The causal perturbation expansion of the fermionic projector is performed with a contour integral method. Different normalization conditions are analyzed. It is shown that the corresponding light-cone expansions are causal in the sense that they only involve bounded line integrals. For the resulting loop diagrams we prove a generalized Furry theorem.

Abstract The invention of the ‘dual resonance model’ N-point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic cont...

We present a semantics-driven contour tree visualization approach to support exploring and comparing cohort-level brain white matter connectivities. A contour tree is a topological method that stores the nesting relationships of the contours in a scalar field, here a brain water molecule movement measure of factional anisotropy (FA) values. Previous contour tree visualizations have lacked the c...

This paper concerns the frequency domain problem of diffraction of a plane wave incident on an infinite right-angled wedge on which impedance (absorbing) boundary conditions are imposed. It is demonstrated that the exact Sommerfeld-Malyuzhinets contour integral solution for the diffracted field can be transformed to a line integral over a physical variable along the diffracting edge. This integ...

The invention of the “dual resonance model” N -point functions BN motivated the development of current string theory. The simplest of these models, the four-point function B4, is the classical Euler Beta function. Many standard methods of complex analysis in a single variable have been applied to elucidate the properties of the Euler Beta function, leading, for example, to analytic continuation...

This paper employs a contour integral method to derive and evaluate the infinite sum of Euler polynomial expressed in terms Hurwitz Zeta function. We provide formulae for several classes sums Riemann function fundamental mathematical constants, including Catalan’s constant. representation constant suggests it could be rational.

Evaluating the power densities emitted by GSM1800 and GSM900 BTS antennas isconducted via two methods. Measurements are carried out in half a square meter grids around twoantennas. CST Microwave STUDIO software is employed to estimate the power densities in order fordetailed antenna and tower modeling and simulation of power density. Finally, measurements obtainedfrom computational and experime...

This paper shows how to apply Leibniz's integral rule calculate the action variables for Kepler problem. method offers an attractive alternative usual technique of complex contour integration. The presented here definite integrals has a broad scope and is especially suitable undergraduates who are unfamiliar with analysis.

Abstract— We present an a-posteriori method for computing rigorous upper and lower bounds of the J-integral in two dimensional linear elasticity. The J-integral, which is typically expressed as a contour integral, is recast as a surface integral which yields a quadratic continuous functional of the displacement. By expanding the quadratic output about an approximate finite element solution, the...

We apply the optimization procedure based on the Principle of Minimal Sensitivity to the third-order calculation of Rτ . Since the effective couplant remains finite, freezing to a value αs/π = 0.26 at low energies, we can actually evaluate the defining integral of Rτ and compare the optimized perturbation theory result to that of the optimized result obtained after the integral has been evaluat...