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1.
We give necessary and sufficient conditions for a module M with a decomposition that complements maximal direct summands to be a lifting module. We apply our results to get a necessary and sufficient condition for a direct sum of modules to be a quasi-discrete (discrete) module. We also give some sufficient conditions for a lifting module to be a direct sum of indecomposables. 相似文献
2.
We study a system of two equations of the parabolic type with two nonlinearities depending on the sum of squares of two unknown functions. We derive conditions under which the system can be reduced to a single equation. We indicate conditions under which this equation can be reduced to a linear heat equation or to semilinear equations. We construct parametric families of exact solutions defined by elementary functions. We derive a control law providing the existence of a wide class of functions that can be realized as exact solutions. 相似文献
3.
Diclehan Tezcaner Murat Köksalan 《Journal of Optimization Theory and Applications》2011,150(2):379-394
We address the route selection problem for Unmanned Air Vehicles (UAV) under multiple objectives. We consider a general case
for this problem, where the UAV has to visit several targets and return to the base. We model this problem as a combination
of two combinatorial problems. First, the path to be followed between each pair of targets should be determined. We model
this as a multi-objective shortest path problem. Additionally, we need to determine the order of the targets to be visited.
We model this as a multi-objective traveling salesperson problem (MOTSP). The overall problem is a combination of these two
problems, which we define as a generalized MOTSP. We develop an exact interactive approach to identify the best paths and
the best tour of a decision maker under a linear utility function. 相似文献
4.
We study semi-convex frontier (SCF) optimization problems where objective functions can be semi-convex and constraint sets can be non-polyhedron, which stem from a growing range of optimization applications such as frontier analysis, multi-objective programming in economics. The new findings of this paper can be summarized as follows: (1) We characterize non-dominated points of a non-polyhedron optimal solution set of a semi-convex frontier program. (2) We obtain optimality conditions of a constant modulus SCF program, of which the objective function is semi-convex with a constant semiconvexity modulus. (3) We obtain a non-smooth Hölder stability of the optimal solutions of a semiconvex frontier program. (4) We use generalized differentiability to establish sensitivity analysis of the optimal value function of a semi-convex frontier program. 相似文献
5.
Frank Natterer Olga Klyubina 《计算数学(英文版)》2007,25(3):368-373
We study the initial value problem of the Helmholtz equation with spatially variable wave number. We show that it can be stabilized by suppressing the evanescent waves. The stabilized Helmholtz equation can be solved numerically by a marching scheme combined with FFT. The resulting algorithm has complexity n^2 log n on a n x n grid. We demonstrate the efficacy of the method by numerical examples with caustics. For the Maxwell equation the same treatment is possible after reducing it to a second order system. We show how the method can be used for inverse problems arising in acoustic tomography and microwave imaging. 相似文献
6.
We give an upper bound of the number of edges of a permutation graph. We introduce some necessary conditions for a graph to be a permutation graph, and we discuss the independence of these necessary conditions. We show that they are altogether not sufficient for a graph to be a permutation graph. 相似文献
7.
Sara Mattia 《Computational Optimization and Applications》2012,51(2):809-834
We address the problem of designing a multi-layer network with survivability requirements. We are given a two-layer network:
the lower layer represents the potential physical connections that can be activated, the upper layer is made of logical connections
that can be set up using physical links. We are given origin-destination demands (commodities) to be routed at the upper layer.
We are also given a set of failure scenarios and, for every scenario, an associated subset of commodities. The goal is to
install minimum cost integer capacities on the links of both layers in order to ensure that the commodities can be routed
simultaneously on the network. In addition, in every failure scenario the routing of the associated commodities must be guaranteed.
We consider two variants of the problem and develop a branch-and-cut scheme based on the capacity formulation. Computational
results on instances derived from the SNDLib for single node failure scenarios are discussed. 相似文献
8.
D. Laroze P.G. Siddheshwar H. Pleiner 《Communications in Nonlinear Science & Numerical Simulation》2013,18(9):2436-2447
We report theoretical and numerical results on thermally driven convection of a magnetic suspension. The magnetic properties can be modeled as those of electrically non-conducting superparamagnets. We perform a truncated Galerkin expansion finding that the system can be described by a generalized Lorenz model. We characterize the dynamical system using different criteria such as Fourier power spectrum, bifurcation diagrams, and Lyapunov exponents. We find that the system exhibits multiple transitions between regular and chaotic behaviors in the parameter space. Transient chaotic behavior in time can be found slightly below their linear instability threshold of the stationary state. 相似文献
9.
P. A. Martin 《Mathematical Methods in the Applied Sciences》2020,43(15):8906-8929
In some circumstances, sound waves in a rarefied gas can be studied using a linearised form of the regularised 13-moment equations of Struchtrup and Torrilhon. We build solutions of those equations in spherical polar coordinates using vector spherical harmonics. We first solve a reduced system of equations (with 11 unknowns) after introduction of a force vector (divergence of the stress). We then show that the stresses themselves can be recovered by solving five additional equations. The results obtained are expected to be useful for problems such as acoustic scattering of a plane wave by a sphere in a rarefied gas. 相似文献
10.
We consider the problem of preemptive scheduling a set of periodically occurring jobs on a set of unrelated processors, that is, processors having different speeds for different jobs. We assume that each occurrence of a job has to be completely processed before the next occurrence of the same job. We provide a system of linear inequalities for testing the existence of a feasible schedule which can be solved in polynomial time. We then use the solution to this linear system, if any, for constructing a feasible schedule in a straightforward way. 相似文献
11.
Walter S. Sizer 《Linear algebra and its applications》1977,16(2):177-187
We define a closure operation on semigroups of matrices over a skew field, and show that a semigroup of matrices can be (upper) triangularized if and only if its closure can be. We then give necessary and sufficient conditions for a closed semigroup to be triangularizable. 相似文献
12.
E. V. Trifonov 《Theoretical and Mathematical Physics》2017,192(1):974-981
We propose a procedure for multiplying solutions of linear and nonlinear one-dimensional wave equations, where the speed of sound can be an arbitrary function of one variable. We obtain exact solutions. We show that the functional series comprising these solutions can be used to solve initial boundary value problems. For this, we introduce a special scalar product. 相似文献
13.
We approach the question of which soluble groups are automatic. We describe a class of nilpotent-by-Abelian groups which need to be studied in order to answer this question. We show that the nilpotent-by-cyclic groups in this class have exponential isoperimetric inequality and so cannot be automatic. 相似文献
14.
We present a new class of high-order variational integrators on Lie groups. We show that these integrators are symplectic and momentum-preserving, can be constructed to be of arbitrarily high order, or can be made to converge geometrically. Furthermore, these methods are capable of taking very large time-steps. We demonstrate the construction of one such variational integrator for the rigid body and discuss how this construction could be generalized to other related Lie group problems. We close with several numerical examples which demonstrate our claims and discuss further extensions of our work. 相似文献
15.
In this paper we carry on the research initiated in [13] and [14]. We consider classes of orthomodular lattices which satisfy
certain state and polynomial conditions. We show that these classes form quasivarieties. We then exhibit basic examples of
these quasivarieties (some of these examples originated in the quantum logic theory). We finally show how the quasivarieties
in question can be described in terms of implicative equations. (It should be noted that in some cases we have not been able
to clarify whether or not a class shown to be a quasivariety is a variety, see Section 2.)
Received May 26, 1998; accepted in final form May 19, 1999. 相似文献
16.
We introduce the notion of a Richman extension of an integral domain, and show its basic properties. We further show that a flat extension need not be a Richman extension, and a Richman extension need not be an LCM-stable extension. 相似文献
17.
人数与任务数不相等的指派问题 总被引:5,自引:2,他引:3
本提出人数与任务数不相等的指派问题应当视为一个多目标决策问题,首先要求指派给各人的任务数目两两之间相差不能超过1,其次要求所需总时间最少;并且给出了该问题的求解方法。 相似文献
18.
We studied transboundary groundwater management problems in the presence of hydraulic fracturing. We found that the presence of risk suggests there should be caution when considering hydraulic fracturing. Our results from the cooperative solution show a decrease in hydraulic fracturing and increase in the steady state survival rate of groundwater. We also provide a Pigouvian type tax that could be imposed on natural gas developers. 相似文献
19.
20.
We consider a queueing system with two stations served by a single server in a cyclic manner. We assume that at most one customer can be served at a station when the server arrives at the station. The system is subject to service interuption that arises from server breakdown. When a server breakdown occurs, the server must be repaired before service can resume. We obtain the approximate mean delay of customers in the system. 相似文献