The Getzler’s formula relates the Sn-equivariant Hodge-Deligne polynomial of the space of ordered tuples of distinct points on a given variety X with the Hodge-Deligne polynomial of X. We obtain the analogue of this formula for the case when X has a nontrivial automorphism group. Collecting together all strata of M2 with different automorphism groups, we derive a formula for the Sn-equivariant ...

We give an explicit formula for the shuffle relation in a general double shuffle framework that specializes to double shuffle relations of multiple zeta values and multiple polylogarithms. As an application, we generalize the well-known decomposition formula of Euler that expresses the product of two Riemann zeta values as a sum of double zeta values to a formula that expresses the product of t...

The formula for the Hirzebruch χy-genus of complex manifolds is a consequence of the Hirzebruch–Riemann–Roch formula. The classical index formulae for Todd genus, Euler number and signature correspond to the case when the complex variable y = 0,−1 and 1 respectively. Here we give a direct derivation of this nice formula based on supersymmetric quantum mechanics. PACS numbers: 12.60.Jv, 02.40.Ma...

A novel procedure to reduce by four the order of Euler–Lagrange equations associated to n-th order variational problems involving single variable integrals is presented. In preparation, a new formula for the commutator of two C∞symmetries is established. The method is based on a pair of variational C∞-symmetries whose commutators satisfy a certain solvability condition. It allows one to recover...

Let {U n } be given by U 0 = 1 and U n = −2 [n/2] k=1 n 2k U n−2k (n ≥ 1), where [·] is the greatest integer function. Then {U n } is an analogy of Euler numbers and U 2n = 3 2n E 2n (1 3), where E m (x) is the Euler polynomial. In a previous paper the author gave many properties of {U n }. In the paper we present a summation formula and several congruences involving {U n }.

In this paper, we investigate the existence and uniqueness of solutions to neutral stochastic differential equations with Markovian switching and jumps (NSDEwMSJs) under non-Lipschitz conditions. On the other hand, we present the Euler approximate solutions for NSDEwMSJs and show that the convergence of the Euler approximate solutions to the true solutions by applying Itô formula, Bihari’s lemm...

In this paper we study that the q-Euler numbers and polynomials are analytically continued to Eq(s). A new formula for the Euler’s q-Zeta function ζE,q(s) in terms of nested series of ζE,q(n) is derived. Finally we introduce the new concept of the dynamics of analytically continued q-Euler numbers and polynomials. 2000 Mathematics Subject Classification 11B68, 11S40 Key wordsq-Bernoulli polynom...

The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér 2004 and R...

Contractible transformations of graphs consist of contractible gluing and deleting of vertices and edges of graphs. They partition all graphs into the family of homotopy classes. Contractible transformations do not change the Euler characteristic and the homology groups of graphs. In this paper we describe the minimal representatives of some homotopy classes and find the formula for computing t...