Kussmaul's (1969) formulation of acoustic scattering problems involves the superposition of a double-layer distribution and a simple-layer distribution on the boundary.This ensured the existence of a unique solution for all wave numbers of the incoming wave. However,the boundary integral equation involves a highly singular kernel which proves difficult to treat numerically. An alternative appro...

‎an  oriented perfect path double cover (oppdc) of a‎ ‎graph $g$ is a collection of directed paths in the symmetric‎ ‎orientation $g_s$ of‎ ‎$g$ such that‎ ‎each arc‎ ‎of $g_s$ lies in exactly one of the paths and each‎ ‎vertex of $g$ appears just once as a beginning and just once as an‎ ‎end of a path‎. ‎maxov{'a} and ne{v{s}}et{v{r}}il (discrete‎ ‎math‎. ‎276 (2004) 287-294) conjectured that ...

A bstract We study Jackiw-Teitelboim gravity with positive cosmological constant as a model for de Sitter quantum gravity. focus on the mechanics of at past and future infinity. There is Hilbert space asymptotic states an infinite-time evolution operator between far future. This not unitary, although we find that it acts unitarily subspace up to non-perturbative corrections. These corrections c...

A gauge group is the topological of automorphisms a principal bundle. We compute integral cohomology ring classifying spaces groups U(n)-bundles over 2-sphere by generalizing operation for free loop spaces, called double suspension.

An anisotropic double crystal (double in short) is a mathematical model of simplest multi-crystal. It consists two connected regions the space enclosing prescribed volumes that contact each other. Its energy integral an density over surface, and depends on normal direction surface at point. A critical point this energy. We derive geometric characterization crystals. In plane, for certain functi...

The purpose of this study was to investigate the potential benefits of using triple-arc volumetric-intensity modulated arc radiotherapy (RapidArc (RA)) for the treatment of early-stage nasopharyngeal carcinoma (NPC). A comprehensive evaluation was performed including plan quality, integral doses, and peripheral doses. Twenty cases of stage I or II NPC were selected for this study. Nine-field sl...

In this study, we prove equality for twice partially differentiable mappings involving the double generalized fractional integral. Using established identity, offer some Simpson?s type inequalities co-ordinated convex functions in a rectangle from plane R2.

A bstract Elliptic multiple polylogarithms occur in Feynman integrals and particular scattering amplitudes. They can be characterized by their symbol, a tensor product the so-called symbol letters. In contrast to non-elliptic case, elliptic letters themselves satisfy highly non-trivial identities, which we discuss this paper. Moreover, introduce prime, an analog of for letters, makes these iden...

A class of functions involving the divided differences of the psi function and the polygamma functions and originating from Kershaw’s double inequality are proved to be completely monotonic. As applications of these results, the monotonicity and convexity of a function involving ratio of two gamma functions and originating from establishment of the best upper and lower bounds in Kershaw’s doubl...