共查询到20条相似文献,搜索用时 93 毫秒
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In this paper, we study the initial-boundary value problem for infinitely degenerate semilinear parabolic equations with logarithmic nonlinearity , where is an infinitely degenerate system of vector fields, and is an infinitely degenerate elliptic operator. Using potential well method, we first prove the invariance of some sets and vacuum isolating of solutions. Then, by the Galerkin method and the logarithmic Sobolev inequality, we obtain the global existence and blow-up at +∞ of solutions with low initial energy or critical initial energy, and we also discuss the asymptotic behavior of the solutions. 相似文献
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Yinghui Wang 《Discrete Mathematics》2019,342(5):1325-1335
We define and study a variant of the Stanley depth which we call total depth for partially ordered sets (posets). This total depth is the most natural variant of Stanley depth from – the poset of nonempty subsets of ordered by inclusion – to any finite poset. In particular, the total depth can be defined for the poset of nonempty submultisets of a multiset ordered by inclusion, which corresponds to a product of chains with the bottom element deleted. We show that the total depth agrees with Stanley depth for but not for such posets in general. We also prove that the total depth of the product of chains with the bottom element deleted is , which generalizes a result of Biró, Howard, Keller, Trotter, and Young (2010). Further, we provide upper and lower bounds for a general multiset and find the total depth for any multiset with at most five distinct elements. In addition, we can determine the total depth for any multiset with distinct elements if we know all the interval partitions of . 相似文献
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We consider the pseudo-Euclidean space , , with coordinates and metric , , where at least one is positive, and also tensors of the form , such that are differentiable functions of x. For such tensors, we use Lie point symmetries to find metrics that solve the Ricci curvature and the Einstein equations. We provide a large class of group-invariant solutions and examples of complete metrics defined globally in . As consequences, for certain functions , we show complete metrics , conformal to the pseudo-Euclidean metric g, whose scalar curvature is . 相似文献
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《Indagationes Mathematicae》2022,33(6):1172-1188
Let be linear recursive sequences of integers with characteristic polynomials respectively. Assume that has a dominating and simple real root , while has a pair of conjugate complex dominating and simple roots . Assume further that and are not roots of unity and . Then there are effectively computable constants such that the inequality holds for all with . We present explicitly. 相似文献
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Ion Grama Ronan Lauvergnat Émile Le Page 《Stochastic Processes and their Applications》2019,129(7):2485-2527
Let be a branching process in a random environment defined by a Markov chain with values in a finite state space . Let be the probability law generated by the trajectories of starting at We study the asymptotic behaviour of the joint survival probability , as in the critical and strongly, intermediate and weakly subcritical cases. 相似文献
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Ryotaro Tanaka 《Journal of Mathematical Analysis and Applications》2022,505(1):125444
A Banach space X is said to be isomorphic to another Y with respect to the structure of Birkhoff-James orthogonality, denoted by , if there exists a (possibly nonlinear) bijection between X and Y that preserves Birkhoff-James orthogonality in both directions. It is shown that if either X or Y is finite dimensional and , and that if . Moreover, if H is a Hilbert space with and , then . In the two-dimensional case, it turns out that , which indicates that nonlinear Birkhoff-James orthogonality preservers between Banach spaces are not necessarily scalar multiples of isometric isomorphisms. 相似文献
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We establish the exponential convergence with respect to the -Wasserstein distance and the total variation for the semigroup corresponding to the stochastic differential equation where is a pure jump Lévy process whose Lévy measure fulfills for some constant , and the drift term satisfies that for any , with some positive constants and positive measurable function . The method is based on the refined basic coupling for Lévy jump processes. As a byproduct, we obtain sufficient conditions for the strong ergodicity of the process . 相似文献
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Kai Wang 《Discrete Mathematics》2019,342(3):888-897
We present formulas to count the set of degree sequences of simple graphs of order , the set of degree sequences of those graphs with no isolated vertices, and the set of degree sequences of those graphs that are -connected for fixed . The formulas all use a function of Barnes and Savage and the associated dynamic programming algorithms all run in time polynomial in and are asymptotically faster than previous known algorithms for these problems. We also show that and are asymptotically equivalent but and as well as and with fixed are asymptotically inequivalent. Finally, we explain why we are unable to obtain the absolute asymptotic orders of these functions from their formulas. 相似文献
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《Discrete Mathematics》2019,342(5):1275-1292
A discrete function of variables is a mapping , where , and are arbitrary finite sets. Function is called separable if there exist functions for , such that for every input the function takes one of the values . Given a discrete function , it is an interesting problem to ask whether is separable or not. Although this seems to be a very basic problem concerning discrete functions, the complexity of recognition of separable discrete functions of variables is known only for . In this paper we will show that a slightly more general recognition problem, when is not fully but only partially defined, is NP-complete for . We will then use this result to show that the recognition of fully defined separable discrete functions is NP-complete for .The general recognition problem contains the above mentioned special case for . This case is well-studied in the context of game theory, where (separable) discrete functions of variables are referred to as (assignable) -person game forms. There is a known sufficient condition for assignability (separability) of two-person game forms (discrete functions of two variables) called (weak) total tightness of a game form. This property can be tested in polynomial time, and can be easily generalized both to higher dimension and to partially defined functions. We will prove in this paper that weak total tightness implies separability for (partially defined) discrete functions of variables for any , thus generalizing the above result known for . Our proof is constructive. Using a graph-based discrete algorithm we show how for a given weakly totally tight (partially defined) discrete function of variables one can construct separating functions in polynomial time with respect to the size of the input function. 相似文献
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Benjamin Schwarz 《Journal of Functional Analysis》2019,276(11):3275-3303
One of the most fundamental operators studied in geometric analysis is the classical Laplace–Beltrami operator. On pseudo-Hermitian manifolds, higher Laplacians are defined for each positive integer m, where coincides with the Laplace–Beltrami operator. Despite their natural definition, these higher Laplacians have not yet been studied in detail. In this paper, we consider the setting of simple pseudo-Hermitian symmetric spaces, i.e., let be a symmetric space for a real simple Lie group G, equipped with a G-invariant complex structure. We show that the higher Laplacians form a set of algebraically independent generators for the algebra of G-invariant differential operators on X, where r denotes the rank of X. For higher rank, this is the first instance of a set of generators for defined explicitly in purely geometric terms, and confirms a conjecture of Engli? and Peetre, originally stated in 1996 for the class of Hermitian symmetric spaces. 相似文献
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《Journal of Pure and Applied Algebra》2023,227(2):107190
Let W be a finite Coxeter group and X a subset of W. The length polynomial is defined by , where ? is the length function on W. If then we call the involution length polynomial of W. In this article we derive expressions for the length polynomial where X is any conjugacy class of involutions, and the involution length polynomial, in any finite Coxeter group W. In particular, these results correct errors in [11] for the involution length polynomials of Coxeter groups of type and . Moreover, we give a counterexample to a unimodality conjecture stated in [11]. 相似文献
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This paper is to derive a new blow-up criterion for the 2D full compressible Navier–Stokes equations without heat conduction in terms of the density and the pressure . More precisely, it indicates that in a bounded domain the strong solution exists globally if the norm for some constant satisfying . The boundary condition is imposed as a Navier-slip boundary one and the initial vacuum is permitted. Our result extends previous one which is stated as . 相似文献
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The tensor product of graphs , and is defined by and Let be the fractional chromatic number of a graph . In this paper, we prove that if one of the three graphs , and is a circular clique, 相似文献