Violation of Bell’s inequality in neutral kaons system

We show by general considerations that it is not possible to test violation of the existing versions of Bell’s inequality in entangled neutral kaons system using experimentally accessible thin regenerators. We point out the loophole in the recent argument (A Bramon and M Nowakowski, Phys. Rev. Lett. 83, 1 (1999)) that claimed such a test to be possible.     

Mixed methods on quadrilaterals and hexahedra

We describe a new family of discrete spaces suitable for use with mixed methods on certain quadrilateral and hexahedral meshes. The new spaces are natural in the sense of differential geometry, so all the usual mixed method theory, including the hybrid formulation, carries over to these new elements with proofs unchanged. Because transforming general quadrilaterals into squares introduces nonlinearity and because mixed methods involve the divergence operator, the new spaces are more complicated than either the corresponding Raviart-Thomas spaces for rectangles or corresponding finite element spaces for quadrilaterals. The new spaces are also limited to meshes obtained from a rectangular mesh through the application of a single global bilinear transformation. Despite this limitation, the new elements may be useful in certain topologically regular problems, where initially rectangular grids are deformed to match features of the physical region. They also illustrate the difficulties introduced into the theory of mixed methods by nonlinear transformations.     

OSCILLATION OF A FORCED SECOND ORDER NONLINEAR EQUATION

ＯＳＣＩＬＬＡＴＩＯＮ ＯＦ Ａ ＦＯＲＣＥＤ ＳＥＣＯＮＤ ＯＲＤＥＲ ＮＯＮＬＩＮＥＡＲ ＥＱＵＡＴＩＯＮ ￥ＫＯＮＧＱＩＮＧＫＡＩ；ＺＨＡＮＧＢＩＮＧＧＥＮＡｂｓｔｒａｃｔ：Ｔｈｉｓｐａｐｅｒｇｉｖｅｓｓｅｖｅｒａｌｃｒｉｔｅｒｉａｏｎｔｈｅｏ...     

带耗散的一阶非线性偏微分方程组的Cauchy问题

本文采用整体迭代法证明了带小初值的一阶非线性耗散偏微分方程组的Cauchy问题的整体经典解的存在性及指数衰减性质。     

Cyclic reduction and FACR methods for piecewise hermite bicubic orthogonal spline collocation

Cyclic reduction and Fourier analysis-cyclic reduction (FACR) methods are presented for the solution of the linear systems which arise when orthogonal spline collocation with piecewise Hermite bicubics is applied to boundary value problems for certain separable partial differential equations on a rectangle. On anN×N uniform partition, the cyclic reduction and Fourier analysis-cyclic reduction methods requireO(N ²log₂ N) andO(N ²log₂log₂ N) arithmetic operations, respectively.     

A convection/reaction/switching system

We consider a spatially distributed hybrid system consisting of a convection/reaction system in which the reaction switches discontinuously in time between modes, independently at each spatial point on reaching “switching thresholds”. The model involves a novel formulation for evolution of the free boundary between the modal regions.     

Existence of a solution for two phase flow in porous media: The case that the porosity depends on the pressure

In this paper we prove the existence of a solution of a coupled system involving a two phase incompressible flow in the ground and the mechanical deformation of the porous medium where the porosity is a function of the global pressure. The model is strongly coupled and involves a nonlinear degenerate parabolic equation. In order to show the existence of a weak solution, we consider a sequence of related uniformly parabolic problems and apply the Schauder fixed point theorem to show that they possess a classical solution. We then prove the relative compactness of sequences of solutions by means of the Fréchet-Kolmogorov theorem; this yields the convergence of a subsequence to a weak solution of the parabolic system.     

迭代的计算与估计

对高次多项式函数这类非线性映射给出了一般 n次迭代的一个计算结果 ,还讨论了一维欧氏空间中一些非多项式型映射的迭代 .在二维欧氏空间中 ,我们给出了几类特殊的非线性迭代的结果 .对于一些难以精确计算迭代表达式的映射 ,我们给出了其迭代的估计 .     

脉冲时滞抛物型偏微分方程组解的振动性

研究一类脉冲时滞抛物型偏微分方程组解的振动性,利用一阶脉冲时滞微分不等式获得了该类方程组在两类不同边值条件下所有解振动的若干充分条件.所得结果充分反映了脉冲和时滞在振动中的影响作用.     

On a model of electromagnetic field propagation in ferroelectric media

The Maxwell system in an anisotropic, inhomogeneous medium with non-linear memory effect produced by a Maxwell type system for the polarization is investigated under low regularity assumptions on data and domain. The particular form of memory in the system is motivated by a model for electromagnetic wave propagation in ferromagnetic materials suggested by Greenberg, MacCamy and Coffman [J.M. Greenberg, R.C. MacCamy, C.V. Coffman, On the long-time behavior of ferroelectric systems, Phys. D 134 (1999) 362-383]. To avoid unnecessary regularity requirements the problem is approached as a system of space-time operator equation in the framework of extrapolation spaces (Sobolev lattices), a theoretical framework developed in [R. Picard, Evolution equations as space-time operator equations, Math. Anal. Appl. 173 (2) (1993) 436-458; R. Picard, Evolution equations as operator equations in lattices of Hilbert spaces, Glasnik Mat. 35 (2000) 111-136]. A solution theory for a large class of ferromagnetic materials confined to an arbitrary open set (with suitably generalized boundary conditions) is obtained.