Stimulated by earlier work by Moll and his coworkers [1], we evaluate various basic log Gamma integrals in terms of partial derivatives of Tornheim– Witten zeta functions and their extensions arising from evaluations of Fourier series. In particular, we fully evaluate

Motivated by the need for new mathematical tools applicable to the study of fractal point-cloud distributions, expectations of complex-valued functions defined over general ‘deterministic’ fractal domains are considered, following the development of a measure-theoretic foundation for their analysis. In particular, we wish to understand and evaluate separation moments as given by integrals of th...

We provide the monotonicity and convexity properties and sharp bounds for the generalized elliptic integrals [Formula: see text] and [Formula: see text] depending on a parameter [Formula: see text], which contains an earlier result in the particular case [Formula: see text].

We consider shape functionals obtained as minima on Sobolev spaces of classical integrals having smooth and convex densities, under mixed Dirichlet-Neumann boundary conditions. We propose a new approach for the computation of the second order shape derivative of such functionals, yielding a general existence and representation theorem. In particular, we consider the p-torsional rigidity functio...

We present an asynchronous algorithm based on Quasi-Monte Carlo methods for the computation of multivari-ate integrals. Randomized Korobov and Richtmyer sequences are applied for problems of moderately high to high dimensions. We propose the use of Sobol rules in those dimensions where the integrand shows particular singular behavior. Timing results on MPI yield good speedup.

We apply path integrals to study nonequilibrium work theorems in the context of Brownian dynamics, deriving in particular the equations of motion governing the most typical and most dominant trajectories. For the analytically soluble cases of a moving harmonic potential and a harmonic oscillator with a time-dependent natural frequency, we find such trajectories, evaluate the work-weighted propa...

We give a summary on the geometry of iterated Stratonovich integrals. For this exposition, we always have the connection to stochastic Taylor expansion in mind. In particular, we believe that “cubature on Wiener space” is best understood in the setting presented in this text. Besides cubature on Wiener space, we also give a second application regarding the heat kernel on nilpotent free Lie groups.

I discuss how a variatonal approach can be extended to systems of identical particles (in particular fermions) within the path-integral treatment. The applicability of the many-body variational principle for path integrals is illustrated for different model systems, and is shown to crucially depend on whether or not a model system possesses the proper symmetry with respect to permutations of id...

Recently, many generalizations and extensions of well-known inequalities were obtained via different kinds of fractional integrals. In this paper, we show that most of those results are particular cases of (or equivalent to) existing inequalities from the literature. As consequence, such results are not real generalizations.

An efficient numerical algorithm to evaluate one-loop amplitudes using tensor integrals is presented. In particular, it is shown by explicit calculations that for ordered QCD amplitudes with a number of external legs up to 10, its performance is competitive with other methods.