Circle theorems for steady Stokes flow

Two circle theorems for two-dimensional steady Stokes flow are presented. The first theorem gives an expression for the stream function for a Stokes flow past a circular cylinder in terms of the stream function for a slow and steady irrotational flow in an unbounded incompressible viscous fluid. The second theorem gives a more general expression for the stream function for another Stokes flow past the circular cylinder in terms of the stream function for a slow and steady rotational flow in the same fluid.     

Representation for the Green’s function of the Dirichlet problem for polyharmonic equations in a ball

We explicitly construct the Green’s function for the Dirichlet problem for polyharmonic equations in a ball in a space of arbitrary dimension. The formulas for the Green’s function are of interest in their own right. In particular, the explicit representations for a solution to the Dirichlet problem for the biharmonic equation are important in elasticity.     

Superconvergence of mixed finite element semi-discretizations of two time-dependent problems

We will show that some of the superconvergence properties for the mixed finite element method for elliptic problems are preserved in the mixed semi-discretizations for a diffusion equation and for a Maxwell equation in two space dimensions. With the help of mixed elliptic projection we will present estimates global and pointwise in time. The results for the Maxwell equations form an extension of existing results. For both problems, our results imply that post-processing and a posteriori error estimation for the error in the space discretization can be performed in the same way as for the underlying elliptic problem.     

Various motivations for managerial (mis)reporting – an experimental study

In the experiment we model all possible consequences from misreporting for both the shareholder and for the manager, since we are interested in patterns in reporting behaviour resulting from different motivations for potential misrepresentation. This allows for examining the stability of the (mis)reporting behaviour in different treatments. Agents are primarily driven by the consequences for themselves rather than by the consequences for the principal, while deciding on misreporting. Participants are willing to sacrifice a small gain for themselves in order to prevent a greater loss for the principal. If agents misreport, they do it in order to generate positive rather than negative consequences for themselves. Reports in favour of the principal, but fruitless or even costly for the agent are very rare. The experiment indicates also that pro-social agents report more truthfully than pro-self agents.     

Sparre Andersen模型中破产概率的边界

研究在Andersen Spaxre模型中,当破产概率的初始边界已知的时候,根据更新方程和更新方程中函数的单调性来改进破产概率的边界,并进一步改进了严重损失函数G（x,y）的边界．     

Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bounds for Shannon and Zipf‐Mandelbrot entropies

Shannon and Zipf‐Mandelbrot entropies have many applications in many applied sciences, for example, in information theory, biology and economics, etc. In this paper, we consider two refinements of the well‐know Jensen inequality and obtain different bounds for Shannon and Zipf‐Mandelbrot entropies. First of all, we use some convex functions and manipulate the weights and domain of the functions and deduce results for Shannon entropy. We also discuss their particular cases. By using Zipf‐Mandelbrot laws for different parameters in Shannon entropies results, we obtain bounds for Zipf‐Mandelbrot entropy. The idea used in this paper for obtaining the results may stimulate further research in this area, particularly for Zipf‐Mandelbrot entropy.     

On the energy flux vector for bending vibrations of a plate : PMM vol. 40, n 6, 1976, pp. 1131–1135

An expression for the energy flux vector of plate bending vibrations is obtained in invariant form. The derivation of expressions for the transverse force, bending and twisting moments in an arbitrary orthogonal coordinate system and the derivation of an orthogonality type condition for normal waves being propagated in a thin elastic strip with free edges are considered as applications.In a number of cases it turns out to be useful to consider the energy flux vector in analyzing the vibrations in systems with distributed parameters. The expressions for the Umov-Poynting vector in electrodynamics and for the energy flux vector in acoustics are well-known. An analogous vector for the bending Vibrations of a plate was mentioned only in [1 – 3], This vector is used in [1] to prove a uniqueness theorem for a two-component acoustic model consisting of an ideal compressible fluid and elastic plates in contact with it. However, the expression for the energy flux in [1] (it was later cited in [2, 3] with a reference to [1]) is erroneous. An exact expression (within the framework of the applicability of the Kirchhoff equation) is found below for the energy flux vector of the bending vibrations of a plate and some applications of the formulas obtained are mentioned.     

City-effects in the atomic bomb survivors data

It was investigated how risk estimates derived from the RERF life span study data sets for cancer incidence and mortality, respectively, differ between the two cities Hiroshima and Nagasaki, and the two sexes. This was done by estimating the excess risk for various age-at-exposure and time-since-exposure groups. The epidemiologically most reliable age group are those aged 20–39 years at the time of exposure. As expected, in this group, the relative risk for females in Hiroshima is higher than that for males; however, in Nagasaki, the relative risk for females is lower than that for males. When comparing the risks in the two cities for the same sex, the risks of cancer incidence and mortality of females exposed in Hiroshima are higher than those in Nagasaki. However, for the males, the risks of cancer incidence in Hiroshima are lower than in Nagasaki, and the risks of cancer mortality of males are very similar between both cities. All differences depend on age-at-exposure and time-since-exposure, and are at the borderline of being statistically significant. The absorbed dose of neutrons, for the same γ-dose, is about three times as high in Hiroshima than in Nagasaki for both sexes. Because of these observed risk differences between both cities, it does not appear to be possible to reliably estimate the relative biological effectiveness of neutrons as compared to that of γ-rays from these epidemiological data sets. No evidence was found in this analysis that the radiation weighting factors w_R presently used for neutrons in radiation protection could severely underestimate the risks for somatic late effects induced by neutrons.     

A NEW NONCONFORMING MIXED FINITE ELEMENT SCHEME FOR THE STATIONARY NAVIER-STOKES EQUATIONS

In this article, a new stable nonconforming mixed finite element scheme is proposed for the stationary Navier-Stokes equations, in which a new low order CrouzeixRaviart type nonconforming rectangular element is taken for approximating space for the velocity and the piecewise constant element for the pressure. The optimal order error estimates for the approximation of both the velocity and the pressure in L2-norm are established, as well as one in broken H1-norm for the velocity. Numerical experiments are given which are consistent with our theoretical analysis.     

流动稳定性弱非线性理论的重新考虑*

弱非性理论已被广泛用于流动稳定性理论及其它领域.然而其应用对某些问题虽是成功的,但对另一些问题,其结果却常不令人满意,特别是对转捩或自由剪切流中涡的演化这类问题,这时理论研究的目的不是寻找稳态解,而是预测演化过程.在本文中,我们将研究不成功的原因并建议一些改进的办法.     

裂缝孔隙介质中二相驱动问题的交替方向有限元方法及理论分析

考虑裂缝孔隙介质中二相驱动问题的数值方法及理论分析。对压力方程采用混合有限元方法,对裂缝和岩块系统上的饱和度方程采用交替方向有限元方法,证明了交替方向有限元格式具有最优Ｌ２模和Ｈ１模误差估计。     

On the convergence of difference schemes for a heat conduction equation

Sufficient conditions are obtained for the convergence of difference schemes for the numerical solution of the Cauchy problem for a heat conduction equation in two space variables. The sufficient conditions are derived in a form similar to those for the convergence of a sequence of linear positive operators in the Korovkin theorem. As an application it is shown that difference schemes that are widely used in practice can easily be checked for convergence by these conditions.     

The effect of receptor site nonuniformity on the measurement of rate constants

The BIAcore is an instrument for measuring rate constants in real time by using a surface–volume geometry. Though current models for the resulting reaction include transport effects for the reactant in solution, they do not account for spatial nonuniformities in the reactant attached to the wall. This work accounts for such nonuniformities and establishes that in the limit of small Damköhler number, such effects are negligible due to the averaging characteristics of the instrumentation.     

Coupled-expanding maps and one-sided symbolic dynamical systems

This paper studies relationships between coupled-expanding maps and one-sided symbolic dynamical systems. The concept of coupled-expanding map is extended to a more general one: coupled-expansion for a transitive matrix. It is found that the subshift for a transitive matrix is strictly coupled-expanding for the matrix in certain disjoint compact subsets; the topological conjugacy of a continuous map in its compact invariant set of a metric space to a subshift for a transitive matrix has a close relationship with that the map is strictly coupled-expanding for the matrix in some disjoint compact subsets. A certain relationship between strictly coupled-expanding maps for a transitive matrix in disjoint bounded and closed subsets of a complete metric space and their topological conjugacy to the subshift for the matrix is also obtained. Dynamical behaviors of subshifts for irreducible matrices are then studied and several equivalent statements to chaos are obtained; especially, chaos in the sense of Li–Yorke is equivalent to chaos in the sense of Devaney for the subshift, and is also equivalent to that the domain of the subshift is infinite. Based on these results, several new criteria of chaos for maps are finally established via strict coupled-expansions for irreducible transitive matrices in compact subsets of metric spaces and in bounded and closed subsets of complete metric spaces, respectively, where their conditions are weaker than those existing in the literature.     

Numerical modelling of the plane problem of the stress state of a tube immersed in a liquid

A numerical method for solving the plane problem of determining the stress state of a tube of arbitrary section immersed in a homogeneous incompressible liquid is proposed. The change from the boundary conditions for this problem to the boundary conditions for a biharmonic stress function is carried out, which enables the algorithm for solving boundary value problems in the case of a polyharmonic function developed earlier to be used to solve the problem under consideration. It is shown that the boundary conditions for doubly-connected domains contain three unknown constants. The conditions for finding these constants in a form that is convenient for the implementation of a numerical algorithm are obtained. Tubes with sections in the form of concentric, eccentric and elliptic rings are considered as examples.     

Error linear complexity measures for multisequences

Complexity measures for sequences over finite fields, such as the linear complexity and the k-error linear complexity, play an important role in cryptology. Recent developments in stream ciphers point towards an interest in word-based stream ciphers, which require the study of the complexity of multisequences. We introduce various options for error linear complexity measures for multisequences. For finite multisequences as well as for periodic multisequences with prime period, we present formulas for the number of multisequences with given error linear complexity for several cases, and we present lower bounds for the expected error linear complexity.     

Stable exact solutions in cosmological models with two scalar fields

We consider the stability of isotropic solutions for two-field models in the Bianchi I metric. We prove that the sufficient conditions for Lyapunov stability in the Friedmann-Robertson-Walker metric ensure the stability under anisotropic perturbations in the Bianchi I metric and also under perturbations of the energy density for cold dark matter. We find sufficient conditions for the Lyapunov stability of isotropic fixed points for the system of Einstein equations. We use the superpotential method to construct stable kink-type solutions and obtain sufficient conditions on the superpotential for the Lyapunov stability of the corresponding exact solutions. We analyze the stability of isotropic kink-type solutions for models related to string field theory.     

A nonlocal boundary value problem for elliptic differential-operator equations and applications

In this paper we give, for the first time, an abstract interpretation of nonlocal boundary value problems for elliptic differential equations of the second order. We prove coerciveness and Fredholmness of nonlocal boundary value problems for the second order elliptic differential-operator equations. We apply then, in section 6, these results for investigation of nonlocal boundary value problems for the second order elliptic differential equations (one can find the references on the subject in the introduction and Chapter V in the book by A. L. Skubachevskii [27]). Abstract results obtained in this paper can be used for study of nonlocal boundary value problems for quasielliptic differential equations.     

Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations

A variety of numerical methods are available for determining the stability of a given solution of a partial differential equation. However for a family of solutions, calculation of boundaries in parameter space between stable and unstable solutions remains a major challenge. This paper describes an algorithm for the calculation of such stability boundaries, for the case of periodic travelling wave solutions of spatially extended local dynamical systems. The algorithm is based on numerical continuation of the spectrum. It is implemented in a fully automated way by the software package wavetrain, and two examples of its use are presented. One example is the Klausmeier model for banded vegetation in semi-arid environments, for which the change in stability is of Eckhaus (sideband) type; the other is the two-component Oregonator model for the photosensitive Belousov–Zhabotinskii reaction, for which the change in stability is of Hopf type.