共查询到20条相似文献,搜索用时 15 毫秒
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William G. Lau 《Journal of Pure and Applied Algebra》1989,60(3):253-268
Let P be a poset, and let γ be a linear order type with |γ| ≥ 3. The γ-deviation of P, denoted by γ-dev P, is defined inductively as follows: (1) γ-dev P=0, if P contains no chain of order type γ; (2) γ-dev P = , if γ-dev P and each chain C of type γ in P contains elements a and b such that a<b and [a, b] as an interval of P has γ-deviation <. There may be no ordinal such that γ-dev P = ; i.e., γ-dev P does not exist. A chain is γ-dense if each of its intervals contains a chain of order type γ. If P contains a γ-dense chain, then γ-dev P fails to exist. If either (1) P is linearly ordered or (2) a chain of order type γ does not contain a dense interval, then the converse holds. For an ordinal ξ, a special set S(ξ) is used to study ωξ-deviation. The depth of P, denoted by δ(P) is the least ordinal β that does not embed in P*. Then the following statements are equivalent: (1) ωξ-dev P does not exist; (2) S(ξ) embeds in P; and (3) P has a subset Q of cardinality ξ such that δ(Q*) = ωξ + 1. Also ωξ-dev P = <ωξ + 1 if and only if |δ(P*)|ξ; if these equivalent conditions hold, then ωβξ < δ(P*) ≤ ω + 1ξ for all β < . Applications are made to the study of chains of submodules of a module over an associative ring. 相似文献
3.
Coxeter H. S. M.; Fisher J. Chris; Wilker J. B. 《Journal London Mathematical Society》1997,55(3):527-548
Certain projections of the real polytopes {3, 3, 4}, {3, 4,3}, {3, 3, 5} suggest highly symmetric coordinates for the self-reciprocalcomplex polygons 3{3}3, 4{3}4, 3{4}3, 5{3}5 and 3{5}3. Althoughthere are a number of interesting complications, this suggestionis essentially correct and leads to elegant coordinates forall the sporadic complex polygons. Among the by-products ofproducing these coordinates we count most significant our newinsights about 2{6}3 and our simple proof that the 600 verticesof the real polytope {5, 3, 3} are quite unrelated to the 600vertices of either 5{6}2 or 5{4}3. 相似文献
4.
Ahmed M. Assaf 《Discrete Mathematics》1991,90(3):221-231
Let X be a finite set of size ν, further let λ be a positive integer and let σ(4,λν) denote the maximum number of quadruples such that each pair of elements of X is contained in at most λ of them. The value of σ(4, 1;ν) has been determined by Brouwer (1979) for all v4. The value of σ(4,λν) has been determined by Billington, Stanton and Stinson (1984) for all ν≡0 (mod 3) and λ>1. In this paper we complete the determination of σ(4,λν) for all ν4 and λ>1. 相似文献
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Jaspal Singh Aujla 《Linear algebra and its applications》1999,290(1-3):109-118
There is one to one correspondence between positive operator monotone functions on (0, ∞) and operator connections. For a symmetric connection σ, it is proved that the map X → (AσX)σ(BσX) from positive operators on a Hilbert space to itself, has a unique fixed point. Here σ denotes the dual of σ. It is also proved that |||AσB||| |||A|||σ|||B||| for all unitarily invariant norms ||| · ||| and for all positive operators A,B. 相似文献
7.
It was proved by Dow and Simon that there are 2ω1 (as many as possible) pairwise nonhomeomorphic compact, T2, scattered spaces of height ω1 and width ω. In this paper, we prove that if is an ordinal withω1 < ω2 and θ = κξ: ξ < is a sequence of cardinals such that either κξ = ω or κξ = ω1 for every ξ < , then there are 2ω1 pairwise nonhomeomorphic compact, T2, scattered spaces whose cardinal sequence is θ. 相似文献
8.
Alan P Sprague 《Journal of Combinatorial Theory, Series A》1979,27(3):223-253
Laskar introduced 3-nets as a 3 dimensional analogue to Bruck's notion of net. Affine 3-spaces are an example of 3-nets, and cubic lattice graphs provide another example. Freeman introduced and Laskar extended a class of examples of 3-nets, here called Freeman-Laskar 3-nets. We show that every finite 3-net is either a cubic lattice 3-net or a Freeman-Laskar 3-net. We also show that every infinite 3-net either is a cubic lattice 3-net or arises from a vector space over a skew field. 相似文献
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In this paper, we give low-dimensional examples of local cocycle 3-Lie bialgebras and double construction 3-Lie bialgebras which were introduced in the study of the classical Yang–Baxter equation and Manin triples for 3-Lie algebras. We give an explicit and practical formula to compute the skew-symmetric solutions of the 3-Lie classical Yang–Baxter equation (CYBE). As an illustration, we obtain all skew-symmetric solutions of the 3-Lie CYBE in complex 3-Lie algebras of dimensions 3 and 4 and then the induced local cocycle 3-Lie bialgebras. On the other hand, we classify the double construction 3-Lie bialgebras for complex 3-Lie algebras in dimensions 3 and 4 and then give the corresponding eight-dimensional pseudo-metric 3-Lie algebras. 相似文献
10.
Iliya Boukliev 《Designs, Codes and Cryptography》1997,12(1):5-11
Let d3(n,k) be the maximum possible minimum Hamming distance of a ternary [ n,k,d;3]-code for given values of n and k. It is proved that d3(44,6)=27, d3(76,6)=48,d3(94,6)=60 , d3(124,6)=81,d3(130,6)=84 , d3(134,6)=87,d3(138,6)=90 , d3(148,6)=96,d3(152,6)=99 , d3(156,6)=102,d3(164,6)=108 , d3(170,6)=111,d3(179,6)=117 , d3(188,6)=123,d3(206,6)=135 , d3(211,6)=138,d3(224,6)=147 , d3(228,6)=150,d3(236,6)=156 , d3(31,7)=17 and d3(33,7)=18 . These results are obtained by a descent method for designing good linear codes. 相似文献
11.
In this paper, by using the Discharging Method, we show that any graph with maximum degree Δ 8 that is embeddable in a surface Σ of characteristic χ(Σ) 0 is class one and any graph with maximum degree Δ 9 that is embeddable in a surface Σ of characteristic χ(Σ) = − 1 is class one. For surfaces of characteristic 0 or −1, these results improve earlier results of Mel'nikov. 相似文献
12.
Song Xu 《Linear and Multilinear Algebra》1993,34(3):353-364
For a set σ with n complex numbers, some sufficient conditions are found for σ to be the spectrum of an n ×n normal (entrywise) nonnegative (positive) matrix. After proving a fundamental theorem and introducing the companion set σ' of σ which consists of real numbers, we prove that if σ' satisfies any known sufficient conditions for a real set to be the spectrum of a nonnegative matrix introduced by Suleimanova, Perfect, Salzmann and Kellogg respectively, then σ is the spectrum of an n×n normal nonnegative matrix. 相似文献
13.
Nian-Zu Li 《Discrete Mathematics》1992,110(1-3):185-196
Frucht and Giudici classified all graphs having quadratic σ-polynomials. Dhurandhar characterized all graphs having quadratic and cubic σ-polynomials. Here, we give a necessary and sufficient condition for the graphs whose σ-polynomials are of degree k where k is any positive integer. By using this condition, we construct all graphs whose σ-polynomials are of degree 2, 3 and 4. For the quadratic and cubic cases, our results are the same as those of Frucht, Giudici and Dhurandhar's. 相似文献
14.
令ρ3(n)=∑n=|m|3-|l|3,(m,l)=1 1.本文研究了和式R3(x)=∑n≤xρ3(n)= A3x2/3+B3x1/2+E3(x),并且在黎曼假设下,得到E3(x)=0(x4/15+ε),从而进一步改进了前人的结果. 相似文献
15.
Amihood Amir Alberto Apostolico Gad M. Landau Giorgio Satta 《Journal of Discrete Algorithms》2003,1(5-6):409-421
We consider the problem of fingerprinting text by sets of symbols. Specifically, if S is a string, of length n, over a finite, ordered alphabet Σ, and S′ is a substring of S, then the fingerprint of S′ is the subset φ of Σ of precisely the symbols appearing in S′. In this paper we show efficient methods of answering various queries on fingerprint statistics. Our preprocessing is done in time O(n|Σ|lognlog|Σ|) and enables answering the following queries:
- (1)Given an integer k, compute the number of distinct fingerprints of size k in time O(1).
- (2)Given a set φΣ, compute the total number of distinct occurrences in S of substrings with fingerprint φ in time O(|Σ|logn).
16.
不含三角形的图的λ3-最优性的充分条件 总被引:1,自引:0,他引:1
设G=(V,E)是一个连通图,边集S(?)E是一个3-限制性边割,如果G-S是不连通的并且G-S的每个分支至少有三个点.图G的3-限制性边连通度λ_3(G)是G中最小的一个3-限制性边割的基数.图G是λ_3(G)连通的,如果3-限制性边割存在.G是λ_3-最优的,如果λ_3(G)=ξ_3(G),其中ξ_3(G)=min{|[U,(?)]|:U(?)V,|U|=3 and G[U]是连通的).G[U]表示V的子集U的导出子图,(?)=V\U表示U的补.[U,(?)]是一条边的一个端点在U中另一个端点在(?)中的边的集合.本文给出了不含三角形的图是λ_3-最优的一些充分条件. 相似文献
17.
Impulsive effects on global existence of solutions for degenerate semilinear parabolic equations 总被引:4,自引:0,他引:4
Let q be a nonnegative real number, and λ and σ be positive constants. This article studies the following impulsive problem: for n = 1, 2, 3,…, . The number λ* is called the critical value if the problem has a unique global solution u for λ < λ*, and the solution blows up in a finite time for λ > λ*. For σ < 1, existence of a unique λ* is established, and a criterion for the solution to decay to zero is studied. For σ > 1, existence of a unique λ* and three criteria for the blow-up of the solution in a finite time are given respectively. It is also shown that there exists a unique T* such that u exists globally for T> T*, and u blows up in a finite time for T < T*. 相似文献
18.
Adolfo Sanchez-Flores 《Discrete Mathematics》1995,140(1-3):281-286
The Ramsey number N(3,3,3,3; 2) is the smallest integer n such that each 4-coloring by edges of the complete graph on n vertices contains monochromatic triangles. It is well known that 51 ≤ N(3, 3, 3, 3; 2) ≤ 65. Here we prove that N(3, 3, 3, 3; 2) ≤ 64. 相似文献
19.
E. R. LamkenS. A. Vanstone 《Discrete Mathematics》1993,120(1-3):135-148
Let V be a set of υ elements. A (1, 2; 3, υ, 1)-frame F is a square array of side v which satisfies the following properties. We index the rows and columns of F with the elements of V, V={x1,x2,…,xυ}. (1) Each cell is either empty or contains a 3-subset of V. (2) Cell (xi, xi) is empty for i=1, 2,…, υ. (3) Row xi of F contains each element of V−{xi} once and column xi of F contains each element of V−{xi} once. (4) The collection of blocks obtained from the nonempty cells of F is a (υ, 3, 2)-BIBD. A (1, 2; 3, υ, 1)-frame is a doubly near resolvable (υ, 3, 2)-BIBD. In this paper, we first present a survey of existence results on doubly near resolvable (υ, 3, 2)-BIBDs and (1, 2; 3, υ, 1)-frames. We then use frame constructions to provide a new infinite class of doubly near resolvable (υ, 3, 2)-BIBDs by constructing (1, 2; 3, υ, 1)-frames. 相似文献
20.
Milo
S. Kurili 《Annals of Pure and Applied Logic》2003,120(1-3):225-236
If a˜cardinal κ1, regular in the ground model M, is collapsed in the extension N to a˜cardinal κ0 and its new cofinality, ρ, is less than κ0, then, under some additional assumptions, each cardinal λ>κ1 less than cc(P(κ1)/[κ1]<κ1) is collapsed to κ0 as well. If in addition N=M[f], where f : ρ→κ1 is an unbounded mapping, then N is a˜|λ|=κ0-minimal extension. This and similar results are applied to generalized forcing notions of Bukovský and Namba. 相似文献