We introduce a new representation scheme for coalitional games, called coalition-flow networks (CF-NETs), where the formation of effective coalitions in a task-based setting is reduced to the problem of directing flow through a network. We show that our representation is intuitive, fully expressive, and captures certain patterns in a significantly more concise manner compared to the conventiona...

The five parameter gamma–Weibull distribution has been introduced by Leipnik and Pearce (2004). Nadarajah and Kotz (2007) have simplified it into four parameter form, using hypergeometric functions in some special cases. We show that the probability distribution function, all moments of positive order and the characteristic function of gamma–Weibull distribution of a random variable can be expl...

Let X be an nelement set, and let k, t, A be positive integers, n ~ k ~ t. A system Y of k-element subsets of X is called an SA (n, k, t) Steiner-system if every t-element subset of X is contained in exactly A members of Y. (Notice that two members of Yare not necessarily distinct.) We denote by hy the characteristic function of Y i.e. hy is defined on all subsets of X, and for any B ~X, h(B) i...

Foldover is a widely used procedure for selecting follow-up experimental runs. As foldover designs require twice as many runs as the initial design, they can be inefficient if the number of effects to be dealiased is smaller than the size of the original experiment. Semifolding refers to adding half of a foldover fraction and is a technique that has been investigated in recent literature for re...

The present work is concerned with cooperative games with transferable utility the characteristic function of which may have fuzzy values. Main attention is devoted to notions of superadditivity, convexity, core, and Shapley value. It turns out that the proposed fuzzy counterparts of these notions eliminate difficulties and disappointing features connected with previous approaches.

In dimension d ≥ 5, we consider the differential operator (1.1) H0 = −∆+ τζ(x)|x|(−∆θ), ε > 0, τ > 0, where ∆θ is the Laplace-Beltrami operator on the unit sphere S = {x ∈ R : |x| = 1} and ζ is the characteristic function of the complement to the unit ball {x ∈ R : |x| ≤ 1}. The standard argument with separation of variables allows one to define this operator as the orthogonal sum of one-dimens...

Let 5 and 8 be Krein spaces. By S(3 ,8 ) we denote the (generalized Schur) class of all functions O, defined and holomorphic at z = 0 and with values in L(5,8), the space of bounded Linear operators from 5 to 8 (we write L ( 8 ) for L(3,S)). It is known, see Section 3 below, that any OeS(3,8) is in some neighborhood of z = 0 the characteristic function On of a unitary colligation A = (J?,S,@;U)...

1 f-vector for convex polytopes Given a convex polytope P of full dimension in R, we can consider the f-vector, fk = number of k-faces, 0 ≤ k ≤ d− 1. A natural question is Question 1. Given an abstract tuple f of d integers, what are necessary and sufficient conditions for f to be the f-vector of a convex polytope? It turns out to be quite difficult to give sufficient conditions, so let’s deter...

We present the main ideas of the proof of the following result: The characteristic function of the unit disc in R is the symbol of a bounded bilinear multiplier operator from L1(R) × L2(R) into L(R) when 2 ≤ p1, p2 < ∞ and 1 < p = p1p2 p1+p2 ≤ 2.

We propose a new representation for coalitional games, called the coalitional skill vector model, where there is a set of skills in the system, and each agent has a skill vector—a vector consisting of values that reflect the agents’ level in different skills. Furthermore, there is a set of goals, each with requirements expressed in terms of the minimum skill level necessary to achieve the goal....