共查询到20条相似文献,搜索用时 15 毫秒
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《随机分析与应用》2013,31(6):1421-1486
Abstract In this article we investigate a class of non-autonomous, semilinear, parabolic systems of stochastic partial differential equations defined on a smooth, bounded domain 𝒪 ? ? n and driven by an infinite-dimensional noise defined from an L 2(𝒪)-valued Wiener process; in the general case the noise can be colored relative to the space variable and white relative to the time variable. We first prove the existence and the uniqueness of a solution under very general hypotheses, and then establish the existence of invariant sets along with the validity of comparison principles under more restrictive conditions; the main ingredients in the proofs of these results consist of a new proposition concerning Wong–Zakaï approximations and of the adaptation of the theory of invariant sets developed for deterministic systems. We also illustrate our results by means of several examples such as certain stochastic systems of Lotka–Volterra and Landau–Ginzburg equations that fall naturally within the scope of our theory. 相似文献
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《代数通讯》2013,41(5):2327-2355
Abstract Let 𝒜 and ? be two Grothendieck categories, R : 𝒜 → ?, L : ? → 𝒜 a pair of adjoint functors, S ∈ ? a generator, and U = L(S). U defines a hereditary torsion class in 𝒜, which is carried by L, under suitable hypotheses, into a hereditary torsion class in ?. We investigate necessary and sufficient conditions which assure that the functors R and L induce equivalences between the quotient categories of 𝒜 and ? modulo these torsion classes. Applications to generalized module categories, rings with local units and group graded rings are also given here. 相似文献
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Let E/F be a Galois extension of number fields with the quaternion Galois group Q 8. In this paper, we prove some relations connecting orders of the odd part of the kernel of the transfer map of the tame kernel of E with the same orders of some of its subfields. Let E/? be a Galois extension of number fields with the Galois group Q 8 and p an odd prime such that p ≡ 3 (mod 4). We prove that if there is at most one quadratic subfield such that the p-Sylow subgroup of the tame kernel is nontrivial, then p r -rank(K 2(E/K)) is even, i.e., 2|p r -rank(K 2(𝒪 E )) ? p r -rank(K 2(𝒪 K )), where K is the quartic subfield of E. 相似文献
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《代数通讯》2013,41(7):2723-2732
Abstract Let L be a line bundle on a smooth curve C, which defines a birational morphism onto Φ(C) ? P r . We prove that, under suitable assumptions on L, which are satisfied by Castelnuovo's curves, a generic section in H 0(C, L 2) can be written as α2 + β2 + γ2, with α, β, γ ∈ H 0(C, L). If there are no quadrics of rank 3 containing Φ(C), this is true for any section. For canonical curves, this gives a non linear version of Noether's Theorem. 相似文献
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Ximei Yang Yinkui Zhang Hongwei Liu Peiping Shen 《Numerical Functional Analysis & Optimization》2016,37(4):499-519
In this article, we propose a new second-order infeasible primal-dual path-following algorithm for symmetric cone optimization. The algorithm further improves the complexity bound of a wide infeasible primal-dual path-following algorithm. The theory of Euclidean Jordan algebras is used to carry out our analysis. The convergence is shown for a commutative class of search directions. In particular, the complexity bound is 𝒪(r5/4log ??1) for the Nesterov-Todd direction, and 𝒪(r7/4log ??1) for the xs and sx directions, where r is the rank of the associated Euclidean Jordan algebra and ? is the required precision. If the starting point is strictly feasible, then the corresponding bounds can be reduced by a factor of r3/4. Some preliminary numerical results are provided as well. 相似文献
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Georgi Vodev 《偏微分方程通讯》2013,38(11):1709-1733
We prove dispersive estimates for solutions to the wave equation with a real-valued potential V ∈ L ∞(R n ), n ≥ 4, satisfying V(x) = O(?x??(n+1)/2?ε), ε > 0. 相似文献
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Pao-Liu Chow 《随机分析与应用》2013,31(3):543-551
This article is concerned with explosive solutions of the initial-boundary problem for a class of nonlinear stochastic wave equations in a domain 𝒟 ? ? d . Under appropriate conditions on the initial data, the nonlinear term and the noise intensity, it is proved in Theorem 3.4 that there cannot exist a global solution and the local solution will blow up at a finite time in the mean L p ? norm for p ≥ 1. An example is given to show the application of this theorem. 相似文献
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Karen E. Smith 《代数通讯》2013,41(12):5915-5929
Abstract For a canonical threefold X, we know that h 0(X, 𝒪 X (nK X )) ≥ 1 for a sufficiently large n. When χ(𝒪 X ) > 0, it is not easy to get such an integer n. Fletcher showed that h 0(X, 𝒪 X (12K X )) ≥ 1 and h 0(X, 𝒪 X (24K X )) ≥ 2 when χ(𝒪 X ) = 1. He inquired about existence of a canonical threefold with given conditions which shows the result sharp. We show that such an example does not exist. Using a different technique, we prove h 0(X, 𝒪 X (12K X )) ≥ 2. 相似文献
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Vladimir Maz'ya 《偏微分方程通讯》2013,38(2):191-207
We consider weak solutions of an elliptic equation of the form ? i ? i (a ij u) = 0 and their asymptotic properties at an interior point. We assume that the coefficients are bounded, measurable, complex-valued functions that stabilize as x → 0 in that the norm of the matrix (a ij (x) ? δ ij ) on the annulus B 2r \ B r is bounded by a function Ω(r), where Ω2(r) satisfies the Dini condition at r = 0, as well as some technical monotonicity conditions; under these assumptions, solutions need not be continuous. Our main result is an explicit formula for the leading asymptotic term for solutions with at most a mild singularity at x = 0. As a consequence, we obtain upper and lower estimates for the L p -norm of solutions, as well as necessary and sufficient conditions for solutions to be bounded or tend to zero in L p -mean as r → 0. 相似文献
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We propose an infeasible Mehrotra-type predictor-corrector algorithm with a new center parameter updating scheme for Cartesian P *(κ)-linear complementarity problem over symmetric cones. Based on the Nesterov-Todd direction, we show that the iteration-complexity bound of the proposed algorithm is 𝒪((1 + κ)3 r 2log ε?1), where r is the rank of the associated Euclidean Jordan algebras and κ is the handicap of the problem and ε > 0 is the required precision. Some numerical results are reported as well. 相似文献
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Frank Loose 《代数通讯》2013,41(7):2395-2416
Abstract A ring R is called left P-injective if for every a ∈ R, aR = r(l(a)) where l( ? ) and r( ? ) denote left and right annihilators respectively. The ring R is called left GP-injective if for any 0 ≠ a ∈ R, there exists n > 0 such that a n ≠ 0 and a n R = r(l(a n )). As a response to an open question on GP -injective rings, an example of a left GP-injective ring which is not left P-injective is given. It is also proved here that a ring R is left FP -injective if and only if every matrix ring 𝕄 n (R) is left GP-injective. 相似文献
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Garrett Johnson 《代数通讯》2013,41(3):1018-1032
We express the double affine Hecke algebra ? associated to the general linear group GL2(k) (here, k is a field with char(k) ≠ 2) as an amalgamated free product of quadratic extensions over the three-dimensional quantum torus 𝒪q((k×)3). With an eye towards proving ring-theoretic results pertaining to ?, a general treatment of amalgamated products of Ore and quadratic extensions is given. We prove an analogue of the Hilbert Basis Theorem for an amalgamated product Q of quadratic extensions and determine conditions for when the one-sided ideals of Q are principal or doubly-generated. Furthermore, we determine sufficient conditions which imply Q is a principal ideal ring. Finally, we construct an explicit isomorphism from ? to the amalgamated free product ring of quadratic extensions over 𝒪q((k×)3), a ring known to be noetherian. Therefore, it follows that ? is noetherian. 相似文献
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Hans Christianson 《偏微分方程通讯》2015,40(4):629-651
We consider quasimodes on planar domains with a partially rectangular boundary. We prove that for any ε0 > 0, an 𝒪(λ?ε0 ) quasimode must have L 2 mass in the “wings” (in phase space) bounded below by λ?2?δ for any δ > 0. The proof uses the author's recent work on 0-Gevrey smooth domains to approximate quasimodes on C 1, 1 domains. There is an improvement for C k, α and C ∞ domains. 相似文献
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《代数通讯》2013,41(5):2381-2401
Abstract Let 𝒪 be a discrete valuation ring whose residue field 𝒪/𝔭 is finite and has odd characteristic. Let l be a positive integer. Set R = 𝒪/𝔭 l and let R = R[θ] be the ring obtained by adjoining to R a square root of a non-square unit. Consider the involution σ of R that fixes R elementwise and sends θ to ? θ. Let V be a free R-module of rank n > 0 endowed with a non-degenerate hermitian form ( , ) relative to σ. Let U n (R) be the subgroup of GL(V) that preserves ( , ). Let SU n (R) be the subgroup of all g ∈ U n (R) whose determinant is equal to one. Let Ψ be the Weil character of U n (R). All irreducible constituents of Ψ are determined. An explicit character formula is given for each of them. In particular, all character degrees are computed. For n > 2 the corresponding results are also obtained for the restriction of Ψ to SU n (R). 相似文献
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Pierre‐Étienne Druet 《Mathematical Methods in the Applied Sciences》2009,32(2):135-166
Accurate modelling of heat transfer in high‐temperature situations requires accounting for the effect of heat radiation. In complex industrial applications involving dissipative heating, we hardly can expect from the mathematical theory that the heat sources will be in a better space than L1. In this paper, we focus on a stationary heat equation with nonlocal boundary conditions and Lp right‐hand side, with p?1 being arbitrary. Thanks to new coercivity results, we are able to produce energy estimates that involve only the Lp norm of the heat sources and to prove the existence of weak solutions. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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《代数通讯》2013,41(5):2095-2140
Abstract We construct an associative algebra A k and show that there is a representation of A k on V ?k , where V is the natural 2n-dimensional representation of the Lie superalgebra 𝔭(n). We prove that A k is the full centralizer of 𝔭(n) on V ?k , thereby obtaining a “Schur-Weyl duality” for the Lie superalgebra 𝔭(n). This result is used to understand the representation theory of the Lie superalgebra 𝔭(n). In particular, using A k we decompose the tensor space V ?k , for k = 2 or 3, and show that V ?k is not completely reducible for any k ≥ 2. 相似文献