In this present work we derive, evaluate and produce a table of definite integrals involving logarithmic exponential functions. Some the closed form solutions derived are expressed in terms elementary or transcendental A substantial part is new.

We discuss the possibility of using multiple shift-invert Lanczos and contour integral based spectral projection method to compute a relatively large number of eigenvalues of a large sparse and symmetric matrix. The key to achieving high parallel efficiency in this type of computation is to divide the spectrum into several intervals in a way that leads to optimal use of computational resources....

In this paper, we compute E[Q(‖X‖], where X is an n × 1 complex circularly Gaussian vector, ‖X‖ is the L norm of X and E[ ] is the expectation operator. This is done by finding the characteristic function of the decision variable and subsequently applying the inversion formula to obtain a one dimensional real integral expression. This integral is then converted to a contour integral which is ev...

The contributions coming from the first two terms correspond to Rτ,V and Rτ,A respectively, while Rτ,S contains the remaining Cabibbo-suppressed contributions. The integrand in Eq. (3) cannot be calculated at present from QCD. Nevertheless the integral itself can be calculated systematically by exploiting the analytic properties of the correlators Π(s). They are analytic functions of s except a...

Three-body resonances in atomic systems are calculated as complexenergy solutions of Faddeev-type integral equations. The homogeneous FaddeevMerkuriev integral equations are solved by approximating the potential terms in a Coulomb-Sturmian basis. The Coulomb-Sturmian matrix elements of the three-body Coulomb Green’s operator has been calculated as a contour integral of two-body Coulomb Green’s ...

The Picard-Lefschetz theory has been attracting much attention as a tool to evaluate multi-variable integral with complex weight, which appears in various important problems theoretical physics. idea is deform the integration contour based on Cauchy's theorem using so-called gradient flow equation. In this paper, we propose fast Hybrid Monte Carlo algorithm for evaluating integral, where "backp...

The factorization theorem mentioned in the title is about matrix-valued functions satisfying the Lipschitz condition on the real line and is related to the Riemann problem. Many questions of mathematical physics reduce to what is called the Riemann problem, which consists in finding a certain scalaror vector-valued piecewise holomorphic function. This function is assumed to be regular inside an...