mm-3179 to choose. Also I won't deal with a discrete Fourier transform but with the Fourier series that the discrete transform is an approximation to. So let's say you're working with s(t) for one period: 0 <= t <= L = 2 pi/w. The Fourier series is s(t) = sum_{k=-infty}^infty c(k) exp(2 pi i k t/L) with c(k) = 1/L int_0^L s(t) exp(-2 pi i k t/L) dt (your conventions may differ) I'll assume 0 < c < a. Note that v(t) = 0 when sin(w t) = -c/a, i.e. t = L/2 + arcsin(c/a)/w or L - arcsin(c/a)/w. Let h = arcsin(c/a)/w. Thus s(t) = - v(t) for L/2 + h < t < L - h, and v(t) elsewhere on the interval [0,L]. Maple tells me c(0) = 2 (c arcsin(c/a) + a sqrt(1-c^2/a^2))/pi c(1) = - i (a arcsin(c/a) + c sqrt(1-c^2/a^2))/pi c(2) = - 2 (a^2 - c^2) sqrt(1-c^2/a^2)/(3 a pi) c(3) = - 2 i c (a^2 - c^2) sqrt(1-c^2/a^2)/(3 a^2 pi) Subject: This week in the mathematics arXiv (12 Sep - 16 Sep) Here are this week's titles in the mathematics arXiv, available at: http://front.math.ucdavis.edu/ http://front.math.ucdavis.edu/submissions This week in the mathematics arXiv may be freely redistributed with attribution and without modification. Titles in the mathematics arXiv (12 Sep - 16 Sep) ------------------------------------------------- AC: Commutative Algebra ----------------------- Mohammad T. Dibaei, Siamak Yassemi: Finiteness of extension functors of local cohomology modules Niels Lauritzen: Truncated Groebner fans and lattice ideals Satoshi Murai, Takayuki Hibi: Combinatorial shifting and graded Betti numbers AG: Algebraic Geometry ---------------------- Markus Reineke: Localization in quiver moduli D. Markushevich: Rational Lagrangian fibrations on punctual Hilbert schemes of K3 surfaces Ivan Cheltsov: Elliptic structures on weighted three-dimensional Fano hypersurfaces John Scherk: The Borel-Serre Compactification for the Classifying Space of Hodge Structures Terence Gaffney: The Multiplicity Polar Theorem and Isolated Singularities E. Artal Bartolo, I. Luengo, A. Melle-Hernandez: Superisolated Surface Singularities Alex Kuronya, Alexandre Wolfe: A Briancon-Skoda type theorem for graded systems of ideals Kenichiro Kimura: Murre's conjectures for certain product varieties Jason Howald, Mircea Mustata, Cornelia Oichi Yuen: On Igusa zeta functions of monomial ideals Piotr Pragacz: Thom polynomials and Schur functions I J.M. Landsberg, Colleen Robles: Fubini's Theorem in codimension two Justin Sawon: Lagrangian fibrations on Hilbert schemes of points on K3 surfaces Justin Sawon: Deformations of holomorphic Lagrangian fibrations Justin Sawon: Twisted Fourier-Mukai transforms for holomorphic symplectic fourfolds Ragnar-Olaf Buchweitz, David Mond: Linear free divisors and quiver representations Kalle Karu: Lefschetz decomposition and the cd-index of fans F. Bihan: Polynomial systems supported on circuits and dessins d'enfants Pelle Salomonsson: Steenrod operations in Gromov--Witten theory: a computation for CP^n D. Barlet: Interaction de strates consecutives pour les cycles evanescents III : Le cas de la valeur propre 1 Volker Braun, Yang-Hui He, Burt A. Ovrut, Tony Pantev: Heterotic Standard Model Moduli AP: Analysis of PDEs -------------------- A. Babin, A. Figotin: Linear superposition in nonlinear wave dynamics D. Iftimie, M. C. Lopes Filho, H. J. Nussenzveig Lopes: Two-dimensional incompressible viscous flow around a small obstacle Volker Elling, Tai-Ping Liu: The ellipticity principle for selfsimilar polytropic potential flow Jason Metcalfe, Ann Stewart: Almost global existence for quasilinear wave equations in waveguides with Neumann boundary conditions Atanas Stefanov: Strichartz estimates for the magnetic Schrodinger equation Yan Guo, Hyung Ju Hwang: Pattern formation (I): The Keller-Segel Model Raphael Ponge: Heisenberg calculus and spectral theory of hypoelliptic operators on Heisenberg manifolds Irina Markina, Sergey Vodopyanov: On Value Distributions for Quasimeromorphic Mappings on $mathbb H$-type Carnot Groups Julien Vovelle, Merlet Benoit: Error estimate for the Finite Volume Scheme applied to the advection equation James Nolen, Jack Xin: Variational Principle of KPP Front Speeds in Temporally Random Shear Flows Erik Ekstrom, Johan Tysk: Properties of option prices in a jump-diffusion model Erik Ekstrom, Johan Tysk: A boundary point lemma for Black-Scholes type operators Jens Wirth: Modified scattering for a wave equation with weak dissipation S. Herr: An improved bilinear estimate for Benjamin-Ono type equations Oliver C. Schnurer, Hartmut R. Schwetlick: Decay at infinity for parabolic equations L. Escauriaza, C. E. Kenig, G. Ponce, L. Vega: On unique continuation of solutions of Schrodinger equations AT: Algebraic Topology ---------------------- Martin Markl: Lie elements in pre-Lie algebras, trees and cohomology operations Gregory Lupton, N. Christopher Phillips, Claude L. Schochet, Samuel B. Smith: Banach Algebras and Rational Homotopy Theory Max Karoubi: Quasi-commutative cochains in algebraic topology Jouko Mickelsson, Juha-Pekka Pellonpaa: Families index theorem in supersymmetric WZW model and twisted K-theory: The SU(2) case Peter J. Eccles, Mark Grant: Self-intersections of Immersions and Steenrod Operations CA: Classical Analysis and ODEs ------------------------------- Matthias R. Gaberdiel, Albrecht O. Klemm, Ingo Runkel: Matrix model eigenvalue integrals and twist fields in the su(2)-WZW model Carlos Cabrelli, Ursula Molter: Density of the Set of Generators of Wavelet Systems Vincent Thilliez: An introduction to quasianalytic local rings Jonathan Bennett, Anthony Carbery, Terence Tao: On the Multilinear Restriction and Kakeya conjectures CO: Combinatorics ----------------- Denis Krotov: On decomposability of 4-ary distance 2 MDS codes, double-codes, and n-quasigroups of order 4 Shalosh B. Ekhad, Vince Vatter, Doron Zeilberger: A Proof of the Loehr-Warrington Amazing TEN to the Power n Conjecture Glenn Hurlbert: Recent Progress in Graph Pebbling Weigen Yan, Yeong-Nan Yeh, Fuji Zhang: Graphical condensation of plane graphs: a combinatorial approach Denis Krotov: Krotov: Z_{2^k}-duality, Z_{2^k}-linear Hadamard codes, and co-Z_{2^k}-linear 1-perfect codes Vadim B. Kuznetsov, Evgeny K. Sklyanin: Eigenproblem for Jacobi matrices: hypergeometric series solution Ian Shipman: The distinguishing number of the iterated line graph William Y.C. Chen, Qing-Hu Hou, Yan-Ping Mu: Nonterminating Basic Hypergeometric Series and the $q$-Zeilberger Algorithm Nantel Bergeron, Christophe Hohlweg, Mike Zabrocki: Posets related to the connectivity set of Coxeter groups Nantel Bergeron, Mike Zabrocki: The Hopf algebra of non-commutative symmetric functions and quasi-symmetric functions are free and cofree Alberto M. Teguia, Anant P. Godbole: Sierpi' nski Gasket Graphs and Some of Their Properties William Y.C. Chen, Nelson Y. Li, Louis W. Shapiro, Sherry H.F. Yan: Matrix Identities on Weighted Partial Motzkin Paths Dan Bernsà¿,^L°{uàÿXEêO 216§.9f#ãó.86oyuô.96:©[ADoub leDot]¨.8fÄÚàA!°èä.87 [Hyphen]Ä©Î.850N.8fÔ427.82.b2,[AH at]T$.9aÚEùØ.b2.8b[Eth]y.88.9d±m.9eÍ1üFE» t.90ÅrmL.82Ø$vOëê[CapitalA DoubleDot]ÈSß.8bû.94.95è&§[Ca pitalUGrave][Times]?gn'`&Ãè¯ßAw[C apitalIAcute]¤hv(f$.8fò'[CapitalIDouble Dot]x¨.95ì[Micro].82£t1-£.85~.87[Capit alATilde]r«.bd.beÉû÷C*.9f23 47.8c#üYÃ'gÊ~Î[Capital EDoubleDot]ÁÈ.a6.b2d;'ñ Ht@@hÿá¬hFï[Thorn]º.b2..81*[ CapitalEGrave]P[Ï#Ï[CapitalYAcute] 235ÍG,ZÙ»pusàJ[Capital EGrave]ì©.87ÄÑ[@.838'1[CapitalID oubleDot]&.87.93Ì.89îÂZÆ[AH at]·.85á'.8dtWtâ+,ßH wÓÑ´}.9c[Eth]¬ê.92.83[NTil de]´)ÆËò.8cn»¬ `hÙ6«<.88¯[CapitalYAcute]ä[A Hat][CapitalEth]Ø.9aoÂ+.9aÒ [CapitalEth]Df^£RKÄ5È[YAcute]#.98N.89[Capital IAcute]-ëN.8d¢.86.90ÿ÷@U[CapitalEth ].beÜSÁ.939+.8dr.a6h[CapitalCCedilla ]º[Eth]0Ì(b.84ɨaª6Ú KÉ.92.88¢.8a.818/ ¸Ñ.8a.86'EË.bd.93K Üi[YAcute].92.96?æÿ¤_[IA cute]ÊFæå#Ú.91ÿ.b2O 224.91t.82C[YAcute]ÒL[NonBreakingSpace]§[IGra ve]Io.90ó(.8a9ÍS÷ÃL[UAcut e].89Dted states Michael Skeide: Spatial E_0-Semigroups are Restrictions of Inner Automorphismgroups Gilles Pisier: Remarks on $B(H)otimes B(H)$ Astrid an Huef, S. Kaliszewski, Iain Raeburn: Covariant representations of Hecke algebras and imprimitivity for crossed products by homogeneous spaces Gelu Popescu: Constrained multivariable operator theory II Narcisse Randrianantoanina: Conditioned square functions for non-commutative martingales OC: Optimization and Control ---------------------------- Amit K. Sanyal: Optimal Attitude Estimation and Filtering Without Using Local Coordinates Part I: Uncontrolled and Deterministic Attitude Dynamics H'{e}l`{e}ne Le Cadre: Robust Routing and Cross-Entropy Estimation Taeyoung Lee, Melvin Leok, N. Harris McClamroch: Attitude Maneuvers of a Rigid Spacecraft in a Circular Orbit Ioannis A. Fotiou, Philipp Rostalski, Bernd Sturmfels, Manfred Morari: An algebraic geometry approach to nonlinear parametric optimization in control J. Eisert: Optimizing linear optics quantum gates Marianne Akian, Stephane Gaubert, Asma Lakhoua: The max-plus finite element method for optimal control problems: further approximation results Tryphon T. Georgiou: The Caratheodory-Fejer-Pisarenko decomposition and its multivariable counterpart PR: Probability --------------- Annie Millet, Marta Sanz-Sol'{e}: Approximation of rough paths of fractional Brownian motion Joseph F. Johnson: Logical Structure of Physical Probability Assertions Mireille Bousquet-M'{e}lou, Svante Janson: The density of the ISE and local limit laws for embedded trees X. Bressaud, A. Maass, S. Martinez, J. San Martin: Stationary processes whose filtrations are standard Ioannis Kontoyiannis, S.P. Meyn: Large deviations asymptotics and the spectral theory of multiplicatively regular Markov processes Didier Dacunha-Castelle, Lisandro Ferm'{i}n: Disaggregation of Long Memory Processes on C^{infty} Class Patrick Cheridito, H. Mete Soner, Nizar Touzi, Nicolas Victoir: Second order backward stochastic differential equations and fully non-linear parabolic PDEs Marianne Akian, Stephane Gaubert, Vassili Kolokoltsov: Solutions of max-plus linear equations and large deviations Shankar Bhamidi, Steven N. Evans, Ron Peled, Peter Ralph: Brownian motion on time scales, basic hypergeometric functions, and some continued fractions of Ramanujan Pierre Mathieu: Carne-Varopoulos bounds for centered random walks Eran Ofek: On the expansion of the giant component in percolated (n,d,lambda) graphs Gady Kozma: Percolation, Perimetry, Planarity Jean Mairesse, Fr'ed'eric Math'eus: Random walks on free products of cyclic groups Jean Mairesse, Fr'ed'eric Math'eus: Appendix to the paper Random walks on free products of cyclic groups QA: Quantum Algebra ------------------- Vijay Kodiyalam, V.S. Sunder: Planar algebras and Kuperberg's 3-manifold invariant Jonathan Block: Duality and equivalence of module categories in noncommutative geometry I Kevin J. Costello: The Gromov-Witten potential associated to a TCFT Israel Gelfand, Sergei Gelfand, Vladimir Retakh, Robert Lee Wilson: Factorizations of Polynomials over Noncommutative Algebras and Sufficient Sets of Edges in Directed Graphs Tom Hadfield, Ulrich Kraehmer: On the Hochschild homology of quantum SL(N) A. P. Isaev, O. V. Ogievetsky, P. N. Pyatov: On R-matrix representations of Birman-Murakami-Wenzl algebras RA: Rings and Algebras ---------------------- Mark Kambites, Friedrich Otto: Uniform decision problems in automatic semigroups Mark Kambites: Automatic Rees matrix semigroups over categories Vasyl Ostrovskyi: Special characters on star graphs and representations of $*$-algebras Michael Pinsker: Monoidal intervals of clones on infinite sets Yunge Xu, Yang Han, Wenfeng Jiang: Hochschild cohomology of truncated quiver algebras RT: Representation Theory ------------------------- G. Lusztig: Character sheaves on disconnected groups, VIII Jean-Yves Charbonnel: Complexe canonique d'une alg`ebre de Lie r'eductive Ghislain Fourier, Peter Littelmann: Weyl modules, affine Demazure modules, fusion products and limit constructions Jean-Yves Charbonnel: Complexe canonique de deuxi`{e}me esp`{e}ce, vari'{e}t'{e} commutante et bic^{o}ne nilpotent d'une alg`{e}bre de Lie r'{e}ductive Raphael Rouquier: q-Schur algebras and complex reflection groups, I Cristian Lenart: On the Combinatorics of Crystal Graphs, I SG: Symplectic Geometry ----------------------- M. J. D. Hamilton, D. Kotschick: Minimality and irreducibility of symplectic four-manifolds SP: Spectral Theory ------------------- V. Guillemin, A. Uribe: Some inverse spectral results for semi-classical Schrodinger operators Fr'{e}d'{e}ric Serier: Inverse spectral problem for radial Schr{o}dinger operator on [0, 1] ST: Statistics -------------- Ana Arribas-Gil, Elisabeth Gassiat, Catherine Matias: Parameter estimation in pair hidden Markov models Andr'{e} Mas: Weak convergence in the functional autoregressive model Arnak Dalalyan: James-Stein Shrinkage and Second Order Efficiency in Semiparametrics -- / Greg Kuperberg (UC Davis) / Home page: http://www.math.ucdavis.edu/~greg/ / Visit the Math ArXiv Front at http://front.math.ucdavis.edu/ / * All the math that's fit to e-print * Subject: embeddability of hyperbolic 3-manifolds in R^n Given a hyperbolic 3-manifold M of finite volume, what conditions on the geometry of M make it embeddable in R^n? For n=5 it embeds by a theorem of C.T.C. Wall (all compact 3-manifolds embed in R^5). So the question is, what does it take to get the dimension down to 4 or 3? For dimension 3, a simple neccessary condition is that you have a non-empty boundary. If you have one boundary torus then a sufficient condition is that M is diffeomorphic to a knot complement. Similarly you can show a sufficient condition is that if there's finitely many boundary components, then M is diffeomorphic to a hyperbolic link complement. Is there a geometric characterisation of the class of hyperbolic 3-manifolds which are link complements, inside of the class of all hyperbolic 3-manifolds? What I'm asking for is a statement of the form a hyperbolic 3-manifold of finite volume is diffeomorphic to the complement of a link in S^3 if and only if it has at least one boundary component and some geometrical conditions are satisfied ie: some condition on something like volumes or cusp shapes, etc... Subject: New Version of 3D-XplorMath Visualization Program Availabhle. This announcement will primarily be of interest to Macintosh users, however note the announcement below of an upcoming Java version. 3D-XplorMath version 10.4.1 is a freeware mathematical visualization tool that is a much improved version of the well-known program 3D-Filmstrip. NOTE: The 3D-XplorMath webserver has moved. The new server, located at the University of California, Irvine Mathematics Department, is vmm.math.uci.edu. The new 3D-XplorMath homepage is at: http://vmm.math.uci.edu/3D-XplorMath/ and the program together with full documentation can be downloaded from there. (There is a Gallery of 3D-XplorMath produced visualizations and animations at: IMPORTANT NEWS!: Professor David Eck of Hobart and William Smith Colleges is creating a cross-platform Java program called VMM (for the Virtual Mathematical Museum) that will eventually include all of the essential functionality of 3D-XplorMath. Work on this is progressing very well, and we hope to have a public release of an early version by Spring of 2006 if not earlierói¨Ò ÃØà8bÂbÎOº $[CapitalEth]-Ñ@í& L÷^ÔV.82Yã[[NonBreakingSpace][CapitalEDoub leDot].87V t.9e.8e.8bên¡Ôfi?[UAcu te]ná.83zÓx(Ø.93ªA©'2 ìhaÔ'g).9c.938}C6$»PB0- [YAcute]©üEé.85ïà NÍ.9aø·÷ü<.91.83[NonBreakingS pace]íT' 2iEá£.99CVß á5 &dH0jA.85.8cO¨hN8º°I.89A$ó.8d¯.97H[Capital ARing]í.85wzSx.9d.8d#bt,tA%d].8cBÔ.89R[Copyrig ht][YAcute]G.83°1.8cFÃÛ[CapitalIDou bleDot].81>G£.9f XP*t^5-1/4*a1^2*t^2+1/8*a1*a0*t-5/64*a0^2 =0 we can find that t = u is always a solution indepenent of v for Spearman and Williams quintics http://mathworld.wolfram.com/QuinticEquation.html a1 = 5*e^4*(3-4*c*k)/(c^2 + 1) a0 = -4*e^5*(11*k + 2*c)/(c^2 + 1) k = +1 or -1 Solving the same sextic a1*t^6+5/2*a0*t^5-1/4*a1^2*t^2+1/8*a1*a0*t-5/64*a0^2 =0 we can find that t = -ke is always a solution indepenent of c