共查询到20条相似文献,搜索用时 437 毫秒
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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 generalize classical Lq, q≥p, estimates of the gradient to the Orlicz space for weak solutions of quasilinear elliptic equations of p-Laplacian type. 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, 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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For a Tychonoff space X , we denote by Cp(X) and Cc(X) the space of continuous real-valued functions on X equipped with the topology of pointwise convergence and the compact-open topology respectively. Providing a characterization of the Lindelöf Σ-property of X in terms of Cp(X), we extend Okunev?s results by showing that if there exists a surjection from Cp(X) onto Cp(Y) (resp. from Lp(X) onto Lp(Y)) that takes bounded sequences to bounded sequences, then υY is a Lindelöf Σ-space (respectively K-analytic) if υX has this property. In the second part, applying Christensen?s theorem, we extend Pelant?s result by proving that if X is a separable completely metrizable space and Y is first countable, and there is a quotient linear map from Cc(X) onto Cc(Y), then Y is a separable completely metrizable space. We study also a non-separable case, and consider a different approach to the result of J. Baars, J. de Groot, J. Pelant and V. Valov, which is based on the combination of two facts: Complete metrizability is preserved by ?p-equivalence in the class of metric spaces (J. Baars, J. de Groot, J. Pelant). If X is completely metrizable and ?p-equivalent to a first-countable Y, then Y is metrizable (V. Valov). Some additional results are presented. 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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Let η be a non-zero scalar. In this paper, we investigate a bijective map ? between two von Neumann algebras, one of which has no central abelian projections, satisfying ?(AB+ηBA∗)=?(A)?(B)+η?(B)?(A)∗ for all A,B in the domain. It is showed that ? is a linear *-isomorphism if η is not real and ? is a sum of a linear *-isomorphism and a conjugate linear *-isomorphism if η is real. 相似文献
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In this paper, a new monotonicity, M-monotonicity, is introduced, and the resolvent operator of an M-monotone operator is proved to be single valued and Lipschitz continuous. With the help of the resolvent operator, an equivalence between the variational inequality VI(C,F+G) and the fixed point problem of a nonexpansive mapping is established. A proximal point algorithm is constructed to solve the fixed point problem, which is proved to have a global convergence under the condition that F in the VI problem is strongly monotone and Lipschitz continuous. Furthermore, a convergent path Newton method, which is based on the assumption that the projection mapping ∏C(⋅) is semismooth, is given for calculating ε-solutions to the sequence of fixed point problems, enabling the proximal point algorithm to be implementable. 相似文献
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This paper introduces a notion of regularity of t=-∞ for the diffusion (or heat) equation and establishes a necessary and sufficient condition for the existence of a unique bounded solution to the first boundary value problem for the diffusion equation in a general domain Ω⊂RN+1 which extends up to t=-∞. 相似文献
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We conjecture that the balanced complete bipartite graph K⌊n/2⌋,⌈n/2⌉ contains more cycles than any other n-vertex triangle-free graph, and we make some progress toward proving this. We give equivalent conditions for cycle-maximal triangle-free graphs; show bounds on the numbers of cycles in graphs depending on numbers of vertices and edges, girth, and homomorphisms to small fixed graphs; and use the bounds to show that among regular graphs, the conjecture holds. We also consider graphs that are close to being regular, with the minimum and maximum degrees differing by at most a positive integer k. For k=1, we show that any such counterexamples have n≤91 and are not homomorphic to C5; and for any fixed k there exists a finite upper bound on the number of vertices in a counterexample. Finally, we describe an algorithm for efficiently computing the matrix permanent (a #P-complete problem in general) in a special case used by our bounds. 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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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