We propose an efficient computation method for an infinite integral ∞ 0 xdx/(1 + x 6 sin 2 x), which has an unbounded integrand with highly oscillated singularity. Computing the value of this integral has been a problem since 1984. We herein demonstrate that the method using the Hilbert transform to change this type of singular function into a smooth function and compute the value of the integr...

The packaging of genomic RNA in members of the Cystoviridae is performed by P4, a hexameric protein with NTPase activity. Across family members such as Phi6, Phi8 and Phi13, the P4 proteins show low levels of sequence identity, but presumably have similar atomic structures. Initial structure-determination efforts for P4 from Phi6 and Phi8 were hampered by difficulties in obtaining crystals that...

In this work we extend the JIMWLK formalism to the two–source problem. The S–matrix for the forward scattering can be written in a double functional integral representation which involves the usual functional integral for the gluon field and the spin path integral for the external color sources. Modifications needed in the light–cone gauge are discussed. Using our source term we compute the pro...

This paper presents an enhanced transillumination radiosity method that can provide accurate solutions at relatively low computational cost. The proposed algorithm breaks down the double integral of the gathered power to an area integral that is computed analytically and to a directional integral that is evaluated by quasi-Monte Carlo or Monte-Carlo techniques. The paper also analyses the requi...

The first-passage time problem through two time-dependent boundaries for one-dimensional Gauss-Markov processes is considered, both for fixed and for random initial states. The first passage time probability density functions are proved to satisfy a system of continuous-kernel integral equations that can be numerically solved by an accurate and computationally simple algorithm. A condition on t...

The generalized Funk transform is a integral transform acting from densities on a manifold X to functions defined on a family Σ of hypersurfaces in X. The dual operator M is again a Funk transform which is defined for densities on the manifold Σ. We state twoside estimates for the operator M and a description of the range of the Funk transform operatorM and approximation theorem for the kernel ...

In our research, we have presented a second-order linear partial differential equation in polar coordinates. Considering this on the unit disk, obtained one-dimensional heat equation. It is well-known that can be solved taking into account boundary condition for general solution circle. paper, boundary-value problem using method called separation of variables. As result, to terms Fourier series...

In the present paper, we evaluate a finite double integral involving product of biorthogonal polynomial, a multivariable general class of polynomial and the H function with general arguments. The integral evaluated is quite general in nature and yields number of known and new integrals as its special cases. Several new interesting integrals of our findings have also been mentioned briefly.

in this paper, a generalized method for accurate full-wave analysis of shielded mic's and the three-layer microstrip structure enclosed in a rectangular cavity based on mixed potential integral equation (mpie) derived in real space have been developed. method of moments (mom) with galerkin technique has been used for the solution of the integral equation to obtain the surface electric currents ...

We construct a family of continuous biorthogonal functions related to an elliptic analogue of the Gauss hypergeometric function. The key tools used for that are the elliptic beta integral and the integral Bailey chain introduced earlier by the author. Relations to the Sklyanin algebra and elliptic analogues of the Faddeev modular double are discussed in detail.