We investigate the equations of motion in the four-dimensional non-anticommutative N=2 supersymmetric U(1) gauge field theory, in the search for BPS configurations. The BPS-like equations, generalizing the abelian (anti)self-duality conditions, are proposed. We prove full solvability of our BPS-like equations, as well their consistency with the equations of motion. Certain restrictions on the a...

This paper deals with a new Gronwall-like integral inequality which is a generalization of integral inequalities proved by Engler (1989) and Pachpatte (1992). The new Gronwall-like integral inequality can be used in various problems in the theory of certain class of ordinary and integral equations. 1. Introduction. It is well known that integral inequalities play a very crucial role in the stud...

Fractonic superfluids are exotic states of matter with spontaneously broken higher-rank $U(1)$ symmetry. The latter is associated conserved quantities that include not only particle number (i.e. charge) but also higher moments, such as dipoles, quadrupoles, and angular moments. Due to the presence quantities, mobility particles restricted either completely or partially. In this work, we systema...

In this study, we present a convergence analysis of Newton-like midpoint method for solving nonlinear equations in Banach space setting. The semilocal is analyzed two different ways. first one shown by replacing the existing conditions with weaker and tighter continuity conditions, thereby enhancing its applicability. second uses more general ?-continuity majorizing principle. This approach inc...