In this article, we first give a modified Schwarz–Pompeiu formula in general sector ring with angle \(\vartheta =\frac{\pi }{\alpha },\ \alpha \ge 1/2\) by proper conformal mappings, and obtain the solution of Schwarz problem for Cauchy–Riemann equation explicit forms. Furthermore, construct some integral operators discuss their properties detail. Finally, virtue these operators, problems an in...

A mathematical model is developed for the steady-state electric current flow through in a homogeneous isotropic conductor whose shape body of rotation. The rotation considered bounded by coordinate surfaces an orthogonal curvilinear system. equations Maxwell’s theory solid are used to formulate corresponding boundary value problem. studied conduction problem axisymmetric. determination steady m...

We describe a framework to build distances by measuring the tightness of inequalities, and introduce the notion of proper statistical divergences and improper pseudo-divergences. We then consider the Hölder ordinary and reverse inequalities, and present two novel classes of Hölder divergences and pseudo-divergences that both encapsulate the special case of the Cauchy-Schwarz divergence. We repo...

The Boolean ring $B$ of measurable subsets of the unit interval, modulo sets of measure zero, has proper radical ideals (for example, ${0})$ that are closed under the natural metric, but has no prime ideal closed under that metric; hence closed radical ideals are not, in general, intersections of closed prime ideals. Moreover, $B$ is known to be complete in its metric. Togethe...

We prove new incidence bounds between a plane point set, which is Cartesian product, and set of translates H the hyperbola xy=??0, over field asymptotically large positive characteristic p. They improve recent by Shkredov, are based on using explicit estimates in early terminated procedure repeated applications Cauchy-Schwarz inequality, underlying many qualitative results related to growth exp...

This paper addresses a new segmentation model for texture image based on active contour and the model is driven by the simplified Cauchy-Schwarz divergence. First, we define a new texture descriptor with the Gauss curvature and the mean curvature of the textural region to represent the textural image space. Then, a novel active contour model has been developed to distinguish between object of i...