We prove a Vasyunin-type formula for an autocorrelation function arising from Nyman-Beurling criterion generalized to probabilistic framework. This can also be seen as reciprocity cotangent sums, related the ones proven in [BC13], [ABB17].

Padé-type approximants are rational functions that approximate a given formal power series. Boutry [Numer. Algorithms, 33 (2003), pp 113–122] constructed correspond to the averaged Gauss quadrature rules introduced by Laurie [Math. Comp., 65 (1996), pp. 739–747]. More recently, Spalević 76 (2007), 1483–1492] proposed optimal rules, have higher degree of precision than corresponding with...

in this research a three dimensional model is explained which simulate the oil spill behavior inseas. this model is the developed version of previous two-dimensional study of aghajanloo et al., 2013.because of three-dimensional nature of the oil dispersion/movement in water, this is a more realistic model of oil spill transport and fate in marine environment. the model is based on eulerian appr...

t-shape profile barriers are one of the most successful barriers among many different profiles. it has been shown that using welled diffusers on the top of t-shaped barriers makes a reactive barrier that shows better performance than that of any other used profile barriers compared with their equivalent absorbent barrier. the contribution of the top surface of reactive t-profile barriers to the...