共查询到20条相似文献,搜索用时 31 毫秒
1.
Eduardo Casas 《Numerical Functional Analysis & Optimization》2013,34(2):117-137
ABSTRACT For a polygonal open bounded subset of ?2, of boundary Γ, we study stability estimates for the projection operator from L 1(Γ) on a convex set K h of continuous piecewise affine functions satisfying bound constraints. We establish stability estimates in L p (Γ) and in W s,p (Γ) for 1 ≤ p ≤ ∞ and 0 < s ≤ 1. This kind of result plays a crucial role in error estimates for the numerical approximation of optimal control problems of partial differential equations with bilateral control constraints. 相似文献
2.
Silvia Montarani 《代数通讯》2013,41(5):1449-1467
Let Γ N : = S N ? Γ N be the wreath product of Γ, a finite subgroup of SL(2,C), by the symmetric group of degree N. In this article we classify all the irreducible representations of S N ? Γ N that can be extended to a representation of the associated symplectic reflection algebra H 1,k,c (Γ N ) (where k is a complex number and c a class function on the nontrivial elements of Γ) for nonzero values of k. 相似文献
3.
4.
Udo Baumgartner James Foster Jacqueline Hicks Helen Lindsay Ben Maloney Iain Raeburn 《代数通讯》2013,41(11):4135-4147
Abstract We describe the Hecke algebra ?(Γ,Γ0) of a Hecke pair (Γ,Γ0) in terms of the Hecke pair (N,Γ0) where N is a normal subgroup of Γ containing Γ0. To do this, we introduce twisted crossed products of unital *-algebras by semigroups. Then, provided a certain semigroup S ? Γ/N satisfies S ?1 S = Γ/N, we show that ? (Γ,Γ0) is the twisted crossed product of ? (N,Γ0) by S. This generalizes a recent theorem of Laca and Larsen about Hecke algebras of semidirect products. 相似文献
5.
Claus Mokler 《代数通讯》2013,41(7):2298-2323
Let (, S) be a Coxeter system. For ?, δ ? {+, ?} we introduce and investigate combinatorially certain partial orders ≤ ?δ, called extended Bruhat orders, on a × -set (N, C), which depends on , a subset N ? S, and a component C ? N. We determine the length of the maximal chains between two elements x, y ? (N, C), x ≤ ?δ y. These posets generalize equipped with its Bruhat order. They include the × -orbits of the Renner monoids of reductive algebraic monoids and of some infinite-dimensional generalizations which are equipped with the partial orders obtained by the closure relations of the Bruhat and Birkhoff cells. They also include the × -orbits of certain posets obtained by generalizing the closure relation of the Bruhat cells of the wonderful compactification. 相似文献
6.
《随机分析与应用》2013,31(4):865-894
Abstract It may happen that there is not a finite maximum order bound for numerical approximations of stochastic processes X = (X t : 0 ≤ t ≤ T) satisfying Stratonovich stochastic differential equations (SDEs) with some commutative structure along an appropriate functional V(t, X t ). This statement can be proven with respect to the concept of mean square convergence under the assumption of “infinite smoothness” of drift a(t, x) and diffusion coefficients b j (t, x) and with finite initial second moments. As a result, we obtain an infinite series expansion of the conditional expectation 𝔼[V(t, X t )|? t N ] on any fixed finite time interval [0, T], provided that the information is collected by discretized σ‐field ? T N = σ{W t 0 , W t 1 , …, W t N?1 , W T } at N + 1 given time instants t i ∈ [0, T] with t 0 ≤ t 1 ≤ ··· ≤ t N?1 ≤ t N = T. 相似文献
7.
ABSTRACT Let R be a commutative ring with nonzero identity and let I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by Γ I (R), is the graph whose vertices are the set {x ? R\I | xy ? I for some y ? R\I} with distinct vertices x and y adjacent if and only if xy ? I. In the case I = 0, Γ0(R), denoted by Γ(R), is the zero-divisor graph which has well known results in the literature. In this article we explore the relationship between Γ I (R) ? Γ J (S) and Γ(R/I) ? Γ(S/J). We also discuss when Γ I (R) is bipartite. Finally we give some results on the subgraphs and the parameters of Γ I (R). 相似文献
8.
We consider an inverse boundary value problem for the heat equation ? t u = div (γ? x u) in (0, T) × Ω, u = f on (0, T) × ?Ω, u| t=0 = u 0, in a bounded domain Ω ? ? n , n ≥ 2, where the heat conductivity γ(t, x) is piecewise constant and the surface of discontinuity depends on time: γ(t, x) = k 2 (x ∈ D(t)), γ(t, x) = 1 (x ∈ Ω?D(t)). Fix a direction e* ∈ 𝕊 n?1 arbitrarily. Assuming that ?D(t) is strictly convex for 0 ≤ t ≤ T, we show that k and sup {e*·x; x ∈ D(t)} (0 ≤ t ≤ T), in particular D(t) itself, are determined from the Dirichlet-to-Neumann map : f → ?ν u(t, x)|(0, T)×?Ω. The knowledge of the initial data u 0 is not used in the proof. If we know min0≤t≤T (sup x∈D(t) x·e*), we have the same conclusion from the local Dirichlet-to-Neumann map. Numerical examples of stationary and moving circles inside the unit disk are shown. The results have applications to nondestructive testing. Consider a physical body consisting of homogeneous material with constant heat conductivity except for a moving inclusion with different conductivity. Then the location and shape of the inclusion can be monitored from temperature and heat flux measurements performed at the boundary of the body. Such a situation appears for example in blast furnaces used in ironmaking. 相似文献
9.
Charef Beddani 《代数通讯》2013,41(11):4671-4678
In this paper, we will show that if (R, 𝔪) is a quasi-unmixed local ring, I an 𝔪-primary ideal of R and ?𝒱(I) is the set of Rees valuations of I, then the number of minimal prime ideals in the 𝔪-adic completion of R equals exactly the number of equivalence classes on the set ?𝒱(I) under the equivalence relation ~defined by: ν1 ~ ν2 if there exist a constant c ≥ 1 such that for all x ∈ R, ν1(x) ≤ cν2(x) and ν2(x) ≤ cν1(x). 相似文献
10.
Let Γ denote a smooth simple curve in ? N , N ≥ 2, possibly with boundary. Let Ω R be the open normal tubular neighborhood of radius 1 of the expanded curve RΓ: = {Rx | x ∈ Γ??Γ}. Consider the superlinear problem ? Δu + λu = f(u) on the domains Ω R , as R → ∞, with homogeneous Dirichlet boundary condition. We prove the existence of multibump solutions with bumps lined up along RΓ with alternating signs. The function f is superlinear at 0 and at ∞, but it is not assumed to be odd. If the boundary of the curve is nonempty our results give examples of contractible domains in which the problem has multiple sign changing solutions. 相似文献
11.
《代数通讯》2013,41(11):5627-5651
12.
Harvey I. Blau 《代数通讯》2017,45(11):4646-4655
We investigate the character values and structures of p-standard table algebras (A,B) with o(B) = pN. If N≤3, then B has a complete normal series. If for every χ∈Irr(B), χ has at most p distinct classes of character values, and if either B has a complete normal series or p = 2, then B is an elementary abelian p-group. 相似文献
13.
Let (S,𝔫) be a 2-dimensional regular local ring and let I = (f, g) be an ideal in S generated by a regular sequence f, g of length two. Let I* be the leading ideal of I in the associated graded ring gr𝔫(S), and set R = S/I and 𝔪 = 𝔫/I. In Goto et al. (2007), we prove that if μ G (I*) = n, then I* contains a homogeneous system {ξ i }1≤i≤n of generators such that deg ξ i + 2 ≤ deg ξ i+1 for 2 ≤ i ≤ n ? 1, and ht G (ξ1, ξ2,…, ξ n?1) = 1, and we describe precisely the Hilbert series H(gr𝔪(R), λ) in terms of the degrees c i of the ξ i and the integers d i , where d i is the degree of D i = GCD(ξ1,…, ξ i ). To the complete intersection ideal I = (f, g)S we associate a positive integer n with 2 ≤ n ≤ c 1 + 1, an ascending sequence of positive integers (c 1, c 2,…, c n ), and a descending sequence of integers (d 1 = c 1, d 2,…, d n = 0) such that c i+1 ? c i > d i?1 ? d i > 0 for each i with 2 ≤ i ≤ n ? 1. We establish here that this necessary condition is also sufficient for there to exist a complete intersection ideal I = (f, g) whose leading ideal has these invariants. We give several examples to illustrate our theorems. 相似文献
14.
《代数通讯》2013,41(3):937-951
ABSTRACT Let k be a field, char k ≠ 2, F = k(x), D a biquaternion division algebra over k, and σ an orthogonal involution on D with nontrivial discriminant. We show that there exists a quadratic form ? ∈ I 2(F) such that dim ? = 8, [C(?)] = [D], and ? does not decompose into a direct sum of two forms similar to two-fold Pfister forms. This implies in particular that the field extension F(D)/F is not excellent. Also we prove that if A is a central simple K-algebra of degree 8 with an orthogonal involution σ, then σ is hyperbolic if and only if σ K(A) is hyperbolic. Finally, let σ be a decomposable orthogonal involution on the algebra M 2 m (K). In the case m ≤ 5 we give another proof of the fact that σ is a Pfister involution. If m ≥ 2 n?2 ? 2 and n ≥ 5, we show that q σ ∈ I n (K), where q σ is a quadratic form corresponding to σ. The last statement is founded on a deep result of Orlov et al. (2000) concerning generic splittings of quadratic forms. 相似文献
15.
Let Φ be a Drinfeld A-module over an A-field K of generic characteristic. We will prove the following two results which are analogous to ones in number fields. Case 1. Φ is of rank one. Suppose that P and Q are two nontorsion points in Φ(K). If for any element a ? A and almost all prime ideals 𝒫 in one has that Φ a (P) ≡ 0 (mod 𝒫) ? Φ a (Q) ≡ 0 (mod 𝒫), then Q = Φ m (P) for some m ? A. Case 2. Φ is of general rank ≥ 1. Let x, y ? Φ(K) be two K-rational points. Denote = End K (Φ) which is commutative and Λ = · y which is a cyclic -module. Let red v :Φ(K) → Φ(k v ) be the reduction map at a place v of K with residue field k v . If red v (x) ? red v (Λ) for almost all places v of K. Then f(x) = g(y), for some nonzero elements f and g in . 相似文献
16.
Jiakuan Lu 《代数通讯》2013,41(10):3726-3732
A subgroup H of a finite group G is called a QTI-subgroup if C G (x) ≤ N G (H) for any 1 ≠ x ∈ H. In this article, the finite groups all of whose second maximal subgroup are QTI-subgroups are classified. 相似文献
17.
We show that if A is a representation-finite selfinjective Artin algebra, then every P ? ? K b(𝒫 A ) with Hom K(Mod?A)(P ?,P ?[i]) = 0 for i ≠ 0 and add(P ?) = add(νP ?) is a direct summand of a tilting complex, and that if A, B are derived equivalent representation-finite selfinjective Artin algebras, then there exists a sequence of selfinjective Artin algebras A = B 0, B 1,…, B m = B such that, for any 0 ≤ i < m, B i+1 is the endomorphism algebra of a tilting complex for B i of length ≤ 1. 相似文献
18.
In this paper we prove a quantitative form of Landis’ conjecture in the plane. Precisely, let W(z) be a measurable real vector-valued function and V(z) ≥0 be a real measurable scalar function, satisfying ‖W‖ L ∞(R 2) ≤ 1 and ‖V‖ L ∞(R 2) ≤ 1. Let u be a real solution of Δu ? ?(Wu) ? Vu = 0 in R 2. Assume that u(0) = 1 and |u(z)| ≤exp (C 0|z|). Then u satisfies inf |z 0| =R sup |z?z 0| <1|u(z)| ≥exp (?CRlog R), where C depends on C 0. In addition to the case of the whole plane, we also establish a quantitative form of Landis’ conjecture defined in an exterior domain. 相似文献
19.
R is any ring with identity. Let Spec r (R) (resp. Max r (R), Prim r (R)) denote the set of all right prime ideals (resp. all maximal right ideals, all right primitive ideals) of R and let U r (eR) = {P ? Spec r (R)| e ? P}. Let = ∪P?Prim r (R) Spec r P (R), where Spec r P (R) = {Q ?Spec r P (R)|P is the largest ideal contained in Q}. A ring is called right quasi-duo if every maximal right ideal is 2-sided. In this article, we study the properties of the weak Zariski topology on and the relationships among various ring-theoretic properties and topological conditions on it. Then the following results are obtained for any ring R: (1) R is right quasi-duo ring if and only if is a space with Zariski topology if and only if, for any Q ? , Q is irreducible as a right ideal in R. (2) For any clopen (i.e., closed and open) set U in ? = Max r (R) ∪ Prim r (R) (resp. = Prim r (R)) there is an element e in R with e 2 ? e ? J(R) such that U = U r (eR) ∩ ? (resp. U = U r (eR) ∩ ), where J(R) is the Jacobson of R. (3) Max r (R) ∪ Prim r (R) is connected if and only if Max l (R) ∪ Prim l (R) is connected if and only if Prim r (R) is connected. 相似文献
20.
André Adler 《随机分析与应用》2013,31(2):339-358
Abstract Consider independent and identically distributed random variables {X nk , 1 ≤ k ≤ m, n ≥ 1} from the Pareto distribution. We randomly select a pair of order statistics from each row, X n(i) and X n(j), where 1 ≤ i < j ≤ m. Then we test to see whether or not Strong and Weak Laws of Large Numbers with nonzero limits for weighted sums of the random variables X n(j)/X n(i) exist where we place a prior distribution on the selection of each of these possible pairs of order statistics. 相似文献