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...

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 at ...

Let G = (V,E), V {1,2,...,n}, be a simple connected graph of order n, size m with vertex degree sequence d1 ? d2 ... dn > 0, di d(vi). The geometric-arithmetic topological index is defined as GA(G) i~j 2? didj/di+dj, whereas the coindex GA?(G) i~/j 2 didj/di+dj . New lower bounds for and in terms some parameters other invariants are obtained.