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 show that a pointwise symmetric pre-isotonic preclosure function is uniquely determined the pairs of sets it separates. We then show that when the preclosure function of the domain is pre-isotonic and the pre-closure function of the codomain is pre-isotonic and pointwise-pre-symmetric, functions which separate only those pairs of sets which are already separated are precontinu...

this paper is an attempt to generalize, simultaneously, the ring of real-valued continuous functions and the ring of real-valued measurable functions.

properties of the hybrid of block-pulse functions and lagrange polynomials based on the legendre-gauss-type points are investigated and utilized to define the composite interpolation operator as an extension of the well-known legendre interpolation operator. the uniqueness and interpolating properties are discussed and the corresponding differentiation matrix is also introduced. the appli...

The initial size of a completely susceptible population in a group of individuals plays a key role in drawing inferences for epidemic models. However, this can be difficult to obtain in practice because, in any population, there might be individuals who may not transmit the disease during the epidemic. This short note describes how to improve the maximum likelihood estimators of the infection r...

An audio-visual (AV) speech presentation mode can significantly improve spoken word identification. Language comprehension and communication in patients with Alzheimer disease (AD) can be compromised; however, little is known about the extent to which patients might benefit from an AV mode. Patients with mild cognitive impairment (MCI) are at risk for developing AD and can demonstrate parallel ...

Normann proved that the domains of the game model of PCF (the domains of sequential functionals) need not be dcpos. Sazonov has defined natural domains for a theory of such incomplete domains. This paper further develops that theory. It defines lub-rules that infer natural lubs from existing natural lubs, and lub-rule classes that describe axiom systems like that of natural domains. There is a ...

In this paper, I would like to propose an idea of semantics for discourse and pictorial representations. The central notion of this paper is function. A representation is a representation of something. A function determines the connection between representation and what is represented. This is true for both discourse and pictorial representations. To properly interpret a representation system m...