On a certain asymptotic expansion

On the asymptotic expansion of certain plane singular integral operators

*Correspondence: [email protected] Chair of Differential Equations, Belgorod National Research University, Studencheskaya 14/1, Belgorod, 308007, Russia Abstract We discuss the problem of the asymptotic expansion for some operators in a general theory of pseudo-differential equations on manifolds with borders. Using the distribution theory one obtains certain explicit representation...

On the Asymptotic Distribution of Certain Sums

An Asymptotic Expansion for the Number of Permutations with a Certain Number of Inversions

Let b(n, k) denote the number of permutations of {1, . . . , n} with precisely k inversions. We represent b(n, k) as a real trigonometric integral and then use the method of Laplace to give a complete asymptotic expansion of the integral. Among the consequences, we have a complete asymptotic expansion for b(n, k)/n! for a range of k including the maximum of the b(n, k)/n!. AMS Subject Classific...

On the Asymptotic Expansion of Bergman Kernel

We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.

New Expansion for Certain Isomers of Various Classes of Fullerenes

This paper is dedicated to propose an algorithm in order to generate the certain isomers of some well-known fullerene bases. Furthermore, we enlist the bipartite edge frustration correlated with some of symmetrically distinct innite families of fullerenes generated by the oered process.