共查询到20条相似文献,搜索用时 31 毫秒
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T. A. Zhereb’eva 《Moscow University Mathematics Bulletin》2010,65(1):16-22
A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered.
It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness
for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative
system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform. 相似文献
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Chau O. Shillor M. Sofonea M. 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2004,55(1):32-47
A model for the dynamic, adhesive, frictionless contact
between a viscoelastic body and a deformable foundation is
described. The adhesion process is modeled by a bonding field on
the contact surface. The contact is described by a modified normal
compliance condition. The tangential shear due to the bonding
field is included. The problem is formulated as a coupled system
of a variational equality for the displacements and a differential
equation for the bonding field. The existence of a unique weak
solution for the problem is established, together with a partial
regularity result. The existence proof proceeds by construction of
an appropriate mapping which is shown to be a contraction on a
Hilbert space. 相似文献
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A. K. Aziz J. B. Bell M. Schneider R. P. Gilbert 《Mathematical Methods in the Applied Sciences》1982,4(1):307-316
A boundary value problem is considered for an equation of mixed type in a rectangle. An energy method is used to prove uniqueness for appropriate boundary conditions. Similar considerations for the adjoint problem allow one to prove the existence of a generalized solution to the problem. It is also shown that the energy method leads naturally to a finite element method. The method is described for a special case and convergence is shown for the resulting numerical procedure. 相似文献
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A. V. Kel’manov L. V. Mikhailova S. A. Khamidullin 《Numerical Analysis and Applications》2008,1(3):255-268
An a posteriori (off-line) approach to solving the problem of maximum-likelihood detection of a recurring tuple containing reference fragments in a numerical quasiperiodic sequence is studied. The case is analyzed where (1) the total number of fragments in a sequence is unknown; (2) the index of a sequence term corresponding to the beginning of a fragment is a deterministic (not random) value; (3) a sequence distorted by additive uncorrelated Gaussian noise is available for observation. It is shown that the problem under consideration is reduced to testing a set of simple hypotheses about the mean of a random Gaussian vector. The cardinality of this totality grows exponentially as the vector dimension (i.e., the length of the sequence under study) increases. It is established that searching for a maximum-likelihood hypothesis is equivalent to finding arguments that yield a maximum for an auxiliary objective function. It is shown that maximizing the objective function reduces to solving a special optimization problem, which is proved to be solvable in polynomial time. An exact algorithm for solving this problem, which underlies the optimal (maximum-likelihood) detection algorithm for a recurring tuple, is substantiated. The kernel of the exact algorithm is an algorithm for solving a special (basic) optimization problem. Results of numerical simulations are presented. 相似文献
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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. 相似文献
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Franciszek Grabski 《Applied mathematics and computation》2011,217(24):9956-9965
Usually, a reliability function is defined by a failure rate which is a real function taking the non-negative real values. In this paper the failure rate is assumed to be a stochastic process with non-negative and right continuous trajectories. The reliability function is defined as an expectation of a function of that random process. Particularly, the failure rate defined by the semi-Markov processes is considered here. The theorems dealing with the renewal equations for the conditional reliability functions with a semi-Markov process as a failure rate are presented in this paper. A system of that kind of equations for the discrete state space semi-Markov process is applied for calculating the reliability function for the 3-states semi-Markov random walk. Using the introduced system of renewal equations for the countable state space, the reliability function for the Furry-Yule failure rate process is obtained. 相似文献
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Cocycles of general form on an arbitrary metric space are considered. The notion of determining modes for cocycles on a Hilbert space is introduced, and a theorem on the existence of finitely many determining modes for such cocycles is proved. The existence of a B-pullback attractor in the problem of microwave heating of a material is proved. The notion of almost periodic integral for a cocycle is introduced, and the existence of such an integral for a certain class of cocycles is proved. 相似文献
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The effective conductivity σ* of a multicomponent composite material is considered. Integral representations for σ* treated as a holomorphic function on a polydisk with values in a half-plane are analyzed. A representation for σ* is introduced which is symmetric in the component conductivities and for which the moments of the positive measure in the integral are directly related to the coefficients in a perturbation expansion of σ* around a homogeneous medium. This second feature, which is important for obtaining bounds on σ*, was previously available only in the two-component case. In addition, a bound valid for any holomorphic function of the above type is proven. 相似文献
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O. L. Bandman 《Numerical Analysis and Applications》2010,3(1):1-10
A cellular-automata (CA) approach for investigating properties of porous media with tortuous channels and different smoothness of pore walls is proposed. This approach is aimed at combining two different CA models: the first one is intended for constructing the morphology of a porous material; the second, for simulating a fluid flow through it. The porous media morphology is obtained as a result of evolution of a cellular automaton, forming a “steady pattern.” The result is then used for simulating a fluid flow through a porous medium by applying the Lattice Gas CA model. The method has been tested on a small fragment of a porous material and implemented for investigating a carbon electrode of a hydrogen fuel cell on a multiprocessor cluster. 相似文献
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讨论了二维非定常不可压Navier-Stokes方程的两重网格方法.此方法包括在粗网格上求解一个非线性问题,在细网格上求解一个Stokes问题.采用一种新的全离散(时间离散用Crank-Nicolson格式,空间离散用混合有限元方法)格式数值求解N-S方程.证明了该全离散格式的稳定性.给出了L2误差估计.对比标准有限元方法,在保持同样精度的前提下,TGM能节省大量的计算量. 相似文献
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V. I. Erokhin 《Computational Mathematics and Mathematical Physics》2007,47(4):564-578
A matrix is sought that solves a given dual pair of systems of linear algebraic equations. Necessary and sufficient conditions for the existence of solutions to this problem are obtained, and the form of the solutions is found. The form of the solution with the minimal Euclidean norm is indicated. Conditions for this solution to be a rank one matrix are examined. On the basis of these results, an analysis is performed for the following two problems: modifying the coefficient matrix for a dual pair of linear programs (which can be improper) to ensure the existence of given solutions for these programs, and modifying the coefficient matrix for a dual pair of improper linear programs to minimize its Euclidean norm. Necessary and sufficient conditions for the solvability of the first problem are given, and the form of its solutions is described. For the second problem, a method for the reduction to a nonlinear constrained minimization problem is indicated, necessary conditions for the existence of solutions are found, and the form of solutions is described. Numerical results are presented. 相似文献
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Max Mintz 《Journal of Optimization Theory and Applications》1972,9(2):99-111
A minimax terminal state estimation problem is posed for a linear plant and a generalized quadratic loss function. Sufficient conditions are developed to insure that a Kalman filter will provide a minimax estimate for the terminal state of the plant. It is further shown that this Kalman filter will not generally be a minimax estimate for the terminal state if the observation interval is arbitrarily long. Consequently, a subminimax estimate is defined, subject to a particular existence condition. This subminimax estimate is related to the Kalman filter, and it may provide a useful estimate for the terminal state when the performance of the Kalman filter is no longer satisfactory. 相似文献
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Y. Nishikawa N. Sannomiya H. Itakura 《Journal of Optimization Theory and Applications》1976,18(2):271-284
A method is developed for the approximate design of an optimal state regulator for a linear periodically varying system with quadratic performance index. The periodic term is taken to be a perturbation to the system. By making use of a power-series expansion in a small parameter, associated with periodic terms, a set of matrix equations is derived for determining successively a feedback gain. Given periodic terms of a Fourier-series form, explicit solutions are obtained for those matrix equations. A sufficient condition for existence and periodicity of the solution is also shown. Further, the performance degradation resulting from a truncation of the power-series solution is investigated. The method may effectively be used in a computer-programmed computation. 相似文献
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L. A. Manita 《Journal of Mathematical Sciences》2011,177(2):257-269
The problem on minimizing a quadratic functional on trajectories of the wave equation is considered. We assume that the density
of external forces is a control function. A control problem for a partial differential equation is reduced to a control problem
for a countable system of ordinary differential equations by use of the Fourier method. The controllability problem for this
countable system is considered. Conditions of the noncontrollability for some wave equations were obtained. 相似文献
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Pasol L; Sellier A; Feuillebois F 《The Quarterly Journal of Mechanics and Applied Mathematics》2006,59(4):587-614
Comprehensive results are provided for the creeping flow arounda spherical particle in a viscous fluid close to a plane wall,when the external velocity is parallel to the wall and variesas a second degree polynomial in the coordinates. By linearityof Stokes equations, the solution is a sum of flows for typicalunperturbed flows: a pure shear flow, a modulated shearflow, for which the rate of shear varies linearly inthe direction normal to the wall, and a quadratic flow. Solutionsconsidered here use the bipolar coordinates technique. Theycomplement the accurate results of Chaoui and Feuillebois (2003)for the pure shear flow. The solution of Goren and O'Neill (1971)for the quadratic flow is reconsidered and a new analyticalsolution is derived for the ambient modulated shear flow. Theperturbed flow fields for these two cases are presented in detailand discussed. Results for the force and torque friction factorsare provided with a 5 x 1017 accuracy as a reference.For the quadratic flow, there is a force and a torque on a fixedsphere. A minimum value of the torque is found for a gap ofabout 0·18a, where a is the sphere radius. This minimumis interpreted in term of the corresponding flow structure.For the modulated shear flow, there is only a torque. The freemotion of a sphere in an ambient quadratic flow is also determined. 相似文献
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Lijun Zhang Sheng Liu Hai Lan 《Journal of Mathematical Analysis and Applications》2007,334(1):414-430
In this paper, the problem of stability of switched homogeneous systems is addressed. First of all, if there is a quadratic Lyapunov function such that nonlinear homogeneous systems are asymptotically stable, a matrix Lyapunov-like equation is obtained for a stable nonlinear homogeneous system using semi-tensor product of matrices, and Lyapunov equation of linear system is just its particular case. Following the previous results, a sufficient condition is obtained for stability of switched nonlinear homogeneous systems, and a switching law is designed by partition of state space. In particular, a constructive approach is provided to avoid chattering phenomena which is caused by the switching rule. Then for planar switched homogeneous systems, an LMI approach to stability of planar switched homogeneous systems is presented. Similar to the condition for linear systems, the LMI-type condition is easily verifiable. An example is given to illustrate that candidate common Lyapunov function is a key point for design of switching law. 相似文献
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Lineu C. Barbosa Moshe Friedman 《The Journal of the Operational Research Society》1979,30(12):1129-1132
The paper is concerned with equipment which is being phased out because it is superseded by a technologically more advanced product. It nevertheless still requires efficient handling for the rest of its life span.An inventory lot size model without backlogs for a single commodity with a vanishing market is used. The vanishing market is represented by- a demand function that decreases with time and eventually reaches zero, implying that the planning horizon is finite and known. It is assumed that there is no lead time for replenishments. The problem is to devise an optimal management scheme for this inventory system, namely, to determine the number of replenishments and their schedule over the predicted survival time horizon of the product.The problem is completely solved for the class of demand functions which can be approximated to by positive powers of time. The solution is given in a nearly closed form and is proven to be unique. 相似文献