排序方式: 共有37条查询结果,搜索用时 15 毫秒
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《Indagationes Mathematicae》2022,33(4):801-815
We consider the irreducibility of polynomial where is a negative integer. We observe that the constant term of vanishes if and only if . Therefore we assume that where is a non-negative integer. Let and more general polynomial, let where with are integers such that . Schur was the first to prove the irreducibility of for . It has been proved that is irreducible for . In this paper, by a different method, we prove: Apart from finitely many explicitly given possibilities, either is irreducible or is linear factor times irreducible polynomial. This is a consequence of the estimate whenever has a factor of degree and . This sharpens earlier estimates of Shorey and Tijdeman and Nair and Shorey. 相似文献
2.
Armen Shirikyan 《Journal of Functional Analysis》2007,249(2):284-306
The paper is devoted to studying the distribution of stationary solutions for 3D Navier-Stokes equations perturbed by a random force. Under a non-degeneracy assumption, we show that the support of such a distribution coincides with the entire phase space, and its finite-dimensional projections are minorised by a measure possessing an almost surely positive smooth density with respect to the Lebesgue measure. Similar assertions are true for weak solutions of the Cauchy problem with a regular initial function. The results of this paper were announced in the short note [A. Shirikyan, Controllability of three-dimensional Navier-Stokes equations and applications, in: Sémin. Équ. Dériv. Partielles, 2005-2006, École Polytech., Palaiseau, 2006]. 相似文献
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In this paper, we present an alternative method to compute the eigenvalue of an irreducible (max,+)-system. The method resembles the well-known simplex method in linear programming in the sense that the eigenvalue and a corresponding eigenvector are obtained by going along the boundary of a polygon-like set, while increasing the number of equalities in some (max,+)-algebraic eigenvalue–eigenvector expression, until only equalities are left over. The latter is unlike the normal linear programming approach where, going along the boundary of a polygon-like set, a linear functional is optimized. 相似文献
5.
By proving an L2-gradient estimate for the corresponding Galerkin approximations, the log-Harnack inequality is established for the semigroup associated to a class of stochastic Burgers equations. As applications, we derive the strong Feller property of the semigroup, the irreducibility of the solution, the entropy-cost inequality for the adjoint semigroup, and entropy upper bounds of the transition density. 相似文献
6.
Damjana Kokol Bukovšek 《Linear algebra and its applications》2007,420(1):34-50
We study non-degenerate irreducible homomorphisms from the multiplicative semigroup of all n-by-n matrices over an algebraically closed field of characteristic zero to the semigroup of m-by-m matrices over the same field. We prove that every non-degenerate homomorphism from the multiplicative semigroup of all n-by-n matrices to the semigroup of (n + 1)-by-(n + 1) matrices when n ? 3 is reducible and that every non-degenerate homomorphism from the multiplicative semigroup of all 3-by-3 matrices to the semigroup of 5-by-5 matrices is reducible. 相似文献
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Lucian Beznea Iulian Cîmpean Michael Röckner 《Stochastic Processes and their Applications》2018,128(4):1405-1437
We analyze the transience, recurrence, and irreducibility properties of general sub-Markovian resolvents of kernels and their duals, with respect to a fixed sub-invariant measure . We give a unifying characterization of the invariant functions, revealing the fact that an -integrable function is harmonic if and only if it is harmonic with respect to the weak dual resolvent. Our approach is based on potential theoretical techniques for resolvents in weak duality. We prove the equivalence between the -irreducible recurrence of the resolvent and the extremality of in the set of all invariant measures, and we apply this result to the extremality of Gibbs states. We also show that our results can be applied to non-symmetric Dirichlet forms, in general and in concrete situations. A second application is the extension of the so called Fukushima ergodic theorem for symmetric Dirichlet forms to the case of sub-Markovian resolvents of kernels. 相似文献
8.
Abdessamad Belhadef 《代数通讯》2013,41(10):3750-3758
Dans cette note, nous établissons le lien entre le nombre de facteurs absolument irréductibles d'un polynôme et la dimension d'un espace vectoriel de formes différentielles fermées. Notre résultat généralise un théorème de Gao. In this note, we establish the relationship between the number of absolutely irreducible factors of a polynomial and the dimension of a space of closed differentials forms. Our result generalizes a theorem of Gao. 相似文献
9.
The p-Laplace equation with random perturbation is studied for the singular case 1<p2 in this paper. Some properties of the invariant measure and transition semigroups are obtained. The main tool is the dimension-free Harnack inequality, which is established by using the coupling argument. As consequences, some ergodicity, compactness and contractive properties are derived for the associated transition semigroups. The main results are applied to stochastic reaction–diffusion equations and the stochastic p-Laplace equation in Hilbert space. 相似文献
10.
李应求 《数学物理学报(A辑)》2007,27(2):269-276
借鉴确定环境中马氏链暂留性的定义,在随机环境中马氏链的研究领域,引入了各种暂留性的概念,在确定环境中这些暂留性是等价的,而在随机环境中它们不等价.讨论了各类暂留性之间的相互关系及其基本性质,给出了链和状态是暂留的一些判别准则. 相似文献