This paper extends the modified affine arithmetic in matrix form method for bivariate polynomial evaluation and algebraic curve plotting in 2D to modified affine arithmetic in tensor form for trivariate polynomial evaluation and algebraic surface plotting in 3D. Experimental comparison shows that modified affine arithmetic in tensor form is not only more accurate but also much faster than affin...

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 ...

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 ...

We extend Meyer’s 1972 investigation of sets of minimal indices. Blum showed that minimal index sets are immune, and we show that they are also immune against high levels of the arithmetic hierarchy. We give optimal immunity results for sets of minimal indices with respect to the arithmetic hierarchy, and we illustrate with an intuitive example that immunity is not simply a refinement of arithm...

The paper describes an efficient method to prove equivalence between two integer arithmetic datapath designs specified at the register transfer level. The method is illustrated with an industrial ALU design. As reported in literature, solving it using a commercial equivalence checking tool required casesplitting, which limits its applicability to larger designs. We show how such a task can be s...

This paper generalizes the speci cation of Basic Interval Arithmetic Subroutines (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 B...

The second geometric-arithmetic index GA2(G) of a graph G was introduced recently by Fath-Tabar et al. [2] and is defined to be ∑ uv∈E(G) √ nu(e,G)nv(e,G) 1 2 [nu(e,G)+nv(e,G)] , where e = uv is one edge in G, and nu(e,G) denotes the number of vertices in G lying closer to u than to v. In this paper, we characterize the tree with the minimum GA2 index among the set of trees with given order and...

This paper begins with a general introduction to the symmetric level-index, SLI, system of number representation and arithmetic. This system provides a robust framework in which experimental computation can be performed without the risk of failure due to overflow/underflow or to poor scaling of the original problem. There follows a brief summary of some existing computational experience with th...