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1.
Let G be a finite group and π(G) be the set of all prime divisors of its order. The prime graph GK(G) of G is a simple graph with vertex set π(G), and two distinct primes p, q ∈ π(G) are adjacent by an edge if and only if G has an element of order pq. For a vertex p ∈ π(G), the degree of p is denoted by deg(p) and as usual is the number of distinct vertices joined to p. If π(G) = {p 1, p 2,...,p k }, where p 1 < p 2 < ... < p k , then the degree pattern of G is defined by D(G) = (deg(p 1), deg(p 2),...,deg(p k )). The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying conditions |H| = |G| and D(H) = D(G). In addition, a 1-fold OD-characterizable group is simply called OD-characterizable. In the present article, we show that the alternating group A 22 is OD-characterizable. We also show that the automorphism groups of the alternating groups A 16 and A 22, i.e., the symmetric groups S 16 and S 22 are 3-fold OD-characterizable. It is worth mentioning that the prime graph associated to all these groups are connected.  相似文献   

2.
Friedrich Kasch 《代数通讯》2013,41(4):1459-1478
ABSTRACT

We define “regular” for maps in a Hom group. This notion specializes to the well-known notions of (Von Neumann) regular in rings and modules. A map f ∈ Hom R (A,M) is regular if and only if Ker(f) ? A and Im(f) ? M. There exists a unique maximal regular End(M)-End(A)-submodule in Hom R (A,M). We study regularity in Hom R (A 1 ⊕ A 2, M 1 ⊕ M 2). The existence of a regular function Hom R (A,M) implies the existence of projective summands of Hom R (A,M) End R (A) and of End R ( M ) Hom R (A,M). We consider regularity in endomorphism rings, and generalize a theorem of Ware-Zelmanowitz. We examine connections between the maximum regular bimodule and other substructures of Hom, mention two generalizations of regularity, and raise some questions.  相似文献   

3.
We consider different types of processes obtained by composing Brownian motion B(t), fractional Brownian motion B H (t) and Cauchy processes C(t) in different manners. We study also multidimensional iterated processes in ? d , like, for example, (B 1(|C(t)|),…, B d (|C(t)|)) and (C 1(|C(t)|),…, C d (|C(t)|)), deriving the corresponding partial differential equations satisfied by their joint distribution. We show that many important partial differential equations, like wave equation, equation of vibration of rods, higher-order heat equation, are satisfied by the laws of the iterated processes considered in the work. Similarly, we prove that some processes like C(|B 1(|B 2(…|B n+1(t)|…)|)|) are governed by fractional diffusion equations.  相似文献   

4.
Let C(f), Q(f), E(f) and A(f) be the sets of all continuity, quasicontinuity, upper and lower quasicontinuity and cliquishness points of a real function f: X → ℝ, respectively. The triplets (C(f),Q(f),A(f)), (C(f),E(f),A(f) and (Q(f),E(f),A(f)are characterized for functions defined on Baire metric spaces without isolated points.  相似文献   

5.
Let V be a vector space, V* its dual space and L(V) the algebra of all linear operators on V. For an operator a?∈?L(V) let a* be its adjoint acting on V*, and for a subset R of L(V) let R″ be its bicommutant. If R is a left noetherian subalgebra of L(V), then {a*: a?∈?R}″?=?{a*: a?∈?R″}. When R is singly generated R″ is described precisely. Further, for any two operators a, b?∈?L(V), b?∈?(a)″ if and only if the derivations d a and d b satisfy d b (F(V))???d a (F(V)), where F(V) is the set of all finite rank operators on V. In this case the inclusion d b (L(V))???d a (L(V)) also holds.  相似文献   

6.
We study z-automorphisms of the polynomial algebra K[x, y, z] and the free associative algebra Kx, y, z〉 over a field K, i.e., automorphisms that fix the variable z. We survey some recent results on such automorphisms and on the corresponding coordinates. For Kx, y, z〉 we include also results about the structure of the z-tame automorphisms and algorithms that recognize z-tame automorphisms and z-tame coordinates.   相似文献   

7.
Using computationally efficient wavelet methods, we study two nonlinear models of financial returns {r t }: linear ARCH (LARCH) and fractionally integrated GARCH (FIGARCH). We estimate the tail index α and the long memory parameter d of the squared returns Xt = rt2{X_t= r_t^2} of LARCH, and of the powers X t = |r t | p of FIGARCH. We find that the X t have infinite variance and long memory, and show how the estimates of α and d depend on the model parameters. These relationships are determined empirically, as the setting is quite complex, and no suitable theory has been developed so far. In particular, we provide empirical relationships between the estimates [^(d)]{\hat d} and the difference parameters in LARCH and FIGARCH. Our computational work uncovers tail and memory properties of LARCH and FIGARCH for practically relevant parameter ranges, and provides some guidance on modeling returns on speculative assets including FX rates, stocks and market indices.  相似文献   

8.
图和线图的谱性质   总被引:5,自引:0,他引:5  
Let G be a simple connected graph with n vertices and m edges,Lo be the line graph of G and λ1(LG)≥λ2 (LG)≥...≥λm(LG) be the eigenvalues of the graph LG,.. In this paper, the range of eigenvalues of a line graph is considered. Some sharp upper bounds and sharp lower bounds of the eigenvalues of Lc. are obtained. In oarticular,it is oroved that-2cos(π/n)≤λn-1(LG)≤n-4 and λn(LG)=-2 if and only if G is bipartite.  相似文献   

9.
V. Guletskii  C. Pedrini 《K-Theory》2003,30(3):243-263
We relate the notion of finite dimensionality of the Chow motive M(X) of a smooth projective variety X (as defined by S. Kimura) with the conjectures of Beilinson, Bloch and Murre on the existence of a filtration on the Chow ring CH*(X). We show (Theorem 3) that finite dimensionality of M(X) implies uniqueness, up to isomorphism, of Murre's decomposition of M(X). Conversely (Theorem 4), Murre's conjecture for X m ×X m (for a suitable m) implies finite-dimensionality of M(X). We also show (Theorem 7) that, for a surface X with p g = 0, the motive M(X) is finite-dimensional if and only if the Chow group of 0-cycles of X is finite-dimensional in the sense of Mumford, i.e. iff the Bloch conjecture holds for X.The second named author is a member of GNSAGA of CNR.  相似文献   

10.
Let f be a nonconstant entire function; let k ≥ 2 be a positive integer; and let a be a nonzero complex number. If f(z) = a→f′(z) = a, and f′(z) = a →f^(k)(z) = a, then either f = Ce^λz + a or f = Ce^λz + a(λ - 1)/)λ, where C and ), are nonzero constants with λ^k-1 = 1. The proof is based on the Wiman-Vlairon theory and the theory of normal families in an essential way.  相似文献   

11.
In this article, we study necessary and sufficient conditions for the invertibility of a linear combination c 1 A k ?+?c 2 B l , in the case when A and B are both commuting generalized or hypergeneralized projectors. We present some results relating different matrix partial orderings and the invertibility of a linear combination c 1 A k ?+?c 2 B l when A and B are hypergeneralized projectors.  相似文献   

12.
Behnam Khosravi 《代数通讯》2018,46(7):3006-3013
For a finite monoid S, let ν(S) (νd(S)) denote the least number n such that there exists a graph (directed graph) Γ of order n with End(Γ)?S. Also let rank(S) be the smallest number of elements required to generate S. In this paper, we use Cayley digraphs of monoids, to connect lower bounds of ν(S) (νd(S)) to the lower bounds of rank(S). On the other hand, we connect upper bounds of rank(S) to upper bounds of ν(S) (νd(S)).  相似文献   

13.
Let (X i , Y i ) be a sequence of i.i.d. random vectors in R with an absolutely continuous distribution function H and let g x (y), y R denote the conditional density of Y given X = x(F), the support of F, assuming that it exists. Also let M(x) be the (unique) conditional mode of Y given X = x defined by M(x) = arg max y (y)). In this paper new classes of smoothed rank nearest neighbor (RNN) estimators of g x (y), its derivatives and M(x) are proposed and the laws of iterated logarithm (pointwise), uniform a.s. convergence over – < y < and x a compact C(F) and the asymptotic normality for the proposed estimators are established. Our results and proofs also cover the Nadayara-Watson (NW) case. It is shown using the concept of the relative efficiency that the proposed RNN estimator is superior (asymtpotically) to the corresponding NW type estimator of M(x), considered earlier in literature.  相似文献   

14.
William C. Brown 《代数通讯》2013,41(8):2401-2417
Let Rbe a commutative ring and A?M m×n . The spanning rank of Ais the smallest positive integer s for which A=PQ(m×s s×n) The spanning rank of the zero matrix is set equal to zero. If Ris a field, then the spanning rank of Ais just the classical rank of A. In the first section of this paper, various theorems and examples are given which indicate how much of the classical theory of rank is still valid for spanning rank over a commutative ring. If A= PQ(n×s s×n) is a spanning rank factorization of a square matrix and D= QP, then Dis called a spanning rank partner of A. In the second part of this paper, the null ideals N Aand N Dof Aand Drespectively are compared. For instance, we show N A=N Dif s= nand N A= XN Dif s<nwhenever Ris a PIDand A≠0. This result sometimes (e.g. s<<n) makes the computation of N Aeasy.  相似文献   

15.
In this note, we revisit the problem of polynomial interpolation and explicitly construct two polynomials in n of degree k + 1, Pk(n) and Qk(n), such that Pk(n) = Qk(n) = fk(n) for n = 1, 2,…?, k, where fk(1), fk(2),…?, fk(k) are k arbitrarily chosen (real or complex) values. Then, we focus on the case that fk(n) is given by the sum of powers of the first n positive integers Sk(n) = 1k + 2k + ??? + nk, and show that Sk(n) admits the polynomial representations Sk(n) = Pk(n) and Sk(n) = Qk(n) for all n = 1, 2,…?, and k ≥ 1, where the first representation involves the Eulerian numbers, and the second one the Stirling numbers of the second kind. Finally, we consider yet another polynomial formula for Sk(n) alternative to the well-known formula of Bernoulli.  相似文献   

16.
In this paper we use the theory of normal families to prove: Let a and b be two complex numbers such that ba, 0, and let f be a non-constant entire function. If f and f′ share the value a CM and if f = b whenever f′ = b, then ff′. This result improves a result due to Rubel and Yang. Received: 13 June 2005  相似文献   

17.
The nth order derivatives of tan x and sec x may be represented by polynomials P n (u) and Q n (u) in u = tan x, which are known as the derivative polynomials for the tangent and secant and have occurred in diverse contexts. In this paper, explicit representations of P n (u) and Q n (u) are derived in terms of the central factorial numbers of the second kind, and the values of the Bernoulli and Euler polynomials at rationals are expressed by means of these polynomials.  相似文献   

18.
A collection ?? = {G1, G2,…,Gn} of spanning subgraphs of Kn is called an orthogonal double cover if (i) every edge of Kn belongs to exactly two of the Gi's and (ii) any two distinct Gi's intersect in exactly one edge. Chung and West conjectured that there exists an orthogonal double cover of Kn, for all n, in which each Gi has maximum degree 2, and proved this result for n in six of the residue classes modulo 12. In another context, Ganter and Gronau showed that for n ≡ 1 mod 3, n ≠ 10, there exists an orthogonal double cover of Kn in which each Gi consists of an isolated vertex and the vertex disjoint union of K3's (actually these orthogonal double covers result from the solution of the directed version of the problem, which reduces to the undirected case when the orientation of the arcs is ignored). Clearly the covers of Ganter and Gronau satisfy the Chung-West requirement. In this article, the configurations of Ganter and Gronau are generalized to include the cases n ≡ 0,2 mod 3, and the results are used to provide a unified solution of the Chung-West problem. For n ≠ 5 mod 6, all the spanning subgraphs in the collection ?? are isomorphic to each other; however, this is not the case when n ≡ 5 mod 6. In addition to solving the Chung-West problem, we also go on to show that for n ≡ 2 mod 3 and n > 287, there exists an orthogonal double cover of Kn in which each spanning subgraph Gi consists of the vertex-disjoint union of an isolated vertex, and quadrilateral, and (n?5)/3 triangles. Of the 96 cases with 2 ? n ? 287, 65 cases are resolved and 31 remain open. © 1995 John Wiley & Sons, Inc.  相似文献   

19.
Necessary and sufficient conditions of the existence and uniqueness of bounded and almost-periodic solutions of nonlinear dif ferential equation dx/dt+f(x)=h(t), tR, are obtained. Here f: RR is continuous, h: RR is continuous and bounded.  相似文献   

20.

We consider difference equations of order k n+k ≥ 2 of the form: yn+k = f(yn,…,yn+k-1), n= 0,1,2,… where f: D kD is a continuous function, and D?R. We develop a necessary and sufficient condition for the existence of a symmetric invariant I(x 1,…,xk ) ∈C[Dk,D]. This condition will be used to construct invariants for linear and rational difference equations. Also, we investigate the transformation of invariants under invertible maps. We generalize and extend several results that have been obtained recently.  相似文献   

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