共查询到20条相似文献,搜索用时 31 毫秒
1.
Jinquan Dong 《Journal of Graph Theory》1999,30(3):235-241
A graph G is said to be Pt‐free if it does not contain an induced path on t vertices. The i‐center Ci(G) of a connected graph G is the set of vertices whose distance from any vertex in G is at most i. Denote by I(t) the set of natural numbers i, ⌊t/2⌋ ≤ i ≤ t − 2, with the property that, in every connected Pt‐free graph G, the i‐center Ci(G) of G induces a connected subgraph of G. In this article, the sharp upper bound on the diameter of G[Ci(G)] is established for every i ∈ I(t). The sharp lower bound on I(t) is obtained consequently. © 1999 John Wiley & Sons, Inc. J Graph Theory 30: 235–241, 1999 相似文献
2.
Esko Turunen 《Mathematical Logic Quarterly》2007,53(2):170-175
Generalizations of Boolean elements of a BL‐algebra L are studied. By utilizing the MV‐center MV(L) of L, it is reproved that an element x ∈ L is Boolean iff x ∨ x * = 1 . L is called semi‐Boolean if for all x ∈ L, x * is Boolean. An MV‐algebra L is semi‐Boolean iff L is a Boolean algebra. A BL‐algebra L is semi‐Boolean iff L is an SBL‐algebra. A BL‐algebra L is called hyper‐Archimedean if for all x ∈ L, xn is Boolean for some finite n ≥ 1. It is proved that hyper‐Archimedean BL‐algebras are MV‐algebras. The study has application in mathematical fuzzy logics whose Lindenbaum algebras are MV‐algebras or BL‐algebras. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
An n × n real matrix A = (aij)n × n is called bi‐symmetric matrix if A is both symmetric and per‐symmetric, that is, aij = aji and aij = an+1?1,n+1?i (i, j = 1, 2,..., n). This paper is mainly concerned with finding the least‐squares bi‐symmetric solutions of matrix inverse problem AX = B with a submatrix constraint, where X and B are given matrices of suitable sizes. Moreover, in the corresponding solution set, the analytical expression of the optimal approximation solution to a given matrix A* is derived. A direct method for finding the optimal approximation solution is described in detail, and three numerical examples are provided to show the validity of our algorithm. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
4.
Let M be an MV‐algebra and ΩM be the set of all σ ‐valuations from M into the MV‐unit interval. This paper focuses on the characterization of MV‐algebras using σ ‐valuations of MV‐algebras and proves that a σ ‐complete MV‐algebra is σ ‐regular, which means that a ≤ b if and only if v (a) ≤ v (b) for any v ∈ ΩM. Then one can introduce in a natural way a fuzzy topology δ on ΩM. The representation theorem forMV‐algebras is established by means of fuzzy topology. Some properties of fuzzy topology δ and its cut topology U are investigated (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
Let L be a finite pseudocomplemented lattice. Every interval [0, a] in L is pseudocomplemented, so by Glivenko’s theorem, the set S(a) of all pseudocomplements in [0, a] forms a boolean lattice. Let B i denote the finite boolean lattice with i atoms. We describe all sequences (s 0, s 1, . . . , s n ) of integers for which there exists a finite pseudocomplemented lattice L with s i = |{ a ∈ L | S(a) ? B i }|, for all i, and there is no a ∈ L with S(a) ? B n+1. This result settles a problem raised by the first author in 1971. 相似文献
6.
Let ? be a symmetric binary function, positive valued on positive arguments. A graph G = (V,E) is a ?‐tolerance graph if each vertex υ ∈ V can be assigned a closed interval Iυ and a positive tolerance tυ so that xy ∈ E ? | Ix ∩ Iy|≥ ? (tx,ty). An Archimedean function has the property of tending to infinity whenever one of its arguments tends to infinity. Generalizing a known result of [15] for trees, we prove that every graph in a large class (which includes all chordless suns and cacti and the complete bipartite graphs K2,k) is a ?‐tolerance graph for all Archimedean functions ?. This property does not hold for most graphs. Next, we present the result that every graph G can be represented as a ?G‐tolerance graph for some Archimedean polynomial ?G. Finally, we prove that there is a ?universal”? Archimedean function ? * such that every graph G is a ?*‐tolerance graph. © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 179–194, 2002 相似文献
7.
Let I = [a , b ] ? ?, let 1 < q ≤ p < ∞, let u and v be positive functions with u ∈ L p ′ (I ) and v ∈ L q (I ), and let T : L p (I ) → L q (I ) be the Hardy‐type operator given by Given any n ∈ ?, let s n stand for either the n ‐th approximation number of T or the n ‐th Kolmogorov width of T . We show that where c pq is an explicit constant depending only on p and q . (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
8.
Hassan Sfouli 《Mathematical Logic Quarterly》2010,56(5):503-507
The main goal of this note is to study for certain o‐minimal structures the following propriety: for each definable C∞ function g0: [0, 1] → ? there is a definable C∞ function g: [–ε, 1] → ?, for some ε > 0, such that g (x) = g0(x) for all x ∈ [0, 1] (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
Let v, k be positive integers and k ≥ 3, then Kk = : {v: v ≥ k} is a 3‐BD closed set. Two finite generating sets of 3‐BD closed sets K4 and K5 are obtained by H. Hanani [5] and Qiurong Wu [12] respectively. In this article we show that if v ≥ 6, then v ∈ B3(K,1), where K = {6,7,…,41,45,46,47,51,52,53,83,84}\{22,26}; that is, we show that K is a generating set for K6. Finally we show that v ∈ B3(6,20) for all v ∈ K\{35,39,40,45}. © 2007 Wiley Periodicals, Inc. J Combin Designs 16: 128–136, 2008 相似文献
10.
A λ‐design is a family ?? = {B1, B2, …, Bv} of subsets of X = {1, 2, …, v} such that |Bi∩Bj| = λ for all i≠jand not all Bi are of the same size. The only known example of λ‐designs (called type‐1 designs) are those obtained from symmetric designs by a certain complementation procedure. Ryser [J Algebra 10 (1968), 246–261] and Woodall [Proc London Math Soc 20 (1970), 669–687] independently conjectured that all λ‐designs are type‐1. Let g = gcd(r ? 1, r* ? 1), where rand r* are the two replication numbers. Ionin and Shrikhande [J Combin Comput 22 (1996), 135–142; J Combin Theory Ser A 74 (1996), 100–114] showed that λ‐designs with g = 1, 2, 3, 4 are type‐1 and that the Ryser–Woodall conjecture is true for λ‐designs on p + 1, 2p + 1, 3p + 1, 4p + 1 points, where pis a prime. Hein and Ionin [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 145–156] proved corresponding results for g = 5 and Fiala [Codes and Designs—Proceedings of Conference honoring Prof. D. K. Ray‐Chaudhuri on the occasion of his 65th birthday, Ohio State University Mathematical Research Institute Publications, 10, Walter de Gruyter, Berlin, 2002, pp. 109–124; Ars Combin 68 (2003), 17–32; Ars Combin, to appear] for g = 6, 7, and 8. In this article, we consider λ designs with exactly two block sizes. We show that in this case, the conjecture is true for g = 9, 11, 12, 13, 15, 16, 17, 19, 20, 21, and for g = 10, 14, 18, 22 with v≠4λ ? 1. We also give two results on such λ‐designs on v = 9p + 1 and 12p + 1 points, where pis a prime. © 2010 Wiley Periodicals, Inc. J Combin Designs 19:95‐110, 2011 相似文献
11.
Petr Hájek 《Mathematical Logic Quarterly》2007,53(6):610-615
First the expansion of the ?ukasiewicz (propositional and predicate) logic by the unary connectives of dividing by any natural number (Rational ?ukasiewicz logic) is studied; it is shown that in the predicate case the expansion is conservative w.r.t. witnessed standard 1‐tautologies. This result is used to prove that the set of witnessed standard 1‐tautologies of the predicate product logic is Π2‐hard. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
12.
A Hilbert space operator S is called (p, k)‐quasihyponormal if S *k ((S *S)p – (SS *)p )Sk ≥ 0 for an integer k ≥ 1 and 0 < p ≤ 1. In the present note, we consider (p, k)‐quasihyponormal operator S ∈ B (H) such that SX = XT for some X ∈ B (K,H) and prove the Fuglede–Putnam type theorems when the adjoint of T ∈ B (K) is either (p, k)‐quasihyponormal or dominant or a spectral operator (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
13.
Ming-Huat Lim 《Linear and Multilinear Algebra》2013,61(4):481-496
Let A be a non-empty set and m be a positive integer. Let ≡ be the equivalence relation defined on A m such that (x 1, …, x m ) ≡ (y 1, …, y m ) if there exists a permutation σ on {1, …, m} such that y σ(i) = x i for all i. Let A (m) denote the set of all equivalence classes determined by ≡. Two elements X and Y in A (m) are said to be adjacent if (x 1, …, x m?1, a) ∈ X and (x 1, …, x m?1, b) ∈ Y for some x 1, …, x m?1 ∈ A and some distinct elements a, b ∈ A. We study the structure of functions from A (m) to B (n) that send adjacent elements to adjacent elements when A has at least n + 2 elements and its application to linear preservers of non-zero decomposable symmetric tensors. 相似文献
14.
Kyriakos Keremedis 《Mathematical Logic Quarterly》2001,47(2):205-210
We show that the axiom of choice AC is equivalent to the Vector Space Kinna‐Wagner Principle, i.e., the assertion: “For every family 𝒱= {Vi : i ∈ k} of non trivial vector spaces there is a family ℱ = {Fi : i ∈ k} such that for each i ∈ k, Fi is a non empty independent subset of Vi”. We also show that the statement “every vector space over ℚ has a basis” implies that every infinite well ordered set of pairs has an infinite subset with a choice set, a fact which is known not to be a consequence of the axiom of multiple choice MC. 相似文献
15.
In any r‐uniform hypergraph for 2 ≤ t ≤ r we define an r‐uniform t‐tight Berge‐cycle of length ?, denoted by C?(r, t), as a sequence of distinct vertices v1, v2, … , v?, such that for each set (vi, vi + 1, … , vi + t ? 1) of t consecutive vertices on the cycle, there is an edge Ei of that contains these t vertices and the edges Ei are all distinct for i, 1 ≤ i ≤ ?, where ? + j ≡ j. For t = 2 we get the classical Berge‐cycle and for t = r we get the so‐called tight cycle. In this note we formulate the following conjecture. For any fixed 2 ≤ c, t ≤ r satisfying c + t ≤ r + 1 and sufficiently large n, if we color the edges of Kn(r), the complete r‐uniform hypergraph on n vertices, with c colors, then there is a monochromatic Hamiltonian t‐tight Berge‐cycle. We prove some partial results about this conjecture and we show that if true the conjecture is best possible. © 2008 Wiley Periodicals, Inc. J Graph Theory 59: 34–44, 2008 相似文献
16.
Let T be a bounded operator on Lp‐space, with 1 ≤ p < ∞. A theorem of W. B. Johnson and L. Jones asserts that after an appropriate change of density, T actually extends to a bounded operator on L2. We show that if 𝒯 ⊂ B (Lp) is an R‐bounded set of operators, then the latter result holds for any T ∈ 𝒯 with a common change of density. Then we give applications including results on R‐sectorial operators. 相似文献
17.
Based on the coincidence degree theory of Mawhin, we prove some existence results for the following third‐order multi‐point boundary value problem at resonance where f: [0, 1] × R3 → R is a continuous function, 0 < ξ1 < ??? < ξm < 1, αi ∈ R, i = 1, …, m, m ≥ 1 and 0 < η1 < η2 < ??? < ηn < 1, βj ∈ R, j = 1, 2, …, n, n ≥ 2. In this paper, the dimension of the linear space Ker L (linear operator L is defined by Lx = x′′′) is equal to 2. Since all the existence results for third‐order differential equations obtained in previous papers are for the case dim Ker L = 1, our work is new. 相似文献
18.
In this study, we take under investigation principal functions corresponding to the eigenvalues and the spectral singularities of the Operator L generated in by the differential expression and the boundary condition (A0 + A1λ + A2λ2)y′(0,λ) ? (B0 + B1λ + B2λ2)y(0,λ) = 0, where Q is a matrix‐valued function and Ai,Bi,i = 0,1,2 are non‐selfadjoint matrices also A2,B2 are invertible. 相似文献
19.
Salah Mecheri 《Mathematische Nachrichten》2007,280(7):794-801
In this paper we use recent results [14] to establish various characterizations of the global minimum of the map Fψ : U → ?+ defined by Fψ (X) = ‖ψ (X)‖p (1 < p < ∞) where ψ: U → Cp is a map defined by ψ (X) = S +? (X), with ?: B (H) → B (H) a linear map and S ∈ Cp , and U = {X ∈ B (H): ? (X) ∈ Cp }. Further, we apply these results to characterize the operators which are orthogonal to the range of elementary operators. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
20.
Michael M. H. Pang 《Mathematische Nachrichten》2008,281(8):1069-1078
We study the properties of essential self‐adjointness on C∞c (ℝN ) and semigroup ultracontractivity of a class of singular second order elliptic operators defined in L2 (ℝN , σ–a –N (x) dx) with Dirichlet boundary conditions, where a, b ∈ ℝ and σ: ℝN → (0, ∞) is a C∞‐function satisfying c‐1(1 + |x |) ≤ σ (x) ≤ c (1 + |x |) (x ∈ ℝN). We also obtain sharp short time upper and lower diagonal bounds on the heat kernel of e –Ht. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献