共查询到20条相似文献,搜索用时 31 毫秒
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2.
Jean MAWHIN 《数学年刊B辑(英文版)》2017,38(2):563-578
The existence of a zero for a holomorphic functions on a ball or on a rectangle under some sign conditions on the boundary generalizing Bolzano's ones for real functions on an interval is deduced in a very simple way from Cauchy's theorem for holomorphic functions.A more complicated proof,using Cauchy's argument principle,provides uniqueness of the zero,when the sign conditions on the boundary are strict.Applications are given to corresponding Brouwer fixed point theorems for holomorphic functions.Extensions to holomorphic mappings from Cn to Cn are obtained using Brouwer degree. 相似文献
3.
We consider uniformly strongly elliptic systems of the second order with bounded coefficients. First, sufficient conditions for the invariance of convex bodies are obtained for linear systems without zero order term on bounded domains and quasilinear systems of special form on bounded domains and on a class of unbounded domains. These conditions are formulated in algebraic form. They describe relation between the geometry of the invariant convex body and the coefficients of the system. Next, necessary conditions, which are also sufficient, for the invariance of some convex bodies are found for elliptic homogeneous systems with constant coefficients in a half-space. The necessary conditions are derived by using a criterion on the invariance of convex bodies for normalized matrix-valued integral transforms also obtained in the paper. In contrast with the previous studies of invariant sets for elliptic systems, no a priori restrictions on the coefficient matrices are imposed. 相似文献
4.
George A. Gravvanis 《Journal of Mathematical Modelling and Algorithms》2002,1(4):269-282
A new class of approximate inverses for arrowhead and special tridiagonal linear systems, based on the concept of sparse approximate Choleski-type factorization procedures, are introduced for computing fast explicit approximate inverses. Explicit preconditioned iterative schemes in conjunction with approximate inverse matrix techniques are presented for the efficient solution of symmetric linear systems. A theorem on the rate of convergence of the explicit preconditioned conjugate gradient scheme is given and estimates of the computational complexity are presented. Applications of the proposed method on linear and nonlinear systems are discussed and numerical results are given. 相似文献
5.
Abdelhamid Meziani 《Journal of Geometric Analysis》1999,9(2):301-315
This paper deals with the integrability problem for structures on the sphere S2 which are elliptic on the upper and lower hemispheres, and which are given by a simple fold on the equator. Criteria for
standardness are given. Existence and factorization of first integrals are studied. 相似文献
6.
Michael Voit 《Journal of Theoretical Probability》1990,3(2):245-266
There are introduced moments on polynomial hypergroups. These moments are used to prove strong laws of large number (SSLLNs) for random walks on the nonnegative integers that are homogeneous with respect to a polynomial hypergroup where SLLNs of different kind appear for polynomial hypergroups thth different properties. Furthermore, we discuss polynomial hypergroups that are associated with some discrete semigroups in a canonical way, and, using SLLNs for polynomial hypergroups, we get SLLNs for isotropic random walks on some discrete semigroups. 相似文献
7.
V. V. Ryazanov 《Computational Mathematics and Mathematical Physics》2007,47(10):1720-1735
The search for logical regularities of classes in the recognition by precedents problems and the use of logical regularities for solving recognition and prediction problems are considered. Logical regularities of classes are defined as conjunctions of one-place predicates that determine the membership of a value of a feature in a certain interval of the real axis. The conjunctions are true on the subsets of reference objects of a certain class and are optimal. Various optimality criteria are considered and the problem of finding logical regularities is formulated as an integer programming problem. A qualitative analysis of these problems is performed. Models for evaluating estimates on the basis of systems of logical regularities are considered. Modifications of linear decision rules for finding estimates of how close the reference objects are to classes are proposed that are based on the search for the maximum gap. Approximations of logical regularities of classes by smooth functions is proposed. The concept of the dynamic logical regularity of classes is introduced, an algorithm for finding dynamic logical regularities is proposed, and a prediction method is developed. 相似文献
8.
Boundary-transmission problems of first order for the Helmholtz equation are considered within the context of wave diffraction by a periodic strip grating and formulated as convolution type operators acting on a Bessel potential periodic space setting. Two boundary-value problems are studied for an arbitrary geometry of the grating: the oblique derivative and the classic Neumann boundary-value problems. The convolution type operators on the grating which correspond to the given boundary-transmission problems are associated with Toeplitz operators acting on spaces of matrix functions defined on composed contours. A Fredholm theory for periodic boundary-value problems of first order is established independently of the grating period and the Fredholm indices for the oblique derivative and the classic Neumann boundary-value problems are given. 相似文献
9.
Initial and initial boundary value problems for first order partial functional differential equations are considered. Explicit
difference schemes of the Euler type and implicit difference methods are investigated. The following theoretical aspects of
the methods are presented. Sufficient conditions for the convergence of approximate solutions are given and comparisons of
the methods are presented. It is proved that assumptions on the regularity of given functions are the same for both the methods.
It is shown that conditions on the mesh for explicit difference schemes are more restrictive than suitable assumptions for
implicit methods. There are implicit difference schemes which are convergent and corresponding explicit difference methods
are not convergent. Error estimates for both the methods are construted. 相似文献
10.
This paper presents an analytical solution to the problem of the optimal rendezvous using power-limited propulsion for a spacecraft
in an elliptic orbit in a gravitational field. The derivation of the result assumes small relative distances, but does not
make any assumption on the eccentricity of the orbit and does not require numerical integration. The results are generalized
to include the possibility of different weights on the control effort for each axis (radial, along-track, and out-of-plane).
When the weights on the control efforts are unequal, several integrals are used whose solutions may be represented by infinite
series in a small parameter dependent on the eccentricity. A methodology is introduced where the series can be extended trivially
to as many terms as desired. Furthermore, for a given numerical tolerance, an upper bound on the number of terms required
to represent the series is also obtained. When the weights are equal for all the three axes, the series representations are
no longer necessary. The results can be used easily to design optimal feedback controls for rendezvous maneuvers, or for generating
initial guesses for two-point boundary-value problems for numerical solutions to the nonlinear rendezvous problem. 相似文献
11.
Some mathematical models of applied problems lead to the need of solving boundary value problems with a fractional power of an elliptic operator. In a number of works, approximations of such a nonlocal operator are constructed on the basis of an integral representation with a singular integrand. In the present article, new integral representations are proposed for operators with fractional powers. Approximations are based on the classical quadrature formulas. The results of numerical experiments on the accuracy of quadrature formulas are presented. The proposed approximations are used for numerical solving a model two‐dimensional boundary value problem for fractional diffusion. 相似文献
12.
In this paper, we consider multiperiod minisum location problems on networks in which demands can occur continuously on links according to a uniform probability density function. In addition, demands may change dynamically over time periods and at most one facility can be located per time period. Two types of networks are considered in conjunction with three behavioral strategies. The first type of network discussed is a chain graph. A myopic strategy and long-range strategy for locatingp-facilities are considered, as is a discounted present worth strategy for locating two facilities. Although these problems are generally nonconvex, effective methods are developed to readily identify all local and global minima. This analysis forms the basis for similar problems on tree graphs. In particular, we construct algorithms for the 3-facility myopic problem and the 2-facility long-range and discounted cost problems on a tree graph. Extensions and suggestions for further research on problems involving more general networks are provided. 相似文献
13.
Stefan Bilbao 《Numerical Methods for Partial Differential Equations》2004,20(3):463-480
This article is devoted to an analysis of simple families of finite difference schemes for the wave equation. These families are dependent on several free parameters, and methods for obtaining stability bounds as a function of these parameters are discussed in detail. Access to explicit stability bounds such as those derived here may, it is hoped, lead to optimization techniques for so‐called spectral‐like methods, which are difference schemes dependent on many free parameters (and for which maximizing the order of accuracy may not be the defining criterion). Though the focus is on schemes for the wave equation in one dimension, the analysis techniques are extended to two dimensions; implicit schemes such as ADI methods are examined in detail. Numerical results are presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 20: 463–480, 2004. 相似文献
14.
Y. Rama Krishna Sarma 《Annals of the Institute of Statistical Mathematics》1987,39(1):497-512
Summary In this note some asymptotically optimum tests for testing hypotheses concerning parameters when the observations are dependent
are obtained. Test statistics based on the score functions, similar to the one proposed by Rao in the case when the observations
are i.i.d. are proposed. Asymptotically UMP tests for one sided hypotheses against one sided alternatives and asymptotically
UMP unbiased test for a simple hypothesis against two sided alternatives are derived. In the multiparameter case tests for
simple hypotheses that have asymptotically best constant power on some family of surfaces in the parameter space are derived. 相似文献
15.
A.M. Abd-AllaS.R. Mahmoud N.A. AL-Shehri 《Applied mathematics and computation》2011,217(22):8914-8922
The present investigation is concerned with a study effect of non-homogeneous on the elastic stresses in rotating orthotropic infinite circular cylinder subjected to certain boundary conditions. Closed form stress solutions are obtained for rotating orthotropic cylinder with constant thickness for three cases: (1) a solid cylinder; (2) cylinder mounted on a circular rigid shaft; and (3) cylinder with a circular hole at the center. Analytical expressions for the components of the displacement and the stress in different cases are obtained. The effect of the rotation and non-homogeneity on the displacement and stress are studied. Numerical results are given and illustrated graphically for each case is considered. The effects rotating and non-homogeneity are discussed. Comparisons are made with the results predicted in the presence and absence of rotation. 相似文献
16.
Kosta Doen 《Mathematical Logic Quarterly》1992,38(1):179-187
Models for the Lambek calculus of syntactic categories surveyed here are based on frames that are in principle of the same type as Kripke frames for intuitionistic logic. These models are extracted from the literature on models for relevant logics, in particular the ternary relationed models introduced in the early seventies. The purpose of this brief survey is to locate some open completeness problems for variants of the Lambek calculus in the context of completeness results based on various types of ternary relational models. 相似文献
17.
The inverse problem of determining the growth rate coefficient of biological objects from additional information on their time-dependent density is considered. Two nonlinear integral equations are derived for the unknown coefficient, which is determined on part of its domain from one equation and on the remaining part from the other equation. The nonlinear integral equations are solved by iterative methods. The convergence conditions for the iterative methods are formulated, and results of numerical experiments are presented. 相似文献
18.
《Communications in Nonlinear Science & Numerical Simulation》2007,12(1):72-82
This study intends to investigate the dynamic behaviour of an all-terrain vehicle travelling on rough terrains. A nonlinear analytical model is established for quantifying the response of the vehicle with spring and damping nonlinearities to various operation and terrain conditions. Focus of the study is on the motion characteristics of the vehicle operating on rough terrains. Stability analyses are performed for the all-terrain vehicles under the operation of surmounting large obstacles and the operation of the vehicle on rough terrain surfaces. Stability conditions are provided and stable and unstable region diagrams are plotted and analyzed with the analytical model developed. Analytical solutions are provided for weakly nonlinear dynamic systems. Numerical simulations for the motion of the all-terrain vehicle are also presented. 相似文献
19.
Based on the rational system of Legendre rational functions, we construct
two set of new interpolation basis functions on the unbounded intervals. Their explicit expressions are derived, and fast and stable algorithms are provided for computing the new basis functions. As applications, new rational collocation methods
based on these new basis functions are proposed for solving various second-order
differential equations on the unbounded domains. Numerical experiments illustrate
that our new methods are more effective and stable than the existing collocation
methods. 相似文献
20.
J. Arnal H. Migalln V. Migalln J. Penads 《Numerical Linear Algebra with Applications》2006,13(7):553-572
Parallel iterative algorithms based on the Newton method and on two of its variants, the Shamanskii method and the Chord method, for solving nonlinear systems are proposed. These algorithms are based on two‐stage multisplitting methods where incomplete LU factorizations are considered as a mean of constructing the inner splittings. Convergence properties of these parallel methods are studied for H‐matrices. Computational results of these methods on two parallel computing systems are discussed. The reported experiments show the effectiveness of these methods. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献