共查询到20条相似文献,搜索用时 31 毫秒
1.
Let F q be a finite field of cardinality q, l and m be positive integers and M l (F q ) the F q -algebra of all l × l matrices over F q . We investigate the relationship between monic factors of X m ? 1 in the polynomial ring M l (F q )[X] and quasi-cyclic (QC) codes of length lm and index l over F q . Then we consider the idea of constructing QC codes from monic factors of X m ? 1 in polynomial rings over F q -subalgebras of M l (F q ). This idea includes ideas of constructing QC codes of length lm and index l over F q from cyclic codes of length m over a finite field F q l, the finite chain ring F q + uF q + · · · + u l ? 1 F q (u l = 0) and other type of finite chain rings. 相似文献
2.
Stefan Samko 《Mediterranean Journal of Mathematics》2013,10(4):2007-2025
We introduce a new type of variable exponent function spaces ? p(·),q(·),α(·)( ${\mathbb{R}^n}$ ) and H p(·),q(·),α(·)( ${\mathbb{R}^n}$ ) of Herz type, homogeneous and non-homogeneous versions, where all the three parameters are variable, and give comparison of continual and discrete approaches to their definition. Under the only assumption that the exponents p, q and α are subject to the log-decay condition at infinity, we prove that sublinear operators, satisfying the size condition known for singular integrals and bounded in L p(·)( ${\mathbb{R}^n}$ ), are also bounded in the nonhomogeneous version of the introduced spaces, which includes the case maximal and Calderón-Zygmund singular operators. 相似文献
3.
Ronglu Li 《Topology and its Applications》2007,154(6):1195-1205
For classical Banach sequence spaces c0(X), l∞(X) and lp(X) (0<p<+∞) we have found the strongest intrinsical meanings of their β-duals, and two basic convergence results are established in the β-duals. 相似文献
4.
A. A. Bondarenko 《Mathematical Notes》2009,85(5-6):638-646
Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n, respectively, over K, char K ≠ 2. The problem of birational composition of f(X) and g(Y) is considered: When is the product f(X) · g(Y) birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The solution of the birational composition problem for anisotropic quadratic forms over K in the case of m = n = 2 is given. The main result of the paper is the complete solution of the birational composition problem for forms f(X) and g(Y) over a local field P, char P ≠ 2. 相似文献
5.
6.
We study minimal immersions of closed surfaces (of genus g ≥ 2) in hyperbolic three-manifolds, with prescribed data (σ, t α), where σ is a conformal structure on a topological surface S, and α dz 2 is a holomorphic quadratic differential on the surface (S, σ). We show that, for each ${t \in (0,\tau_0)}$ for some τ 0 > 0, depending only on (σ, α), there are at least two minimal immersions of closed surface of prescribed second fundamental form Re(t α) in the conformal structure σ. Moreover, for t sufficiently large, there exists no such minimal immersion. Asymptotically, as t → 0, the principal curvatures of one minimal immersion tend to zero, while the intrinsic curvatures of the other blow up in magnitude. 相似文献
7.
D. Shanks [11] has given a heuristical argument for the fact that there are “more” primes in the non-quadratic residue classes modq than in the quadratic ones. In this paper we confirmShanks' conjecture in all casesq<25 in the following sense. Ifl 1 is a quadratic residue,l 2 a non-residue modq, ε(n, q, l 1,l 2) takes the values +1 or ?1 according ton?l 1 orl 2 modq, then $$\mathop {\lim }\limits_{x \to \infty } \sum\limits_p {\varepsilon (p,q,l_1 ,l_2 )} \log pp^{ - \alpha } \exp ( - (\log p)^2 /x) = - \infty$$ for 0≤α<1/2. In the general case the same holds, if all zeros ?=β+yγ of allL(s, χ modq),q fix, satisfy the inequality β2?γ2<1/4. 相似文献
8.
Suppose that (X 0, X 1) is a Banach couple, X 0 ∩ X 1 is dense in X 0 and X 1, (X0,X1)θq (0 < θ < 1, 1 ≤ q < ∞) are the spaces of the real interpolation method, ψ ∈ (X 0 ∩ X 1), ψ ≠ 0, is a linear functional, N = Ker ψ, and N i stands for N with the norm inherited from X i (i = 0, 1). The following theorem is proved: the norms of the spaces (N0,N1)θ,q and (X0,X1)θ,q are equivalent on N if and only if θ ? (0, α) ∪ (β∞, α0 ∪ (β0, α∞) ∪ (β, 1), where α, β, α0, β0, α∞, and β ∞ are the dilation indices of the function k(t)=K(t,ψ;X 0 * ,X 1 * ). 相似文献
9.
V. V. Korableva 《Siberian Mathematical Journal》2008,49(2):273-286
We determine the ranks of the permutation representations of the simple groups B l (q), C l (q), and D l (q) on the cosets of the parabolic maximal subgroups. 相似文献
10.
We show that if a finite simple group G, isomorphic to PSLn(q) or PSUn(q) where either n ≠ 4 or q is prime or even, acts on a vector space over a field of the defining characteristic of G; then the corresponding semidirect product contains an element whose order is distinct from every element order of G. We infer that the group PSLn(q), n ≠ 4 or q prime or even, is recognizable by spectrum from its covers thus giving a partial positive answer to Problem 14.60 from the Kourovka Notebook. 相似文献
11.
For a normal space X, α (i.e. the nonempty player) having a winning strategy (resp. winning tactic) in the strong Choquet game Ch(X) played on X is equivalent to α having a winning strategy (resp. winning tactic) in the strong Choquet game played on the hyperspace CL(X) of nonempty closed subsets endowed with the Vietoris topology τ V . It is shown that for a non-normal X where α has a winning strategy (resp. winning tactic) in Ch(X), α may or may not have a winning strategy (resp. winning tactic) in the strong Choquet game played on the Vietoris hyperspace. If X is quasi-regular, then having a winning strategy (resp. winning tactic) for α in the Banach-Mazur game BM(X) played on X is sufficient for α having a winning strategy (resp. winning tactic) in BM(CL(X), τ V ), but not necessary, not even for a separable metric X. In the absence of quasi-regularity of a space X where α has a winning strategy in BM(X), α may or may not have a winning strategy in the Banach-Mazur game played on the Vietoris hyperspace. 相似文献
12.
We describe the atoms of the complete lattice (q(X),⊆) of all quasi-uniformities on a given (nonempty) set X. We also characterize those anti-atoms of (q(X),⊆) that do not belong to the quasi-proximity class of the discrete uniformity on X. After presenting some further results on the adjacency relation in (q(X),⊆), we note that (q(X),⊆) is not complemented for infinite X and show how ideas about resolvability of (bi)topological spaces can be used to construct complements for some elements of (q(X),⊆). 相似文献
13.
Cecilia H. Brook William H. Graves 《Journal of Mathematical Analysis and Applications》1980,73(1):219-237
Let X be a completely regular Hausdorff space and E be a locally convex Hausdorff space. Then Cb(X) ? E is dense in (Cb(X, E), β0), (Cb(X), β) ??E = (Cb(X) ? E, β) and (Cb(X), β1) ??E = (Cb(X) ? E, β1). For a separable space E, (Cb(X, E), β0) is separable if and only if X is separably submetrizable. As a corollary, for a locally compact paracompact space X, if (Cb(X, E), β0) is separable, then X is metrizable. 相似文献
14.
Eliza P. de Jager Hans-Peter A. Künzi 《Topology and its Applications》2011,158(17):2287-2293
We continue our investigations on the lattice (q(X),⊆) of quasi-uniformities on a set X. Improving on earlier results, we show that the Pervin quasi-uniformity (resp. the well-monotone quasi-uniformity) of an infinite topological T1-space X does not have a complement in (q(X),⊆). We also establish that a hereditarily precompact quasi-uniformity inducing the discrete topology on an infinite set X does not have a complement in (q(X),⊆). 相似文献
15.
A.R. Sourour 《Journal of Functional Analysis》1978,30(2):276-285
Let (Ω, ∑, μ) be a finite measure space and X a separable Banach space. We characterize the linear isometries of onto itself for 1 ? p < ∞, p ≠ 2 under the condition that X is not the lp-direct sum of two nonzero spaces (for the same p). It is shown that T is such an isometry if and only if (Tf)(·) = S(·)h(·)(Φ(f))(·), where Φ is a set isomorphism of ∑ onto itself, S is a strongly measurable operator-valued map such that S(t) is a.e. an isometry of X onto itself, and h is a scalar function which is related to Φ. It is further shown that for a big class of measure spaces (perhaps all nontrivial ones) the condition on X is also a necessary condition for the above conclusion to hold. In the case when X is a Hilbert space the injective isometries of are also characterized. They have the same form as above, except that Φ and S(t) are not necessarily onto. 相似文献
16.
This is a continuation of our previous work. We classify all the simple ?q(D n )-modules via an automorphismh defined on the set { λ | Dλ ≠ 0}. Whenf n(q) ≠ 0, this yields a classification of all the simple ? q (D n)- modules for arbitrary n. In general ( i. e., q arbitrary), if λ(1) = λ(2),wegivea necessary and sufficient condition ( in terms of some polynomials ) to ensure that the irreducible ?q,1(B n )- module Dλ remains irreducible on restriction to ?q(D n ). 相似文献
17.
L Drewnowski 《Journal of Functional Analysis》1977,26(4):315-332
An F-space (complete metric linear space) is minimal if it admits no strictly weaker linear Hausdorff topology, and quotient (q-) minimal if all of its Hausdorff quotients are minimal. Two F-spaces are (q-minimally) minimally s-comparable if they have no isomorphic (q-) nonminimal closed linear subspaces. It is proved that if X, Y are (q-minimally (resp., minimally) s-comparable F-subspaces of an arbitrary topological linear space E (resp., with X ∩ Y = {0}), then X + Y is an F-subspace of E. Also, if X1,…, Xn are F-subspaces of E, then X1 + ··· + Xn is an F-subspace of E, provided that are minimally s-comparable whenever F and G are closed minimal subspaces of Xi and Xj, i ≠ j. These are analogs of some results due to Gurariǐ and Rosenthal concerning totally incomparable Banach spaces. 相似文献
18.
Shige Peng 《Applied Mathematics and Optimization》1993,27(2):125-144
We study the existence and uniqueness of the following kind of backward stochastic differential equation, $$x(t) + \int_t^T {f(x(s),y(s),s)ds + \int_t^T {y(s)dW(s) = X,} }$$ under local Lipschitz condition, where (Ω, ?,P, W(·), ?t) is a standard Wiener process, for any given (x, y),f(x, y, ·) is an ?t-adapted process, andX is ?t-measurable. The problem is to look for an adapted pair (x(·),y(·)) that solves the above equation. A generalized matrix Riccati equation of that type is also investigated. A new form of stochastic maximum principle is obtained. 相似文献
19.
Pal-Andrej Nitsche 《Constructive Approximation》2006,24(1):49-70
We consider best N term approximation using anisotropic tensor product wavelet bases ("sparse grids"). We introduce a tensor
product structure ⊗q on certain quasi-Banach spaces. We prove that the approximation
spaces Aαq(L2) and Aαq(H1) equal tensor products of Besov spaces Bαq(Lq), e.g.,
Aαq(L2([0,1]d)) = Bαq(Lq([0,1])) ⊗q · ⊗q Bαq · ·(Lq([0,1])). Solutions to elliptic partial differential equations on polygonal/polyhedral domains belong to these new scales
of Besov spaces. 相似文献
20.
Solutions of second order degenerate integro-differential equations in vector-valued function spaces
We study the well-posedness of the second order degenerate integro-differential equations(P2):(Mu)(t)+α(Mu)(t) = Au(t)+ft-∞ a(ts)Au(s)ds + f(t),0t2π,with periodic boundary conditions M u(0)=Mu(2π),(Mu)(0) =(M u)(2π),in periodic Lebesgue-Bochner spaces Lp(T,X),periodic Besov spaces B s p,q(T,X) and periodic Triebel-Lizorkin spaces F s p,q(T,X),where A and M are closed linear operators on a Banach space X satisfying D(A) D(M),a∈L1(R+) and α is a scalar number.Using known operatorvalued Fourier multiplier theorems,we completely characterize the well-posedness of(P2) in the above three function spaces. 相似文献