共查询到20条相似文献,搜索用时 296 毫秒
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We show that the class of all delta-convex selfmappings of R (differences of two convex functions) enjoys the difference property in the sense of N.G. de Bruijn. The Q-differentiability technique has been applied as a proof tool. 相似文献
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We introduce the notion of the (one-parameter subgroup) γ-condition for a map f from a Lie group to its Lie algebra and establish α-theory and γ-theory for Newton’s method for a map f satisfying this condition. Applications to analytic maps are provided, and Smale’s α-theory and γ-theory are extended and developed. Examples arising from initial value problems on Lie group are presented to illustrate applications of our results. 相似文献
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We analyze the MAP/PH/1 vacation system at arbitrary times using the matrix-analytic method, and obtain decomposition results for the R and G matrices. The decomposition results reduce the amount of computational effort needed to obtain these matrices. The results for the G matrix are extended to the BMAP/PH/1 system. We also show that in the case of the Geo/PH/1 and M/PH/1 systems with PH vacations both the G and R matrices can be obtained explicitly. 相似文献
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In this paper, the approximation characteristic of a diagonal matrix in probabilistic and average case settings is investigated. And the asymptotic degree of the probabilistic linear (n,δ)-width and p-average linear n-width of diagonal matrix M are determined. 相似文献
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Starting with a regular symmetric Dirichlet form on a locally compact separable metric space X, our paper studies elements of vector analysis, Lp-spaces of vector fields and related Sobolev spaces. These tools are then employed to obtain existence and uniqueness results for some quasilinear elliptic PDE and SPDE in variational form on X by standard methods. For many of our results locality is not assumed, but most interesting applications involve local regular Dirichlet forms on fractal spaces such as nested fractals and Sierpinski carpets. 相似文献
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We introduce (n+1)-preprojective algebras of algebras of global dimension n. We show that if an algebra is n-representation-finite then its (n+1)-preprojective algebra is self-injective. In this situation, we show that the stable module category of the (n+1)-preprojective algebra is (n+1)-Calabi–Yau, and, more precisely, it is the (n+1)-Amiot cluster category of the stable n-Auslander algebra of the original algebra. In particular this stable category contains an (n+1)-cluster tilting object. We show that even if the (n+1)-preprojective algebra is not self-injective, under certain assumptions (which are always satisfied for n∈{1,2}) the results above still hold for the stable category of Cohen–Macaulay modules. 相似文献
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In this paper, we analyze a real-valued reflected backward stochastic differential equation (RBSDE) with an unbounded obstacle and an unbounded terminal condition when its generator f has quadratic growth in the z-variable. In particular, we obtain existence, uniqueness, and stability results, and consider the optimal stopping for quadratic g-evaluations. As an application of our results we analyze the obstacle problem for semi-linear parabolic PDEs in which the non-linearity appears as the square of the gradient. Finally, we prove a comparison theorem for these obstacle problems when the generator is concave in the z-variable. 相似文献
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A purely topological characterization of relatively compact sets is given for the metric space (K(Y),D) of upper semicontinuous, compact-supported, normal fuzzy subsets of a metric space Y. The considered metric D is that of the distance between fuzzy subsets, which is the supremum of the Hausdorff distances of the corresponding level sets. In the given proof the compactness of a variational convergence which was introduced by De Giorgi and Franzoni is fundamental. 相似文献
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In this paper, we present a new one-step smoothing Newton method proposed for solving the non-linear complementarity problem with P0-function based on a new smoothing NCP-function. We adopt a variant merit function. Our algorithm needs only to solve one linear system of equations and perform one line search per iteration. It shows that any accumulation point of the iteration sequence generated by our algorithm is a solution of P0-NCP. Furthermore, under the assumption that the solution set is non-empty and bounded, we can guarantee at least one accumulation point of the generated sequence. Numerical experiments show the feasibility and efficiency of the algorithm. 相似文献
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By using the generalized Borsuk theorem in coincidence degree theory, some criteria for guaranteeing the existence of ω-periodic solutions for a Rayleigh system of p-Laplacian type are derived. 相似文献
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Let T:D⊂X→X be an iteration function in a complete metric space X. In this paper we present some new general complete convergence theorems for the Picard iteration xn+1=Txn with order of convergence at least r≥1. Each of these theorems contains a priori and a posteriori error estimates as well as some other estimates. A central role in the new theory is played by the notions of a function of initial conditions of T and a convergence function of T. We study the convergence of the Picard iteration associated to T with respect to a function of initial conditions E:D→X. The initial conditions in our convergence results utilize only information at the starting point x0. More precisely, the initial conditions are given in the form E(x0)∈J, where J is an interval on R+ containing 0. The new convergence theory is applied to the Newton iteration in Banach spaces. We establish three complete ω-versions of the famous semilocal Newton–Kantorovich theorem as well as a complete version of the famous semilocal α-theorem of Smale for analytic functions. 相似文献
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In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the ?-constraint method, the Benson method, the hybrid method and the elastic ?-constraint method can be subsumed under these two problems. Then, considering approximate solutions, some relationships between ε-(weakly, properly) efficient points of a general (without any convexity assumption) multiobjective optimization problem and ?-optimal solutions of the introduced scalarized problem are achieved. 相似文献