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951.
Ricardo Almeida 《Applied mathematics and computation》2010,217(3):956-5111
Based on a method introduced by Leitmann [G. Leitmann, A note on absolute extrema of certain integrals, Int. J. Non-Linear Mech. 2 (1967) 55-59], we exhibit exact solutions for some fractional optimization problems of the calculus of variations and optimal control. 相似文献
952.
基于金属纤维烧结结点的几何模型,运用Caputo分数阶微分方程,建立时间分数阶表面扩散模型,使用有限差分法求数值解,实现金属纤维烧结过程的数值模拟.对不同的阶数进行模拟,得到0~1阶烧结过程数值结果及颈长变化规律;在阶数为0.9阶时,模拟初始夹角为0°、30°、60°、90°时的烧结过程.结果表明:阶数等于1时的结果与整数阶扩散模型一致;烧结的初始阶段,整数阶与分数阶模拟的颈半径迅速生长,随着烧结的进行,分数阶模拟的烧结颈长出现局部波动,最后以大于整数阶的增长速率增长;阶数固定时,初始夹角越小,增长速率越大.分数阶表面扩散模型比整数阶表面扩散模型能更好地描述纤维烧结过程中烧结结点的复杂变化. 相似文献
953.
Yulin SONG 《Frontiers of Mathematics in China》2018,13(1):161-172
We consider a real-valued doubly-perturbed stochastic differential equation driven by a subordinated Brownian motion. By using classic Malliavin calculus, we prove that the law of the solution is absolutely continuous with respect to the Lebesgue measure on . 相似文献
954.
The task of designing the geometry of a set of current-carrying coils that produce the magnetic field required to confine a given plasma equilibrium in stellarators is expressed as a minimization principle, namely that the coils minimize a suitably defined error expressed as a surface integral, which is recognized as the quadratic-flux. A penalty on the coil length is included to avoid pathological solutions. A simple expression for how the quadratic-flux and coil length vary as the coil geometry varies is derived, and an expression describing how this varies with variations in the surface geometry is derived. These expressions allow efficient coil-design algorithms to be implemented, and also enable efficient algorithms for varying the shape of the plasma surface in order to simplify the coil geometry, and a numerical illustration of this is given. 相似文献
955.
In chemical reaction process, mathematical modeling of certain experiments lead to Brusselator system of equations. In this article, the dynamical behaviors of reaction Brusselator system with fractional Caputo derivative is studied. Also, Its stability and chaotic attractors of the commensurate fractional dynamical Brussleator system are discussed. The fractional derivative operators are nonlocal and having weak singularity as compare to the classical derivative operators. To find the analytical solutions of fractional dynamical systems is a big challenge, therefore, new techniques are worth demanding to solve such problems. To overcome this difficulty, the optimal homotopy asymptotic method is extended in this study to the system of fractional partial differential equations. A numerical example is presented as well to investigate the convergence, performance, and effectiveness of this method. 相似文献
956.
Numerical simulation of antennae is a topic in computational electromagnetism, which is concerned with the numerical study of Maxwell equations. By discrete exterior calculus and the lattice gauge theory with coefficient R, we obtain the Bianchi identity on prism lattice. By defining an inner product of discrete differential forms, we derive the source equation and continuity equation. Those equations compose the discrete Maxwell equations in vacuum case on discrete manifold, which are implemented on Java development platform to simulate the Gaussian pulse radiation on antennaes. 相似文献
957.
958.
The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium
statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that
relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics
of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics,
but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we
do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics
of the full system 相似文献
959.
H. Idrissi P. Loridan C. Michelot 《Journal of Optimization Theory and Applications》1988,56(1):127-143
This paper is devoted to a class of location problems with polyhedral norms. The objective function is shown to be a piecewise convex function which has to be maximized. We prove that the optimal locations belong to a finite set of intersection points, and we present an efficient method operating upon this finite set and providing a strict local maximum with few computational effort. 相似文献
960.
The constructive functional calculus for a sequence of commuting selfadjoint operators on a separable Hilbert space is shown to be independent of the orthonormal basis used in its construction. The proof requires a constructive criterion for the absolute continuity of two positive measures in terms of test functions. Mathematics Subject Classification: 03F60, 46S30, 47S30. 相似文献