iosr-Jm   Volume-6 ~ Issue-2

Abstract: Recently, the concept of 𝛽-statistical Convergence was introduced considering a sequence of infinite matrices 𝛽 = (𝑏𝑛𝑘 𝑖 ). Later, it was used to define and study 𝛽-statistical limit point, 𝛽-statistical cluster point, 𝑠𝑡𝛽 − 𝑙𝑖𝑚𝑖𝑡 inferior and 𝑠𝑡𝛽 − 𝑙𝑖𝑚𝑖𝑡 superior. In this paper we analogously define and study 2𝛽-statistical limit, 2𝛽-statistical cluster point, 𝑠𝑡2𝛽 − 𝑙𝑖𝑚𝑖𝑡 inferior and 𝑠𝑡2𝛽 − 𝑙𝑖𝑚𝑖𝑡 superior for double sequences. Keywords: Double sequences, Statistical convergence, 𝛽-statistical Convergence Regular matrices, RHregular matrices.

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Abstract: In graph theory, a connected component of an undirected graph is a sub graph in which any two vertices are connected to each other by paths. For a graph G, if the subgraph of G itself is a connected component then the graph is called connected, else the graph G is called disconnected and each connected component sub graph is called it's components. A dominating set Dst of graph G=(V,E) is a non-split strong dominating set if the induced sub graph < V-Dst > is connected. The non-split strong domination number of G is the minimum cardinality of a non-split strong dominating set . In this paper constructed a verification method algorithm for finding a non-split strong dominating set of an interval graph.

Keywords: Domination number, Interval graph, Strong dominating set, Strong domination number , split dominating set.

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Abstract: Background: Pneumonia associated with mechanical ventilation (VAP) is one of the important causes of nosocomial infections in pediatric intensive care units (PICU). VAP is the leading cause of morbidity and mortality in PICUs. Aim: To assess the compliance to ventilator bundle components: elevation of the head of bed >30, sedation interruption, spontaneous breathing trial, peptic ulcer prophylaxis and its effect on the prevention of VAP. Subjects and Methods: A case control study at PICU of Abo EL Reish El Moneira Hospital, including all mechanically ventilated patients admitted over a period of one year. The study tested the effect of implementation of this bundle as regard the rate of VAP in both group, compliance to bundle and most affecting component of it. Results: There was decrease incidence of VAP after implementation of the bundle, from (50%) to (14%). Development of VAP was mostly affected by being in supine position, long duration of mechanical ventilation and presence of pump failure. (p<0.05) The compliance to bundle components was statistically significant, p= 0.001. Conclusion: VAP rate decreased after implementation of this bundle. Elevation of the head of bed was the most compliant component of bundle in the PICU.

Key words: Effective, Pediatric Intensive Care, Ventilator-associated pneumonia, Ventilator bundle

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Abstract: The object of this paper is to discuss certain integral properties of a I -function and H -function, proposed by Inayat-Hussain which contain a certain class of Feynman integrals, the exact partition of a Gaussian model in Statistical Mechanics and several other functions as its particular cases. During the course of finding, we establish certain new double integral relation pertaining to a product involving I function and H function. These double integral relations are unified in nature and act as a key formulae from which we can obtain as their special case, double integral relations concerning a large number of simple special functions. For the sake of illustration, we record here some special cases of our main results which are also new and of interest by themselves. All the result which are established in this paper are basic in nature and are likely to find useful applications in several fields notably electrical network, probability theory and statistical mechanics.

Key words. I function, H -function, Hermite polynomials, Laguerre polynomials.

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