We study the distribution of Mahler’s measures of reciprocal polynomials with complex coefficients and bounded even degree. We discover that the distribution function associated to Mahler’s measure restricted to monic reciprocal polynomials is a reciprocal (or anti-reciprocal) Laurent polynomial on [1,∞) and identically zero on [0, 1). Moreover, the coefficients of this Laurent polynomial are r...

hydrological drought refers to a persistently low discharge and volume of water in streams and reservoirs, lasting months or years. hydrological drought is a natural phenomenon, but it may be exacerbated by human activities. hydrological droughts are usually related to meteorological droughts, and their recurrence interval varies accordingly. this study pursues to identify a stochastic model (o...

We analyse the asymptotic behaviour in the mean of a non-commutative rational series, which originates from differential cryptanalysis, using elementary tools from analysis and linear algebra, and more sophisticated tools from analytic number theory. We show that a probability distribution function describes the asymptotic behaviour of the rational series according to the length of words. As a ...

Psychological factors are commonly believed to play a role on cyclical economic fluctuations, but they are typically omitted from state-of-the-art macroeconomic models. This paper introduces “sentiment” in a medium-scale DSGE model of the U.S. economy and tests the empirical contribution of sentiment shocks to business cycle fluctuations. The assumption of rational expectations is relaxed. The ...

Based on the principles of equalized sliding coefficients and equalized teeth bending strength, the optimization mathematical model for calculating and allocating the addendum modification coefficients of involute cylindrical gear is firstly established. Then the measures to calculate the tooth parameters in real-time during the optimization steps are achieved. Finally, the optimization program...

In this paper we first intend to examine the probability of falling into the realm of child labor by using conditional probability theorem. Furthermore, we will compare the extent of each factor’s effect on boys and girls using a TOBIT regression model. Finally we will analyze aspects of Iran’s labor market to assess the future ahead of the children who work at present. As the results will show...

In this research study, energy, exergy and economic analyses is performed for a combined cycle power plant (CCPP) with a supplementary firing system. The purpose of this analyses is to evaluate the economic feasibility of a CCPP by applying an optimization techniques based on Evolutionary algorithms. Actually, the evolutionary algorithms of Firefly, PSO and NSGA-II are applied to minimize the c...

Based on his study of the Hilbert scheme from algebraic geometry, Haiman [Invent. Math. 149 (2002), pp. 371–407] obtained a formula for the character of the space of diagonal harmonics under the diagonal action of the symmetric group, as a sum of Macdonald polynomials with rational coefficients. In this paper we show how Haiman’s formula, combined with identities involving plethystic symmetric ...