9] for example, and, in this paper, we introduce an index In this paper we present a rigorous theoretical analysis of the main properties of a double base number system, using bases 2 and 3; in particular we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus fo...

Investigating banks’ status has always been a concern to its management and regulatory decisions, which can be carried out by means of income diversification and CAMEL composite. The importance of income diversification is to decline the operation risk. The soundness of banking is also another essential component in the banking industry that can be evaluated by CAMEL. This article’s two primary...

Shape analyses are often imprecise in their numerical reasoning, whereas numerical static analyses are often largely unaware of the shape of a program’s heap. In this paper we propose a lazy method of combining a shape analysis based on separation logic with an arbitrary arithmetic analysis. When potentially spurious counterexamples are reported by our shape analysis, the method constructs a pu...

The use of arithmetic coding for binary image compression achieves a high compression ratio while the running time remains rather slow. A composite modelling method presented in this paper reduces the size of the data to be coded by arithmetic coding. The method is to code the uniform areas with less computation and apply arithmetic coding to the areas with more variation.

A new method (the ‘binary indexed tree’) is presented for maintaining the cumulative frequencies which are needed to support dynamic arithmetic data compression. It is based on a decomposition of the cumulative frequencies into portions which parallel the binary representation of the index of the table element (or symbol). The operations to traverse the data structure are based on the binary co...

Arithmetic complexity has a main role in the performance of algorithms for spectrum evaluation. Arithmetic transform theory offers a method for computing trigonometrical transforms with minimal number of multiplications. In this paper, the proposed algorithms for the arithmetic Fourier transform are surveyed. A new arithmetic transform for computing the discrete Hartley transform is introduced:...

quantum-dot cellular automaton (qca) is a novel nanotechnology with a very different computational method in compared with cmos, whereas placement of electrons in cells indicates digital information. this nanotechnology with specifications such as fast speed, high parallel processing, small area, low power consumption and higher switching frequency becomes a promising candidate for cmos technol...

Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient manifold as the integral over the index form plus a sum of orbital integrals. For the Euler operator these orbital integrals are shown to vanish for products of certain rank one spaces. In this case the index theorem looks exactly as in the compact case.