We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in terms Δ-integral for convex (concave) functions scale sets and investigate its properties such as superadditivity monotonicity. The obtained are used to derive bounds given those results provide a refinement converse known scales. Further, we define new types functionals weighted generalized powe...

MC-nets constitute a natural compact representation scheme for cooperative games in multiagent systems. In this paper, we study the complexity of several natural computational problems that concern solution concepts such as the core, the least core and the nucleolus. We characterize the complexity of these problems for a variety of subclasses of MC-nets, also considering constraints on the game...

We study properties of the minimal cross section of entanglement wedge which connects two disconnected subsystems in holography. In particular we focus on various inequalities which are satisfied by this quantity. They suggest that it is a holographic counterpart of the quantity called entanglement of purification, which measures a bipartite correlation in a given mixed state. We give a heurist...

Abstract This paper formally introduces Hart–Mas-Colell consistency for general (possibly multi-valued) solutions cooperative games with transferable utility. notion is used to axiomatically characterize the core on domain of convex games. Moreover, we all nonempty satisfying individual rationality, anonymity, scale covariance, superadditivity, weak consistency, and converse consistency. family...

Topological measures and quasi-linear functionals generalize linear functionals. We define study deficient topological on locally compact spaces. A measure a space is set function open closed sets which finitely additive sets, inner regular outer sets. Deficient measures. First we investigate positive, negative, total variation of signed that only assumed to be These variations turn out Then ex...

The functional properties of the entropy gives rise to 6 possible types of thermodynamics. Additivity or superadditivity or subadditivity are closely related to extensivity and this is one of the characteristics used to distinguish the 6 types. We give examples (some are somewhat academic) of all of these, except one. For this purpose we draw also on black hole systems which have been proposed....

As shown by Peleg (1993), the core of market games is characterized by nonemptiness, individual rationality, superadditivity, the weak reduced game property, the converse reduced game property, and weak symmetry. It was not known whether weak symmetry was logically independent. With the help of a certain transitive 4-person TU game, it is shown that weak symmetry is redundant in this result. He...

In quantum information theory, there are several important open problems which center around whether certain quantities are additive or not. Especially, additivity conjecture about Holevo capacity and additivity/strong superadditivity conjecture about entanglement of formation have been attracting many researchers. It recently turned out that these are equivalent to the additivity of the minimu...