The rhizosphere, the narrow zone of soil around plant roots, is a complex network of interactions between plants, bacteria, and a variety of other organisms. The absolute dependence on host-derived signals, or xenognosins, to regulate critical developmental checkpoints for host commitment in the obligate parasitic plants provides a window into the rhizosphere's chemical dynamics. These sessile ...

Although classic valve-sparing root repair yields excellent results (survival at 10 years of 93.5%, freedom from structural valve deterioration at 10 years of 96.1% [1]), I agree with Siepe and colleagues [2] that extensive skeletonization of the aortic root might jeopardize an abnormal circumflex artery arising from the right coronary sinus and crossing the dorsal aspect of the annulus. I also...

In this paper, based in the L ukasiewicz logic, the definition offuzzifying soft neighborhood structure and fuzzifying soft continuity areintroduced. Also, the fuzzifying soft proximity spaces which are ageneralizations of the classical soft proximity spaces are given. Severaltheorems on classical soft proximities are special cases of the theorems weprove in this paper.

In this paper‎, ‎we introduce a new type of graph contraction using a special class of functions and give a best proximity point theorem for this contraction in complete metric spaces endowed with a graph under two different conditions‎. ‎We then support our main theorem by a non-trivial example and give some consequences of best proximity point of it for usual graphs.

Abstract Background The proximity of the maxillary sinus floor to molar roots increases probability oroantral communication on conducting any surgical or endodontic procedure in involved area. aim this study is evaluate relationship between each root and using cone beam computed tomography. Predicting protrusion into will consequently predict occurrence fistula a sample Egyptian population. Res...

University of Perugia 4.

In this paper, we establish some best proximity point theorems using new proximal contractive mappings in asymmetric $G_{p}$-metric spaces. Our motive is to find an optimal approximate solution of a fixed point equation. We provide best proximity points for cyclic contractive mappings in $G_{p}$-metric spaces. As consequences of these results, we deduce fixed point results in $G_{p}$-metric spa...