In this paper, we considered the problem of finding the upper bound Haus-dorff matrix operator from sequence spaces l p (v) (or d(v, p)) into l p (w) (or d(w, p)). Also we considered the upper bound problem for matrix operators from d(v, 1) into d(w, 1), and matrix operators from e(w, ∞) into e(v, ∞), and deduce upper bound for Cesaro, Copson and Hilbert matrix operators, which are recently con...

In this paper we define the weighted Cesaro sequence spaces ces (p, q).We prove the space ces(p, q) is a complete paranorm space. In section-2 we determine its Kothe-Toeplitz dual and continuous dual. In section-3 we establish necessary and sufficient condition for a matrix A to map ces (p, q) to and ces(p, q) to , where is the space of all bounded sequences and is the space of all convergent s...

We present a model of two-sided matching where utility is non-transferable and information about individuals’ skills is private, utilities are strictly increasing in the partner’s skill and satisfy increasing differences. Skills can be either revealed or kept hidden, but while agents on one side have verifiable skills, agents on the other side have skills that are unverifiable unless certified,...

Supermodularity has long been regarded as a natural notion of complementarities in individual decision making; it was introduced as such in the nineteenth century by Edgeworth and Pareto. But supermodularity is not an ordinal property. We study the ordinal content of assuming a supermodular utility, i.e. what it means for the individual’s underlying preferences. We show that supermodularity is ...

This paper defines weak-α-supermodularity for set functions. It shows that minimizing such functions under cardinality constrains is a common task in machine learning and data mining. Moreover, any problem whose objective function exhibits this property benefits from a greedy extension phase. Explicitly, let S∗ be the optimal set of cardinality k that minimizes f and let S0 be an initial soluti...

We introduce a constrained optimal transport problem where origins x can only be transported to destinations y≥x. Our statistical motivation is describe the sharp upper bound for variance of treatment effect Y−X given marginals when monotone, or Y≥X. thus focus on supermodular costs (or submodular rewards) and coupling P∗ that all such yields bound. This admits manifold characterizations—geomet...

Community partition is an important problem in many areas, such as biology networks and social networks. The objective of this to analyze the relationships among data via network topology. In article, we consider community under independent cascade (IC) model We formulate a combinatorial optimization that aims at partitioning given into disjoint <inline-formula xmlns:mml="http://www.w3.org/1998...