mm-3039 === Subject: projective ideals Originator: israel@math.ubc.ca (Robert Israel) Are there projective ideals (of rings) which are not finitely generated? -- http://www.iecn.u-nancy.fr/~gaillard/ === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) Here is a mild simplification of Ojanguren's argument. Let B be a nonzero ring, let A be the ring of sequences a_1, a_2, ... in B, let I be the ideal of finitely supported such sequences; in particular I is not finitely generated. Let F be the free A-module with basis e_1, e_2, ... Define p : F --> I by letting p(e_i) be the characteristic fonction of the integral interval [1,i], and s : I --> F by putting s(x) := sum d_i x e_i where d_i is the characteristic fonction of the singleton {i}. Then ps is the identity of I. === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) > Are there projective ideals (of rings) which are not finitely generated? Manuel Ojanguren has just given me an example of a projective ideal which is not finitely generated. His text (in French) is available in pdf format at http://www.iecn.u-nancy.fr/~gaillard/DIVERS/ojanguren.pdf -- http://www.iecn.u-nancy.fr/~gaillard/ === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) > Are there projective ideals (of rings) which are not finitely generated? Yes, there are in non-noetherian graded rings. Take, e.g., in the polynomial ring k[X1,...,Xn,...] generated by countably many indeterminates Xn the ideal generated by {Xm : m e S} for any infinite subset S of IN. J. === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) >>Are there projective ideals (of rings) which are not finitely generated? >> >Yes, there are in non-noetherian graded rings. Take, e.g., in the >polynomial ring k[X1,...,Xn,...] generated by countably many >indeterminates Xn the ideal generated by {Xm : m e S} for any infinite >subset S of IN. Yes, but it is not PROJECTIVE ... === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) >> >Are there projective ideals (of rings) which are not finitely generated? > >> Yes, there are in non-noetherian graded rings. Take, e.g., in the >> polynomial ring k[X1,...,Xn,...] generated by countably many >> indeterminates Xn the ideal generated by {Xm : m e S} for any infinite >> subset S of IN. >> > Yes, but it is not PROJECTIVE ... I interpreted PROJECTIVE to HOMOGENEOUS or to be an element of the associated projective scheme Proj(S) - if S denotes the positively graduated algebra S. So what is your notion of PROJECTIVE IDEALS? J. === Subject: Re: Rational solutions family Originator: israel@math.ubc.ca (Robert Israel) > Is there a rational solutions family for > (x - 1/x)*(y - 1/y)*(z - 1/z) = 8 > There are infinite solutions e.g. > x = 11/5; y = 5/2; z = 18/7 > x = 8/3; y = 7/3; z = 25/11 > x = 21/11; y = 4/3; z = 10 > x = 16/5; y = 7; z = 11/9 > Also > if x1 ; y1 ; z1 is a solutions then > x = (x1+1)/(x1-1) ; y = (y1+1)/(y1-1); z = > (z1+1)/(z1-1) is a solution An altenative solution for (x - 1/x)*(y - 1/y)*(z - 1/z) = 8 Let x = x1/x2; y = y1/y2; z = z1/z2 where x1,x2,y1,y2,z1,z2 are rationals (x1^2 - x2^2)*(y1^2 - y2^2)*(z1^2 - z2^2) = 8*x1*x2*y1*y2*z1*z2 Let x1 + x2 = 2*t1*z1 x1 - x2 = 2*t2*z2 y1 + y2 = 2*t3*x1 y1 - y2 = 2*t4*x2 z1 + z2 = 2*t5*y1 z1 - z2 = 2*t6*y2 where t1,t2,t3,t4,t5,t6 are rationals such that t1*t2*t3*t4*t5*t6=1/8 Solving for x1,x2,y1,y2,z1,z2 x1 = t1*z1 + t2*z2 x2 = t1*z1 - t2*z2 y1 = t3*x1 + t4*x2 = t3*(t1*z1 + t2*z2) + t4*(t1*z1 - t2*z2) y2 = t3*x1 - t4*x2 = t3*(t1*z1 + t2*z2) - t4*(t1*z1 - t2*z2) z1 = t5*y1 + t6*y2=t5*(t3*(t1*z1 + t2*z2) + t4*(t1*z1 - t2*z2)) + t6*(t3*(t1*z1 + t2*z2) - t4*(t1*z1 - t2*z2)) z2 = t5*y1 - t6*y2=t5*(t3*(t1*z1 + t2*z2) + t4*(t1*z1 - t2*z2)) - t6*(t3*(t1*z1 + t2*z2) - t4*(t1*z1 - t2*z2)) z1*(-1 + t5*t3*t1 + t5*t4*t1 + t6*t3*t1 - t6*t4*t1) + z2*(t5*t3*t2 - t5*t4*t2 + t6*t3*t2 + t6*t4*t2) = 0 z1*(t5*t3*t1 + t5*t4*t1 - t6*t3*t1 + t6*t4*t1) + z2*(-1 + t5*t3*t2 - t5*t4*t2 - t6*t3*t2 - t6*t4*t2) = 0 Then (-1 + t5*t3*t1 + t5*t4*t1 + t6*t3*t1 - t6*t4*t1)=k*(t5*t3*t1 + t5*t4*t1 - t6*t3*t1 + t6*t4*t1) (t5*t3*t2 - t5*t4*t2 + t6*t3*t2 + t6*t4*t2)=k*(-1 + t5*t3*t2 - t5*t4*t2 - t6*t3*t2 - t6*t4*t2) Taking k = 1 and solving for t1 and t2 t1 = 1/2/t6/(t3 - t4) t2 = -1/2/t6/(t3 + t4) t5 = 1/8/(t1*t2*t3*t4*t6) z1 = -(t5*t3*t2 - t5*t4*t2 + t6*t3*t2 + t6*t4*t2)*z2/(-1 + t5*t3*t1 + t5*t4*t1 + t6*t3*t1 - t6*t4*t1) y1 = t3*(t1*z1 + t2*z2) + t4*(t1*z1 - t2*z2) y2 = t3*(t1*z1 + t2*z2) - t4*(t1*z1 - t2*z2) x1 = t1*z1 + t2*z2 x2 = t1*z1 - t2*z2 z =z2/z1; y=y2/y1; x=x2/x1 z = (t4^2 - 4*t3*t4 + t3^2)/(t4^2 + 4*t3*t4 + t3^2) y = -1/2*(t4^2 + t3^2)/(-t3^2 + t4^2) x = -t4*(-3*t3^2 + t4^2)/(-t3^2 + 3*t4^2)/t3 taking t = t4/t3 z = (t^2 - 4*t + 1)/(t^2 + 4*t + 1) y = 1/2*(t^2 + 1)/(1 - t^2) x = t*(3 - t^2)/(3*t^2 -1) Example -------- t = 3 z = -1/11 ; y= -5/8; x=-9/13 === Subject: This week in the mathematics arXiv (2 Jan - 6 Jan) Originator: israel@math.ubc.ca (Robert Israel) 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 (2 Jan - 6 Jan) ----------------------------------------------- AC: Commutative Algebra ----------------------- math.AC/0601101 Jerome W. Hoffman, Haohao Wang: Regularity and Resolutions for Multigraded Modules math.AC/0601022 Kwankyu Lee, Michael E. O'Sullivan: Sudan's List Decoding of Reed-Solomon Codes from a Groebner Basis Perspective AG: Algebraic Geometry ---------------------- math.AG/0601100 Yoichi Mieda: On l-independence for the etale cohomology of rigid spaces over local fields math.AG/0601097 J.M. Landsberg, L. Manivel: Generalizations of Strassen's equations for secant varieties of Segre varieties math.AG/0601075 Sergei Shadrin, Dimitri Zvonkine: Intersection numbers with Witten's top Chern class math.AG/0601072 Yuri G. Zarhin: Superelliptic jacobians math.AG/0601063 Francesco Polizzi: Surfaces of general type with $p_g=q=1$ which are isogenous to a product of curves math.AG/0601052 Salman Abdulali: Hodge structures of CM-type math.AG/0601047 A. Shapiro, S. Kaplan, M. Teicher: Several Applications of Bezout Matrices math.AG/0601041 Grigory Mikhalkin: Tropical Geometry and its applications math.AG/0601037 Steven Dale Cutkosky: Strong Toroidalization of Dominant Morphisms of 3-folds hep-th/0512205 Tomas L. Gomez, Sergio Lukic, Ignacio Sols: Constraining the Kahler Moduli in the Heterotic Standard Model math.AG/0601023 Ivan V. Losev: Algebraic Hamiltonian actions math.AG/0601014 Timothy Logvinenko: Natural G-Constellation Families math.AG/0512648 Yukinobu Toda: Stability conditions and crepant small resolutions math.AG/0512645 Giuseppe Pareschi, Mihnea Popa: M-regularity and the Fourier-Mukai transform math.AG/0512640 Kai Behrend, Ajneet Dhillon: On the Motive of the Stack of Bundles math.AG/0512632 Allen Knutson: Balanced normal cones and Fulton-MacPherson's intersection theory math.AG/0512631 Tommaso de Fernex: Negative curves on very general blow-ups of P^2 AP: Analysis of PDEs -------------------- math.AP/0601086 Neil S Trudinger, Xu-jia Wang: On the second boundary value problem for Monge-Ampere type equations and optimal transportation math.AP/0601074 Alexey Cheskidov: Blow-up in finite time for the dyadic model of the Navier-Stokes equations math.AP/0601060 Dongho Chae: Nonexistence of self-similar singularities for the 3D incompressible Euler equations gr-qc/0512119 Mihalis Dafermos, Igor Rodnianski: The red-shift effect and radiation decay on black hole spacetimes math.AP/0601030 Davide Catania: A dispersive estimate for the linear wave equation with an electromagnetic potential math.AP/0601018 Leonid Berlyand, Dmitry Golovaty, Volodymyr Rybalko: Capacity of a multiply-connected domain and nonexistence of Ginzburg-Landau minimizers with prescribed degrees on the boundary math.AP/0512644 V. Beresnevich, M. Dodson, S. Kristensen, J. Levesley: Diophantine approximation with perfect squares and the solvability of an inhomogeneous wave equation math.AP/0512639 Ramona Anton: Strichartz Inequalities for Lipschitz Metrics on Manifolds and Nonlinear Schrodinger Equation on Domains math.AP/0512629 Abderrahmane El Hachimi, Moulay Rchid Sidi Ammi, Delfim F. M. Torres: Existence and uniqueness of solutions for a nonlocal parabolic thermistor-type problem AT: Algebraic Topology ---------------------- math.AT/0601085 Benoit Fresse: The bar construction of an E-infinite algebra math.AT/0601079 Thomas Kahl: Relative directed homotopy theory of partially ordered spaces math.AT/0512658 Ernesto Lupercio, Bernardo Uribe, Miguel A. Xicotencatl: Orbifold String Topology CA: Classical Analysis and ODEs ------------------------------- math.CA/0601078 Diego Dominici: Asymptotic analysis of the Hermite polynomials from their differential-difference equation math.CA/0601044 J. M. Aldaz, J. P'erez L'azaro: Functions of bounded variation, the derivative of the one dimensional maximal function, and applications to inequalities math.CA/0601021 Gady Kozma, Ferenc Oravecz: On the gaps between zeros of trigonometric polynomials math.CA/0512659 Palle E. T. Jorgensen, Anilesh Mohari: Localized bases in L^2(0,1) and their use in the analysis of Brownian motion math.CA/0512647 Nets Hawk Katz: The Grone Merris Conjecture and a quadratic eigenvalue problem math.CA/0512642 Holger Rauhut: Random Sampling of Sparse Trigonometric Polynomials CO: Combinatorics ----------------- math.CO/0601094 K. De Naeghel, N. Marconnet: An inequality on broken chessboards math.CO/0601081 Anisse Kasraoui, Jiang Zeng: Distribution of crossings, nestings and alignments of two edges in matchings and partitions math.CO/0601019 Alexei Borodin: Periodic Schur process and cylindric partitions math.CO/0601009 Seunghyun Seo, Heesung Shin: A Generalized Enumeration of Labeled Trees and Reverse Prufer Algorithm math.CO/0512653 Lin Hu, Hao Li, Xueliang Li: Best lower bound for the maximum heterochromatic matchings in edge-colored bipartite graphs math.CO/0512650 Helene Barcelo, Bruce Sagan, Sheila Sundaram: Counting permutations by congruence class of major index math.CO/0512636 D. Falik, A. Samorodnitsky: Edge-isoperimetric inequalities and influences CV: Complex Variables --------------------- math.CV/0601080 Pietro Poggi-Corradini: Mapping properties of analytic functions on the disk math.CV/0512652 Bernard Shiffman, Steve Zelditch: Number variance of random zeros DG: Differential Geometry ------------------------- math.DG/0601106 Sema Salur: Deformations of Special Lagrangian Submanifolds; An Approach via Fredholm Alternative math.DG/0601093 Yuri Kordyukov: Noncommutative spectral geometry of Riemannian foliations: some results and open problems math.DG/0601066 Marcin Bobienski: The topological obstructions to the existence of an irreducible SO(3) structure on a five manifold math.DG/0601062 A.E. Mironov, I.A. Taimanov: Orthogonal curvilinear coordinate systems corresponding to singular spectral curves math.DG/0601002 Diego Conti, Adriano Tomassini: Special symplectic six-manifolds math.DG/0512634 Shengda Hu: Reduction and duality in generalized geometry math.DG/0512633 B.Y.Wu, Y.L.Xin: Comparison Theorems in Finsler Geometry and their Applications DS: Dynamical Systems --------------------- math.DS/0601103 L. Berezansky, L. Idels: Population Models With Delay in Dynamic Environment cond-mat/0011396 Pedro Castelo Ferreira: Fractal Structure of the Harper Map Phase Diagram from Topological Hierarchical Classification math.DS/0601043 Yulij Ilyashenko: Variation of argument and Bernstein index for holomorphic functions on Riemann surfaces math.DS/0601039 N.S. Dairbekov, G.P. Paternain: Entropy production in Gaussian thermostats math.DS/0601033 Patrick Boily: Spiral Waves and the Dynamical System Approach math.DS/0601015 Araceli Bonifant, Marius Dabija, John Milnor: Elliptic Curves as Attractors in ${mathbb P}^2$ Part 1: Dynamics math.DS/0601013 M. U. Akhmet, M.A. Tleubergenova, A. Zafer: Asymptotic equivalence of differential equations and asymptotically almost periodic solutions FA: Functional Analysis ----------------------- math.FA/0601090 A.J.E.M. Janssen & Peter L. Soendergaard: Iterative algorithms to approximate canonical Gabor windows: Computational aspects math.FA/0601011 C. Baak, M. S. Moslehian: $theta$-derivations on $JB^*$-triples GM: General Mathematics ----------------------- math.GM/0601059 Friedrich Wehrung: A solution to Dilworth's Congruence Lattice Problem math.GM/0601058 Friedrich Wehrung: Poset representations of distributive semilattices math.GM/0601053 M. Brozos-Vazquez, M. A. Campo-Cabana, J. C. Diaz-Ramos, J. Gonzalez-Diaz: Ranking Participants in Tournaments by means of Rating Functions math.GM/0601020 Pawel Nurowski: Distinguished dimensions for special Riemannian geometries math.GM/0601016 A.K.Kwasniewski: Ivan Bernoulli Series Universalissima GR: Group Theory ---------------- math.GR/0601077 Tomav{s} Kepka, Michael K. Kinyon, J.D. Phillips: F-quasigroups isotopic to groups math.GR/0601061 Mark Kambites: Formal languages and groups as memory math.GR/0601050 David Fisher: $Out(F_n)$ and the spectral gap conjecture math.GR/0601042 Mark Kambites: On commuting elements and embeddings of graph groups and monoids math.GR/0512646 Sorin Popa: Cocycle and Orbit Equivalence Superrigidity for Bernoulli Actions of Kazhdan Groups GT: Geometric Topology ---------------------- math.GT/0601105 Selman Akbulut: Real algebraic structures math.GT/0601034 Luis G. Valdez-Sanchez: Toroidal and Klein bottle boundary slopes math.GT/0601006 Natasha Harrell, Sam Nelson: Detecting non-classicality with quandle difference invariants math.GT/0601005 Jan Dymara: Thin buildings math.GT/0601004 Maciej Niebrzydowski, Jozef H. Przytycki: Burnside kei math.GT/0512630 Jozef H. Przytycki: Khovanov Homology: categorification of the Kauffman bracket relation KT: K-Theory and Homology ------------------------- math.KT/0601008 Mircea Voineagu: Semi-topological K-theory for certain projective varieties LO: Logic --------- math.LO/0601087 Saka'{e} Fuchino, Noam Greenberg, Saharon Shelah: Models of real-valued measurability math.LO/0601083 Jakob Kellner, Saharon Shelah: Decisive creatures and large continuum MG: Metric Geometry ------------------- math.MG/0601084 Mathieu Dutour Sikiric, Achill Schuermann, Frank Vallentin: A generalization of Voronoi's reduction theory and its application math.MG/0601067 D. Frettloh, B. Sing: Computing modular coincidences math.MG/0601064 D. Frettloh: Duality of Model Sets Generated by Substitutions math.MG/0512649 Oleg R. Musin: An extension of Delsarte's method. The kissing problem in three and four dimensions math.MG/0512638 Anders Karlsson: On the dynamics of isometries MP: Mathematical Physics ------------------------ nlin.SI/0601007 Oksana Ye. Hentosh: Lax Integrable Supersymmetric Hierarchies on Extented Phase Spaces math-ph/0601009 Thomas Chen, Juerg Froehlich: Coherent infrared representations in non-relativistic QED quant-ph/0601011 Oded Kenneth, Israel Klich: Opposites Attract - A Theorem About The Casimir Force math-ph/0601008 Yulia Karpeshina, Young-Ran Lee: Spectral Properties of Polyharmonic Operators with Limit-Periodic Potential in Dimension Two math-ph/0601007 David W. Farmer, Mark Yerrington: Crystallization of random trigonometric polynomials hep-th/0601014 J.F. Gomes, L.H. Ymai, A.H. Zimerman: The Super mKdV and sinh-Gordon Hierarchy: Solitons and Backlund Defects nlin.SI/0601001 Aristophanes Dimakis, Folkert Muller-Hoissen: Nonassociativity and Integrable Hierarchies math-ph/0601006 Alex H. Barnett: Quasi-orthogonality on the boundary for Euclidean Laplace eigenfunctions hep-th/0512349 Takayoshi Ootsuka, Erico Tanaka, Eugene Loginov: Non-associative Gauge Theory quant-ph/0512239 Pavel Hejcik, Taksu Cheon: Irregular Dynamics in Solvable One-Dimensional Quantum Graph math-ph/0601005 Christian Fleischhack: Construction of Generalized Connections math-ph/0601004 Y. Brihaye, J. Ndimubandi, B. Prasad Mandal: QES systems, invariant spaces and polynomials recursions math-ph/0601003 J. Kiukas: Covariant observables on a nonunimodular group math-ph/0601002 Gorazd Cvetic, Igor Kondrashuk, Ivan Schmidt: On the effective action of dressed mean fields for N =4 super-Yang-Mills theory math-ph/0601001 Sergey Dobrokhotov, Sergey Sekerzh-Zenkovich, Brunello Tirozzi, Timur Tudorovskiy: Generalized Maslov canonical operator and tsunami asymptotics over nonuniform bottom. I math-ph/0512095 M.V. Feigin, A.P. Veselov: Coxeter discriminants and logarithmic Frobenius structures math-ph/0512094 Emmanuel Serie: Gauge theories in noncommutative geometry and generalization of the Born-Infeld model math-ph/0512093 Anthony M. Bloch, Arieh Iserles, Jerrold E. Marsden, Tudor S. Ratiu: A Class of Integrable Geodsic Flows on the Symplectic Group math-ph/0512092 Vladimir Dragovic, Milena Radnovic: On Closed Geodesics on Ellipsoids math-ph/0512091 Tobias Schlegelmilch: Local Scattering Operators for P(phi)_2 Models and the Time-dependent Schrodinger Equation math-ph/0512090 Konstantin Pankrashkin: Equilateral quantum graphs and their decorations NA: Numerical Analysis ---------------------- math.NA/0601031 Norbert Roehrl: Recovering boundary conditions in inverse Sturm-Liouville problems math.NA/0601029 H. Lamba, J.C. Mattingly, A.M. Stuart: An Adaptive Euler-Maruyama Scheme For SDEs: Convergence and Stability NT: Number Theory ----------------- math.NT/0601082 Mathew D. Rogers: A study of inverse trigonometric integrals associated with three-variable Mahler measures, and some related identities math.NT/0601073 Dan Yasaki: On the existence of spines for Q-rank 1 groups math.NT/0601071 Dan Yasaki: Explicit reduction theory for SU(2,1;Z[i]) math.NT/0601046 Matthew Baker: A finiteness theorem for canonical heights attached to rational maps over function fields math.NT/0601026 Hao Pan: A remark on Zoloterav's theorem math.NT/0601017 Zhi-Wei Sun: On covering numbers math.NT/0512643 Roland Queme: On Kummer and Stickelberger relations math.NT/0512637 Leonid G. Fel: Arnold's Conjectures on Weak Asymptotics and Statistics of Numerical Semigroups S(d_1,d_2,d_3) OA: Operator Algebras --------------------- math.OA/0601069 Ping Wong Ng, Wilhelm Winter: A Note On Subhomogeneous C*-Algebras math.OA/0601051 Siegfried Echterhoff, Dana P. Williams: Inducing Primitive Ideals math.OA/0601045 Andreas Thom: A remark about the Connes fusion tensor product math.OA/0601024 Erik Christensen, Cristina Ivan: Sums of two dimensional spectral triples math.OA/0601003 M. Anoussis, A. Katavolos, I. G. Todorov: Lattices of Projections and Operator Ranges in C*-algebras OC: Optimization and Control ---------------------------- math.OC/0601088 Heng-Qing Ye, David D. Yao: Heavy-Traffic Optimality of a Stochastic Network under Utility-Maximizing Resource Control math.OC/0601025 Eitan Bachmat: Analysis of disk scheduling, increasing subsequences and space-time geometry PR: Probability --------------- math.PR/0601102 Nadine Guillotin-Plantard, Arnaud Le Ny: Transient random walks on 2d-oriented lattices math.PR/0601095 M. Hairer, A. M. Stuart, J. Voss, P. Wiberg: Analysis of SPDEs Arising in Path Sampling Part I: The Gaussian Case math.PR/0601092 M. Hairer, A. M. Stuart, J. Voss: Analysis of SPDEs Arising in Path Sampling Part II: The Nonlinear Case math.PR/0601076 A. Faggionato: Bulk diffusion of 1D exclusion process with bond disorder math.PR/0601040 Alice Guionnet, 'Edouard Maurel-Segala: Second order asymptotics for matrix models math.PR/0601038 Andreas Neuenkirch, Ivan Nourdin: Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion math.PR/0601036 Randal Douc, Arnaud Guillin, Eric Moulines: Bounds on Regeneration Times and Limit Theorems for Subgeometric Markov Chains math.PR/0601035 Shige Peng: $G$--Expectation, $G$--Brownian Motion and Related Stochastic Calculus of It^{o}'s type math.PR/0601032 Julien Berestycki, Nathanael Berestycki, Jason Schweinsberg: Small-time behavior of beta coalescents math.PR/0601027 Richard F. Bass, Alexander Lavrentiev: The submartingale problem for a class of degenerate elliptic operators math.PR/0601010 Anatolii A. Puhalskii, Alexander A. Vladimirov: A large deviation principle for join the shortest queue math.PR/0601007 Jason Swanson: Variations of the Solution to a Stochastic Heat Equation math.PR/0512660 Laurent Decreusefond, Pascal Moyal: Fluid limit of a heavily loaded EDF queue with impatient customers QA: Quantum Algebra ------------------- math.QA/0601056 Aaron Lauve: Flag varieties for the Yangian Y(gl_n) math.QA/0601055 PoNing Chen: On The Formality Theorem for the Differential Graded Lie Algebra of Drinfeld math.QA/0601054 Alain Connes, Matilde Marcolli: A walk in the noncommutative garden math.QA/0601049 Yuuki Abe, Toshiki Nakashima: Evaluation representations of quantum affine algebras at roots of unity math.QA/0601012 Siu-Hung Ng, Peter Schauenburg: Frobenius-Schur Indicators and Exponents of Spherical Categories math.QA/0601001 Lars Kadison: Codepth Two and Related Topics math.QA/0512657 Masaki Kashiwara, Toshiki Nakashima, Masato Okado: Affine Geometric Crystals and Limit of Perfect Crystals RA: Rings and Algebras ---------------------- math.RA/0601096 K. De Naeghel, N. Marconnet: Ideals of cubic algebras and an invariant ring of the Weyl algebra math.RA/0601068 Emily Burgunder: Infinite magmatic bialgebras math.RA/0512655 L. El Kaoutit: Corings over rings with local units math.RA/0512654 Alberto Elduque: Some new simple modular Lie superalgebras RT: Representation Theory ------------------------- math.RT/0601104 Meinolf Geck, Nicolas Jacon: Canonical basic sets in type B math.RT/0601089 Piotr Sniady: Gaussian fluctuations of representations of wreath products math.RT/0601028 M.Rovinsky: On maximal proper subgroups of field automorphism groups math.RT/0512661 Steven P. Diaz, Mark Kleiner: Almost Split Morphisms, Preprojective Algebras and Multiplication Maps of Maximal Rank math.RT/0512656 Shashidhar Jagadeeshan, Mark Kleiner: Finite-dimensional algebras with smallest resolutions of simple modules math.RT/0512651 A.A.Lopatin, A.N.Zubkov: Semi-invariants of $ast$-representations of quivers SP: Spectral Theory ------------------- math.SP/0601057 Vladimir Kondratiev, Vladimir Maz'ya, Mikhail Shubin: Gauge optimization and spectral properties of magnetic Schrodinger operators ST: Statistics -------------- math.ST/0601099 Anestis Antoniadis, Jeremie Bigot: Poisson inverse problems math.ST/0601098 Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin: Finite sample penalization in adaptive density deconvolution math.ST/0601091 Fabienne Comte, Yves Rozenholc, Marie-Luce Taupin: Penalized contrast estimator for adaptive density deconvolution math.ST/0601070 Eric Moulines, Franc{c}ois Roueff, Murad S. Taqqu: A Wavelet Whittle estimator of the memory parameter of a non-stationary Gaussian time series math.ST/0601065 Jean-Michel Billiot, Jean-Franc{c}ois Coeurjolly, R'{e}my Drouilhet: Maximum pseudo-likelihood estimator for nearest-neighbours Gibbs point processes math.ST/0601048 M. Grendar: Conditioning by rare sources math.ST/0512641 Fuchang Gao, Jon A. Wellner: Entropy Estimate For High Dimensional Monotonic Functions math.ST/0512635 Eric Moulines, Franc{c}ois Roueff, Murad Taqqu: On the spectral density of the wavelet coefficients of long memory time series with application to the log-regression estimation of the memory parameter -- / 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: Re: Pointwise Convergence Originator: israel@math.ubc.ca (Robert Israel) In metric spaces, sequential convergence has the following property: if M is any set, and seqclM is the extension of M by all limits of convergent sequences taking values in M, then seqcl(seqclM) = seqclM. This property fails, however, for pointwise convergence of functions on a real interval: the second Baire class is a proper extension of the first Baire class; more specifically, if f is a pointwise limit of a sequence of continuous functions then f is continuous except on a meager set; however, by repeating this operation one obtains, e.g., the characteristic function of the rationals which is everywhere discontinuous. === Subject: limit of (1-b)*sum b^k x_k Originator: israel@math.ubc.ca (Robert Israel) since Robert convinced me that the answer to my last question is no (thank's a lot Robert, although I would have liked yes much better), I have to try a different strategy: Suppose that x_t is a strictly stationary process, with a finite r-th moment, all x_t are positive. In particular, x_t does *not* necessarily have a first moment! If x_t even has a second moment, rumour has it that lim (1-b) sum_{t>=0} b^t x_t b->1 should be finite and non-zero. (Under certain conditions, it should tend to the expectation of x_t.) Of course, I cannot expect the above limit to be finite, if E(x_t) is infinite. However, might it be true -- since E(x_t^r) is finite -- that there is always a real number s such that lim (1-b)^s sum_{t>=0} b^t x_t b->1 is finite and non-zero? Martin === Subject: Re: Virtually nilpotent groups Originator: israel@math.ubc.ca (Robert Israel) > Hi. I am wondering if a virtually nilpotent group can be icc (if each > non-trivial conjugacy-class is infinite). > I have already seen, that each nilpotent group will have non-trivial > center. Is the same true for virtually nilpotent groups? This will of > course imply a negative answer to the first question I asked. The infinite dihedral group (or holomorph of the integers) is virtually nilpotent (even virtually abelian) but its center is trivial. Werner Nickel === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) > >> > Are there projective ideals (of rings) which are > not finitely generated? >> >> Yes, there are in non-noetherian graded rings. > Take, e.g., in the >> polynomial ring k[X1,...,Xn,...] generated by > countably many >> indeterminates Xn the ideal generated by {Xm : m e > S} for any infinite >> subset S of IN. >> > Yes, but it is not PROJECTIVE ... > > I interpreted PROJECTIVE to HOMOGENEOUS or to be an > element of the > associated projective scheme Proj(S) - if S denotes > the positively > graduated algebra S. > So what is your notion of PROJECTIVE IDEALS? > J. An ideal is projective if it is projective as a module. H === Subject: Re: projective ideals Originator: israel@math.ubc.ca (Robert Israel) It seems to me that the s is not A-linear, just B-linear. === Subject: 3 Parameters family for solvable polynomials of degree P(prime) = 6*k+1 Originator: israel@math.ubc.ca (Robert Israel) The following method can be applied to design 3 Parameters family for any solvable polynomials of degree P, where P is a prime number of the form 6*k+1 ; k is intger. i.e P = 7, 13, 19, 31,...... Let t1, t2 and t3 are the roots for t^3 + 3*g*n*t^2 + n^2*(3*g^2 - (m^2+27))*t + n^3*(g^3 - (m^2+27)*g - 2*(m^2+27)) = 0 where g, m and n are rational numbers and m>0 This cubic is designed to get rational values for t1^2*t2+t2^2*t3+t3^2*t1 and t2^2*t1+t3^2*t2+t1^2*t3 Alternatively, rational values for t1, t2 and t3 can be used directly as another choice solve the gollowing Diophantine equation to get intger q z*P = 1 + q + q^2 h = mod(q^2,P) c1 = sign(t1*t2^q*t3^h) c2 = sign(t1^q*t2^h*t3) c3 = sign(t1^h*t2*t3^q) u1 = c1*(c1*t1*t2^q*t3^h)^(1/p) u2 = c2*(c2*t1^q*t2^h*t3)^(1/p) u3 = c3*(c3*t1^h*t2*t3^q)^(1/p) w = exp(2*pi*i/p) r1 =u1 + u2 + u3 r2 =u1*w^1 + u2*w^q + u3*w^h r3 =u1*w^2 + u2*w^(2*q) + u3*w^(2*h) r4 =u1*w^3 + u2*w^(3*q) + u3*w^(3*h) r5 =u1*w^4 + u2*w^(4*q) + u3*w^(4*h) r_j =u1*w^(j-1) + u2*w^((j-1)*q) + u3*w^((j-1)*h) r_P =u1*w^(p-1) + u2*w^((p-1)*q) + u3*w^((p-1)*h) r_j shall be the roots of irreducible solvable polynomial of degree P of rational coefficients for any rational numbers g, m>0 & n Example ------- Let k=2 ; then P = 13 1 + q + q^2 = z*13 q=3; z=1 h = mod(9,13) = 9 Let g=2 m=1 n=1 t1, t2 and t3 are the roots for t^3 + 6*t^2 -16*t -104 = 0 Then f(x)=x^13 - 2704*x^10 - 91936*x^8 + 1546688*x^7 - 10167040*x^6 + 47806720*x^5 - 509303808*x^4 + 4049510400*x^3 -18029666304*x^2 + 41943928832*x - 44500631552 See also http://mathforum.org/kb/thread.jspa?threadID=1307779&tstart=75 http://mathforum.org/kb/thread.jspa?threadID=1301741&tstart=105 === Subject: Re: Minima of Phi(m) over m Originator: israel@math.ubc.ca (Robert Israel) Below is a copy of an answer to my posting about phi(m)/m from Gerd Verbouwe (Belgium). For technical reasons, he could not get it posted here, and he e-mailed it to me the day of my posting, on June 30, 2005. After a long delay due to emergencies, I checked his answer, and with his agreement, I submit it for posting here. Jean-Claude Evard Department of Mathematics Western Kentucky University ----------------------------------------------------- First, I recall the notation that I used: ----------------------------------------------------- Phi(m) = [The Euler`s function] = [The number of integers k such that 0Conjecture 1. The relative minimum values of r(m) occur at the points >where m is a primorial, and the sequence of values of r(m) at these >points is strictly decreasing. Isn't observing that r(m) = Phi(m) / m = prod_{primes p_i | m} (1 - 1/p_i) (*) enough? Say p# < m < q# (p prime, q the next prime larger than p). [a] The number of distinct prime factors of m is less than or equal to pi(p) = the number of prime factors of p#. (because p# is the smallest number with pi(p) prime factors) (or the number of distinct prime factors of m is strictly smaller than pi(q).) [b] Since all factors in (*) are less than one; if a prime P|m, P > p occurs, it can be replaced by a smaller one, hence no minimum in this case. [c] Hence (*) is a relative minimum, when as much factors (1-1/prime) as possible occur, and since 1-1/P > 1-1/p for P>p, one needs the first N primes.83 . Of course these are local minima, since, e.g. r(2* 17#) = r(17#) and (*) shows immediately that it is strictly decreasing. (Also, >Conjecture 2. The relative maximum values of r(m) occur at the points >where m is a prime, the sequence of values of r(m) at these points is >strictly increasing, and its limit when m goes to infinity is 1. becomes clear: it's maximal when only one factor (1-1/p) appears, this happens first for the prime p itself; the limit of these is of course 1.) Am I missing something here? gv ----------------------------------------------------------------------- I think that this proof is 100% OK. I have not checked my third conjecture yet, and I intend to come back to all this during next summer. Jean-Claude Evard === Subject: Need help for subset problem Originator: israel@math.ubc.ca (Robert Israel) Given N sets as A1, A2,..., An, find a subset Bi for each Ai, i = 1, 2,..., n, subject to that for each i != j, the intersection of Bi and Bj is empty. The target is to maiximize the size of the subset Bk that has minimal number of elements among all the subset Bi, that is: max min{|Bi|, i = 1, 2,..., n}. What kind problem cat this problem categorized to? Any one can give me some ideas about how to solve this problem? === Subject: Efficient gcd-tuple construction? Originator: israel@math.ubc.ca (Robert Israel) given a prime p, a natural number N, and two integers x,y in {0,...,N-1}, please give an efficient way to describe all integers a,b such that x=a mod N y=b mod N y =< b =< x, (here =< means lower equal) x =< a =< sqrt(p), gcd(a,b)=1 Especially: is there a way to reduce the number of gcd-computations? Best, Oswald