Modular arithmetic is the underlying integer computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of modular arithmetic formulae over the finite ring Z2ω . Although an upper bound of 2 2 4) can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Further, we give an effi...

Modular arithmetic is the underlying integral computation model in conventional programming languages. In this paper, we discuss the satisfiability problem of propositional formulae in modular arithmetic over the finite ring Z2ω . Although an upper bound of 2 2 O(n4) can be obtained by solving alternation-free Presburger arithmetic, it is easy to see that the problem is in fact NP-complete. Fur...

Local authorities in the UK have been set challenging new targets for recycling household waste for 2003/4. This means many of them are urgently trying to determine which parameters in kerbside schemes are most important for increasing recycling rates. In this work information from previous kerbside schemes was used to plan significant improvements in an existing scheme in Horsham District, UK,...

Arithmetic Transform (AT) has been known under various names, including Inverse Integer Reed-Muller (IRM) transform. We outline the developments that place AT in the center of very practical arithmetic circuit applications, and explain the conditions for making the AT practical. We show that AT allows the only known scheme of treating all the approximation and imprecision sources of arithmetic ...

Part II deals in some detail with practical methods of individualising the study of reading, poetry, composition, grammar, spelling, arithmetic, history and geography. The suggestions are not all of equal value. The methods suggested for individual work in reading are on the whole the most valuable, although there is perhaps a tendency to stress the testing, by means of written answers, of what...

Approximating a binomial distribution by a suitable normal distribution is a well known practice, and widely discussed in introductory level statistics books. Recently it has been shown (in Chang et al. (2008)) that the skew-normal distributions can provide a far better approximation than the normal ones. This article revisits the approximation issue and other related inferential aspects. Thoug...

The nonlinear solvers in numerical solution of water flow in variably saturated soils are prone to convergence difficulties. Many aspects can give rise to such difficulties, like very dry initial conditions, a steep pressure gradient and great variation of hydraulic conductivity occur across the wetting front during the infiltration of water.  So, the averaging method applied to compute hydraul...

This paper is a summary of the historical measurement system that was used by the Telugu people before it was replaced by the modern metric system. Measures of volume, weight and length along with the arithmetic notation used to write the measures are described here. Many of the words that represent a unit of a certain measurement are still used; most often their original meaning is lost. The s...