CONSTRUCTION OF SOME KIESSWETTER-LIKE FUNCTIONS-THE CONTINUOUS BUT NON-DIFFERENTIABLE FUNCTION DEFINED BY QUINARY DECIMAL

In this paper, we construct some continuous but non-differentiable functions defined by quinary decimal, that are Kiesswetter-like functions. We discuss their properties, then investigate the Hausdorff dimensions of graphs of these functions and give a detailed proof.     

Partially Classical States of a Boson Field

Employing positive-definiteness arguments we analyse Boson field states, which combine classical and quantum mechanical features (signal and noise), in a constructive manner. Mathematically, they constitute Bauer simplexes within the convex, weak-*-compact state space of the C*-Weyl algebra, defined by a presymplectic test function space (smooth one-Boson wave functions) and are affinely homeomorphic to a state space of a classical field. The regular elements are expressed in terms of weak distributions (probability premeasures) on the dual test function space. The Bauer simplex arising from the bare vacuum is shown to generalize the quantum optical photon field states with positive P-functions.     

正交变换在重积分中某些应用

正交变换是代数学的基本内容 ,其用途十分广泛 .重积分的计算往往存在技术性的困难 ,若利用“正交变换”的有关理论去解决某些重积分的计算问题是颇有功效的 .本文将以“正交变换”为工具 ,简洁的处理重积分的某些问题     

Comparison of higher-order accurate schemes for solving the two-dimensional unsteady Burgers' equation

This paper is devoted to the testing and comparison of numerical solutions obtained from higher-order accurate finite difference schemes for the two-dimensional Burgers' equation having moderate to severe internal gradients. The fourth-order accurate two-point compact scheme, and the fourth-order accurate Du Fort Frankel scheme are derived. The numerical stability and convergence are presented. The cases of shock waves of severe gradient are solved and checked with the fourth-order accurate Du Fort Frankel scheme solutions. The present study shows that the fourth-order two-point compact scheme is highly stable and efficient in comparison with the fourth-order accurate Du Fort Frankel scheme.     

Formula 1 – A Mathematical Microworld with CAS: Analysis of Learning Opportunities and Experiences with Students

In this article we describe a mathematical microworld for investigating car motion on a racing course and its use with a group of grade 12 students. The microworld is concerned with the mathematical construction of courses and functions which describe car motion. It is implemented in the computer algebra system, Maple^®, which provides the means to represent courses and functions symbolically and graphically. We describe the learning opportunities offered by the microworld in relation to the research literature on functions. Various facets and layers of the function concept are addressed in the microworld, and we suggest how work in the microworld might help in overcoming some well-known misconceptions.This revised version was published online in September 2005 with corrections to the Cover Date.     

Regularity of Harmonic Functions in Cheeger-Type Sobolev Spaces

We give a geometric approach to the study of the regularity of harmonic functions in Cheeger-type Sobolev spaces, and prove the Hölder continuity of such functions. In the proof, we give a definition of an upper curvature bound of the unit sphere of a Banach space, which seems to be of independent interest.     

Solving a class of multiplicative programming problems via c-programming

In this note we show that many classes of global optimization problems can be treated most satisfactorily by classical optimization theory and conventional algorithms. We focus on the class of problems involving the minimization of the product of several convex functions on a convex set which was studied recently by Kunoet al. [3]. It is shown that these problems are typical composite concave programming problems and thus can be handled elegantly by c-programming [4]–[8] and its techniques.     

Hyers–Ulam stability of linear differential operator with constant coefficients

Let P(z) be a polynomial of degree n with complex coefficients and consider the n–th order linear differential operator P(D). We show that the equation P(D)f = 0 has the Hyers–Ulam stability, if and only if the equation P(z) = 0 has no pure imaginary solution. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The regularizing properties of anisotropic radial basis functions

In the present work we consider the problem of interpolating scattered data using radial basis functions (RBF). In general, it is well known that this leads to a discrete linear inverse problem that needs to be regularized in order to provide a meaningful solution. The work focuses on a metric-regularization approach, based on a new class of RBF, called anisotropic RBF. The work provides theoretical justifications for the regularization approach and it considers a suitable proposal for the metric, supporting it by numerical examples.     

Sufficient optimality conditions and duality in vector optimization with invex-convexlike functions

We prove the Kuhn-Tucker sufficient optimality condition, the Wolfe duality, and a modified Mond-Weir duality for vector optimization problems involving various types of invex-convexlike functions. The class of such functins contains many known generalized convex functions. As applications, we demonstrate that, under invex-convexlikeness assumptions, the Pontryagin maximum principle is a sufficient optimality condition for cooperative differential games. The Wolfe duality is established for these games.The author is indebted to the referees and Professor W. Stadler for valuable remarks and comments, which have been used to revise considerably the paper.