Jackson’s integral of the Hurwitz zeta function

We give a Jacksonq-integral analogue of Euler’s logarithmic sine integral established in 1769 from several points of view, specifically from the one relating to the Hurwitz zeta function. Partially supported by Grant-in-Aid for Exploratory Research No. 15654003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340003. Partially supported by Grant-in-Aid for Scientific Research (B) No. 15340012.     

Toward the Determination of the Minimum Distance of Two-Point Codes on a Hermitian Curve

This is a first step toward the determination of the parameters of two-point codes on a Hermitian curve. We describe the dimension of such codes and determine the minimum distance of some two-point codes.AMS Classification: 94B27, 14H50, 11T71, 11G20Masaaki Homma - Partially supported by Grant-in-Aid for Scientific Research (15500017), JSPS.Seon Jeong Kim - Partially supported by Korea Research Foundation Grant (KRF-2002-041-C00010).     

Finite element analysis of pressure formulation of the elastoacoustic problem

In this paper we analyze the non symmetric pressure/displacement formulation of the elastoacoustic vibration problem and show its equivalence with the (symmetric) stiffness coupling formulation. We introduce discretizations for these problems based on Lagrangian finite elements. We show that both formulations are also equivalent at discrete level and prove optimal error estimates for eigenfunctions and eigenvalues. Both formulations are rewritten such as to be solved with a standard Matlab eigensolver. We report numerical results comparing the efficiency of the methods over some test examples. Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by Xunta de Galicia (Spain) through grant No. PGIDT00-PXI20701PR and by MCYT Research Project DPI2001-1613-C02-02Partially supported by FONDAP in Applied Mathematics (Chile) and by MCYT Research Projects DPI2001-1613-C02-02 and BFM2001-3261-C02-02Partially supported by FONDECYT (Chile) through grant No. 1.990.346 and FONDAP in Applied Mathematics (Chile)Mathematics Subject Classification (1991):65N30     

On Legal Semigroups

A new class of semigroups with a two variable regularity law is introduced. These semigroups are non-regular semigroups but they are closely related to regular semigroups. The local and global structures of this class of semigroups are investigated.AMS Subject Classification (2000): 20M10Partially supported by a Chinese University of Hong Kong Direct Research grant, Hong Kong (98/99) # 2060152.Partially supported by a grant of the National Science Foundation, China.     

Free construction of CAT(1) spaces

We construct several non-trivial examples of CAT(1) spaces by using the idea of free construction. Received: 29 August 2005 Partially supported by the MEXT Grant-in-Aid for scientific research, and by the 2004 JSPS Postdoctoral Fellowships for Research Abroad.     

Proper action on a homogeneous space of reductive type

Partially supported by Grant-in-Aid for Scientific Research (No. 63740074)     

Local geometry of smooth curves passing through rational double points

Partially supported by a fellowship from the University of Nebraska Research Council     

Involutions of compact Klein surfaces

Partially supported by British-Spanish Joint Research Program     

Homogeneous almost disjoint families

An almost disjoint family is constructed which is isomorphic to any almost disjoint family which can be constructed from it by taking subsets and finite unions. This is applied to the construction of a Boolean algebra with related properties.Presented by R. McKenzie.Partially supported by Israel-US Binational Research Fund.Partially supported by NSERC.     

Inequivalent frame-spun knots with the same complement

Partially supported by a Northeastern University Junior Research Fellowship     

A generalization of the corona theorem in the unit disc

Partially supported by the Swedish Natural Science Research Council     

Ideals and Clots in Pointed Regular Categories

We clarify the relationship between ideals, clots, and normal subobjects in a pointed regular category with finite coproducts. Partially supported by South African NRF Research partially supported by the Hungarian National Foundation for Scientific Research grant no. K61007.     

A note on extensions of algebraic and formal groups II

Partially supported by Grant-in-Aid for Scientific Research #05640063     

Inequivalent fibred knots whose homotopy Seifert pairings are isometric

Partially supported by a Northeastern University Jonior Research Fellowship     

Hamiltonian / Gauge theoretical Gromov-Witten invariants of toric varieties

We present a purely algebraic approach to the Hamiltonian / Gauge theoretical invariants associated to torus actions on affine spaces. Secondly, we address the issue of computing the invariants: a localization and a genus recursion formula are deduced. Partially supported by: EAGER - European Algebraic Geometry Research Training Network, contract No. HPRN-CT-2000-00099 (BBW).     

Non-existence of wave operators for Stark effect Hamiltonians

Partially supported by Grant-in-Aid for Scientific Research, Ministry of Education     

A note on extensions of algebraic and formal groups I

Partially supported by Grant-in-Aid for Scientific Research #62540066     

Rate of convergence to the semi-circular law

A stochastic bound of order O _P (n ^–1/2 ) for the Kolmogorov distance between the spectral distribution function of an n×n matrix from Wigner ensemble and the distribution function of the semi-circular law is obtained. The result holds assuming that the twelfth moment of the entries of the matrix is uniformly bounded.Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken'.Research supported by the DFG-Forschergruppe FOR 399/1-1 ``Spektrale Analyse, Asymptotische Verteilungen und Stochastische Dynamiken'.Partially supported by Russian Foundation for Fundamental Research Grants NN02-01-00233, 00-15-96019. Partially supported by INTAS N99-01317, DFG-RFBR N99-01-04027. Mathematics Subject Classification (2000): 60F05     

Long-time behaviour of arbitrary order continuous time Galerkin schemes for some one-dimensional phase transition problems

The long-time behaviour of continuous time Galerkin (CTG) approximationsof some well-known one-dimensional non-linear evolution problemswhich model phase transitions are analyzed. These numericalschemes are fully discrete and of arbitrary order. Partially supported by the Army Research Office through grant28535-MA. Partially supported by the ONR Contract No N00014-90-J-1238.     

The strong summability of Fourier transforms

Partially supported by the Hungarian National Foundation for Scientific Research under Grant #234.