‎We study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎These equations will be converted to a system of‎ ‎singular integral equations with Cauchy type kernels‎. ‎Using‎ ‎Chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of Cauchy type singular integral equation which will ...

We define signed dual volumes at all dimensions for circumcentric dual meshes. We show that for pairwise Delaunay triangulations with mild boundary assumptions these signed dual volumes are positive. This allows the use of such Delaunay meshes for Discrete Exterior Calculus (DEC) because the discrete Hodge star operator can now be correctly defined for such meshes. This operator is crucial for ...

The Aleksandrov-Fenchel inequalities from the theory of mixed volumes are used to prove that certain sequences of combinatorial interest are log concave (and therefore unimodal). 1. MIXED VOLUMES We wish to show how the Aleksandrov-Fenchel inequalities from the theory of mixed volumes can be used to prove that certain sequences of combinatorial interest are log concave (and therefore unimodal)....

Introduction: Transient cavitations induced by low frequency irradiation of ultrasound can be used to treat tumors. Previous studies in in-vitro experiments have shown that induced cavitation by dual or multiple frequencies of ultrasound is greater than induced cavitation by single frequency irradiation. In this study, we compared and evaluated the treatment effects of dual frequency irradiatio...