We consider the Schrödinger operator in the plane with δ-potential supported by a curve Γ. For the cases of an infinite curve and a finite loop we give estimates on the lower bound of the spectrum expressed explicitly through the strength of the interaction and a parameter c(Γ) which characterizes geometry of the curve Γ. Going further we cut the curve into finite number of pieces Γi and estima...

IT is intuitively obvious that if a simple continuous curve is given in the (x, 2/)-plane, and a continuous distribution of values along the curve, there will exist functions of x and y which are continuous in both variables together, and which take on the prescribed values along the curve. It is the purpose of the present note to give an analytic proof of this fact, by elementary means, and, i...

background: human dental stem cells have high proliferative potential for self-renewal that is important to the regenerative capacity of the tissue. objective: the aim was to isolate human dental pulp stem cells (dpsc), periodontal ligament stem cells (pdlsc) and periapical follicle stem cells (pafsc) for their potential role in tissue regeneration. materials and methods: in this experimental s...

Computing curve skeletons of 3D shapes is a challenging task. Recently, a high-potential technique for this task was proposed, based on integrating medial information obtained from several 2D projections of a 3D shape (Livesu et al., 2012). However effective, this technique is strongly influenced in terms of complexity by the quality of a so-called skeleton probability volume, which encodes pot...

Abstract-Consider the motion of a curve in the plane under its mean curvature. It is a very interesting problem to investigate what happens when there are intersection points on the curve at which the mean curvature is singular. In this paper, we study this issue numerically by solving the Allen-Cahn equation and the nonlocal evolution equation with Kac potential. The Allen-Cahn equation is dis...

In this paper we have down three theoretical study by using Monte Carlo simulation and Mm+,AMBER and OPLS force field. The calculations were carried out using Hyper Chem professional,release 7.01 package of program. first we have studied the interaction of H2 molecule and He atomwith single-walled carbon nanotube at different temperature. For doing this study we placed H2 andHe in the center an...

The Gentzen-Kripke construction of the semantics for intermediate logic LQ, which is obtainable from the intuitionistic propositional logic H by adding the weak law of excluded middle -*A v —• —1>4, is presented. Our construction spans the Gentzen system and the Kripke semantics for LQ by providing the way from the cut-elimination theorem to model-theoretic results. The completeness and decidab...