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...

Arithmetic subgroups are finite index subgroups of the modular group. Classically, congruence arithmetic subgroups, which can be described by congruence relations, are playing important roles in group theory and modular forms. In reality, the majority of arithmetic subgroups are noncongruence. These groups as well as their modular forms are central players of this survey article. Differences be...

This paper is a blueprint for the use of a massively parallel SIMD computer architecture for the simulation of various forms of computer arithmetic. The particular system used is a DEC/MasPar MP-1 with 4096 processors in a square array. This architecture has many advantages for such simulations due largely to the simplicity of the individual processors. Arithmetic operations can be spread acros...

Symmetric level-index arithmetic was introduced to overcome recognized limitations of oating-point systems, most notably overrow and un-derrow. The original recursive algorithms for arithmetic operations could be parallelized to some extent, particularly when applied to extended sums or products, and a SIMD software implementation of some of these algorithms is described. The main purpose of th...

Ranking of triangular intuitionistic fuzzy numbers (TIFNs) is an important problem, which is solved by the value and ambiguity based ranking method developed in this paper. Firstly, the concept of TIFNs is introduced. Arithmetic operations and cut sets over TIFNs are investigated. Then, the values and ambiguities of the membership degree and the non-membership degree for TIFNs are defined as we...