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排序方式: 共有197条查询结果,搜索用时 62 毫秒
61.
The effect of discontinuity in the state variables on optimization problems is investigated on the quasi-one-dimensional Euler equations in the discrete level. A pressure minimization problem and a pressure matching problem are considered. We find that the objective functional can be smooth in the continuous level and yet be non-smooth in the discrete level as a result of the shock crossing grid points. Higher resolution can exacerbate that effect making grid refinement counter productive for the purpose of computing the discrete sensitivities. First and second order sensitivities, as well as the adjoint solution, are computed exactly at the shock and its vicinity and are compared to the continuous solution. It is shown that in the discrete level the first order sensitivities contain a spike at the shock location that converges to a delta function with grid refinement, consistent with the continuous analysis. The numerical Hessian is computed and its consistency with the analytical Hessian is discussed for different flow conditions. It is demonstrated that consistency is not guaranteed for shocked flows. We also study the different terms composing the Hessian and propose some stable approximation to the continuous Hessian. 相似文献
62.
Muhammed Talat Sariaydin Talat Krpinar 《Mathematical Methods in the Applied Sciences》2019,42(16):5154-5158
In this paper, we study the Bäcklund transformations for the adjoint curve in the Euclidean 3‐space. Firstly, it is obtained some essential equations of the Bäcklund transformation. After this, we give a new theorem, the Bäcklund transformations for the adjoint curve in Euclidean 3‐space. 相似文献
63.
This paper is mainly concerned with the solutions to both forward
and backward mean-field stochastic partial differential equation and
the corresponding optimal control problem for mean-field stochastic
partial differential equation. The authors first prove the
continuous dependence theorems of forward and backward mean-field
stochastic partial differential equations and show the existence
and uniqueness of solutions to them. Then they establish necessary
and sufficient optimality conditions of the control problem in the
form of Pontryagin''s maximum principles. To illustrate the
theoretical results, the authors apply stochastic maximum principles
to study the infinite-dimensional linear-quadratic control problem
of mean-field type. Further, an application to a Cauchy problem for
a controlled stochastic linear PDE of mean-field type is studied. 相似文献
64.
《Expositiones Mathematicae》2019,37(2):104-144
This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent orbits. It is intended to build a foundation for more specialized settings in which adjoint orbits feature prominently (ex. hyperkähler geometry, Landau–Ginzburg models, and the theory of symplectic singularities). Also included are a few arguments and observations that, to the author’s knowledge, have not yet appeared in the research literature. 相似文献
65.
Aziz Belmiloudi 《Journal of Mathematical Analysis and Applications》2007,327(1):620-642
This paper considers the bilinear minimax control problem of an important class of parabolic systems with Robin boundary conditions. Such systems are linear on state variables when the control and disturbance are fixed, and linear on the control or disturbance when the state variables are fixed. The objective is to maintain target state variables by taking account the influence of noises in data, while a desired power level and adjustment costs are taken into consideration. Firstly we introduce some classes of bilinear systems and obtain the existence and the uniqueness of the solution, as well as stability under mild assumptions. Afterwards the minimax control problem is formulated. We show the existence of an optimal solution, and we also find necessary optimality conditions. Finally, to illustrate the abstract results, we present two examples of neutron fission systems. 相似文献
66.
Adjoint techniques are a common tool in the numerical treatment of optimal control problems. They are used for efficient evaluations
of the gradient of the objective in gradient-based optimization algorithms. Different adjoint techniques for the optimal control
of Burgers equation with Neumann boundary control are studied. The methods differ in the point in the numerical algorithm
at which the adjoints are incorporated. Discretization methods for the continuous adjoint are discussed and compared with
methods applying the application of the discrete adjoint. At the example of the implicit Euler method and the Crank Nicolson
method it is shown that a discretization for the adjoint problem that is adjoint to the discretized optimal control problem
avoids additional errors in gradient-based optimization algorithms. The approach of discrete adjoints coincides with that
of automatic differentiation tools (AD) which provide exact gradient calculations on the discrete level. 相似文献
67.
《数学物理学报(A辑)》2003,23(1):84
研究周期环境下具时滞的Volterra Lotka捕食 食饵系统,利用持久性理论,积分均值和微分不等式的方法,建立了关于一致持久的
充分必要判别准则。得到新的结果。 相似文献
68.
69.
引入伴随多项式是为了从补图的角度研究色多形式,图的伴随多项式的极小根可用于判定色等价图.β(G)表示图G的伴随多项式的极小根.n表示n个顶点的单圈图的集合.分别确定了具有max{β(G)|G∈Ωn}和min{β(G)|G∈Ωn}的所有单圈图. 相似文献
70.
Robert G. Donnelly 《代数通讯》2013,41(10):3705-3742
We construct n distinct weight bases, which we call extremal bases, for the adjoint representation of each simple Lie algebra 𝔤 of rank n: One construction for each simple root. We explicitly describe actions of the Chevalley generators on the basis elements. We show that these extremal bases are distinguished by their “supporting graphs” in three ways. (In general, the supporting graph of a weight basis for a representation of a semisimple Lie algebra is a directed graph with colored edges that describe the supports of the actions of the Chevalley generators on the elements of the basis.) We show that each extremal basis constructed is essentially the only basis with its supporting graph (i.e., each extremal basis is solitary), and that each supporting graph is a modular lattice. Each extremal basis is shown to be edge-minimizing: Its supporting graph has the minimum number of edges. The extremal bases are shown to be the only edge-minimizing as well as the only modular lattice weight bases (up to scalar multiples) for the adjoint representation of 𝔤. The supporting graph for an extremal basis is shown to be a distributive lattice if and only if the associated simple root corresponds to an end node for a “branchless” simple Lie algebra, i.e., type A, B, C, F, or G. For each extremal basis, basis elements for the Cartan subalgebra are explicitly expressed in terms of the h i Chevalley generators. 相似文献