in this paper, we introduce the  probabilistic normed groups. among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. we also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

In this paper, we define the concepts of modified intuitionistic probabilistic metric spaces, the property (E.A.) and  the common property (E.A.) in   modified  intuitionistic probabilistic metric spaces.Then, by the commonproperty (E.A.), we prove some common fixed point theorems in modified intuitionistic Menger probabilistic metric spaces satisfying an implicit relation.

The complex structure of human skin and its physicochemical properties turn it into an efficient outermost defence line against exogenous factors, and help maintain homeostasis of the human body. This role is played by the epidermal barrier with its major part - stratum corneum. The condition of the epidermal barrier depends on individual and environmental factors. The most important biophysica...

Many product lines are critical, and therefore reliability is a vital part of their requirements. Reliability is a probabilistic property. We therefore propose a model for featureaware discrete-time Markov chains as a basis for verifying probabilistic properties of product lines, including reliability. We compare three verification techniques: The enumerative technique uses PRISM, a state-of-th...

In this paper, we introduce the  probabilistic normed groups. Among other results, we investigate the continuityof inner automorphisms of a group and the continuity of left and right shifts in probabilistic group-norm. We also study midconvex functions defined  on probabilistic normed groups and  give  some results about locally boundedness of such  functions.

Pathobiont expansion, such as that of adherent-invasive Escherichia coli (AIEC), is an emerging factor associated with inflammatory bowel disease. The intestinal epithelial barrier is the first line of defense against these pathogens. Inflammation plays a critical role in altering the epithelial barrier and is a major factor involved in promoting the expansion and pathogenesis of AIEC. AIEC in ...

Membrane-anchored mucins are present in the apical surface glycocalyx of mucosal epithelial cells, each mucosal epithelium having at least two of the mucins. The mucins have been ascribed barrier functions, but direct comparisons of their functions within the same epithelium have not been done. In an epithelial cell line that expresses the membrane-anchored mucins, MUC1 and MUC16, the mucins we...

We deene the notion of self-concordance of order two for the restriction f of a logarithmic barrier function to a given line. Based on this notion we prove an inner approximation of the domain of f, as well as a lower bound of the distance from a point t to the minimum of f. These results provide the theoretical tools to develop a simple and eecient search step for nding the minimum of the barr...

The energy barrier for the cross slip of screw dislocations in face-centered cubic (FCC) nickel as a function of multiple stress components is predicted by both continuum line tension and discrete atomistic models. Contrary to Escaig's claim that the Schmid stress component has a negligible effect on the energy barrier, we find that the line tension model, when solved numerically, predicts comp...

BACKGROUND Functional diffusion mapping (fDM) is a cancer imaging technique that uses voxel-wise changes in apparent diffusion coefficients (ADC) to evaluate response to treatment. Despite promising initial results, uncertainty in image registration remains the largest barrier to widespread clinical application. The current study introduces a probabilistic approach to fDM quantification to over...