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.     

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.     

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．     

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.     

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.     

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.     

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.     

Numerical Simulation of Incompressible Flows Within Simple Boundaries. I. Galerkin (Spectral) Representations

Galerkin (spectral) methods are explored for the numerical simulation of incompressible flows within simple boundaries. A major part of the paper is devoted to the development of transform methods for efficient simulation of flows in box geometries with periodic and free-slip boundary conditions. Techniques for incorporating known symmetries and invariances into transform methods are illustrated for the Taylor-Green vortex. Galerkin methods for accurate and efficient representation of rigid no-slip boundary conditions are also explained. A class of pseudospectral approximations is introduced in order to handle more complicated dynamical interactions in more complicated geometries. Later papers in this series will demonstrate the important advantages of spectral methods over finite-difference methods for simulation of many of the flows of current interest and will present specific numerical results for various transition and turbulent flows.     

Necessary conditions for optimal controls for systems governed by parabolic partial delay-differential equations in divergence form with first boundary conditions

In this paper, we consider the question of necessary conditions for optimality for systems governed by second-order parabolic partial delay-differential equations with first boundary conditions. All the coefficients of the system are assumed bounded measurable and contain controls and delays in their arguments. The second-order parabolic partial delay-differential equation is in divergence form. In Theorem 4.1, we present results on the existence and uniqueness of weak solutions in the sense of Ladyzhenskaya-Solonnikov-Ural'ceva for this class of systems. An integral maximum principle and its point-wise version for the corresponding controlled system are established in Theorem 5.1 and Corollary 5.1, respectively.The authors wish to thank Dr. E. Noussair for his stimulating discussion and valuable comments in the preparation of this paper. Further, they also wish to acknowledge the referee of the paper for his valuable suggestions and comments. The discussion presented in Section 6 is in response to his suggestions.     

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.     

Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data

Summary. A semidiscrete mixed finite element approximation to parabolic initial-boundary value problems is introduced and analyzed. Superconvergence estimates for both pressure and velocity are obtained. The estimates for the errors in pressure and velocity depend on the smoothness of the initial data including the limiting cases of data in and data in , for sufficiently large. Because of the smoothing properties of the parabolic operator, these estimates for large time levels essentially coincide with the estimates obtained earlier for smooth solutions. However, for small time intervals we obtain the correct convergence orders for nonsmooth data. Received July 30, 1995 / Revised version received October 14, 1996     

Functionals for the means of observables for one-dimensional infinite-particle systems

We study the problem of the existence of means of observables for infinite-particle systems. Using solutions of the Cauchy problems for the BBGKY hierarchy and for its dual, we prove the local existence in time of the mean-value functionals in the cases where either the observables or the states vary in time. We also discuss the problem of the existence of such functionals for several different classes of observables and for an arbitrary time interval.     

Polytope Lyapunov Functions for Stable and for Stabilizable LSS

We present a new approach for constructing polytope Lyapunov functions for continuous-time linear switching systems (LSS). This allows us to decide the stability of LSS and to compute the Lyapunov exponent with a good precision in relatively high dimensions. The same technique is also extended for stabilizability of positive systems by evaluating a polytope concave Lyapunov function (“antinorm”) in the cone. The method is based on a suitable discretization of the underlying continuous system and provides both a lower and an upper bound for the Lyapunov exponent. The absolute error in the Lyapunov exponent computation is estimated from above and proved to be linear in the dwell time. The practical efficiency of the new method is demonstrated in several examples and in the list of numerical experiments with randomly generated matrices of dimensions up to 10 (for general linear systems) and up to 100 (for positive systems). The development of the method is based on several theoretical results proved in the paper: the existence of monotone invariant norms and antinorms for positively irreducible systems, the equivalence of all contractive norms for stable systems and the linear convergence theorem.     

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.     

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.     

Effective equidistribution of twisted horocycle flows and horocycle maps

We prove bounds for twisted ergodic averages for horocycle flows of hyperbolic surfaces, both in the compact and in the non-compact finite area case. From these bounds we derive effective equidistribution results for horocycle maps. As an application of our main theorems in the compact case we further improve on a result of Venkatesh, recently already improved by Tanis and Vishe, on a sparse equidistribution problem for classical horocycle flows proposed by Shah and Margulis, and in the general non-compact, finite area case we prove bounds on Fourier coefficients of cusp forms which are comparable to the best known bounds of Good in the holomorphic case, and of Bernstein and Reznikov in the Maass (non-holomorphic) case. Our approach is based on Sobolev estimates for solutions of the cohomological equation and on scaling of invariant distributions for twisted horocycle flows.     

圆管层流与湍流进口段效应修正系数的研究

本文对于光滑圆管层流与湍流进口段长度以及压力损失和流量进口段效应修正系数.提出统一的计算方法通过具体算例,提供了层流与湍流进口段效应压力损失和流量修正系数的理论计算公式.并且给出计及湍流进口段效应的流量计算方法.理论计算结果与实验数据比较表明,本文提供的公式.是简便而又可靠的.     

RISK-BASED MULTIATTRIBUTE DECISION-MAKING IN PROPERTY AND WATERSHED MANAGEMENT

ABSTRACT. Determining best management systems for properties and evaluating their sustainability at the watershed scale are useful and important aspects of integrated watershed management. Multiattribute decision-making (MADM) is very useful for modeling the selection of best management systems for properties in a watershed. This paper reviews four MADM approaches including utility theory, surrogate worth tradeoff, free iterative search and stochastic dominance with respect to a function (SDWF). Emphasis is on determining how the first three methods could be used to determine the best (most preferred) combinations of attributes and associated management systems for a property. An application of the expected utility method with risk neutral preferences is presented in which farmer's preferences for five attributes are used to rank five farming systems for an agricultural watershed in Missouri. A framework is presented for assessing the sustainability of the best management systems for all properties in a watershed and the cost-effectiveness of policies for enhancing sustainable resource management at the watershed scale.