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1.
Regularity of the Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities 总被引:2,自引:0,他引:2
Zheng-de DaiDepartment of Mathematics Yunnan University Kunming China 《应用数学学报(英文版)》2002,18(2):263-272
Abstract In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equationgoverning the modulated wave instabilities in E_0 is considered.By a decomposition of solution operator,it isshown that the global attractor in E_0 is actually equal to a global attractor in E_1. 相似文献
2.
Chengming Bai 《代数通讯》2013,41(11):4277-4321
We introduce notions of 𝒪-operators of the Loday algebras including the dendriform algebras and quadri-algebras as a natural generalization of Rota–Baxter operators. The invertible 𝒪-operators give a sufficient and necessary condition on the existence of the 2 n+1 operations on an algebra with the 2 n operations in an associative cluster. The analogues of the classical Yang–Baxter equation in these algebras can be understood as the 𝒪-operators associated to certain dual bimodules. As a byproduct, the constraint conditions (invariances) of nondegenerate bilinear forms on these algebras are given. 相似文献
3.
We construct a natural bijection between the set of admissible pictures and the set of Uq(𝔤𝔩(m, n))–Littlewood–Richardson tableaux. 相似文献
4.
Zhanqiang Bai 《代数通讯》2018,46(9):3689-3710
In this paper, we give a method to compute the Gelfand–Kirillov dimensions of some polynomial–type weight modules. These modules are infinite-dimensional irreducible 𝔬(n,?)-modules and 𝔰𝔭(2n,?)-modules that appeared in the ?-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. We also found that some of these modules have the secondly minimal GK-dimension, and some of them have the larger GK-dimension than the maximal GK-dimension apearing in unitary highest-weight modules. 相似文献
5.
Apoorva Khare 《代数通讯》2013,41(12):4431-4475
This article aims to contribute to the study of algebras with triangular decomposition over a Hopf algebra, as well as the BGG Category 𝒪. We study functorial properties of 𝒪 across various setups. The first setup is over a skew group ring, involving a finite group Γ acting on a regular triangular algebra A. We develop Clifford theory for A?Γ, and obtain results on block decomposition, complete reducibility, and enough projectives. 𝒪 is shown to be a highest weight category when A satisfies one of the “Conditions (S);” the BGG Reciprocity formula is slightly different because the duality functor need not preserve each simple module. Next, we turn to tensor products of such skew group rings; such a product is also a skew group ring. We are thus able to relate four different types of Categories 𝒪; more precisely, we list several conditions, each of which is equivalent in any one setup, to any other setup, and which yield information about 𝒪. 相似文献
6.
ABSTRACT Let X be the surface 𝕋 × 𝕋, where 𝕋 is the complex torus. This article is the third in a series studying the fundamental group of the Galois cover of X with respect to a generic projection onto ??2. Van Kampen Theorem gives a presentation of the fundamental group of the complement of the branch curve, with 54 generators and more than 2000 relations. Here we introduce a certain natural quotient (obtained by identifying pairs of generators), prove it is a quotient of a Coxeter group related to the degeneration of X, and show that this quotient is virtually nilpotent. Communicated by C. Pedrini. 相似文献
7.
Motivated by the identity t (K n+2; 1, –1) = t (K n ; 2, –1), where t(G; x, y) is the Tutte polynomial of a graph G, we search for graphs G having the property that there is a pair of vertices u, v such that t(G; 1, –1) = t(G – {u, v}; 2, –1). Our main result gives a sufficient condition for a graph to have this property; moreover, it describes the graphs for which the property still holds when each vertex is replaced by a clique or a coclique of arbitrary order. In particular, we show that the property holds for the class of threshold graphs, a well-studied class of perfect graphs. 相似文献
8.
《代数通讯》2013,41(5):2043-2052
Abstract Let 𝔤 be a complex semisimple Lie algebra. Let K be an algebraic group acting on the flag variety of 𝔤 with finitely many orbits. We give a geometric interpretation of the coherent continuation on the category of finitely generated (𝔤, K )-modules in terms of the intertwining functors on the category of K-equivariant 𝒟-modules. 相似文献
9.
We prove that if f belongs to the Morrey space
, with λ ∊ [0, n−2], and u is the solution of the problem
then Du belongs to the space
, for any
Mathematics Subject Classification (2000) 35J25, 35D10 相似文献
10.
11.
Joe Gildea 《代数通讯》2013,41(9):3311-3317
The Structure of the Unit Group of the Group Algebra of the group C 3 × D 6 over a finite field of characteristic 3 is established in terms of split extensions of cyclic groups. 相似文献
12.
Seung Jun Chang 《Integral Transforms and Special Functions》2020,31(4):323-338
ABSTRACTIn this paper, we define a transform which has the kernel in its definition and a concept of derivative for functionals on Wiener space. We then establish some results and formulas for the transforms of functionals on Wiener space. We also establish the Cameron–Storvick type theorem for the transform. Finally, we obtain the recurrence formula for the transforms to evaluate formulas involving the multi-dimensional derivative. 相似文献
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15.
V. V. Chugunova 《Mathematical Notes》2011,89(3-4):421-437
We prove that, in the basis {x 1 & x 2 & x 3, x 1 ∨ x 2 ∨ x 3, $ \bar x_1 $ }, for inverse faults at the inputs of functional elements, all Boolean functions f(x 1, x 2, ..., x n ) can be realized by asymptotically optimally reliable circuits operating with unreliability asymptotically (as ? → 0) equal to: ? 3 for the constants 0 and 1, ? for the functions $ \bar x_i $ , and 3? for f(x 1, x 2, ..., x n ) ≠ 0, 1, $ \bar x_i $ , x i , where ? is the error probability at each input of the functional element and i = 1, ..., n. The functions xi, i = 1, ..., n, can be realized absolutely reliably. The complexity of asymptotically optimally reliable circuits is equal in order to the complexity of minimal circuits constructed only from reliable elements. 相似文献
16.
In a previous paper [2] we studied the zeros of hypergeometric polynomials F(−n, b; 2b; z), where b is a real parameter. Making connections with ultraspherical polynomials, we showed that for b > − 1/2 all zeros of F(−n, b; 2b; z) lie on the circle |z − 1| = 1, while for b < 1 − n all zeros are real and greater than 1. Our purpose now is to describe the trajectories of the zeros as b descends below the critical value − 1/2 to 1 − n. The results have counterparts for ultraspherical polynomials and may be said to “explain” the classical formulas of Hilbert
and Klein for the number of zeros of Jacobi polynomials in various intervals of the real axis. These applications and others
are discussed in a further paper [3]. 相似文献
17.
Theodora Bourni 《Journal of Geometric Analysis》2011,21(4):982-1035
In this work we study solutions of the prescribed mean curvature equation over a general domain that do not necessarily attain
the given boundary data. With such a solution we can naturally associate a current with support in the closed cylinder above
the domain and with boundary given by the prescribed boundary data and which inherits a natural minimizing property. Our main
result is that its support is a C
1,α
manifold-with-boundary, with boundary equal to the prescribed boundary data, provided that both the initial domain and the
prescribed boundary data are of class C
1,α
. 相似文献
18.
We prove that the mixed problem for the Klein–Gordon–Fock equation u tt (x, t) ? u xx (x, t) + au(x, t) = 0, where a ≥ 0, in the rectangle Q T = [0 ≤ x ≤ l] × [0 ≤ t ≤ T] with zero initial conditions and with the boundary conditions u(0, t) = μ(t) ∈ L p [0, T ], u(l, t) = 0, has a unique generalized solution u(x, t) in the class L p (Q T ) for p ≥ 1. We construct the solution in explicit analytic form. 相似文献
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20.
Friedrich Sauvigny 《Lithuanian Mathematical Journal》2018,58(3):320-328
When we consider surfaces of prescribed mean curvature H with a one-to-one orthogonal projection onto a plane, we have to study the nonparametric H-surface equation. Now the H-surfaces with a one-to-one central projection onto a plane lead to an interesting elliptic differential equation, which has been discovered for the case H = 0 already by T. Radó in 1932. We establish the uniqueness of the Dirichlet problem for this H-surface equation in central projection and develop an estimate for the maximal deviation of large H-surfaces from their boundary values, resembling an inequality by J. Serrin from 1969.We solve the Dirichlet problem for nonvanishing H with compact support via a nonlinear continuity method. Here we introduce conformal parameters into the surface and study the well-known H-surface system. Then we combine these investigations with a differential equation for its unit normal, which has been developed by the author for variable H in 1982. Furthermore, we construct large H-surfaces bounding extreme contours by an approximation.Here we only provide an overview on the relevant proofs; for the more detailed derivations of our results, we refer the readers to the author’s investigations in the Pacific Journal of Mathematics and the Milan Journal of Mathematics. 相似文献