This paper generalizes the speciication of Basic Interval Arithmetic Sub-routines (BIAS) to support interval arithmetic on directed (i.e. proper and improper) intervals. This is due to our understanding that the arithmetic involving improper intervals will be increasingly used in future applications and the corresponding interval arithmetic implementations require no additional cost. We extend ...

In this paper we give mathematical proofs of two new results relevant to evaluating algebraic functions over a box-shaped region: (i) using interval arithmetic in centered form is always more accurate than standard affine arithmetic, and (ii) modified affine arithmetic is always more accurate than interval arithmetic in centered form. Test results show that modified affine arithmetic is not onl...

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...

A general method of interpreting weak higher-type theories of nonstandard arithmetic in their standard counterparts is presented. In particular, this provides natural nonstandard conservative extensions of primitive recursive arithmetic, elementary recursive arithmetic, and polynomial-time computable arithmetic. A means of formalizing basic real analysis in such theories is sketched. §

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