (i.e. a mean rotation>matrix)? I seem to recall there being a trick involved but beyond>re-normalizing the resuling (averaged) quaternion, I cannot remember>what it is.> I am sure I will be scolded by somebody, but I believe that you can> average the quaternion components, and then normalize as you say.> This is assumes that you are noise dominated.Averaging components is a bad idea no matter what, since the result is nevera quaternion. The OP doesn't imply anything about noise.> Also, there is one trick that I can think of, which is that> quaternions are degenerate. For each unique rotation, there are two> possible quaternions whose components have opposite signs. This is> because a positive rotation about axis V is identical to a negative> rotation about axis -V.> If your system is capable of both signs indiscriminately, then you> must make the sign conventions uniform. For example, by always making> one component positive.You are correct that q and -q represent the same rotation - that's notdegenerate, it's just not unique. Typically, the scalar part of thequaternion, cos(theta/2), is chosen to be the component that's alwayspositive.=== === Subject: : Re: Averaging quaternions>Does anyone know if it is possible to take an average of regularly>sampled quaternions to get a mean orientation (i.e. a mean rotation>matrix)? I seem to recall there being a trick involved but beyond>re-normalizing the resuling (averaged) quaternion, I cannot remember>what it is.>quaternions are degenerate. For each unique rotation, there are two>possible quaternions whose components have opposite signs. This is>because a positive rotation about axis V is identical to a negative>rotation about axis -V.>If your system is capable of both signs indiscriminately, then you>must make the sign conventions uniform. For example, by always making>one component positive.This will not work if the component is zero.Averaging (0,q) and (0,-q) which are the same rotation gives 0,which is meaningless.Thus the average and scale procedure makes only sense if all quaternionsare oriented the same way. One way to achieve this for any set ofunit quaternions that do not stray too much is the following:1. apply to all quaternions a rotation that moves one of them to 1 (for example one that is closest to the trivial average),2. orient all results to positive real part,3. average the results,4. rotate back the result,5. normalize.More costly but completely reliable.Arnold Neumaier=== === Subject: : Re: Averaging quaternionsSorry, I didn't finish before sending. I should have mentioned, however,that Craig's suggestion to just average the components and normalize is,Rotations, International Journal of Computer Vision 42(1/2), 7-16, 2001).So Craig's suggestion is certainly one method (just not one I happen to likevery much).No scolding intended.>Does anyone know if it is possible to take an average of regularly>sampled quaternions to get a mean orientation (i.e. a mean rotation>matrix)? I seem to recall there being a trick involved but beyond>re-normalizing the resuling (averaged) quaternion, I cannot remember>what it is.>I am sure I will be scolded by somebody, but I believe that you can>average the quaternion components, and then normalize as you say.>This is assumes that you are noise dominated.> Averaging components is a bad idea no matter what, since the result isnever> a quaternion. The OP doesn't imply anything about noise.>Also, there is one trick that I can think of, which is that>quaternions are degenerate. For each unique rotation, there are two>possible quaternions whose components have opposite signs. This is>because a positive rotation about axis V is identical to a negative>rotation about axis -V.>If your system is capable of both signs indiscriminately, then you>must make the sign conventions uniform. For example, by always making>one component positive.> You are correct that q and -q represent the same rotation - that's notdegenerate, it's just not unique. Typically, the scalar part of the> quaternion, cos(theta/2), is chosen to be the component that's always> positive.> === === Subject: : Re: Averaging quaternions> Does anyone know if it is possible to take an average of regularly> sampled quaternions to get a mean orientation (i.e. a mean rotation> matrix)? I seem to recall there being a trick involved but beyond> re-normalizing the resuling (averaged) quaternion, I cannot remember> what it is.> Cheers,> :Maybe you could try the SLERP (Spherical Linear IntERPolation) method to average the quaternions. Here's a link that describes the SLERP method: http://www.theory.org/software/qfa/writeup/node12.htmlGood luck,OUP=== === Subject: : Re: ill-conditioned system of linear equationsHi Sam,> I have a big problem concerning the solution of an ill-conditioned> system of linear equations. It is of the form A.x=b, where A can be> square or rectangular depending on the application. The problem is> that really small errors in the experimentally obtained values of A> and x result in absurd values of the solution x. I solve the system by> taking the inverse of the matrix A (if a is square) and then> multiplying b by this inverse.This is perhaps the worst possible way to solve a system of equations.Never do this. Get Golub and Van Loan's Matrix Computations forexplanations as to why (or any book on numerical analysis for that matter).If you want good code for solving this problem, use LAPACK (Fortran code) orCLAPACK (C code) from www.netlib.org. LAPACK is not only free, but it'swritten by the best numerical linear algebra specialists in the world. Ifyou have access to Matlab, just use x = A b, which will work regardless ofwhether A is square or not (Matlab uses LAPACK by the way).Sorry I can't help with your experimental data issues.=== === Subject: : Re: Why mcc compiled windows exe is 20 times slower than m-files??What is this mcc compiler?Is there any way to see what executable it is?jacobluigi a .8ecrit dans le message de> I have a matlab code that does a lot of matrix operations, things> like A.*B.*C etc. in the main loop.> The Windows EXE compiled with mcc runs 20 times SLOWER than the> m-file script. I used default options for mcc and mbuild, which> according to ther manual, has all optimizations turned on.> Is this specific to the mcc compiler? Is there something I can do to> speed it up?=== === Subject: : Re: Why mcc compiled windows exe is 20 times slower than m-files??mcc is the Matlab function that takes a relatively arbitrary Matlab .m script or function (there are constraints) and turns it into an executable. Usually this greatly improves the execution time of the script.Different compilers can be used by mcc to generate the executable, including VC++, lcc (provided by Mathworks with matlab), gcc (*nix only) and some Fortran compilers.Luigi didn't specify which compiler he is using so I'm guessing it is the default lcc compiler..> What is this mcc compiler?> Is there any way to see what executable it is?> jacobluigi a .8ecrit dans le message de> I have a matlab code that does a lot of matrix operations, things>like A.*B.*C etc. in the main loop.> The Windows EXE compiled with mcc runs 20 times SLOWER than the>m-file script. I used default options for mcc and mbuild, which>according to ther manual, has all optimizations turned on.> Is this specific to the mcc compiler? Is there something I can do to>speed it up?=== === Subject: : Workshop Global and Geometric Aspects in Nonlinear PDEOriginator: bergv@math.uiuc.edu (Maarten Bergvelt)Workshop Global and Geometric Aspects in Nonlinear PDEDedicated to the 85th anniversary of the Yerevan State University Scientific Committee: Luis Caffarelli, Peter Markowich, Henrik ShahgholianOrganizing Committee: A. Hakobyan, M. Poghosyan Tentative list of speakers: Amandine Aftalion (France), Ioannis Athanasopoulos (Greece), Henri Berestycki (France), Yann Brenier (France), Xavier Cabre (Spain), Michel Chipot (Switzerland), Claudia Lederman (Argentina), Ki-ahm Lee (South Korea), Fanghua Lin (USA), Nicola Garofalo (USA), Francois Hamel (France), Regis Monneau (France), Louis Nirenberg (USA), Stanley Osher (USA), Sandro Salsa (Italy), Sylvia Serfaty (USA),James Sethian (USA), Halil Mete Soner (Turkey), Takis Souganidis (USA), Neil Trudinger (Australia), Nina Uraltseva (Russia), Juan Luis Vazquez Suarez (Spain), Noemi Wolanski (Argentina)Information: http://math.sci.am http://www.math.kth.se/~henriksh/armenia04.htmlContact: mathconf@ysu.am A. Hakobyan, Department of Mathematics, Yerevan State University, 1, Al. Manoogian Str. Yerevan 375025, ARMENIASponsored by Yerevan State University Institute of Mathematics of National Academy of Sciences of Armenia Swedish Royal Academy of Sciences Wolfgang Pauli Institute in Vienna Wittgenstein Award 2000 of Peter Markowich, funded by the Austrian Science Fund=== === Subject: : Reviews in Mathematical Physics - Vol 15 No 10Originator: bergv@math.uiuc.edu (Maarten Bergvelt)Reviews in Mathematical PhysicsView table-of-contents and abstracts at http://www.worldscinet.com/rmp.htmlAspects Of Noncommutative Lorentzian Geometry For Globally Hyperbolic SpacetimesValter MorettiConfinement To Lowest Landau Band And Application To Quantum CurrentS. FournaisEssential Properties Of The Vacuum Sector For A Theory Of Superselection SectorsGiuseppe RuzziWigner Measures And Molecular Propagation Through Generic Energy Level CrossingsClotilde Fermanian KammererFor more information, go to http://www.worldscinet.com/rmp.html=== === Subject: : This week in the mathematics arXiv (1 Mar - 5 Mar)Originator: bergv@math.uiuc.edu (Maarten Bergvelt)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 Mar - 5 Mar)-----------------------------------------------AC: Commutative Algebra-----------------------math.AC/0403058 hi, everyone>Suppose now we have N normal distributed r.v's X1, X2, ..., Xn>with mean ui and variance v2i. Is there an analytical approximation>of Prob[X1 <= min(X2, ..., Xn)] ?> The function is clearly an analytic function of the> u's and v2's.> But I do not know of any easy computational method, even> asuming the X's are independent, for n > 2. In the> independent case, it can be done by one integration of a> product of normal probabilities with respect to a normal> density.> --> This address is for information only. I do not claim that these views> are those of the Statistics Department or of Purdue University.> Herman Rubin, Department of Statistics, Purdue University> hrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558=== === Subject: : Re: The distribution of the minimum of several normal distributed r.v's?Originator: bergv@math.uiuc.edu (Maarten Bergvelt)>hi, Rubin>Did you see the paper?>Clark, C. (1961), The Greatest of a Finite Set of Random Variables,>Operations Research, Vol. 9, issue 2, page 145-162.>He showed that the minimum of two normal distributed r.v's>Y = min{X1,X2} is approximation of a normal distribution.>However, for multiple r.v's, it needs more work to combine>them togather. Is there any easier way to deal with multiple>r.v's?Getting the probability that one of two jointly normalrandom variable is the smallest is trivial, as thedifference is normal. The cdf of the minimum of anyfinite number of independent random variables is alsoquite easy. Not much else is obtainable in any sortof closed form.>Fan>hi, everyone>Suppose now we have N normal distributed r.v's X1, X2, ..., Xn>with mean ui and variance v2i. Is there an analytical approximation>of Prob[X1 <= min(X2, ..., Xn)] ?> The function is clearly an analytic function of the> u's and v2's.> But I do not know of any easy computational method, even> asuming the X's are independent, for n > 2. In the> independent case, it can be done by one integration of a> product of normal probabilities with respect to a normal> density.-- 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 Universityhrubin@stat.purdue.edu Phone: (765)494-6054 FAX: (765)494-0558=== === Subject: : Re: Cohomology of manifoldsOriginator: bergv@math.uiuc.edu (Maarten Bergvelt)> I received an e-mail from someone whose name I will not reveal unless > I dont know a reference but I believe that a manifold M of dimension n> with your conditions has the homotopy type of a CW complex of> dimension n-1.It was Bruce Westbury who kindly provided me with this information. -- Marc Nardmann(To reply, remove every occurrence of a certain letter from my e-mail address.)=== === Subject: : This week in the mathematics arXiv (8 Mar - 12 Mar)Originator: bergv@math.uiuc.edu (Maarten Bergvelt)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 (8 Mar - 12 Mar)------------------------------------------------AC: Commutative Algebra-----------------------math.AC/0403156