检测线性函数与线性变量的表格方法

讨论了线性函数、部分线性函数和线性变量的定义、性质和定理,提出了检测基于最小项展开的逻辑函数的线性变量与线性函数的表格方法.提出了直接从RM型逻辑函数的Reed-Muller展开出发以及直接从OC型OC展开出发检测RM型逻辑函数和OC型逻辑函数的线性变量及线性函数的表格方法.文中提出的表格方法具有简单、方便和易于计算机编程操作等优点.     

Shift,Rotation and Limited Scale Invariant Pattern Recognition Using Synthetic Discriminant Functions

Making use of the idea of synthetic discriminant functions (SDF), a simple way to synthesize a shift, rotation and limited size correlation filter is proposed. The SDF is synthesized by superimposing four 2nd order circular harmonics of a training reference pattern in 4 different sizes. Computer simulation experiments have shown that the filter is indeed shift, full rotation and limited size invariant over a size range from 1 to 1.82. The invariant range can be increased if more training patterns are used.     

The Minimax Equality; Sufficient and Necessary Conditions

The paper produces new versions of the minimax theorem based on original conditions. Moreover, we investigate not only the sufficiency, but also the necessity of such conditions. The proofs are very simple and preclude any topological technique.     

p-version hybrid/mixed finite element method

In this paper, the p-version hybrid/mixed finite element formulation using the Hu–Washizu principle is presented. The shape functions are assumed to be hierarchical for the displacement variables. The stresses and the strains are interpolated using Legendre polynomials so that the computation of the stiffness matrix will be simplified. For 2-D problems, the higher-order hierarchical shape functions start following the 8-node, quadrilateral shape functions. The geometry mapping of each element is also performed using an 8-node parametric mapping. Numerical examples for a plate with a circular hole and circular inclusion are included.     

Nonsmooth analysis on smooth manifolds

We study infinitesimal properties of nonsmooth (nondifferentiable) functions on smooth manifolds. The eigenvalue function of a matrix on the manifold of symmetric matrices gives a natural example of such a nonsmooth function.

A subdifferential calculus for lower semicontinuous functions is developed here for studying constrained optimization problems, nonclassical problems of calculus of variations, and generalized solutions of first-order partial differential equations on manifolds. We also establish criteria for monotonicity and invariance of functions and sets with respect to solutions of differential inclusions.

     

The evaluation of Legendre functions of the second kind

A method of evaluating Legendre functions of the second kind by applying the trapezoidal rule to Heine's integral representation is described. An error analysis is given, and some numerical results are obtained.Dedicated to Professor Luigi Gatteschi     

Fluctuations in the Bose Gas with Attractive Boundary Conditions

In this paper limiting distribution functions of field and density fluctuations are explicitly and rigorously computed for the different phases of the Bose gas. Several Gaussian and non-Gaussian distribution functions are obtained and the dependence on boundary conditions is explicitly derived. The model under consideration is the free Bose gas subjected to attractive boundary conditions, such boundary conditions yield a gap in the spectrum. The presence of a spectral gap and the method of the coupled thermodynamic limits are the new aspects of this work, leading to new scaling exponents and new fluctuation distribution functions.     

Lie Representations and an Algebra Containing Solomon's

We introduce and study a Hopf algebra containing the descent algebra as a sub-Hopf-algebra. It has the main algebraic properties of the descent algebra, and more: it is a sub-Hopf-algebra of the direct sum of the symmetric group algebras; it is closed under the corresponding inner product; it is cocommutative, so it is an enveloping algebra; it contains all Lie idempotents of the symmetric group algebras. Moreover, its primitive elements are exactly the Lie elements which lie in the symmetric group algebras.     

On the Existence of Solutions of Quasi-equilibrium Problems with Constraints

The quasi-equilibrium problems with constraints are formulated and some sufficient conditions on the existence of their solutions are shown. As special cases, we obtain several results on the existence of solutions of some vector quasivariational inequality and vector optimization problems. An application of the obtained results is given to show the existence of solutions of quasi-optimization problems with constraints.