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1.
The foundations of the incomplete statistics recently proposed by Wang is rediscussed in the context of the canonical statistical ensemble. It is found that the incomplete normalization condition, ∑pqi=1 (i=1,…,w), where pi is the probability of a given microstate, is not compatible with the entropic non-extensive formula proposed by Tsallis. It is proved that the entropic function proposed by Wang must be written as Sq=−kBpi2q−1lnqpi, whereas the form proposed by Tsallis namely, Sq=−kBpiqlnqpi, is directly associated with the standard normalization condition (∑ipi=1).  相似文献   

2.
The parametric resource allocation problem asks to minimize the sum of separable single-variable convex functions containing a parameter λ, Σi = 1ni(xi + λgi(xi)), under simple constraints Σi = 1n xi = M, lixiui and xi: nonnegative integers for i = 1, 2, …, n, where M is a given positive integer, and li and ui are given lower and upper bounds on xi. This paper presents an efficient algorithm for computing the sequence of all optimal solutions when λ is continuously changed from 0 to ∞. The required time is O(GMlog2 n + n log n + n log(M/n)), where G = Σi = 1n ui − Σi = 1n li and an evaluation of ƒi(·) or gi(·) is assumed to be done in constant time.  相似文献   

3.
In this paper we study the existence, the uniqueness, the boundedness and the asymptotic behavior of the positive solutions of the fuzzy difference equation xn+1=∑i=0kAi/xnipi, where k{1,2,…,}, Ai, i{0,1,…,k}, are positive fuzzy numbers, pi, i{0,1,…,k}, are positive constants and xi, i{−k,−k+1,…,0}, are positive fuzzy numbers.  相似文献   

4.
Given S1, a starting set of points in the plane, not all on a line, we define a sequence of planar point sets {Si}i=1 as follows. With Si already determined, let Li be the set of all the lines determined by pairs of points from Si, and let Si+1 be the set of all the intersection points of lines in Li. We show that with the exception of some very particular starting configurations, the limiting point set i=1Si is everywhere dense in the plane.  相似文献   

5.
MEROMORPHIC FUNCTIONS SHARING TWO FINITE SETS   总被引:1,自引:1,他引:0  
Let S1 = {∞} and S2 = {w: Ps(w)= 0}, Ps(w) being a uniqueness polynomial under some restricted conditions. Then, for any given nonconstant meromorphic function f, there exist at most finitely many nonconstant meromorphic functions g such that f-1(Si) = g-1(Si)(i = 1,2), where f-1(Si) and g-1(Si) denote the pull-backs of Si considered as a divisor, namely, the inverse images of Si counted with multiplicities, by f and g respectively.  相似文献   

6.
Let W be an n-dimensional vector space over a field F; for each positive integer m, let the m-tuples (U1, …, Um) of vector subspaces of W be uniformly distributed; and consider the statistics Xm,1 dimF(∑i=1m Ui) and Xm,2 dimF (∩i=1m Ui). If F is finite of cardinality q, we determine lim E(Xm,1k), and lim E(Xm,2k), and hence, lim var(Xm,1) and lim var(Xm,2), for any k > 0, where the limits are taken as q → ∞ (for fixed n). Further, we determine whether these, and other related, limits are attained monotonically. Analogous issues are also addressed for the case of infinite F.  相似文献   

7.
A mapping ƒ : n=1InI is called a bag mapping having the self-identity if for every (x1,…,xn) ε i=1In we have (1) ƒ(x1,…,xn) = ƒ(xi1,…,xin) for any arrangement (i1,…,in) of {1,…,n}; monotonic; (3) ƒ(x1,…,xn, ƒ(x1,…,xn)) = ƒ(x1,…,xn). Let {ωi,n : I = 1,…,n;n = 1,2,…} be a family of non-negative real numbers satisfying Σi=1nωi,n = 1 for every n. Then one calls the mapping ƒ : i=1InI defined as follows an OWA bag mapping: for every (x1,…,xn) ε i=1In, ƒ(x1,…,xn) = Σi=1nωi,nyi, where yi is the it largest element in the set {x1,…,xn}. In this paper, we give a sufficient and necessary condition for an OWA bag mapping having the self-identity.  相似文献   

8.
We present a characterization of those Euclidean distance matrices (EDMs) D which can be expressed as D=λ(EC) for some nonnegative scalar λ and some correlation matrix C, where E is the matrix of all ones. This shows that the cones
where is the elliptope (set of correlation matrices) and is the (closed convex) cone of EDMs.

The characterization is given using the Gale transform of the points generating D. We also show that given points , for any scalars λ12,…,λn such that

j=1nλjpj=0, ∑j=1nλj=0,
we have
j=1nλjpipj2= forall i=1,…,n,
for some scalar independent of i.  相似文献   

9.
Let C1,…, Cn and C1,…, Cn be two collections of equal disks in the plane, with centers c1,…, cn and c1,…, cn. According to a well-known conjecture of Klee and Wagon (1991), if |cicj| ≥ |cicj| for all i, j, then Area(∩i Ci) ≤ Area(∩i Ci).

We prove this statement in the special case when there is a continuous contraction of {c1,…, cn} onto {c1,…, cn}.  相似文献   


10.
We prove that to every positive integer n there exists a positive integer h such that the following holds: If S is a set of h elements and ƒ a mapping of the power set of S into such that ƒ(T)T for all T , then there exists a strictly increasing sequence T1Tn of subsets of S such that one of the following three possibilities holds: (a) all sets ƒ(Ti), i= 1,…,n, are equal; (b) for all i=1,…, n, we have ƒ(Ti)=Ti; (c) Ti=ƒ(Ti+1) for all i= 1,…,n-1. This theorem generalizes theorems of the author, Rado, and Leeb. It has applications for subtrees in power sets.  相似文献   

11.
In this paper we investigate the behaviour of the solutions of equations ΣI=1n aixi = b, where Σi=1n, ai = 0 and b ≠ 0, with respect to colorings of the set N of positive integers. It turns out that for any b ≠ 0 there exists an 8-coloring of N, admitting no monochromatic solution of x3x2 = x2x1 + b. For this equation, for b odd and 2-colorings, only an odd-even coloring prevents a monochromatic solution. For b even and 2-colorings, always monochromatic solutions can be found, and bounds for the corresponding Rado numbers are given. If one imposes the ordering x1 < x2 < x3, then there exists already a 4-coloring of N, which prevents a monochromatic solution of x3x2 = x2x1 + b, where b ε N.  相似文献   

12.
We prove the following theorem. Let m≥2 and q≥1 be integers and let S and T be two disjoint sets of points in the plane such that no three points of ST are on the same line, |S|=2q and |T|=mq. Then ST can be partitioned into q disjoint subsets P1,P2,…,Pq satisfying the following two conditions: (i) conv(Pi)∩conv(Pj)=φ for all 1≤i<jq, where conv(Pi) denotes the convex hull of Pi; and (ii) |PiS|=2 and |PiT|=m for all 1≤iq.  相似文献   

13.
Suppose we are given a family of sets , where S(j) = ∩ki=1 Hi(j), and suppose each collection of sets Hi(j1),…,Hi(jk+1) has a lower bound under the partial ordering defined by inclusion, then the maximal size of an independent subcollection of is k. For example, for a fixed collection of half-spaces H1,…,Hk in , we define to be the collection of all sets of the form
where χi, I=1,…, k are points in . Then the maximal size of an independent collection of such sets us k. This leads to a proof of the bound of 2d due to Rényi et al. (1951) for the maximum size of an independent family of rectangles in with sides parallel to the coordinate axes, and to a bound of d+1 for the maximum size of an independent family of simplices in with sides parallel to given hyperplanes H1,…,Hd+1.  相似文献   

14.
A bisequence of complex numbers {μn}−∞ determines a strong moment functional satisfying L[xn] = μn. If is positive-definite on a bounded interval (a,b) R{0}, then has an integral representation , n=0, ±1, ±2,…, and quadrature rules {wni,xni} exist such that μk = ∑i=innsnikwni. This paper is concerned with establishing certain extremal properties of the weights wni and using these properties to obtain maximal mass results satisfied by distributions ψ(x) representing when only a finite bisequence of moments {μk}k=−nn−1 is given.  相似文献   

15.
Given an infinite sequence t=(k)k of −1 and +1, we consider the oriented walk defined by Sn(t)=∑k=1n12k. The set of t's whose behaviors satisfy Sn(t)bnτ is considered ( and 0<τ1 being fixed) and its Hausdorff dimension is calculated. A two-dimensional model is also studied. A three-dimensional model is described, but the problem remains open.  相似文献   

16.
In 1994, van Trung (Discrete Math. 128 (1994) 337–348) [9] proved that if, for some positive integers d and h, there exists an Sλ(t,k,v) such that
then there exists an Sλ(vt+1)(t,k,v+1) having v+1 pairwise disjoint subdesigns Sλ(t,k,v). Moreover, if Bi and Bj are any two blocks belonging to two distinct such subdesigns, then d|BiBj|<kh. In 1999, Baudelet and Sebille (J. Combin. Des. 7 (1999) 107–112) proved that if, for some positive integers, there exists an Sλ(t,k,v) such that
where m=min{s,vk} and n=min{i,t}, then there exists an
having pairwise disjoint subdesigns Sλ(t,k,v). The purpose of this paper is to generalize these two constructions in order to produce a new recursive construction of t-designs and a new extension theorem of t-designs.  相似文献   

17.
We partially characterize the rational numbers x and integers n 0 for which the sum ∑k=0 knxk assumes integers. We prove that if ∑k=0 knxk is an integer for x = 1 − a/b with a, b> 0 integers and gcd(a,b) = 1, then a = 1 or 2. Partial results and conjectures are given which indicate for which b and n it is an integer if a = 2. The proof is based on lower bounds on the multiplicities of factors of the Stirling number of the second kind, S(n,k). More specifically, we obtain for all integers k, 2 k n, and a 3, provided a is odd or divisible by 4, where va(m) denotes the exponent of the highest power of a which divides m, for m and a> 1 integers.

New identities are also derived for the Stirling numbers, e.g., we show that ∑k=02nk! S(2n, k) , for all integers n 1.  相似文献   


18.
An up–down permutation P=(p1,p2,…,pn) is a permutation of the integers 1 to n which satisfies constraints specified by a sequence C=(c1,c2,…,cn−1) of U's and D's of length n−1. If ci is U then pi<pi+1 otherwise pi−1>pi. A loopless algorithm is developed for generating all the up–down permutations satisfying any sequence C. Ranking and unranking algorithms are discussed.  相似文献   

19.
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.
Length-bounded disjoint paths in planar graphs   总被引:1,自引:0,他引:1  
The following problem is considered: given: an undirected planar graph G=(V,E) embedded in , distinct pairs of vertices {r1,s1},…,{rk,sk} of G adjacent to the unbounded face, positive integers b1,…,bk and a function ; find: pairwise vertex-disjoint paths P1,…,Pk such that for each i=1,…,k, Pi is a risi-path and the sum of the l-length of all edges in Pi is at most bi. It is shown that the problem is NP-hard in the strong sense. A pseudo-polynomial-time algorithm is given for the case of k=2.  相似文献   

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