We consider the problem of minimizing the size of a family of sets G such that every subset of {1, . . . , n} can be written as a disjoint union of at most k members of G, where k and n are given numbers. This problem originates in a real-world application aiming at the diversity of industrial production. At the same time, the question of finding the minimum of |G| so that every subset of {1, ....

Consider the sequences fX i g m i=1 and fY i g n j=1 of independent random variables , which take values in a nite alphabet, and assume that the variables X 1 ; X 2 ; : : : and Y 1 ; Y 2 ; : : : follow the distributions and , respectively. Two variables X i and Y j are said to match if X i = Y j. Let the number of matching subsequences of length k between the two sequences, when r, 0 r < k, mis...

Most accounts of statistical learning (e.g., Saffran et al., 1996) assume that the learner computes cooccurrence statistics over units, such as syllables, that abstract away from the physical features of the input. This assumption need not hold when the units are underlearned, unfamiliar, or uncategorizable. We tested statistical learning with variable, unfamiliar units and show that if the fea...

We introduce the notion of Burkill-Cesari (BC) differentiability for transferable utility (TU) games and compare it with some other analogous established notions existing in cooperative game theoretical literature. We also apply our notion to the study of the core of a new class of TU games.

We construct a variation map on homotopy groups associated to a pencil with isolated stratified singularities on a singular space. As application, we prove a far reaching Zariski-van Kampen-Lefschetz type theorem, for higher homotopy groups of nongeneric pencils on singular (open) complex spaces.

By using functions of bounded variation we generalize the class of strongly starlike functions and related classes. The main object is to obtain characterizations and inclusion properties of these classes of functions.

the aim of this paper is to study the behaviour of certain sequence of nonlinear durrmeyer operators $nd_{n}f$ of the form $$(nd_{n}f)(x)=intlimits_{0}^{1}k_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{n}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% k_{n}left( x,t,uright) $ satisfies some suitable assumptions. here we estimate the rate...

In this paper we prove a new chain rule formula for the distributional derivative of the composite function v(x) = B(x, u(x)), where u :]a, b[→ Rd has bounded variation, B(x, ·) is continuously differentiable and B(·, u) has bounded variation. We propose an application of this formula in order to deal in an intrinsic way with the discontinuous flux appearing in conservation laws in one space va...

A supermartingale deflator (resp. local martingale deflator) multiplicatively transforms nonnegative wealth processes into supermartingales (resp. local martingales). A supermartingale numéraire (resp. local martingale numéraire) is a wealth process whose reciprocal is a supermartingale deflator (resp. local martingale deflator). It has been established in previous works that absence of arbitra...