Nonclassical states of light play a central role in many quantum information protocols. Very recently, their quantum features have been exploited to improve the readout of information from digital memories, modeled as arrays of microscopic beam splitters [Pirandola, Phys. Rev. Lett. 106, 090504 (2011)]. In this model of “quantum reading,” a nonclassical source of light with Einstein-Podolski-Ro...

Vehicle crashes account for over one million fatalities and many more millions of injuries annually worldwide. Some roads are safer than others, so driving routes optimized for safety may reduce the number of crashes. We have developed a method to estimate the probability of a crash on any road as a function of the traffic volume, road characteristics, and environmental conditions. We trained a...

This work, Bernoulli wavelet method is formed to solve nonlinear fuzzy Volterra-Fredholm integral equations. Bernoulli wavelets have been Created by dilation and translation of Bernoulli polynomials. First we introduce properties of Bernoulli wavelets and Bernoulli polynomials, and then we used it to transform the integral equations to the system of algebraic equations. We compared the result o...

Let {Bn(x)} denote Bernoulli polynomials. In this paper we generalize Kummer’s congruences by determining Bk(p−1)+b(x)=(k(p − 1) + b) (modp), where p is an odd prime, x is a p-integral rational number and p − 1 b. As applications we obtain explicit formulae for ∑p−1 x=1 (1=x ) (modp ); ∑(p−1)=2 x=1 (1=x ) (modp ); (p − 1)! (modp ) and Ar(m;p) (modp), where k ∈ {1; 2; : : : ; p− 1} and Ar(m;p) i...

• Axioms: A proposition that is not proven or demonstrated but considered either to be self-evident or to define and delimit the realm of analysis. • Bernoulli Distribution: A discrete binary distribution determined by the probability of success or failure. • Bernoulli Random Variable: Typically a binomial random variable expressed as the function of two parameters: the number of trials and the...