共查询到20条相似文献,搜索用时 31 毫秒
1.
Leslie E Shader 《Journal of Combinatorial Theory, Series A》1974,16(2):221-229
The problem of determining the number of finite central groupoids (an algebraic system satisfying the identity (x · y) · (y ? z) = y) is equivalent to the problem of determining the number of solutions of the matrix equation A2 = J, where A is a 0, 1 matrix and J is a matrix of 1's.The existence of solutions of A2 = J of all ranks r, where , and A is n2 × n2, is proven. Since these are the only possible values, the question of existence solutions of all possible ranks is completely answered. The techniques and proofs are of a constructive nature. 相似文献
2.
Let J=Ir⊕-In-r,0<r<n. An n×n complex matrix A is said to be J-Hermitian if JA=A∗J. An extension of the classical theory of Courant and Fischer on the Rayleigh ratio of Hermitian matrices is stated for J-Hermitian matrices. Applications to the theory of small oscilations of a mechanical system are presented. 相似文献
3.
Kai Wang 《Journal of Combinatorial Theory, Series A》1980,29(2):134-141
In this paper, we will study the h-circulants which satisfy the matrix equation Am = λJ of n × n matrices. We will determine all the (0, 1) h-circulant solutions for 0 < h < n so that hm ≡ 0 (mod n). 相似文献
4.
Gennian Ge 《Journal of Combinatorial Theory, Series A》2007,114(4):747-760
Frames are useful in dealing with resolvable designs such as resolvable balanced incomplete block designs and triplewhist tournaments. Z-cyclic triplewhist tournament frames are also useful in the constructions of Z-cyclic triplewhist tournaments. In this paper, the concept of an (h1,h2,…,hn;u)-regular Z-cyclic triplewhist tournament frame is defined, and used to establish several quite general recursive constructions for Z-cyclic triplewhist tournaments. As corollaries, we are able to unify many known constructions for Z-cyclic triplewhist tournaments. As an application, some new Z-cyclic triplewhist tournament frames and Z-cyclic triplewhist tournaments are obtained. The known existence results of such designs are then extended. 相似文献
5.
Greg W. Anderson 《Advances in Mathematics》2002,172(2):169-205
The abeliant is a polynomial rule which to each n×n by n+2 array with entries in a commutative ring with unit associates an n×n matrix with entries in the same ring. The theory of abeliants, first introduced in an earlier paper of the author, is simplified and extended here. Now let J be the Jacobian of a nonsingular projective algebraic curve defined over an algebraically closed field. With the aid of the theory of abeliants we obtain explicit defining equations for J and its group law. 相似文献
6.
Let Mn(F) denote the algebra of n×n matrices over the field F of complex, or real, numbers. Given a self-adjoint involution J∈Mn(C), that is, J=J*,J2=I, let us consider Cn endowed with the indefinite inner product [,] induced by J and defined by [x,y]?〈Jx,y〉,x,y∈Cn. Assuming that (r,n-r), 0?r?n, is the inertia of J, without loss of generality we may assume J=diag(j1,?,jn)=Ir⊕-In-r. For T=(|tik|2)∈Mn(R), the matrices of the form T=(|tik|2jijk), with all line sums equal to 1, are called J-doubly stochastic matrices. In the particular case r∈{0,n}, these matrices reduce to doubly stochastic matrices, that is, non-negative real matrices with all line sums equal to 1. A generalization of Birkhoff’s theorem on doubly stochastic matrices is obtained for J-doubly stochastic matrices and an application to determinants is presented. 相似文献
7.
The scrambling index of an n×n primitive matrix A is the smallest positive integer k such that Ak(At)k=J, where At denotes the transpose of A and J denotes the n×n all ones matrix. For an m×n Boolean matrix M, its Boolean rank b(M) is the smallest positive integer b such that M=AB for some m×b Boolean matrix A and b×n Boolean matrix B. In this paper, we give an upper bound on the scrambling index of an n×n primitive matrix M in terms of its Boolean rank b(M). Furthermore we characterize all primitive matrices that achieve the upper bound. 相似文献
8.
Let Kn denote the set of all n × n nonnegative matrices whose entries have sum n, and let ϕ be a real function on Kn defined by ϕ (X) = Πni=1Σnj=1xij + Πnj=1Σni=1xij − per X for X = [xij] ϵ Kn. A matrix A ϵ Kn is called a ϕ -maximizing matrix on Kn if ϕ (A) ⩾ ϕ (X) for all X ϵ Kn. It is conjectured that Jn = [1/n]n × n is the unique ϕ-maximizing matrix on Kn. In this note, the following are proved: (i) If A is a positive ϕ-maximizing matrix, then A = Jn. (ii) If A is a row stochastic ϕ-maximizing matrix, then A = Jn. (iii) Every row sum and every column sum of a ϕ-maximizing matrix lies between 1 − √2·n!/nn and 1 + (n − 1)√2·n!/nn. (iv) For any p.s.d. symmetric A ϵ Kn, ϕ (A) ⩽ 2 − n!/nn with equality iff A = Jn. (v) ϕ attains a strict local maximum on Kn at Jn. 相似文献
9.
Vedran Šego 《Linear algebra and its applications》2010,433(7):1265-1275
In this paper, we propose the two-sided hyperbolic SVD (2HSVD) for square matrices, i.e., A=UΣV[∗], where U and V[∗] are J-unitary (J=diag(±1)) and Σ is a real diagonal matrix of “double-hyperbolic” singular values. We show that, with some natural conditions, such decomposition exists without the use of hyperexchange matrices. In other words, U and V[∗] are really J-unitary with regard to J and not some matrix which is permutationally similar to matrix J. We provide full characterization of 2HSVD and completely relate it to the semidefinite J-polar decomposition. 相似文献
10.
Assaf Libman 《Topology》2003,42(3):555-568
For a coaugmented functor J on spaces, we consider J-modules and finite J-limits. The former are spaces X which are retracts of JX via the natural map. The latter are homotopy limits of J-modules arranged in diagrams whose shape is finite dimensional. Familiar examples are generalised Eilenberg MacLane spaces, which are the SP∞-modules. Finite SP∞-limits are nilpotent spaces with a very strong finiteness property. We show that the cofacial Bousfield-Kan construction of the functors Jn is universal for finite J-limits in the sense that every map X→Y where Y is a finite J-limit, factors through such natural map X→JnX, for some n<∞. 相似文献
11.
Modeling genetic regulatory interactions is an important issue in systems biology. Probabilistic Boolean networks (PBNs) have been proved to be a useful tool for the task. The steady-state probability distribution of a PBN gives important information about the captured genetic network. The computation of the steady-state probability distribution involves the construction of the transition probability matrix of the PBN. The size of the transition probability matrix is 2n×2n where n is the number of genes. Although given the number of genes and the perturbation probability in a perturbed PBN, the perturbation matrix is the same for different PBNs, the storage requirement for this matrix is huge if the number of genes is large. Thus an important issue is developing computational methods from the perturbation point of view. In this paper, we analyze and estimate the steady-state probability distribution of a PBN with gene perturbations. We first analyze the perturbation matrix. We then give a perturbation matrix analysis for the captured PBN problem and propose a method for computing the steady-state probability distribution. An approximation method with error analysis is then given for further reducing the computational complexity. Numerical experiments are given to demonstrate the efficiency of the proposed methods. 相似文献
12.
Zuhong Zhang 《Journal of Pure and Applied Algebra》2010,214(5):622-137
Let R be a commutative ring with identity in which 2 is invertible. Let H denote a subgroup of the unitary group U(2n,R,Λ) with n≥4. H is normalized by EU(2n,J,ΓJ) for some form ideal (J,ΓJ) of the form ring (R,Λ). The purpose of the paper is to prove that H satisfies a “sandwich” property, i.e. there exists a form ideal (I,ΓI) such that
EU(2n,IJ8ΓJ,Γ)⊆H⊆CU(2n,I,ΓI). 相似文献
13.
Maria Malejki 《Central European Journal of Mathematics》2010,8(1):114-128
We consider the problem of approximation of eigenvalues of a self-adjoint operator J defined by a Jacobi matrix in the Hilbert space l
2(ℕ) by eigenvalues of principal finite submatrices of an infinite Jacobi matrix that defines this operator. We assume the
operator J is bounded from below with compact resolvent. In our research we estimate the asymptotics (with n → ∞) of the joint error of approximation for the eigenvalues, numbered from 1 to N; of J by the eigenvalues of the finite submatrix J
n
of order n × n; where N = max{k ∈ ℕ: k ≤ rn} and r ∈ (0; 1) is arbitrary chosen. We apply this result to obtain an asymptotics for the eigenvalues of J. The method applied in this research is based on Volkmer’s results included in [23]. 相似文献
14.
The scrambling index of an n × n primitive Boolean matrix A is the smallest positive integer k such that A k (A T) k = J, where A T denotes the transpose of A and J denotes the n×n all ones matrix. For an m×n Boolean matrix M, its Boolean rank b(M) is the smallest positive integer b such that M = AB for some m × b Boolean matrix A and b×n Boolean matrix B. In 2009, M. Akelbek, S. Fital, and J. Shen gave an upper bound on the scrambling index of an n×n primitive matrix M in terms of its Boolean rank b(M), and they also characterized all primitive matrices that achieve the upper bound. In this paper, we characterize primitive Boolean matrices that achieve the second largest scrambling index in terms of their Boolean rank. 相似文献
15.
Habtu Zegeye 《Journal of Mathematical Analysis and Applications》2008,343(2):663-671
Let E be a uniformly convex and 2-uniformly smooth real Banach space with dual E∗. Let be a Lipschitz continuous monotone mapping with A−1(0)≠∅. For given u,x1∈E, let {xn} be generated by the algorithm xn+1:=βnu+(1−βn)(xn−αnAJxn), n?1, where J is the normalized duality mapping from E into E∗ and {λn} and {θn} are real sequences in (0,1) satisfying certain conditions. Then it is proved that, under some mild conditions, {xn} converges strongly to x∗∈E where Jx∗∈A−1(0). Finally, we apply our convergence theorems to the convex minimization problems. 相似文献
16.
R.P Anstee 《Journal of Combinatorial Theory, Series B》1981,30(1):11-20
We study graphs whose adjacency matrix S of order n satisfies the equation S + S2 = J ? K + kI, where J is a matrix of order n of all 1's, K is the direct sum on matrices of order l of all 1's, and I is the identity matrix. Moore graphs are the only solutions to the equation in the case l = 1 for which K = I. In the case k = l we can obtain Moore graphs from a solution S by a bordering process analogous to obtaining (ν, κ, λ)-designs from some group divisible designs. Other parameters are rare. We are able to find one new interesting graph with parameters k = 6, l = 4 on n = 40 vertices. We show that it has a transitive automorphism group isomorphic to C4 × S5. 相似文献
17.
Summary We consider linear systems whose associated block Jacobi matricesJ
p are weakly cyclic of indexp. In a recent paper, Pierce, Hadjidimos and Plemmons [13] proved that the block two-cyclic successive overrelaxation (SOR) iterative method is numerically more effective than the blockq-cyclic SOR-method, 2<qp, if the eigenvalues ofJ
p
p
are either all non-negative or all non-positive. Based on the theory of stationaryp-step methods, we give an alternative proof of their theorem. We further determine the optimal relaxation parameter of thep-cyclic SOR method under the assumption that the eigenvalues ofJ
p
p
are contained in a real interval, thereby extending results due to Young [19] (for the casep=2) and Varga [15] (forp>2). Finally, as a counterpart to the result of Pierce, Hadjidimos and Plemmons, we show that, under this more general assumption, the two-cyclic SOR method is not always superior to theq-cyclic SOR method, 2<qp.Dedicated to R. S. Varga on the occasion of his 60th birthdayResearch supported in part by the Deutsche Forschungsgemeinschaft 相似文献
18.
Enkelejd Hashorva 《Journal of multivariate analysis》2007,98(8):1583-1591
Let {Xn,n?1} be iid elliptical random vectors in Rd,d≥2 and let I,J be two non-empty disjoint index sets. Denote by Xn,I,Xn,J the subvectors of Xn with indices in I,J, respectively. For any a∈Rd such that aJ is in the support of X1,J the conditional random sample Xn,I|Xn,J=aJ,n≥1 consists of elliptically distributed random vectors. In this paper we investigate the relation between the asymptotic behaviour of the multivariate extremes of the conditional sample and the unconditional one. We show that the asymptotic behaviour of the multivariate extremes of both samples is the same, provided that the associated random radius of X1 has distribution function in the max-domain of attraction of a univariate extreme value distribution. 相似文献
19.
Harald K. Wimmer 《Linear algebra and its applications》1978,20(2):101-110
If the inverse of a square polynomial matrix L(s) is proper rational, then L(s)-1 can be written as C(sI–J)-1B. The result of this note states that if J is an nXn Jordan matrix, with n=degreedetL(s), then C consists of Jordan chains of L(s), and BT of Jordan chains of L(s)T. This is a generalization of the fact that each matrix which transforms a complex matrix A into Jordan form is made up of eigenvectors and generalized eigenvectors of A. The proof of our result relies on the realization theory of rational matrices. 相似文献
20.
J. Conde 《Discrete Mathematics》2009,309(10):3166-1344
In the context of the degree/diameter problem, the ‘defect’ of a graph represents the difference between the corresponding Moore bound and its order. Thus, a graph with maximum degree d and diameter two has defect two if its order is n=d2−1. Only four extremal graphs of this type, referred to as (d,2,2)-graphs, are known at present: two of degree d=3 and one of degree d=4 and 5, respectively. In this paper we prove, by using algebraic and spectral techniques, that for all values of the degree d within a certain range, (d,2,2)-graphs do not exist.The enumeration of (d,2,2)-graphs is equivalent to the search of binary symmetric matrices A fulfilling that AJn=dJn and A2+A+(1−d)In=Jn+B, where Jn denotes the all-one matrix and B is the adjacency matrix of a union of graph cycles. In order to get the factorization of the characteristic polynomial of A in Q[x], we consider the polynomials Fi,d(x)=fi(x2+x+1−d), where fi(x) denotes the minimal polynomial of the Gauss period , being ζi a primitive ith root of unity. We formulate a conjecture on the irreducibility of Fi,d(x) in Q[x] and we show that its proof would imply the nonexistence of (d,2,2)-graphs for any degree d>5. 相似文献