共查询到20条相似文献,搜索用时 46 毫秒
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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
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Pieter C. Allaart 《随机分析与应用》2013,31(3):531-554
Abstract Let X 1, X 2,… be any sequence of [0,1]-valued random variables. A complete comparison is made between the expected maximum E(max j≤n Y j ) and the stop rule supremum sup t E Y t for two types of discounted sequences: (i) Y j = b j X j , where {b j } is a nonincreasing sequence of positive numbers with b 1 = 1; and (ii) Y j = B 1… B j?1 X j , where B 1, B 2,… are independent [0,1]-valued random variables that are independent of the X j , having a common mean β. For instance, it is shown that the set of points {(x, y): x = sup t E Y {(x, y): x=sup t E Y and y = E(max j≤n Y j ), for some sequence X 1,…,X n and Y j = b j X j }, is precisely the convex closure of the union of the sets {(b j x, b j y): (x, y) ∈ C j }, j = 1,…,n, where C j = {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ x[1 + (j ? 1)(1 ? x 1/(j?1))]} is the prophet region for undiscounted random variables given by Hill and Kertz [8]. As a special case, it is shown that the maximum possible difference E(max j≤n β j?1 X j ) ? sup t E(β t?1 X t ) is attained by independent random variables when β ≤ 27/32, but by a martingale-like sequence when β > 27/32. Prophet regions for infinite sequences are given also. 相似文献
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Patricia J.Y. Wong 《Journal of Difference Equations and Applications》2013,19(9):765-797
We offer criteria for the existence of single, double and multiple positive symmetric solutions for the boundary value problem ?2m y(k-m)= f(y(k), ?²y(k-1)….,?SUP>2i y(k-i),…,?2(m-1) y(k-(m-1))), k∈{a+1,…,b+1} ?2i y(a+1-m)=?2i y(b+1+m-2i)=0, 0≤i≤m-1 where m ≥ 1 and (-1)m f can either be positive or the condition can be relaxed. 相似文献
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We investigate properties of entire solutions of differential equations of the form
znw(n) + ?j = n - m + 1n - 1 an - j + 1(j)zjw(j) + ?j = 0n - m ( an - j - m + 1(j)zm + an - j + 1(j) )zjw(j) = 0, {z^n}{w^{(n)}} + \sum\limits_{j = n - m + 1}^{n - 1} {a_{n - j + 1}^{(j)}{z^j}{w^{(j)}}} + \sum\limits_{j = 0}^{n - m} {\left( {a_{n - j - m + 1}^{(j)}{z^m} + a_{n - j + 1}^{(j)}} \right){z^j}{w^{(j)}}} = 0, 相似文献
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Let L be the infinitesimal generator of an analytic semigroup on L2(?n ) with Gaussian kernel bound, and let L–α /2 be the fractional integral of L for 0 < α < n. Suppose that b = (b1, b2, …, bm ) is a finite family of locally integral functions, then the multilinear commutator generated by b and L–α /2 is defined by L–α /2 b f = [bm , …, [b2, [b1, L–α /2]], …, ] f, where m ∈ ?+. When b1, b2, …, bm ∈ BMO or bj ∈ Λ (0 < βj < 1) for 1 ≤ j ≤ m, the authors study the boundedness of L–α /2 b . (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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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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Jennifer Seberry Wallis 《Linear and Multilinear Algebra》2013,61(3):197-207
Recent advances in the construction of Hadamard matrices have depeaded on the existence of Baumert-Hall arrays and four (1, ?1) matrices A B C Dof order m which are of Williamson type, that is they pair-wise satisfy i) MNT = NMT , ∈ {A B C D} and ii) AAT + BBT + CCT + DDT = 4mIm . It is shown that Williamson type matrices exist for the orders m = s(4 ? 1)m = s(4s + 3) for s∈ {1, 3, 5, …, 25} and also for m = 93. This gives Williamson matrices for several new orders including 33, 95,189. These results mean there are Hadamard matrices of order i) 4s(4s ?1)t, 20s(4s ? 1)t,s ∈ {1, 3, 5, …, 25}; ii) 4s(4:s + 3)t, 20s(4s + 3)t s ∈ {1, 3, 5, …, 25}; iii) 4.93t, 20.93t for t ∈ {1, 3, 5, … , 61} ∪ {1 + 2 a 10 b 26 c a b c nonnegative integers}, which are new infinite families. Also, it is shown by considering eight-Williamson-type matrices, that there exist Hadamard matrices of order 4(p + 1)(2p + l)r and 4(p + l)(2p + 5)r when p ≡ 1 (mod 4) is a prime power, 8ris the order of a Plotkin array, and, in the second case 2p + 6 is the order of a symmetric Hadamard matrix. These classes are new. 相似文献
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Given m × n matrices A = [ajk ] and B = [bjk ], their Schur product is the m × n matrix A ○ B = [ajkbjk ]. For any matrix T, define ‖T‖ S = maxX ≠O ‖T ○ X ‖/‖X ‖ (where ‖·‖ denotes the usual matrix norm). For any complex (2n – 1)‐tuple μ = (μ –n +1, μ –n +2, …, μ n –1), let Tμ be the Hankel matrix [μ –n +j +k –1]j,k and define ??μ = {f ∈ L 1[–π, π] : f? (2j ) = μj for –n + 1 ≤ j ≤ n – 1} . It is known that ‖Tμ‖ S ≤ infequation/tex2gif-inf-18.gif ‖f ‖1. When equality holds, we say Tμ is distinguished. Suppose now that μ j ∈ ? for all j and hence that Tμ is hermitian. Then there is a real n × n hermitian unitary X and a real unit vector y such that 〈(Tμ ○ X )y, y 〉 = ‖Tμ ‖S . We call such a pair a norming pair for Tμ . In this paper, we study norming pairs for real Hankel matrices. Specifically, we characterize the pairs that norm some distinguished Schur multiplier Tμ . We do this by giving necessary and suf.cient conditions for (X, y ) to be a norming pair in the n ‐dimensional case. We then consider the 2‐ and 3‐dimensional cases and obtain further results. These include a new and simpler proof that all real 2 × 2 Hankel matrices are distinguished, and the identi.cation of new classes of 3 × 3 distinguished matrices. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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A t-(v, k, λ) covering design is a pair (X, B) where X is a v-set and B is a collection of k-sets in X, called blocks, such that every t element subset of X is contained in at least λ blocks of B. The covering number, Cλ(t, k, v), is the minimum number of blocks a t-(v, k, λ) covering design may have. The chromatic number of (X, B) is the smallest m for which there exists a map φ: X → Zm such that ∣φ((β)∣ ≥2 for all β ∈ B, where φ(β) = {φ(x): x ∈ β}. The system (X, B) is equitably m-chromatic if there is a proper coloring φ with minimal m for which the numbers ∣φ?1(c)∣ c ∈ Zm differ from each other by at most 1. In this article we show that minimum, (i.e., ∣B∣ = C λ (t, k, v)) equitably 3-chromatic 3-(v, 4, 1) covering designs exist for v ≡ 0 (mod 6), v ≥ 18 for v ≥ 1, 13 (mod 36), v ≡ 13 and for all numbers v = n, n + 1, where n ≡ 4, 8, 10 (mod 12), n ≥ 16; and n = 6.5a 13b 17c ?4, a + b + c > 0, and n = 14, 62. We also show that minimum, equitably 2-chromatic 3-(v, 4, 1) covering designs exist for v ≡ 0, 5, 9 (mod 12), v ≥ 0, v = 2.5a 13b 17c + 1, a + b + c > 0, and v = 23. © 1993 John Wiley & Sons, Inc. 相似文献
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J.P. May 《Journal of Pure and Applied Algebra》1982,26(1):1-69
Let G be a finitely presented group given by its pre-abelian presentation <X1,…,Xm; Xe11ζ1,…,Xemmζ,ζm+1,…>, where ei≥0 for i = 1,…, m and ζj?G′ for j≥1. Let N be the subgroup of G generated by the normal subgroups [xeii, G] for i = 1,…, m. Then Dn+2(G)≡γn+2(G) (modNG′) for all n≥0, where G” is the second commutator subgroup of G,γn+2(G) is the (n+2)th term of the lower central series of G and Dn+2(G) = G∩(1+△n+2(G)) is the (n+2)th dimension subgroup of G. 相似文献
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Let Ls 1 (s ∈ ?) be the s-th differential group, that is the set {(x1,…,xs): x1 ≠ 0, xn ∈ K, n =1,2,…,s} (K ∈ {?,?}) together with the group operation which describes the chain rules (up to order s) for Cs-functions with fixed point 0. We consider homomorphisms Φs, Φs = (f1,…,fs) from an abelian group (G,+) into Ls 1 such that f1 = 1, f2 = … = fp+2 = 0, 0p+2 ≠ 0 for a fixed, but arbitrary p ≥ 0 such that p + 2 ≤ s (then fp+2 is necessarily a homomorphism from (G, +) to (K, +). Let l ∈ ? or l = ∞. We present a criterion for the extensibility of Φs to a homomorphism Φs+l from (G, +) to Ls+1 1 (L∞ 1, if l = ∞), by proving that such an extension (continuation) exists iff the component functions fn of Φs with s - p ≤ n ≤ min(s - p + l - 1,s) are certain polynomials in fP+2 (see Theorem 1). We also formulate the problem in the language of truncated formal power series in one indeterminate X over K. The somewhat easier situation f 1 ≠ 1 will be studied in a separate paper. 相似文献
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Let X, X1, X2, … be i.i.d. random variables with nondegenerate common distribution function F, satisfying EX = 0, EX2 = 1. Let Xi and Mn = max{Xi, 1 ≤ i ≤ n }. Suppose there exists constants an > 0, bn ∈ R and a nondegenrate distribution G (y) such that Then, we have almost surely, where f (x, y) denotes the bounded Lipschitz 1 function and Φ(x) is the standard normal distribution function (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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《随机分析与应用》2013,31(3):491-509
Abstract Let X 1, X 2… and B 1, B 2… be mutually independent [0, 1]-valued random variables, with EB j = β > 0 for all j. Let Y j = B 1 … sB j?1 X j for j ≥ 1. A complete comparison is made between the optimal stopping value V(Y 1,…,Y n ):=sup{EY τ:τ is a stopping rule for Y 1,…,Y n } and E(max 1≤j≤n Y j ). It is shown that the set of ordered pairs {(x, y):x = V(Y 1,…,Y n ), y = E(max 1≤j≤n Y j ) for some sequence Y 1,…,Y n obtained as described} is precisely the set {(x, y):0 ≤ x ≤ 1, x ≤ y ≤ Ψ n, β(x)}, where Ψ n, β(x) = [(1 ? β)n + 2β]x ? β?(n?2) x 2 if x ≤ β n?1, and Ψ n, β(x) = min j≥1{(1 ? β)jx + β j } otherwise. Sharp difference and ratio prophet inequalities are derived from this result, and an analogous comparison for infinite sequences is obtained. 相似文献
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Motivated by a question of Sárközy, we study the gaps in the product sequence B = A · A = {b 1 < b 2 < …} of all products a i a j with a i , a j ∈ A when A has upper Banach density α > 0. We prove that there are infinitely many gaps b n+1 ? b n ? α ?3 and that for t ≥ 2 there are infinitely many t-gaps b n+t ? b n ? t 2 α ?4. Furthermore, we prove that these estimates are best possible.We also discuss a related question about the cardinality of the quotient set A/A = {a i /a j , a i , a j ∈ A} when A ? {1, …, N} and |A| = αN. 相似文献
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In this paper we introduce for an arbitrary algebra (groupoid, binary system) (X; *) a sequence of algebras (X; *) n = (X; °), where x ° y = [x * y] n = x * [x * y] n?1, [x * y]0 = y. For several classes of examples we study the cycloidal index (m, n) of (X; *), where (X; *) m = (X; *) n for m > n and m is minimal with this property. We show that (X; *) satisfies the left cancellation law, then if (X; *) m = (X; *) n , then also (X; *) m?n = (X; *)0, the right zero semigroup. Finite algebras are shown to have cycloidal indices (as expected). B-algebras are considered in greater detail. For commutative rings R with identity, x * y = ax + by + c, a, b, c ∈ ? defines a linear product and for such linear products the commutativity condition [x * y] n = [y * x] n is observed to be related to the golden section, the classical one obtained for ?, the real numbers, n = 2 and a = 1 as the coefficient b. 相似文献
17.
Pierre Fraisse 《Journal of Graph Theory》1986,10(4):553-557
Let G = (V, E) be a digraph of order n, satisfying Woodall's condition ? x, y ∈ V, if (x, y) ? E, then d+(x) + d?(y) ≥ n. Let S be a subset of V of cardinality s. Then there exists a circuit including S and of length at most Min(n, 2s). In the case of oriented graphs we obtain the same result under the weaker condition d+(x) + d?(y) ≥ n – 2 (which implies hamiltonism). 相似文献
18.
M. I. Nagnybida 《Ukrainian Mathematical Journal》1996,48(7):1084-1098
In the space A (θ) of all one-valued functions f(z) analytic in an arbitrary region G ? ? (0 ∈ G) with the topology of compact convergence, we establish necessary and sufficient conditions for the equivalence of the operators L 1=α n z n Δ n + ... + α1 zΔ+α0 E and L 2= z n a n (z)Δ n + ... + za 1(z)Δ+a 0(z)E, where δ: (Δ?)(z)=(f(z)-?(0))/z is the Pommier operator in A(G), n ∈ ?, α n ∈ ?, a k (z) ∈ A(G), 0≤k≤n, and the following condition is satisfied: Σ j=s n?1 α j+1 ∈ 0, s=0,1,...,n?1. We also prove that the operators z s+1Δ+β(z)E, β(z) ∈ A R , s ∈ ?, and z s+1 are equivalent in the spaces A R, 0?R?-∞, if and only if β(z) = 0. 相似文献
19.
Simeon M. Berman 《纯数学与应用数学通讯》2007,60(8):1238-1259
Let f(x), x ∈ ?M, M ≥ 1, be a density function on ?M, and X1, …., Xn a sample of independent random vectors with this common density. For a rectangle B in ?M, suppose that the X's are censored outside B, that is, the value Xk is observed only if Xk ∈ B. The restriction of f(x) to x ∈ B is clearly estimable by established methods on the basis of the censored observations. The purpose of this paper is to show how to extrapolate a particular estimator, based on the censored sample, from the rectangle B to a specified rectangle C containing B. The results are stated explicitly for M = 1, 2, and are directly extendible to M ≥ 3. For M = 2, the extrapolation from the rectangle B to the rectangle C is extended to the case where B and C are triangles. This is done by means of an elementary mapping of the positive quarter‐plane onto the strip {(u, v): 0 ≤ u ≤ 1, v > 0}. This particular extrapolation is applied to the estimation of the survival distribution based on censored observations in clinical trials. It represents a generalization of a method proposed in 2001 by the author [2]. The extrapolator has the following form: For m ≥ 1 and n ≥ 1, let Km, n(x) be the classical kernel estimator of f(x), x ∈ B, based on the orthonormal Legendre polynomial kernel of degree m and a sample of n observed vectors censored outside B. The main result, stated in the cases M = 1, 2, is an explicit bound for E|Km, n(x) ? f(x)| for x ∈ C, which represents the expected absolute error of extrapolation to C. It is shown that the extrapolator is a consistent estimator of f(x), x ∈ C, if f is sufficiently smooth and if m and n both tend to ∞ in a way that n increases sufficiently rapidly relative to m. © 2006 Wiley Periodicals, Inc. 相似文献
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In this paper, the following two are considered: Problem IQEP Given Ma∈ SR n×n, Λ=diag{λ1, …, λp}∈ C p×p, X=[x1, …, xp]∈ C n×p, and both Λ and X are closed under complex conjugation in the sense that $\lambda_{2j} = \bar{\lambda}_{2j-1} \in {\mathbf{C}}
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