We prove the arithmetic Hodge index and hard Lefschetz conjectures for the Grassmannian G = G(2, N) parametrizing lines in projective space, for the natural arithmetic Lefschetz operator defined via the Plücker embedding of G in projective space. The analysis of the Hodge index inequality involves estimates on values of certain Racah polynomials. 0. Introduction Let X be an arithmetic variety, ...

We address the intractable multi-armed bandit problem with switching costs, for which Asawa and Teneketzis introduced in [M. Asawa and D. Teneketzis. 1996. Multi-armed bandits with switching penalties. IEEE Trans. Automat. Control, 41 328–348] an index that partially characterizes optimal policies, attaching to each project state a “continuation index” (its Gittins index) and a “switching index...

In this paper, we present necessary and sufficient conditions for the existence of positive C3[0, 1]∩C4(0, 1) solutions for the singular boundaryvalue problem x′′′′(t) = p(t)f(x(t)), t ∈ (0, 1); x(0) = x(1) = x′(0) = x′(1) = 0, where f(x) is either superlinear or sublinear, p : (0, 1) → [0,+∞) may be singular at both ends t = 0 and t = 1. For this goal, we use fixed-point index results.

The geometric-arithmetic index of graph G is defined as GA(G) = ∑ uv∈E(G) 2 √ dudv du+dv , du (or dv) is the degree the vertex u (or v). The GA index of benzenoid systems and phenylenes are computed, a simple relation is established between the geometric-arithmetic of a phenylene and the corresponding hexagonal squeeze in this paper. Mathematics Subject Classification: 05C05, 05C12

Ap(X,H) is called the hard Lefschetz conjecture and Hp(X,H) is called the Hodge index conjecture. When the characteristic of k is zero, the Hodge index conjecture is already proved. On the other hand, for an arithmetic variety the intersection theory of cycles was established by Arakelov [1] for surfaces and Gillet and Soulé [5] for higher dimensional varieties. It is quite natural to ask wheth...

In this paper a set of de nitions describing general real number representation sys tems is presented Our purpose is to nd a su ciently wide model de nition including classical systems signed digit notation linear numeration systems p adic numbers symmetric level index arithmetic but speci c enough to make it possible to build some practical results We focuse on the redundancy property and the ...

Background: The seeds of some medicinal plants and their compounds have long been valued for their numerous health benefits. Objective:To investigate some physical and chemical properties of Salvia spp. Methods: Some physico-chemical properties in five species of Salvia seeds (consisted of S. officinalis L., S. macrosiphon L., S. hypoleuca L., S. sclarea L. and S. nemorosa L.) were measured ...

In many problems, such as the analysis of electrical circuits, one has to deal with Differential-Algebraic Equations (DAE’s). Knowing their generic index is of interest for practical and numerical as well as for theoretical reasons. In this paper we give an algorithm that determines the generic index of the Circuit Equations of linear active electrical networks in polynomial time from tlie netw...