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1.
Jürgen Herzog 《manuscripta mathematica》1974,12(3):217-248
Let R be a commutative noetherian ring with unit. To a sequencex:=x1,...,xn of elements of R and an m-by-n matrix α:=(αij) with entries in R we assign a complex D*(x;α), in case that m=n or m=n?1. These complexes will provide us in certain cases with explicit minimal free resolutions of ideals, which are generated by the elements ai:=∑αijxj and the maximal minors of α. 相似文献
2.
A Skolem sequence of order n is a sequence S = (s1, s2…, s2n) of 2n integers satisfying the following conditions: (1) for every k ∈ {1, 2,… n} there exist exactly two elements si,Sj such that Si = Sj = k; (2) If si = sj = k,i < j then j ? i = k. In this article we show the existence of disjoint Skolem, disjoint hooked Skolem, and disjoint near-Skolem sequences. Then we apply these concepts to the existence problems of disjoint cyclic Steiner and Mendelsohn triple systems and the existence of disjoint 1-covering designs. © 1993 John Wiley & Sons, Inc. 相似文献
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Aviezri S Fraenkel 《Journal of Combinatorial Theory, Series A》1973,14(1):8-20
The following is proved (in a slightly more general setting): Let α1, …, αm be positive real, γ1, …, γm real, and suppose that the system [nαi + γi], i = 1, …, m, n = 1, 2, …, contains every positive integer exactly once (= a complementing system). Then is an integer for some i ≠ j in each of the following cases: (i) m = 3 and m = 4; (ii) m = 5 if all αi but one are integers; (iii) m ? 5, two of the αi are integers, at least one of them prime; (iv) m ? 5 and αn ? 2n for n = 1, 2, …, m ? 4.For proving (iv), a method of reduction is developed which, given a complementing system of m sequences, leads under certain conditions to a derived complementing system of m ? 1 sequences. 相似文献
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Let A be an n × n normal matrix over , and Qm, n be the set of strictly increasing integer sequences of length m chosen from 1,…,n. For α, β ? Qm, n denote by A[α|β] the submatrix obtained from A by using rows numbered α and columns numbered β. For k ? {0, 1,…, m} we write |α∩β| = k if there exists a rearrangement of 1,…, m, say i1,…, ik, ik+1,…, im, such that α(ij) = β(ij), i = 1,…, k, and {α(ik+1),…, α(im) } ∩ {β(ik+1),…, β(im) } = ?. A new bound for |detA[α|β ]| is obtained in terms of the eigenvalues of A when 2m = n and |α∩β| = 0.Let n be the group of n × n unitary matrices. Define the nonnegative number where | α ∩ β| = k. It is proved that Let A be semidefinite hermitian. We conjecture that ρ0(A) ? ρ1(A) ? ··· ? ρm(A). These inequalities have been tested by machine calculations. 相似文献
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Jorge L.C Sanz Thomas S Huang 《Journal of Mathematical Analysis and Applications》1984,104(1):302-308
In this paper, the problem of phase reconstruction from magnitude of multidimensional band-limited functions is considered. It is shown that any irreducible band-limited function f(z1…,zn), zi ? , i=1, …, n, is uniquely determined from the magnitude of f(x1…,xn): | f(x1…,xn)|, xi ? , i=1,…, n, except for (1) linear shifts: i(α1z1+…+αn2n+β), β, αi?, i=1,…, n; and (2) conjugation: . 相似文献
7.
Suppose G is a finite group of complex n × n matrices, and let RG be the ring of invariants of G: i.e., those polynomials fixed by G. Many authors, from Klein to the present day, have described RG by writing it as a direct sum Σδj=1 ηj[θ1 ,…, θn]. For example, if G is a unitary group generated by reflections, δ = 1. In this note we show that in general this approach is hopeless by proving that, for any ? > 0, the smallest possible δ is greater than | G |n-1-? for almost all primitive groups. Since for any group we can choose δ ? | G |n-1, this means that most primitive groups are about as bad as they can be. The upper bound on δ follows from Dade's theorem that the θi can be chosen to have degrees dividing | G |. 相似文献
8.
H.J Ryser 《Journal of Combinatorial Theory, Series A》1974,17(1):59-77
In this paper we study de Bruijn-Erdös type theorems that deal with the foundations of finite geometries. The following theorem is one of our main conclusions. Let S1,…, Sn be n subsets of an n-set S. Suppose that |Si| ? 3 (i = 1,…,n) and that |Si ∩ Sj| ? 1 (i ≠ j;i,j = 1,…,n). Suppose further that each Si has nonempty intersection with at least n ? 2 of the other subsets. Then the subsets S1,…,Sn of S are one of the following configurations. (1) They are a finite projective plane. (2) They are a symmetric group divisible design and each subset has nonempty intersection with exactly n ? 2 of the other subsets. (3) We have n = 9 or n = 10 and in each case there exists a unique configuration that does not satisfy (1) or (2). 相似文献
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Let ∏1,…,∏k denote k independent populations, where a random observation from population ∏ i has a uniform distribution over the interval (0,θ i ) and θ i is a realization of a random variable having an unknown prior distribution G i . Population ∏ i is said to be a good population if θ i ≥θ0, where θ0 is a given, positive number. This paper provides a sequence of empirical Bayes procedures for selecting the good populationsamong ∏1,…,∏ k . It is shown that these procedures are asymptotically optimal and that the order of associated convergence rates is O(n-r/4) for some r, 0<r<2, where n is the number of accumulated past observations at hand 相似文献
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John Goldwasser 《Linear and Multilinear Algebra》2013,61(3-4):185-188
Let Ωn be the set of all n × n doubly stochastic matrices, let Jn be the n × n matrix all of whose entries are 1/n and let σ k (A) denote the sum of the permanent of all k × k submatrices of A. It has been conjectured that if A ε Ω n and A ≠ JJ then gA,k (θ) ? σ k ((1 θ)Jn 1 θA) is strictly increasing on [0,1] for k = 2,3,…,n. We show that if A = A 1 ⊕ ⊕At (t ≥ 2) is an n × n matrix where Ai for i = 1,2, …,t, and if for each i gAi,ki (θ) is non-decreasing on [0.1] for kt = 2,3,…,ni , then gA,k (θ) is strictly increasing on [0,1] for k = 2,3,…,n. 相似文献
12.
Vikas Bist 《代数通讯》2013,41(6):1747-1761
By a right (left resp.) S2n-polynomial we mean a multilinear polynomial f(X1,…, Xt) over the ring of integers with noncommuting in-determinates Xisuch that for any prime ring R if f( X1,…, X t) is a PI of some nonzero right (left resp.) ideal of R, then R satisfies S2nthe standard identity of degree 2n. In this paper we prove the theorem:Let R be a prime ring, d a nonzero derivation of R, L a noncommutative Lie ideal of R and f(X1,…, Xt) a right or left S2n-polynomial. Suppose that f(d( u1)n1,…,d(ut)nt)=0 for all uiu,i[d] L, where n1,…,ntare fixed positive integers. Then R satisfies S2n+2. Also, the one-sided version of the theorem is given. 相似文献
13.
Let xi ≥ 0, yi ≥ 0 for i = 1,…, n; and let aj(x) be the elementary symmetric function of n variables given by aj(x) = ∑1 ≤ ii < … <ij ≤ nxii … xij. Define the partical ordering x <y if aj(x) ≤ aj(y), j = 1,… n. We show that , where {xα}i = xαi. We also give a necessary and sufficient condition on a function f(t) such that x <y ? f(x) <f(y). Both results depend crucially on the following: If x <y there exists a piecewise differentiable path z(t), with zi(t) ≥ 0, such that z(0) = x, z(1) = y, and z(s) <z(t) if 0 ≤ s ≤ t ≤ 1. 相似文献
14.
Marcel Erné 《Algebra Universalis》1980,11(1):295-311
Given a certain construction principle assigning to each partially ordered setP some topology θ(P) onP, one may ask under what circumstances the topology θ(P) of a productP = ?j∈J P j of partially ordered setsP i agrees with the product topology ?j∈Jθ(P i) onP. We shall discuss this question for several types ofinterval topologies (Part I), forideal topologies (Part II), and fororder topologies (Part III). Some of the results contained in this first part are listed below:
- Let θi(P) denote thesegment topology. For any family of posetsP j ?j∈Jθs(Pj)=θs(?j∈JPi) iff at most a finite number of theP j has more than one element (1.1).
- Let θcs(P) denote theco-segment topology (lower topology). For any family of lower directed posetsP j ?j∈Jθcs(Pi)=θcs(?j∈JPi) iff eachP j has a least element (1.5).
- Let θi(P) denote theinterval topology. For a finite family of chainsP j,P j ?j∈Jθi(Pi)=θi(?j∈JPi) iff for allj∈k, P j has a greatest element orP k has a least element (2.11).
- Let θni(P) denote thenew interval topology. For any family of posetsP j,P j ?j∈Jθni(Pj)=θni(?j∈JPj) whenever the product space is ab-space (i.e. a space where the closure of any subsetY is the union of all closures of bounded subsets ofY) (3.13).
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Given a set of M × N real numbers, can these always be labeled as xi,j; i = 1,…, M; j = 1,…, N; such that xi+1,j+1 ? xi+1,j ? xi,j+1 + xij ≥ 0, for every (i, j) where 1 ≤ i ≤ M ? 1, 1 ≤ j ≤ N ? 1? For M = N = 3, or smaller values of M, N it is shown that there is a “uniform” rule. However, for max(M, N) > 3 and min(M, N) ≥ 3, it is proved that no uniform rule can be given. For M = 3, N = 4 a way of labeling is demonstrated. For general M, N the problem is still open although, for a special case where all the numbers are 0's and 1's, a solution is given. 相似文献
18.
Jarmila Chvátalová 《Discrete Mathematics》1975,11(3):249-253
If G is a graph with p vertices and at least one edge, we set φ (G) = m n max |f(u) ? f(v)|, where the maximum is taken over all edges uv and the minimum over all one-to-one mappings f : V(G) → {1, 2, …, p}: V(G) denotes the set of vertices of G.Pn will denote a path of length n whose vertices are integers 1, 2, …, n with i adjacent to j if and only if |i ? j| = 1. Pm × Pn will denote a graph whose vertices are elements of {1, 2, …, m} × {1, 2, …, n} and in which (i, j), (r, s) are adjacent whenever either i = r and |j ? s| = 1 or j = s and |i ? r| = 1.Theorem.If max(m, n) ? 2, thenφ(Pm × Pn) = min(m, n). 相似文献
19.
It is shown that if F1, F2, …, Ft are bipartite 2‐regular graphs of order n and α1, α2, …, αt are positive integers such that α1 + α2 + ? + αt = (n ? 2)/2, α1≥3 is odd, and αi is even for i = 2, 3, …, t, then there exists a 2‐factorization of Kn ? I in which there are exactly αi 2‐factors isomorphic to Fi for i = 1, 2, …, t. This result completes the solution of the Oberwolfach problem for bipartite 2‐factors. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:22‐37, 2011 相似文献
20.
Stephen L. Lipscomb 《Semigroup Forum》1992,45(1):249-260
One presentation of the alternating groupA n hasn?2 generatorss 1,…,sn?2 and relationss 1 3 =s i 2 =(s1?1si)3=(sjsk)2=1, wherei>1 and |j?k|>1. Against this backdrop, a presentation of the alternating semigroupA n c )A n is introduced: It hasn?1 generatorss 1,…,S n?2,e, theA n-relations (above), and relationse 2=e, (es 1)4, (es j)2=(es j)4,es i=s i s 1 -1 es 1, wherej>1 andi≥1. 相似文献