共查询到20条相似文献,搜索用时 31 毫秒
1.
Peter Schenzel 《manuscripta mathematica》1981,35(1-2):173-193
In this paper we describe necessary and sufficient conditions for a system of elements a1,...,at of a local Noetherian ring A such that the sequence a1T,a1–a2T,...,at–1– atT, atin the Rees algebra A[a1T,...,atT], T is an indeterminate, constitutes a regular sequence. 相似文献
2.
Andreas Huck 《Graphs and Combinatorics》1991,7(4):323-351
We consider graphs, which are finite, undirected, without loops and in which multiple edges are possible. For each natural numberk letg(k) be the smallest natural numbern, so that the following holds:LetG be ann-edge-connected graph and lets
1,...,s
k,t
1,...,t
k be vertices ofG. Then for everyi {1,..., k} there existsa pathP
i froms
i tot
i, so thatP
1,...,P
k are pairwise edge-disjoint. We prove
相似文献
3.
Optimum super-simple mixed covering arrays of type <Emphasis Type="Italic">a</Emphasis><Superscript>1</Superscript><Emphasis Type="Italic">b</Emphasis><Superscript><Emphasis Type="Italic">k</Emphasis>−1</Superscript> 下载免费PDF全文
Ce Shi 《数学学报(英文版)》2017,33(1):153-164
A mixed covering array (MCA) of type (v 1, v 2,..., v k ), denoted by MCAλ (N; t, k, (v 1, v 2,..., v k )), is an N × k array with entries in the i-th column from a set V i of v i symbols and has the property that each N × t sub-array covers all the t-tuples at least λ times, where 1 ≤ i ≤ k. An MCA λ (N; t, k, (v 1, v 2,..., v k )) is said to be super-simple, if each of its N × (t + 1) sub-arrays contains each (t + 1)-tuple at most once. Recently, it was proved by Tang, Yin and the author that an optimum super-simple MCA of type (a, b, b,..., b) is equivalent to a mixed detecting array (DTA) of type (a, b, b,..., b) with optimum size. Such DTAs can be used to generate test suites to identify and determine the interaction faults between the factors in a component-based system. In this paper, some combinatorial constructions of optimum super-simple MCAs of type (a, b, b,..., b) are provided. By employing these constructions, some optimum super-simple MCAs are then obtained. In particular, the spectrum across which optimum super-simple MCA2(2b 2; 2, 4, (a, b, b, b))′s exist, is completely determined, where 2 ≤ a ≤ b. 相似文献
4.
Adhemar Bultheel Pablo González-Vera Erik Hendriksen Olav Njåstad 《Numerical Algorithms》1992,3(1):91-104
Leta 1,...,a p be distinct points in the finite complex plane ?, such that |a j|>1,j=1,..., p and let \(b_j = 1/\bar \alpha _j ,\) j=1,..., p. Let μ0, μ π (j) , ν π (j) j=1,..., p;n=1, 2,... be given complex numbers. We consider the following moment problem. Find a distribution ψ on [?π, π], with infinitely many points of increase, such that $$\begin{array}{l} \int_{ - \pi }^\pi {d\psi (\theta ) = \mu _0 ,} \\ \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - a_j )^n }} = \mu _n^{(j)} ,} \int_{ - \pi }^\pi {\frac{{d\psi (\theta )}}{{(e^{i\theta } - b_j )^n }} = v_n^{(j)} ,} j = 1,...,p;n = 1,2,.... \\ \end{array}$$ It will be shown that this problem has a unique solution if the moments generate a positive-definite Hermitian inner product on the linear space of rational functions with no poles in the extended complex plane ?* outside {a 1,...,a p,b 1,...,b p}. 相似文献
5.
Wieslaw Kubiak 《Journal of Global Optimization》2003,27(2-3):333-347
Consider the Product Rate Variation problem. Given n products 1,...,i,...,n, and n positive integer demands d
1,..., di,...,dn. Find a sequence =1,...,T, T =
i=1
n
d
i, of the products, where product i occurs exactly d
i times that always keeps the actual production level, equal the number of product i occurrences in the prefix 1,..., t, t=1,...,T, and the desired production level, equal r
i
t, where r
i=di/T, of each product i as close to each other as possible. The problem is one of the most fundamental problems in sequencing flexible just-in-time production systems. We show that if is an optimal sequence for d
1,...,di,...,dn, then concatenation m of m copies of is an optimal sequence for md
1,..., mdi,...,mdn. 相似文献
6.
This paper provides new necessary and sufficient conditions for a Gaussian random field to have a Gohberg-Krein representation in terms of an n-parameter Wiener process (n > 1). As an application, it demonstrates the nonexistence of a Gohberg-Krein representation of Ws,t ? stW1,1 in terms of the two-parameter Wiener process Ws,t with (s, t) ? [0, a] × [0, b] for 0 < a < 1, 0 < b < 1. 相似文献
7.
Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t
1,..., t
p
) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T
1,..., t
p
) of pairwise edge-disjoint closed trails in G such that T
i
is of length T
i
for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M
a,a
is a perfect matching in K
a,a
, then the graph K
a,a
-M
a,a
is arbitrarily decomposable into closed trails.
相似文献
8.
G. R. Wood 《Journal of Optimization Theory and Applications》1988,58(2):331-350
A two-dimensional analogue of the well-known bisection method for root finding is presented in order to solve the following problem, related to the dispersion function of a set of random variables: given distribution functionsF
1,...,F
n and a probabilityp, find an interval [a,b] of minimum width such thatF
i(b)–F
i(a
–)p, fori=1,...,n.The author wishes to thank Dr. I. D. Coope, for helpful advice offered during the preparation of this paper, and the referee, whose comments contributed to a clearer presentation. 相似文献
9.
WU SHIQUAN 《高校应用数学学报(英文版)》1995,10(2):223-228
MAXIMUMTREESOFFINITESEQUENCES¥WUSHIQUANAbstract:Letn,s1,s2,...,snbenon-negativeintegersandM(s1,s2,...,sn)={(a1,a2,...,a.)|aii... 相似文献
10.
The weight hierarchy of a linear [n,k;q] code C over GF(q) is the sequence (d1,d2,...,dk) where dr is the smallest support of an r–dimensional subcode of C. By explicit construction, it is shown that if a sequence (a1,a2,...,ak) satisfies certain conditions, then it is the weight hierarchy of a code satisfying the chain condition. 相似文献
11.
Vladimir Gurvich 《Discrete Applied Mathematics》2010,158(14):1496-302
Consider an electrical circuit, each edge e of which is an isotropic conductor with a monomial conductivity function . In this formula, ye is the potential difference and current in e, while μe is the resistance of e; furthermore, r and s are two strictly positive real parameters common for all edges. In particular, the case r=s=1 corresponds to the standard Ohm’s law.In 1987, Gvishiani and Gurvich [A.D. Gvishiani, V.A. Gurvich, Metric and ultrametric spaces of resistances, in: Communications of the Moscow Mathematical Society, Russian Math. Surveys 42 (6 (258)) (1987) 235-236] proved that, for every two nodes a,b of the circuit, the effective resistance μa,b is well-defined and for every three nodes a,b,c the inequality holds. It obviously implies the standard triangle inequality μa,b≤μa,c+μc,b whenever s≥r. For the case s=r=1, these results were rediscovered in the 1990s. Now, after 23 years, I venture to reproduce the proof of the original result for the following reasons:
- •
- It is more general than just the case r=s=1 and one can get several interesting metric and ultrametric spaces playing with parameters r and s. In particular, (i) the effective Ohm resistance, (ii) the length of a shortest path, (iii) the inverse width of a bottleneck path, and (iv) the inverse capacity (maximum flow per unit time) between any pair of terminals a and b provide four examples of the resistance distances μa,b that can be obtained from the above model by the following limit transitions: (i) r(t)=s(t)≡1, (ii) r(t)=s(t)→∞, (iii) r(t)≡1,s(t)→∞, and (iv) r(t)→0,s(t)≡1, as t→∞. In all four cases the limits μa,b=limt→∞μa,b(t) exist for all pairs a,b and the metric inequality μa,b≤μa,c+μc,b holds for all triplets a,b,c, since s(t)≥r(t) for any sufficiently large t. Moreover, the stronger ultrametric inequality μa,b≤max(μa,c,μc,b) holds for all triplets a,b,c in examples (iii) and (iv), since in these two cases s(t)/r(t)→∞, as t→∞.
- •
- Communications of the Moscow Math. Soc. in Russ. Math. Surveys were (and still are) strictly limited to two pages; the present paper is much more detailed.Although a translation in English of the Russ. Math. Surveys is available, it is not free in the web and not that easy to find.
- •
- The last but not least: priority.
12.
Let {X(t): t [a, b]} be a Gaussian process with mean μ L2[a, b] and continuous covariance K(s, t). When estimating μ under the loss ∫ab (
(t)−μ(t))2 dt the natural estimator X is admissible if K is unknown. If K is known, X is minimax with risk ∫ab K(t, t) dt and admissible if and only if the three by three matrix whose entries are K(ti, tj) has a determinant which vanishes identically in ti [a, b], i = 1, 2, 3. 相似文献
13.
Extremes of independent Gaussian processes 总被引:1,自引:0,他引:1
Zakhar Kabluchko 《Extremes》2011,14(3):285-310
For every n ∈ ℕ, let X
1n
,..., X
nn
be independent copies of a zero-mean Gaussian process X
n
= {X
n
(t), t ∈ T}. We describe all processes which can be obtained as limits, as n→ ∞, of the process a
n
(M
n
− b
n
), where M
n
(t) = max
i = 1,...,n
X
in
(t), and a
n
, b
n
are normalizing constants. We also provide an analogous characterization for the limits of the process a
n
L
n
, where L
n
(t) = min
i = 1,...,n
|X
in
(t)|. 相似文献
14.
E. V. Podsypanin 《Journal of Mathematical Sciences》1979,11(2):306-311
A system of Diophantine equations is considered for integers n1,...,2, $$\phi ^{\left( k \right)} \left( {x_1 , \ldots ,x_s } \right) = n_k \left( {k = 1, \ldots ,2} \right)$$ , Ф(k)(x1,...,xs)=nk (k=1,...,ρ), where Ф(k) are integral forms of degree d is s variables. The singular integral and singular series of this problem are investigated. 相似文献
15.
Vyacheslav V. Chistyakov Dušan Repovš 《Journal of Mathematical Analysis and Applications》2007,331(2):873-885
Let X be a metric space with metric d, c(X) denote the family of all nonempty compact subsets of X and, given F,G∈c(X), let e(F,G)=supx∈Finfy∈Gd(x,y) be the Hausdorff excess of F over G. The excess variation of a multifunction , which generalizes the ordinary variation V of single-valued functions, is defined by where the supremum is taken over all partitions of the interval [a,b]. The main result of the paper is the following selection theorem: If,V+(F,[a,b])<∞,t0∈[a,b]andx0∈F(t0), then there exists a single-valued functionof bounded variation such thatf(t)∈F(t)for allt∈[a,b],f(t0)=x0,V(f,[a,t0))?V+(F,[a,t0))andV(f,[t0,b])?V+(F,[t0,b]). We exhibit examples showing that the conclusions in this theorem are sharp, and that it produces new selections of bounded variation as compared with [V.V. Chistyakov, Selections of bounded variation, J. Appl. Anal. 10 (1) (2004) 1-82]. In contrast to this, a multifunction F satisfying e(F(s),F(t))?C(t−s) for some constant C?0 and all s,t∈[a,b] with s?t (Lipschitz continuity with respect to e(⋅,⋅)) admits a Lipschitz selection with a Lipschitz constant not exceeding C if t0=a and may have only discontinuous selections of bounded variation if a<t0?b. The same situation holds for continuous selections of when it is excess continuous in the sense that e(F(s),F(t))→0 as s→t−0 for all t∈(a,b] and e(F(t),F(s))→0 as s→t+0 for all t∈[a,b) simultaneously. 相似文献
16.
17.
Let A=(aij) be a real symmetric matrix of order n. We characterize all nonnegative vectors x=(x1,...,xn) and y=(y1,...,yn) such that any real symmetric matrix B=(bij), with bij=aij, i≠jhas its eigenvalues in the union of the intervals [bij?yi, bij+ xi]. Moreover, given such a set of intervals, we derive better bounds for the eigenvalues of B using the 2n quantities {bii?y, bii+xi}, i=1,..., n. 相似文献
18.
Jennifer Seberry Wallis 《Journal of Combinatorial Theory, Series A》1976,21(2):188-195
Given any natural number q > 3 we show there exists an integer t ? [2log2(q ? 3)] such that an Hadamard matrix exists for every order 2sq where s > t. The Hadamard conjecture is that s = 2.This means that for each q there is a finite number of orders 2υq for which an Hadamard matrix is not known. This is the first time such a statement could be made for arbitrary q.In particular it is already known that an Hadamard matrix exists for each 2sq where if q = 2m ? 1 then s ? m, if q = 2m + 3 (a prime power) then s ? m, if q = 2m + 1 (a prime power) then s ? m + 1.It is also shown that all orthogonal designs of types (a, b, m ? a ? b) and (a, b), 0 ? a + b ? m, exist in orders m = 2t and 2t+2 · 3, t ? 1 a positive integer. 相似文献
19.
Gini, Lehmer, Beckenbach, and others studied the meanG
s
(a, b) = (a
s
+b
s
)/(a
s 1 +b
s-1
) We proveTheorem 1 The identity (ina, b)G
s
(G
t
,G
u
) =G
v
holds if and only if (s, t, u, v) is (s, t, t, t) (the trivial solution) or one of (1, 1 –k, 1 +k, 1), (1/2, 1 –k, k, 1/2), or (0,–k, k, 0) (the exotic solutions,k is any real number)Theorem 2 IfP
s
(a, b) is the power mean [(a
s
+b
s
)/2]1/s
, thenP
s
(P
t
,P
u
) =P
v
has only the trivial solution (s, t, u, v) = (s, t, t, t) and the exotic solution (0,t, –t, 0) The family of meansG
s
(respP
s
) includes the classical arithmetic, geometric, and harmonic means 相似文献
20.
Josepii Weier 《Annali dell'Universita di Ferrara》1959,9(1):123-148
Riassunto Sianos, t dei campi tensoriali antisi metrici sopra unan-varietà riamanniana orientata. Siano, rispettivamente,a eb i gradi dis et. Allora rot(s·t)=±(a+1)(grads)·(dual
n−(b−a)−1
dual
b−a
t) ±s·(dual
n−(b−a)−1
div dual
b−a
t), dove dual
i
sono delle modificazioni dell’operatore ben noto dual. Cons⋎t=(duals)·t, il prodottos⋎t possiede delle proprità, sotto certi aspetti duali a quelle dei prodotto esterno,s⋏t. Discutendo il prodottos⋏t, si vede: l'operatore div ed il prodotto ⋎ corrispondono all’operatore rot e al prodotto ⋏.
Résumé Soients, t des champs tensoriels antisy métriques sur unen-variété riemannienne orientée. Soient, respectivement,a etb les degrés des ett. Alors rot(s·t)=±(a+1)(grads)·(dual n−(b−a)−1 dual b−a t) ±s·(dual n−(b−a)−1 div dual b−a t), où dual i sont des modifications de l'opérateur connu dual. Avecs⋎t=(duali)·t, le produits⋎t possède des propriétés à certains égards duales à ceux du produit extérieur,s⋏t. En discutant le produits⋎t, l'on voit de plus: l'opérateur div et le produit ⋎ correspondent à l'opérateur rot et au produit ⋏.相似文献