-In this paper we have estimate bounds of the number of level crossings of the random algebraic polynomials     n k k k n x t a x f 0 0 ) ( ) 1 , ( where , 1 0 , ) (    t t t ak are dependent random variables assuming real values only and following the normal distribution with mean zero and joint density function      M M s a ' ) 2 / 1 ( exp ) 2 ( / 2 / 1   . There exists an integ...

We investigate the dynamic stochastic multicriteria decision making (SMCDM) problems, in which the criterion values take the form of log-normally distributed random variables, and the argument information is collected from different periods. We propose two new geometric aggregation operators, such as the log-normal distribution weighted geometric (LNDWG) operator and the dynamic log-normal dist...

The logarithmic-exponential (log-exp) function has been widely used in convex analysis and mathematical programming. This paper studies a natural generalization of the log-exp function. Certain necessary and sufficient conditions are obtained for establishing such a generalization. The derived sufficient conditions are explicitly expressed in terms of the first and second derivatives of the fun...

This paper shows, assuming standard heuristics regarding the number-field sieve, that a “batch NFS” circuit of area L factors L separate B-bit RSA keys in time L. Here L = exp((log 2)(log log 2)). The circuit’s area-time product (priceperformance ratio) is just L per key. For comparison, the best area-time product known for a single key is L. This paper also introduces new “early-abort” heurist...

Let m(n) be the number of ordered factorizations of n ≥ 1 in factors larger than 1. We prove that for every ε > 0 m(n) < nρ exp ( (log n)1/ρ/(log log n)1+ε ) holds for all integers n > n0, while, for a constant c > 0, m(n) > nρ exp ( c(log n/ log log n)1/ρ ) holds for infinitely many positive integers n, where ρ = 1.72864 . . . is the real solution to ζ(ρ) = 2. We investigate also arithmetic pr...

In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and unit-Gompertz model, which named unit Gompertz distribution. The key feature of such novel is that it adds tuning parameter to using in order make more flexible. Diagrams numerical results are used look at model’s mathematical statistical aspects. efficiency estimating distribution para...

Let $E/\\mathbb{Q}$ be an elliptic curve over the rational numbers. It is known, by work of Bombieri and Zannier, that if $E$ has full 2-torsion, number $N_E(B)$ points with Weil height bounded $B$ $\\operatorname{exp}\\big(O \\big(\\frac{\\operatorname{log}B}{\\sqrt{\\operatorname{log}\\operatorname{log} B}}\\big)\\big)$. In this paper we exploit method descent via 2-isogeny to extend result c...

This study analyses the sources of atrazine contamination in the Brusselian sandy aquifer of central Belgium. Atrazine has in the past been used for both agricultural and non-agricultural applications, but it is difficult to distinguish the contamination originating from these two sources. The spatial and temporal covariance of atrazine concentrations was studied by fitting semi-variogram model...