(Generalized) Riemann Hypothesis (that all non-trivial zeros of the (Dirichlet L-function) zeta function have real part one-half) is arguably the most important unsolved problem in contemporary mathematics due to its deep relation to the fundamental building blocks of the integers, the primes. The proof of the Riemann hypothesis will immediately verify a slew of dependent theorems ([BRW], [SA])...

We study the roles of quark-pair correlations for baryon properties, in particular on non-leptonic weak decay of hyperons. We construct the quark wave function of baryons by solving the three body problem explicitly with confinement force and the short range attraction for a pair of quarks with their total spin being 0. We show that the existence of the strong quark-quark correlations enhances ...

In many practical situations, we are not satisfied with the accuracy of the existing measurements. There are two possible ways to improve the measurement accuracy: • first, instead of a single measurement, we can make repeated measurements; the additional information coming from these additional measurements can improve the accuracy of the result of this series of measurements; • second, we can...

The class of games for which the core coincides with the core cover (compromise stable games) is characterized. Moreover an easy explicit formula for the nucleolus for this class of games is developed, using an approach based on bankruptcy problems. Also, the class of convex and compromise stable games is characterized. The relation between the core cover and the Weber set is studied and it is ...

Let A be a standard graded Artinian K-algebra, with char K = 0. We prove the following. 1. A has the Weak Lefschetz Property (resp. Strong Lefschetz Property) if and only if Gr(z)(A) has the Weak Lefschetz Property (resp. Strong Lefschetz Property) for some linear form z of A. 2. If A is Gorenstein, then A has the Strong Lefschetz Property if and only if there exists a linear form z of A such t...

The Fudenberg and Maskin (1986) folk theorem for discounted repeated games assumes that the set of feasible payoffs is full dimensional. We obtain the same conclusion using a weaker condition. This condition is that no pair of players has equivalent von Neumann-Morgenstern utilities over outcomes. We term this condition NEU "non-equivalent utilities". The condition is weak, easily interpreted, ...

recently, choudhury and metiya [fixed points of weak contractions in cone metric spaces, nonlinear analysis 72 (2010) 1589-1593] proved some fixed point theorems for weak contractions in cone metric spaces. weak contractions are generalizations of the banach's contraction mapping, which have been studied by several authors. in this paper, we introduce the notion of $f$-weak contractions and als...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...