the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

An array of different types of hyaluronic acid (HA)- and collagen-based products is available for filling soft-tissue defects. A major drawback of the current soft-tissue fillers is their inability to induce cell infiltration and new tissue formation. Our aim is to develop novel biodegradable injectable gels which induce soft tissue regeneration, initially resulting in integration and finally r...

The main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (briefly soft rgb-closed set) Moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g$alpha$-closed, soft g$alpha$b-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and w...

We study new renormalization-group invariant quantities of soft supersymmetry breaking parameters other than the ratio of gaugino mass to gauge coupling squared by using the spurion method. The obtained invariants are useful to probe supersymmetry breaking and μ-term generation mechanisms at high-energy scale. We also discuss the convergence behavior of fixed points of supersymmetry breaking pa...

We derive one-loop renormalization group (RG) invariant observables and analyze their phenomenological implications in the MSSM and its μ problem solving extensions, U(1) model and NMSSM. We show that there exist several RG invariants in the gauge, Yukawa and soft-breaking sectors of each model. In general, RG invariants are highly useful for projecting experimental data to messenger scale, for...

We show that the results for the soft couplings in supersymmetric gauge theories recently derived via the superconformal anomaly are equivalent to results obtained earlier from a consideration of exact RG-invariant trajectories. We give a full proof of these results for a general multi-coupling theory. Moreover, we demonstrate the existence of a distinct finite RG-invariant solution for the sof...

Skin and soft tissue infections caused by rapidly growing non-tuberculous mycobacteria (RG-NTM) have become a growing clinical concern over the past decades. These RG-NTM are ubiquitous environmental organisms and most are resistant to traditional antituberculous agents. In this report, we describe 3 cutaneous infections caused by RG-NTM, namely, Mycobacterium abscessus, M. chelonae, and M. con...

We demonstrate that soft SUSY breaking introduced via replacement of the couplings of a rigid theory by spurion superfields has far reaching consequences. Substituting these modified couplings into renormalization constants, RG equations, solutions to these equations, fixed points, finiteness conditions, etc., one can get corresponding relations for the soft terms by a simple Taylor expansion o...