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1.
刘修生 《数学杂志》2016,36(5):981-986
本文研究了环Fpm+uFpm+u2Fpm上长度为ps的循环码分类.通过建立环Fpm+uFpm+u2Fpm到环Fpm+uFpm的同态,给出了环Fpm+uFpm+u2Fpm上长度为ps的循环码的新分类方法.应用这种方法,得到了环Fpm+uFpm+u2Fpm长度为ps的循环码的码词数.  相似文献   

2.
It is proved that if the differential equations y ( n )=f(x, y, y′, …, y ( n ?1 )) and y ( m )=g(x, y, y′, …, y ( n ?1 )) have the same particular solutions in a suitable region where f and g are continuous real-valued functions with continuous partial derivatives (alternatively, continuous functions satisfying the classical Lipschitz condition), then n?=?m and the functions f and g are equal. This note could find classroom use in a course on differential equations as enrichment material for the unit on the existence and uniqueness theorems for solutions of initial value problems.  相似文献   

3.
We prove that the maps from S 2 intoS 1 having a finite number of isolated singularities ofdegree ±1 are dense for the strong topology inH 1/2(S 2, S 1). We also prove that smooth maps are densein H 1/2(S 2, S 1)for the sequentially weak topology andthat this is no more the case in H s (S 2, S 1) for s> 1/2.  相似文献   

4.
This paper presents procedures for constructing irreducible polynomials over GF(2s) with linearly independent roots (or normal polynomials or N-polynomials). For a suitably chosen initial N-polynomial F0(x)GF(2s) of degree n, polynomials Fk(x)GF(2s) of degrees n2k are constructed by iteratively applying the transformation xx+x-1, and their roots are shown to form a normal basis of GF(2sn2k) over GF(2s). In addition, the sequences are shown to be trace compatible, i.e., the trace map TGF(2sn2k+1)/GF(2sn2k) fromGF(2sn2k+1) onto GF(2sn2k) maps the roots of Fk+1(x) onto those of Fk(x).  相似文献   

5.
n -2 integers 2 n -2+2 n -3+2 s, where s=0,1,2,..., n-3, in the interval (2 n -2+2 n -3,2 n -1] such that these integers are the cardinalities of row spaces R(A) of non-full rank Boolean matrices A of order n. We also show that for each s, where s=0,1,2,..., n-3, there exists A epsilon B n such that A is non-full rank and the cardinality of R(A) equals 2 n -2+2 n -3+2 s.  相似文献   

6.
The authors establish the boundedness of Marcinkiewicz integrals from the Hardy space H 1 (ℝ n × ℝ m ) to the Lebesgue space L 1(ℝ n × ℝ m ) and their commutators with Lipschitz functions from the Hardy space H 1 (ℝ n × ℝ m ) to the Lebesgue space L q (ℝ n × ℝ m ) for some q > 1.  相似文献   

7.
A class of regular semigroups with regular *- transversals   总被引:6,自引:0,他引:6  
Let S be a regular semigroup. If there is a subsemigroup S * of S and a unary operation * in S satisfying: (1) x * ∈ S * \cap V_ S * (x) for all x∈ S; (2) (x * ) * =x for all x∈ S * ; (3) (x * y) * =y * x ** and (xy * ) * =y ** x * for all x,y∈ S, then S * is called a regular *- transversal of S ; if (3) is replaced with (xy) * =y * x * for all x,y∈ S, then S * is called a strongly regular *- transversal of S. In this paper we consider the class of regular semigroups with a strongly regular *- transversal. It is proved that these semigroups are P - regular semigroups. We characterize the structure of the regular semigroups with a strongly regular *- transversal.  相似文献   

8.
In the present paper we discuss the stability of semilinear problems of the form Aαu + Gα(u) = ? under assumption of an a priori bound for an energy functional Eα(u) ? E, where α is a parameter in a metric space M. Following [11] the problem Aαu + Gα(u) = ?, Eα(u) ? E is called stable in a Hilbert space H at a point α ? M if for any ??H, E, ? > 0 there exists δ > 0 such that for any functions uα1, uα2 satisfying Aαjuαj + Gαj(uαj) = ?αj, Eαj(uαj) ? E, j = 1,2 we have ‖uα1 ? uα2H ? ? provided ρMj, α) ? δ, ‖?αj ? ?‖H ? δ, j = 1,2. In the present paper we obtain stability conditions for the problem Aαu + Gα(u) = ?, Eα(u) ? E.  相似文献   

9.
Ganea comonads     
We construct for all topological space X and all nN a natural section e n X :G n XG n G n X of the Ganea projection :G n G n XG n X and show that the triple (G n ,g n ,e n ) is a comonad on Top *. Received: 6 March 2000  相似文献   

10.
We study the Riesz potentials Iαf on the generalized Lebesgue spaces Lp(·)(?d), where 0 < α < d and Iαf(x) ? ∫equation/tex2gif-inf-3.gif |f(y)| |xy|αd dy. Under the assumptions that p locally satisfies |p(x) – p(x)| ≤ C/(– ln |xy|) and is constant outside some large ball, we prove that Iα : Lp(·)(?d) → Lp?(·)(?d), where . If p is given only on a bounded domain Ω with Lipschitz boundary we show how to extend p to on ?d such that there exists a bounded linear extension operator ? : W1,p(·)(Ω) ? (?d), while the bounds and the continuity condition of p are preserved. As an application of Riesz potentials we prove the optimal Sobolev embeddings Wk,p(·)(?d) ?Lp*(·)(Rd) with and W1,p(·)(Ω) ? Lp*(·)(Ω) for k = 1. We show compactness of the embeddings W1,p(·)(Ω) ? Lq(·)(Ω), whenever q(x) ≤ p*(x) – ε for some ε > 0. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

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