We present a study on strong t-continuity and measure of discontinuity on PN spaces. As an application, we prove a fixed point theorem for a discontinuous self mapping on PN spaces by means of measure of discontinuity.

this paper deals with the boundary value problem involving the differential equationbegin{equation*}    ell y:=-y''+qy=lambda y, end{equation*} subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$ begin{equation*}    y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0),end{equation*}where $q(x),  a_1 , a_2$ are  real, $qin l...

We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the rate of mutational inactivation, selection coefficient, invasion rate (i.e., rate of arrival of a novel sequence from outside of the recipient population), wit...

We address the 3D volume reconstruction problem from depth adjacent sub-volumes acquired by a confocal laser scanning microscope (CLSM). Our goal is to align the sub-volumes by estimating a set of optimal global transformations that preserve morphological continuity of medical structures, e.g., blood vessels, in the reconstructed 3D volume. We approach the problem by learning morphological char...

A key issue in the creation of error-free tool path for numerically controlled (NC) surface machining is gouging (over-cut> prevention. In the case of solid-based machining, where the creation of tool paths across several surfaces in a single pass is imperative, the major sources for gouging are the tangent discontinuity (C’ discontinuity) and the surface gap (Co discontinuity) occurred in the ...

Abstract. We rigorously prove results on spiky patterns for the Gierer-Meinhardt system [8] with a jump discontinuity in the diffusion coefficient of the inhibitor. Using numerical computations in combination with a Turing-type instability analysis, this system has been investigated by Benson, Maini and Sherratt [1], [3], [11]. Firstly, we show the existence of an interior spike located away fr...

There are different models that explain growth during development. One model is based on insect and amphibian regeneration studies. This model proposes that growth is directed by pattern, and growth takes place by intercalation at a growth discontinuity; therefore, proliferation should surround the discontinuity. Currently, this model, apart from regenerative studies on mostly adult patterning,...

Behavioral experiments with infants, adults, and nonhuman animals converge with neurophysiological findings to suggest that there is a discontinuity in auditory processing of stimulus components differing in onset time by about 20 ms. This discontinuity has been implicated as a basis for boundaries between speech categories distinguished by voice onset time (VOT). Here, it is investigated how t...

We show that the recently demonstrated absence of the usual discontinuity for massive spin 2 with a Λ term is an artifact of the tree approximation, and that the discontinuity reappears at one loop.