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.

[1]. T. W. Haynes, S.T. Hedetniemi and P.J.Slater, Fundamentals of domination in graphs, Marcel Dekker, Inc., New York (1998).

[2]. T. W. Haynes, S.T. Hedetniemi and P.J.Slater, Domination in Graphs: advanced topics , Marcel Dekker, Inc., New York (1998).
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[4]. Sampathkumar, E., and Pushpa Latha, Strong weak domination and domination balance in graph, Discrete Math. Vol. 161, 1996, p. 235-242.

[5]. Domke et.al, On parameters related to strong and weak domination in graphs, Discrete Math. Vol. 258, (2002) p. ,1-11.

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[7]. Rautenbach, D., Bounds on the strong domination number, Discrete Math. Vol. 215, (2000) p. 201-212.

[8]. Kulli, V. R. and Janakiram, B., The Non-Split domination number of graph, International Journal of management and systems. Vol.19. No.2, p. 145-156, 2000.

[9]. Maheswari, B., Nagamuni Reddy, L., and A. Sudhakaraiah , Split and Non-split dominating set of circular-arc graphs, J. curr. Sci Vol 3. No.2, (2003)p. 369-372 .

[10]. Dr. A. Sudhakaraiah, V. Rama Latha, E. Gnana Deepika and T.Venkateswarulu, To Find Strong Dominating Set and Split Strong Dominating Set of an Interval Graph Using an Algorithm, IJSER , Vol. 2,(2012), 1026-1034.

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

[1]. Cordero L, Ayers LW, Miller RR, Seguin JH, Coley BD: Surveillance of ventilator-associated pneumonia in very-low-birth infants. Am J Infect Control. 2002; 30: 32-39.
[2]. Fogelia E, Dawn M, Elward A: Ventilator-associated pneumonia in neonatal and pediatric intensive care unit patients. Clin Micro Rev. 2007; 20:409-425.
[3]. Ibrahim EH, Mehringer L, Prentice D: Early versus late enteral feeding of mechanically ventilated patients: results of a clinical trial. JPEN J Parenter Enteral Nutr. 2002; 26: 174-181.
[4]. Tablan OC, Anderson LJ, Besser R: Guidelines for prevention of health-care-associated pneumonia, 2003: recommendations of CDC and the Healthcare Infection Control Practices Advisory Committee. Am J Crit Care. 2004; 53: 1-36.
[5]. Elward AM, Warren DK,Frases VJ: Ventilator-associated pneumonia in pediatric intensive care unit patients: risk factors and outcome. J Pediatr. 2002; 109: 758-764.
[6]. Curley MA, Schwalenstocker E, Deshpande JK, Ganser CC, Bertoch D, Brandon J, Kurtin P: Tailoring the institute for Health care improvement 100,000 lives Campaign to pediatric settings: the example of ventilator-associated pneumonia. Pediatr.Clin.N.Am. 2006; 53: 1231-1251.
[7]. Yildizdas D, Yapicioglu H, Yilmaz HL: Occurrence of ventilator-associated pneumonia in mechanically ventilated pediatric intensive care patients during stress ulcer prophylaxis with sucralfate, ranitidine and omeprazole. J Crit Care. 2002; 17: 240-245.
[8]. Nolan T, Berwick DM: ALL or none measurement raises the bar on performance. JAMA. 2006; 295: 1168-1170.
[9]. Almuneef M, Memish ZA, Balkhy HH, Alalem H, Abutaleb A: Ventilator-associated pneumonia in a pediatric intensive care unit in Saudi Arabia: a 30 – month prospective surveillance. Infect Control Hosp Epidemiol. 2004; 25: 753-758.
[10]. Yuan TM, Chen LH, Yu HM: Risk factors and outcomes for ventilator-associated pneumonia in neonatal intensive care unit patients. J perinat Med. 2007; 35: 334-8.

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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formulae, J. Phys. A: Math. Gen. 20 (1987), 4109-4117.
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Abstract: Non-linear Cellular Automata model is a simulation tool which can be used to diagnosis the intensity of the disease. This paper aims to study the Heart rate behavior between normal respiratory patients and healthy controls/unhealthy controls. We also discuss about Heart Rate Variability (HRV) of employee's through non-linear Cellular Automata model. Cellular Automata model gives us striking results for further studies.

Keywords: Cellular Automata (CA), Heart rate variability (HRV), Time domain method and Frequency domain method.

[1] Cerutti, S.; Bianchi, A. M.; Mainardi, L. T. (1995): Spectral Analysis of the Heart Rate Variability Signal, in: Malik, M.; Camm, A. J. (1995): Heart Rate Variability, Futura Publishing Company Inc., New York, p. 64

[2] Majercak, I. (2002): The Use of Heart Rate Variability in Cardiology, in: Bratisl Lek Listy 2002, Vol. 103(10), p.368

[3] Malliani, A. (1995): Association of Heart Rate Variability Components with Physiological Regulatory Mechanisms, in: Malik, M.; Camm, A. j. (1995): Heart Rate Variability, Future Publishing Company Inc., New York, p. 147

[4] Task Force of The European Society of Cardiology and The North American Societyof Pacing and Electrophysiology (1996): Heart Rate Variability - Standardsof Measurement, Physiological Interpretation, and Clinical Use, in: European Heart Journal, Vol. 17, pp. 354-355

[5] Tommaso Toffoli [1984], "Cellular automata as an alternative to differential equations".

[6] URL: http://hrvconsultants.com/documents/HeartRateVariabilityforClinicians2.ppt (7th October 2007)

[7] Wolfrom S. [1986], "Theory and Application of Cellular automata".

Abstract: We develop and analyze a mathematical model on malaria dynamics using ordinary differential equations, in order to investigate the effect of certain parameters on the transmission and spread of the disease. We introduce dimensionless variables for time, fraction of infected human and fraction of infected mosquito and solve the resulting system of ordinary differential equations numerically. Equilibrium points are established and stability criteria analyzed. The results reveal that the parameters play a crucial role in the interaction between human and infected mosquito.

Keywords – Endemic, Epidemic, Epidemiology, Equilibrium, Malaria

[1] R. Ross, The prevention of malaria (London: John Murray, 1911).

[2] G. Macdonald, The epidemiology and control of malaria (London: Oxford University Press, 1957).

[3] J. L. Aron and R. M. May, The population dynamics of malaria, in R. M. Anderson (Ed.), The population dynamics of infectious disease: theory and applications, (London: Chapman and Hall, 1982), 139-179.

[4] R. M. Anderson and R. M. May, Infectious diseases of humans: dynamics and control (Oxford: Oxford Unversity Press, 1991).

[5] M. G. Roberts and J. A. P. Heesterbeek, A new method for estimating the effort required to control an infectious disease, Proc. 270th Royal Society of London Series B, London, 2003, 1359-1364. [

6] N. R. Chitnis, Using mathematical models in controlling the spread of malaria, doctoral diss., the University of Arizona, Tucson, AZ, 2005.

Abstract: The set of complex eigenvalues of unistochastic matrices of order three forms a deltoid. A cross-section of the set of unistochastic matrices of order three forms a deltoid. The set of possible traces of unitary matrices belonging to the group SU(3) forms a deltoid. The intersection of two deltoids parametrizes a family of Complex Hadamard matrices of order six. The set of all Simson lines of given triangle, form an envelope in the shape of a deltoid. This is known as the Steiner deltoid or Steiner's hypocycloid after Jakob Steiner who described the shape and symmetry of the curve in 1856. The envelope of the area bisectors of a triangle is a deltoid (in the broader sense defined above) with vertices at the midpoints of the medians. The sides of the deltoid are arcs of hyperbolas that are asymptotic to the triangle's sides.

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Abstract: In this paper, we have studied on the topic of "Corruption‟. Also, I will try to find or study the effect of corruption on the Development of the country or any country of the world. Therefore, how find the solution of the problem of corruption will be destroyed completely from the society. We have observed that the Development of the country depends upon Corruption. That is, when the Corruption increases, Development decreases automatically of any country of the world. Therefore, I will try to find the formula on the problem of "Relation between the Corruption and Development of any field or any country of the world‟. Also, I have to highlight the concept of "Application of Mathematical modeling in the interesting problem "corruption" in every field of our country or world .Also, Applied Mathematics focuses on the formulation and study of Mathematical Models .Thus the activity of Applied Mathematics is vitally connected with Research in Pure Mathematics. So I will try to study on it and find, what is corruption and quantity of corruption and also find the growth of corruption and how it will decay? Now we convert this areal world problem to mathematics problem and find some formulae on it such as Mathematical Corruption Growth formula, Mathematical Constant corruption level formula and Mathematical decay of corruption formula.

Keyword: applied, modelling, fuzy, mathematical thinking, corruption mentality.

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Abstract: Sufficient conditions are obtained for every solution of first order nonlinear neutral delay forced impulsive differential equations with positive and negative coefficients tends to a constant as t ∞. Mathematics Subject Classification [MSC 2010]:34A37 Keywords: Asymptotic behavior, neutral, non linear, forced, differential equation, impulse

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[2] D.D. Bainov and P.S. Simeonov, Impulsive Differential Equations: Periodic Solutions and Applications, Longman, Harlow, 1993.
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impulses, Nonlinear Anal. 51 (2002) 633–647.
[7] Gengping Wei and Jianhua Shen, Asymptotic behavior of solutions of nonlinear impulsive delay differential equations positive and
negative coefficients, Math. & Comp. Modeling, 44(2006), 1089-1096.
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impulses J. Appl. Math. & Computing, 12(2003),39-47.
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Abstract: Environmental pollution, high cost and high energy consumption associated with thermal regeneration of activated carbon polluted with hydrocarbon necessitated the search for a better way of regenerating activated carbon, bioregeneration. Spent granular activated carbon was regenerated having been initially characterized using cultured Pseudomonas Putida. The rate of bioregeneration was studied by varying the volume of bacteria from 10ml, 20ml, 30ml and 40ml. The regeneration temperature was also varied from 25oC to ambient temperature of 27oC, 35oC and further at 40 and 45oC over a period of 21 days. The experimental results showed clear correlation when validated using the Langmuir-Hinshelwood kinetic model. The experiment at ambient temperature showed a negative correlation due to the fluctuation in the ambient temperature unlike all other experiment where temperature was controlled in an autoclave machine.

Keywords: Bioregeneration, GAC, Model, Nigeria and Pollution.

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[10]. Lin Y. H and Leu J. Y (2008): Kinetics of reactive azo-dye decolorization by Pseudomonas luteola in a biological activated carbon process. Biochemical Engineering Journal 39:457–467