Generalised regularity and compactness of matrix operators

A well-known result by Cohen and Dunford ([2], 1937) characterises the class of all regular compact linear operators. It follows that a regular matrix transformation cannot be compact. This means that if c denotes the set of all complex sequences of complex numbers, then an infinite matrix that maps c into c and preserves the limits cannot be compact. We obtained this result in a different way applying the theory of BK spaces from functional analysis and summability, and using the Hausdorff measure of noncompactness. Furthermore, we present the extension of this result to matrix transformations between the spaces c and the spaces of strongly summable sequences by the Cesaro method of order 1, and of strongly convergent sequences. We present new unified proofs for our main results.

Selective properties of fuzzy 2-metric spaces

We introduce and study some selective covering properties in fuzzy 2-metric spaces. These properties are related to the classical covering properties of Menger, Hurewicz and Rothberger which are well known in selection principles theory.

Control charts based on quantiles: New approaches

Contemporary development of Statistical quality control includes researches on different control charts, which could be easily implemented in production processes due to facilities offered by computers. New control charts give more information about production processes than the conventional ones, that's why there is a lot of investigation in this area of applied statistics. In this paper, we shall explain some new ideas concerning the construction of control charts based on quantiles, empirical distribution function and p-value.

On some mathematical properties of the general zeroth-order Randić coindex of graphs

Let G = (V,E), V = {v1, v2,..., vn}, be a simple connected graph of order n, size m with vertex degree sequence ∆ = d1 ≥ d2 ≥ ··· ≥ dn = d > 0, di = d(vi). Denote by G a complement of G. If vertices vi and v j are adjacent in G, we write i ~ j, otherwise we write i j. The general zeroth-order Randic coindex of ' G is defined as 0Ra(G) = ∑i j (d a-1 i + d a-1 j ) = ∑ n i=1 (n-1-di)d a-1 i , where a is an arbitrary real number. Similarly, general zerothorder Randic coindex of ' G is defined as 0Ra(G) = ∑ n i=1 di(n-1-di) a-1 . New lower bounds for 0Ra(G) and 0Ra(G) are obtained. A case when G has a tree structure is also covered.

Software engineering a forty years research retrospective

This paper presents author experience with software development during last forty years. It is divided into three eras: closed and open -systems and Internet of Everything, each covered by challenges, issues and solutions. The main stream is given from the interoperability perspective and flavored by security issues. Variety of applications domains, that author faced during his carrier, each with own challenges, is presented. Example include computer graphics systems, special-purpose solutions, business-to-business, business process management, e-government, and smart cities.

Empirical distribution function as a tool in quality control

In this paper, we are introducing two new methods for Quality Control. Those methods rely on using the Empirical distribution function of a given sample (or several samples). The first method we use for one sample, i.e. we can determine if each given sample is adequate. We use the second method to determine whether several samples are "in control" or not. For the sample to be "in control" state, the normal distribution is required.

Generalized 2-proximal C-contraction mappings in complete ordered 2-metric space and their best proximity points

In this paper, we extend the concept of best proximity point to 2-metric spaces and prove the existence of such points for contraction type non-self mappings in the setting of complete 2-metric spaces. Also, we presented an example to support our results.

Fixed point theorems for Cyclic-Ćirić-Reich-Rus contraction mapping in quasi-partial b-metric spaces

In this paper, Cirić-Reich-Rus cyclic contraction mapping is defined in the setting of quasi-partial b-metric spaces and fixed point results are proved. Some examples are given to validate our results.

Some remarks on general sum-connectivity coindex

Let G = (V,E), V = {v1, v2,..., vn} be a simple connected graph with n vertices, m edges and a sequence of vertex degrees d1 ≥ d2 ≥ ··· ≥ dn > 0, di = d(vi). The general sumconnectivity coindex is defined as Ha(G) = ∑i j (di + dj) a , while multiplicative first Zagreb coindex is defined as P1(G) = ∏i j (di + dj). Here a is an arbitrary real number, and i j denotes that vertices i and j are not adjacent. Some relations between Ha(G) and P1(G) are obtained.

Earth's shadowing effects by computer algebra

The short-periodic perturbations of orbits of an artificial satellite due to the radiation pressure during one orbital period are influenced by Earth's shadow. For the semi-analytical theories it is necessary to calculate great number of coefficients. Using computer algebra we have computed them for some of applicable semi-analytical theories.