We derive non-abelian Toda field theories (NATFTs) from a 4d Chern-Simons (CS) theory with two order defects by employing certain asymptotic boundary condition. The CS is characterized meromorphic 1-form $\omega$\,. adopt $\omega$ simple poles and no zeros, each of the located at pole. As result, an anisotropy parameter $\beta^2$ can be identified distance between defects. examples, we (complex...

and some related integrals, where γ denotes imaginary parts of complex zeros of ζ(s), and where every zero is counted with its multiplicity (see also [5] and [7]). The interest is in obtaining unconditional bounds for the above sum, since assuming the Riemann Hypothesis (RH) the sum trivially vanishes. A more general sum than the one in (1.1) was treated by S.M. Gonek [3]. He proved, under the ...

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...

We give a simple proof of an isomorphism between two C[t]-modules corresponding to bivariate polynomial H with nondegenerate highest homogeneous part: the module of relative cohomologies Λ 2 /dH ∧ Λ 1 and the module of Abelian integrals. Using this isomorphism, we prove existence and deduce some properties of the corresponding Picard-Fuchs system.

A new class of exact solutions to the axisymmetric and stationary vacuum Einstein equations containing n arbitrary complex parameters and one arbitrary real solution of the axisymmetric three–dimensional Laplace equation is presented. The solutions are related to Jacobi's inversion problem for hyperelliptic Abelian integrals.

Using a direct approach the return map near a focus of a planar vector field with nilpotent linear part is found as a convergent power series which is a perturbation of the identity and whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals.

The return map for planar vector fields with nilpotent linear part (having a center or a focus and under an assumption generically satisfied) is found as a convergent power series whose terms can be calculated iteratively. The first nontrivial coefficient is the value of an Abelian integral, and the following ones are explicitly given as iterated integrals built with algebraic functions.

In this paper an algorithm is presented for the regularization of singular integrals with any degrees of singularity, which may be employed in all three-dimensional problems analyzed by Boundary Elements. The integrals in Boundary Integrals Equations are inherently singular. For example, one can mention the integrals confronted in potential problems to evaluate the flow or the gradient of the f...