A Note on the all Nearest-Neighbor Problem for Convex Polygons

title: Global Classical Solutions for Nonlinear Evolution Equations
abstract: This text represents the results originally obtained by S. Lainerman, D. Christodoulou, Y. Choquet-Bruhat, T. Nishida and A. Matsumara on the global existence of classical solutions to the Cauchy problem with small initial data for nonlinear evolution equations.

title: LOCAL SOLVABILITY OF THE BOUNDARY VALUE PROBLEMS FOR QUASILINEAR HYPERBOLIC SYSTEMS
abstract: This paper discusses the boundary value problems (including free boundary problems) for quasilinear hyperbolic systems of partial differential equations in two independent variables. These problems are considered on an angular region and within the class of sufficiently smooth functions. The local solvable condition obtained may be described briefly as follows: at the vertex of the angular region, derivatives of any orders for the solution can be determined uniquely by the equations and the boundary value conditions. It allows no contraction. An application of this resnlt to one-dimensional problems in aerodynamics is also given.

title: Global classical solutions for quasilinear hyperbolic systems
abstract: Problem with Boundary Dissipation for Quasilinear Hyperbolic Systems Typical Boundary Value Problem and Typical Free Boundary Problem for Reducible Quasilinear Hyperbolic Systems Generalized Riemann Problem for the System of One-Dimensional Isentropic Flow Typical Free Boundary Problem and Generalized Riemann Problem for General Quasilinear Hyperbolic Systems Bibliography Index.

title: Initial value problems for nonlinear heat equations

title: Proceedings of the workshop on qualitative aspects and applications of nonlinear evolution equations : ICTP, Trieste, Italy, May 3-14, 1993
abstract: Heat Flow Method (Y-M Chen) Integrable Systems and Solitons in Space-Time Rn+l (C-H Gu) Geometric Aspects of Soliton-Like Equations (H-S Hu) Microlocal Order of Singularities for Distributions and Trace Formulas of Hyperbolic Type (S Miyatake) Mixed Problems for Linear Symmetric Hyperbolic Systems with Characteristic Boundary Conditions (P Secchi) The Initial Boundary Value Problem for Symmetric Hyperbolic Systems with Characteristic Boundary (Y Shizuta) Qualitative Behaviour of Global Solutions for lnhomogeneous Quasilinear Hyperbolic Systems (L Xiao) Global Dynamics and Control of a Comprehensive Nonlinear Beam Equation (Y-C You) Weak Linear Degeneracy and Lifespan of Classical Solutions for First Order Quasilinear Hyperbolic Systems (T-T Li) The Differential Equation for the Interface in a Porous Media-Type Equation (J Goncerzewicz) Existence and Regularity of Solutions to Nonlinear Thermoelastic Systems (R Racke). (Part contents).

title: On faithful representations of the holomorph of Lie groups
abstract: Let G be a Lie group and let Aut(G) denote the group of all automorphisms of the Lie group G, endowed with its natural structure of a Lie group. The natural semidirect product G >~ Aut(G) is called the holomorph of G. In , Hochschild has shown that if the nilradical (that is, the maximum nilpotent analytic normal subgroup) N of a real or complex analytic group G is simply connected, then the holomorph of G is faithfully representable. Moreover, one of the authors in  has given an intrinsic characterization of those complex analytic groups whose holomorph is faithfully representable. In this paper, we are interested in determining when the holomorph of a Lie group G is faithfully representable (that is, admits a faithful finite-dimensional continuous representation). Our first result (Theorem 1) answers this question when G is an f.c.c. Lie group. Also in this work, we extend the result of  to real analytic groups (Theorem 2). Our method is entirely different from that of [4] and may be adapted to cover the complex case as well. We would like to thank the referee for making valuable suggestions for improvements of this paper.