关于控制系统的绝对稳定性准则

本文:1.给出非线性控制系统第二标准型[2]平凡解绝对稳定性准则,特别地给出了飞机纵向运动方程平凡解绝对稳定性准则,文[8][9]中关于飞机纵向运动方程的结果是本文推论2.2的特例;2.给出非线性控制系统第一标准型[2]平凡解在通常情况和一种临界情况下绝对稳定准则;3.给出了Lure型直接控制系统一般型平凡解绝对稳定若干准则,全文结果均根据系统本身的参数,具体构造函数,给出显式判据.     

Boundedness of the solution of the third problem for the Laplace equation

A necessary and sufficient condition for the boundedness of a solution of the third problem for the Laplace equation is given. As an application a similar result is given for the third problem for the Poisson equation on domains with Lipschitz boundary.Supported by GACR, Grant No. 201/00/1515.     

Formula for the fundamental solution of the heat equation on the sphere

This paper is devoted to the derivation of a simple asymptotic formula for the fundamental solution of the heat equation on the sphere. This formula is efficient for small values of the evolution parameter, and thus, complements the well-known formula for the fundamental solution in terms of Legendre polynomials that is efficient for relatively large values of the evolution parameter. The method relies on constructing a self-similar solution.     

On the domino-parity inequalities for the STSP

One method which has been used very successfully for finding optimal and provably good solutions for large instances of the symmetric travelling salesman problem (STSP) is the branch and cut method. This method requires knowledge of classes of useful valid inequalities for the polytope associated with the STSP, as well as efficient separation routines for these classes of inequalities. Recently a new class of valid inequalities called the domino-parity inequalites were introduced for the STSP. An efficient separation routine is known for these constraints if certain conditions are satisfied by the point to be separated. This separation routine has never been implemented or tested. We present several performance enhancements for this separation routine, and discuss our implementation of this improved algorithm. We test our implementation and provide results which we believe demonstrate the practical usefulness of these constraints and the separation routine for the STSP within a branch and cut framework. This research was partially supported by grants from the Natural Sciences and Engineering Research Council of Canada     

On the complexity of the Leibniz hierarchy

We prove that the problem of determining whether a finite logical matrix determines an algebraizable logic is complete for EXPTIME. The same result holds for the classes of order algebraizable, weakly algebraizable, equivalential and protoalgebraic logics. Finally, the same problem for the class of truth-equational logic is shown to be hard for EXPTIME.     

On the Passage to the Limit in the Construction of Geometric Solutions of the Riemann Problem

Mathematical Notes - A method for constructing geometric solutions of the Riemann problem for an impulsively perturbed conservation law is described. A complete classification of the possible...     

On the convergence of the secant method under the gamma condition

We provide sufficient convergence conditions for the Secant method of approximating a locally unique solution of an operator equation in a Banach space. The main hypothesis is the gamma condition first introduced in [10] for the study of Newton’s method. Our sufficient convergence condition reduces to the one obtained in [10] for Newton’s method. A numerical example is also provided.      

On the arithmetic triangle arising from the solvability conditions for the Neumann problem

We study the arithmetic triangle arising from the solvability conditions for the Neumann problem for the polyharmonic equation in the unit ball. Recurrence relations for the elements of this triangle are obtained.     

On the regularity of the axisymmetric solutions of the Navier-Stokes equations

We obtain improved regularity criteria for the axisymmetric weak solutions of the three dimensional Navier-Stokes equations with nonzero swirl. In particular we prove that the integrability of single component of vorticity or velocity fields, in terms of norms with zero scaling dimension give sufficient conditions for the regularity of weak solutions. To obtain these criteria we derive new a priori estimates for the axisymmetric smooth solutions of the Navier-Stokes equations. Received: 11 April 2000; in final firm: 26 November 2000 / Published online: 28 February 2002     

On the bound of proximity of the binomial distribution to the normal one

Bounds for the error of the Gaussian approximation for the binomial distribution are stated, depending from the probability of success and the number of observations. As a consequence, the upper bound for a constant in the Berry-Esseen inequality is deduced which differs from asymptotical one slightly more than 0.01.     

On the spectrum of the Laplacian

In this article we prove a generalization of Weyl’s criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for its essential spectrum.     

On the convergence of the block principal pivotal algorithm for the LCP

We show that the block principal pivot algorithm (BPPA) for the linear complementarity problem (LCP) solves the problem for a special class of matrices in at most n block principal pivot steps. We provide cycling examples for the BPPA in which the matrix is positive definite or symmetric positive definite. For LCP of order three, we prove that strict column (row) diagonal dominance is a sufficient condition to avoid cycling.     

From the neutrino to the edge of the universe

Two recent findings necessitate a closer look at the existing standard models of particle physics and cosmology. These are the discovery of neutrino oscillation, and hence a non-zero mass on the one hand and, on the other, observations of distant supernovae which indicate that contrary to popular belief, the universe would continue to expand for ever, possibly accelerating in the process. In this paper it is pointed out that relatively recent studies which indicate a stochastic, quantum vacuum underpinning and a fractal structure for space time, reconcile both of the recent observations, harmoniously.     

m-可乘序列谱测度的关联维数

作者利用关联函数的递减速度与Fourier谱特征之间的关系,计算出无穷m -可乘序列谱测度的关联维数. 且通过对m -可乘序列关联函数的研究,验证了其谱测度是奇异连续的结论.     

On the explicit resolution of the mushy zone in the modelling of the continuous casting of alloys

In the continuous casting of alloys, it is well-known that the mushy zone is decisive for the final properties of the casting. Most numerical models for the process use enthalpy-based methods on fixed grids which determine the extent the mushy zone implicitly. Here, on the other hand, we develop a methodology for explicitly resolving the geometrical extent of the mushy zone; this involves a sharp-interface formulation to solve a dual moving boundary problem to locate the solidus and liquidus isotherms. The results compare favourably with those from enthalpy-based methods, and the advantages of our approach with respect to future multiphysics calculations are discussed.     

On the validity of the Ginzburg-Landau equation

Summary The famous Ginzburg-Landau equation describes nonlinear amplitude modulations of a wave perturbation of a basic pattern when a control parameterR lies in the unstable regionO(ε ²) away from the critical valueR _c for which the system loses stability. Hereε>0 is a small parameter. G-L's equation is found for a general class of nonlinear evolution problems including several classical problems from hydrodynamics and other fields of physics and chemistry. Up to now, the rigorous derivation of G-L's equation for general situations is not yet completed. This was only demonstrated for special types of solutions (steady, time periodic) or for special problems (the Swift-Hohenberg equation). Here a mathematically rigorous proof of the validity of G-L's equation is given for a general situation of one space variable and a quadratic nonlinearity. Validity is meant in the following sense. For each given initial condition in a suitable Banach space there exists a unique bounded solution of the initial value problem for G-L's equation on a finite interval of theO(1/ε²)-long time scale intrinsic to the modulation. For such a finite time interval of the intrinsic modulation time scale on which the initial value problem for G-L's equation has a bounded solution, the initial value problem for the original evolution equation with corresponding initial conditions, has a unique solutionO(ε²) — close to the approximation induced by the solution of G-L's equation. This property guarantees that, for rather general initial conditions on the intrinsic modulation time scale, the behavior of solutions of G-L's equation is really inherited from solutions of the original problem, and the other way around: to a solution of G-L's equation corresponds a nearby exact solution with a relatively small error.     

On the Majorant Method for the Cauchy--Kovalevskaya Problem

We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution.     

On the determination of the control parameters of the optimal can-order policy

This paper considers the well-known class of can-order policies. This type of coordinated replenishment policies accounts for a joint set-up cost structure, where a major set-up cost is incurred for any order and an individual minor set-up cost is charged for each item in the replenishment. Recent comparative studies have pointed out that the performance of the optimal can-order policy is poor, compared to other coordinated replenishment strategies, when the major set-up cost is high. This paper shows that it is the approximate decomposition method to calculate the optimal canorder parameters which performs bad in such situations and not the policy itself. Attention is focused to a subclass of can-order policies, which is close to the optimal can-order policy for high major set-up costs. A solution procedure is developed to calculate the optimal control parameters of this policy. It is shown that a properly chosen combination of the solution procedures to calculate can-order parameters leads to a can-order strategy which performs as well as other coordinated replenishment policies.     

Operator methods in the problem of estimating the asymptotics of the time of the first hit for the birth and death process

Estimates are established for the exponential asymptotics of the time of the first hit of a certain leveln for the birth and death process.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 8, pp. 1104–1108, August, 1993.     

On the complexity of the dualization problem

The computational complexity of discrete problems concerning the enumeration of solutions is addressed. The concept of an asymptotically efficient algorithm is introduced for the dualization problem, which is formulated as the problem of constructing irreducible coverings of a Boolean matrix. This concept imposes weaker constraints on the number of “redundant” algorithmic steps as compared with the previously introduced concept of an asymptotically optimal algorithm. When the number of rows in a Boolean matrix is no less than the number of columns (in which case asymptotically optimal algorithms for the problem fail to be constructed), algorithms based on the polynomialtime-delay enumeration of “compatible” sets of columns of the matrix is shown to be asymptotically efficient. A similar result is obtained for the problem of searching for maximal conjunctions of a monotone Boolean function defined by a conjunctive normal form.