We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.

Positive solutions of systems of Hammerstein integral equations are studied by using the theory of the fixed-point index for compact maps defined on cones in Banach spaces. Criteria for the fixed-point index of the Hammerstein integral operators being 1 or 0 are given. These criteria are generalizations of previous results on a single Hammerstein integral operator. Some of criteria are new and ...

Symmetric level-index arithmetic was introduced to overcome the problems of overflow and underflow in the floating-point system. The purpose of this paper is to improve the algorithm performance of SLI arithmetic by introducing an approximation scheme using Taylor’s expansion. Following a brief summary of the SLI system and its algorithm for addition/subtraction, the deduction and analysis of T...

let $f$ be a finite extension of $bbb q$‎, ‎${bbb q}_p$ or a global‎ ‎field of positive characteristic‎, ‎and let $e/f$ be a galois extension‎. ‎we study the realization fields of‎ ‎finite subgroups $g$ of $gl_n(e)$ stable under the natural‎ ‎operation of the galois group of $e/f$‎. ‎though for sufficiently large $n$ and a fixed‎ algebraic number field $f$ every its finite extension $e$ is‎ ‎re...

By some analysis of the neutral operator (Ax)(t) = x(t)− ∑n i=1 cix(t− δi) and an application of the fixed-point index theorem, we obtain sufficient conditions for the existence, multiplicity and nonexistence of periodic solutions to a second-order differential equation with the prescribed neutral operator, which improve and extend some recent results of Lu-Ge, WuWang, and Zhang. An example is ...

We discuss the existence of solutions for the first-order multipoint BVPs on time scale T: uΔ t p t u σ t λf t, u σ t , t ∈ 0, T T , u 0 − ∑mi 1 αiu ξi 0, where λ > 0 is a parameter, T > 0 is a fixed number, 0, T ∈ T, f : 0, T T × 0,∞ → 0,∞ is continuous, p is regressive and rdcontinuous, αi ≥ 0, ξi ∈ T, i 1, 2, . . . , m, 0 ξ0 < ξ1 < ξ2 < · · · < ξm−1 < ξm σ T , and 1 −∑mi 1 αi/ep ξi, 0 > 0. F...

The total version of geometric–arithmetic (GA) index of graphs is introduced based on the end-vertex degrees of edges of their total graphs. In this paper, the total GA index is computed for zigzag polyhex nanotubes by using some results on GA index and mentioned nanotubes. Also, we compute the edge GA index for the subdivision graphs of TUC C (R) and TUAC [p',q'] nanotubes. 4 8 6

This paper discusses the use of a recently introduced index calculus Double-Base Number System (IDBNS) for representing and processing numbers for non-linear digital signal processing; the target application is a digital hearing aid processor. The IDBNS representation uses 2 orthogonal bases (2 and 3) to represent real numbers with arbitrary precision. By restricting the number of digits to one...

This paper proposes the development of an index to assess rural based on a set 25 demographic, economic, environmental, and social welfare indicators previously selected through Delphi approach. Three widely accepted aggregation methods were then tested: mixed arithmetic/geometric mean without weightings for each indicator; weighted arithmetic using weights generated by panel Principal Componen...

Let G be a simple connected graph and di be the degree of its ith vertex. In a recent paper [D. Vukičević, B. Furtula, Topological index based on the ratios of geometrical and arithmetical means of end-vertex degrees of edges, J. Math. Chem. 46 (2009) 1369–1376] the ‘‘first geometric–arithmetic index’’ of a graph Gwas defined as GA1 = − di dj (di + dj)/2 with summation going over all pairs of ...