共查询到20条相似文献,搜索用时 31 毫秒
1.
Consider a real-analytic orientable connected complete Riemannian manifold M with boundary of dimension n ≥ 2 and let k be an integer 1 ≤ k ≤ n. In the case when M is compact of dimension n ≥ 3, we show that the manifold and the metric on it can be reconstructed, up to an isometry, from the set of the Cauchy data for harmonic k-forms, given on an open subset of the boundary. This extends a result of [14] when k = 0. In the two-dimensional case, the same conclusion is obtained when considering the set of the Cauchy data for harmonic 1-forms. Under additional assumptions on the curvature of the manifold, we carry out the same program when M is complete non-compact. In the case n ≥ 3, this generalizes the results of [13] when k = 0. In the two-dimensional case, we are able to reconstruct the manifold from the set of the Cauchy data for harmonic 1-forms. 相似文献
2.
Thomas Laurent 《偏微分方程通讯》2013,38(12):1941-1964
The purpose of this work is to develop a satisfactory existence theory for a general class of aggregation equations. An aggregation equation is a non-linear, non-local partial differential equation that is a regularization of a backward diffusion process. The non-locality arises via convolution with a potential. Depending on how regular the potential is, we prove either local or global existence for the solutions. Aggregation equations have been used recently to model the dynamics of populations in which the individuals attract each other (Bodnar and Velazquez, 2005; Holm and Putkaradze, 2005; Mogilner and Edelstein-Keshet, 1999; Morale et al., 2005; Topaz and Bertozzi, 2004; Topaz et al., 2006). 相似文献
3.
Stefania Aqué 《代数通讯》2013,41(4):1405-1416
Let F be a field of characteristic 0 and A = M 2, 1(F) the algebra of 3 × 3 matrices over F endowed with the only non trivial ?2-grading. Aver'yanov in [1] determined a set of generators for the T 2-ideal of graded identities of A. Here we study the identities in variables of homogeneous degree 1 via the representation theory of the symmetric group, and we determine the decomposition of the corresponding character into irreducibles. 相似文献
4.
Let R be a Noetherian ring and let C be a semidualizing R-module. In this paper, we impose various conditions on C to be dualizing. For example, as a generalization of Xu [21, Theorem 3.2], we show that C is dualizing if and only if for an R-module M, the necessary and su?cient condition for M to be C-injective is that πi(𝔭,M) = 0 for all 𝔭∈Spec (R) and all i≠ht (𝔭), where πi is the invariant dual to the Bass numbers defined by Enochs and Xu [8]. 相似文献
5.
Jeremy Marzuola 《偏微分方程通讯》2013,38(5):775-790
In this note, we further develop the methods of Burq and Zworski (2005) to study eigenfunctions for billiards which have rectangular components: these include the Bunimovich billiard, the Sinai billiard, and the recently popular pseudointegrable billiards (Bogomolny et al., 1999). The results are an application of a “black-box” point of view as presented in Burq and Zworski (2004). 相似文献
6.
《代数通讯》2013,41(6):3001-3020
Abstract Let L be a positive definite even lattice and let g ∈ Aut L be a fixed point free automorphism of order 3. We determine the twisted Zhu's algebra A ? (V L ) for the lattice vertex operator algebra V L , where ? is an automorphism of V L induced from g. As a result, we show that the set of all irreducible ?-twisted modules for V L (up to isomorphism) are exactly those constructed by Dong and Lepowsky (1996) and Lepowsky (1985). 相似文献
7.
Julia Porcino 《代数通讯》2015,43(1):84-101
We analyze the structure of ideals generated by some classes of 2 × 2 permanents of hypermatrices, generalizing [9] on 2 × 2 permanental ideals of generic matrices. We compare the obtained structure to that of the corresponding determinantal ideals in [11]: as expected, the permanental ideals have many more (minimal) components. In the last two sections, we examine a few related classes of permanental ideals. 相似文献
8.
Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this paper, we introduce and study Gorenstein coresolving categories, which unify the following notions: Gorenstein injective modules [8], Gorenstein FP-injective modules [20], Gorenstein AC-injective modules [3], and so on. Then we define a resolution dimension relative to the Gorenstein coresolving category 𝒢?𝒳(𝒜). We investigate the properties of the homological dimension and unify some important properties possessed by some known homological dimensions. In addition, we study stability of the Gorenstein coresolving category 𝒢?𝒳(𝒜) and apply the obtained properties to special subcategories and in particular to module categories. 相似文献
9.
We investigate the long-time behavior of solutions to the classical mean-field model for coarsening by Lifshitz–Slyozov and Wagner (LSW). In the original work (Lifshitz and Slyozov, 1961; Wagner 1961) convergence of solutions to a uniquely determined self-similar solution was predicted. However, it is by now well known (Giron et al., 1998; Niethammer and Pego 1999 2001) that the long-time behavior of solutions depends sensitively on the initial data. In Niethammer and Pego (1999 2001) a necessary criterion for convergence to any self-similar solution which behaves like a finite power at the end of its (compact) support is given. It says that the data have to be regularly varying at the end of their support with the same power. This criterion is also shown to be sufficient if the power is sufficiently small and for data which are close to self-similar. In this article we extend the local stability result to the whole range of self-similar solutions with compact support. Our first main result establishes global stability of self-similar solutions with not too large power. The proof relies on a global contraction argument for the spreading of characteristics. In addition, we also establish upper and lower bounds for the coarsening rates of the system for a suitable class of initial data whose variation is bounded at the end of the support but not necessarily regular. 相似文献
10.
Melissa Tacy 《偏微分方程通讯》2013,38(8):1538-1562
Let P = P(h) be a semiclassical pseudodifferential operator on a Riemannian manifold M. Suppose that u(h) is a localized, L 2 normalized family of functions such that P(h)u(h) is O(h) in L 2, as h → 0. Then, for any submanifold Y ? M, we obtain estimates on the L p norm of u(h) restricted to Y, with exponents that are sharp for h → 0. These results generalize those of Burq et al. [4] on L p norms for restriction of Laplacian eigenfunctions. As part of the technical development we prove some extensions of the abstract Strichartz estimates of Keel and Tao [8]. 相似文献
11.
This paper is a continuation of [9], where short range perturbations of the flat Euclidian metric where considered. Here, we generalize the results of [9] to long-range perturbations (in particular, we can allow potentials growing like ?x?2?? at infinity). More precisely, we construct a modified quantum free evolution G 0(?s, hD z ) acting on Sjöstrand's spaces, and we characterize the analytic wave front set of the solution e ?itH u 0 of the Schrödinger equation, in terms of the semiclassical exponential decay of G 0(?th ?1, hD z )T u 0, where T stands for the Bargmann-transform. The result is valid for t < 0 near the forward non trapping points, and for t > 0 near the backward non trapping points. It is an extension of [12] to the analytic framework. 相似文献
12.
Viktoriya Ozornova 《代数通讯》2017,45(4):1760-1784
A recent theorem of Dobrinskaya [20] states that the K(π,1)-conjecture holds for an Artin group G if and only if the canonical map BM→BG is a homotopy equivalence, where M denotes the Artin monoid associated to G. The aim of this paper is to give an alternative proof by means of discrete Morse theory and abstract homotopy theory. Moreover, we exhibit a new model for the classifying space of an Artin monoid, in the spirit of [13], and a small chain complex for computing its monoid homology, similar to the one of [44]. 相似文献
13.
In [4] anisotropic inverse problems were considered in certain admissible geometries, that is, on compact Riemannian manifolds with boundary which are conformally embedded in a product of the Euclidean line and a simple manifold. In particular, it was proved that a bounded smooth potential in a Schrödinger equation was uniquely determined by the Dirichlet-to-Neumann map in dimensions n ≥ 3. In this article we extend this result to the case of unbounded potentials, namely those in L n/2. In the process, we derive L p Carleman estimates with limiting Carleman weights similar to the Euclidean estimates of Jerison and Kenig [8] and Kenig et al. [9]. 相似文献
14.
Marjan Sheibani Abdolyousefi 《代数通讯》2017,45(5):1983-1995
A commutative ring R is J-stable provided that R∕aR has stable range 1 for all a?J(R). A commutative ring R in which every finitely generated ideal principal is called a Bézout ring. A ring R is an elementary divisor ring provided that every matrix over R admits a diagonal reduction. We prove that a J-stable ring is a Bézout ring if and only if it is an elementary divisor ring. Further, we prove that every J-stable ring is strongly completable. Various types of J-stable rings are provided. Many known results are thereby generalized to much wider class of rings, e.g. [3, Theorem 8], [4, Theorem 4.1], [7, Theorem 3.7], [8, Theorem], [9, Theorem 2.1], [14, Theorem 1] and [18, Theorem 7]. 相似文献
15.
Dikran Dikranjan 《代数通讯》2015,43(1):212-224
Using the nice properties of the w-divisible weight and the w-divisible groups, we prove a factorization theorem for compact abelian groups K; namely, K = K tor × K d , where K tor is a bounded torsion compact abelian group and K d is a w-divisible compact abelian group. By Pontryagin duality this result is equivalent to the same factorization for discrete abelian groups proved in [9]. 相似文献
16.
We study the long time behavior of solutions of the Cauchy problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator in ? N . The long time behavior in the main results is stated with help of the corresponding to ergodic problem, which complements, in the case of unbounded domains, the recent developments on long time behaviors of solutions of (viscous) Hamilton–Jacobi equations due to Namah (1996), Namah and Roquejoffre (1999), Roquejoffre (1998), Fathi (1998), Barles and Souganidis (2000 2001). We also establish existence and uniqueness results for solutions of the Cauchy problem and ergodic problem for semilinear parabolic equations with the Ornstein–Uhlenbeck operator. 相似文献
17.
Nicholas D. Alikakos 《偏微分方程通讯》2013,38(12):2093-2115
Recently, Giorgio Fusco and the author in [2] studied the system Δu ? W u (u) = 0 for a class of potentials that possess several global minima and are invariant under a general finite reflection group, and established existence of equivariant solutions connecting the minima in certain directions at infinity, together with an estimate. In this paper a new proof is given which, in particular, avoids both the introduction of a pointwise constraint in the minimization process and the equivariant extensions of the various test functions. 相似文献
18.
《Numerical Functional Analysis & Optimization》2013,34(7-8):941-952
We extend the results of Pollard [7] and give asymptotic estimates for the norm of the Fourier-Jacobi projection operator in the appropriate weighted Lp space. 相似文献
19.
Dewen Xiong 《随机分析与应用》2013,31(5):793-819
We construct a market of bonds with jumps driven by a general marked point process as well as by a ? n -valued Wiener process based on Björk et al. [6], in which there exists at least one equivalent martingale measure Q 0. Then we consider the mean-variance hedging of a contingent claim H ∈ L 2(? T 0 ) based on the self-financing portfolio based on the given maturities T 1,…, T n with T 0 < T 1 < … <T n ≤ T*. We introduce the concept of variance-optimal martingale (VOM) and describe the VOM by a backward semimartingale equation (BSE). By making use of the concept of ?*-martingales introduced by Choulli et al. [8], we obtain another BSE which has a unique solution. We derive an explicit solution of the optimal strategy and the optimal cost of the mean-variance hedging by the solutions of these two BSEs. 相似文献
20.
《代数通讯》2013,41(9):3179-3193
ABSTRACT If X and Y are sets, we let P(X, Y ) denote the set of all partial transformations from X into Y (that is, all mappings whose domain and range are subsets of X and Y, respectively). We define an operation * on P(X, Y ) by choosing θ ∈ P(Y, X) and writing: α*β = α °θ°β, for each α, β ∈ P(X, Y ). Then (P(X, Y ), *) is a semigroup, and some authors have determined when this is regular (Magill and Subbiah, 1975), when it contains a “proper dense subsemigroup” (Wasanawichit and Kemprasit, 2002) and when it is factorisable (Saengsura, 2001). In this paper, we extend the latter work to certain subsemigroups of (P(X, Y ), *). We also consider the corresponding idea for partial linear transformations from one vector space into another. In this way, we generalise known results for total transformations and for injective partial transformations between sets, and we establish new results for linear transformations between vector spaces. 相似文献