iosr-Jm   Volume-12 ~ Issue-5 ~ Sep-Oct 2016

Abstract: In this paper, we introduce a new class of sets, namely semi*δ-open sets, using δ-open sets and the generalized closure operator. We find characterizations of semi*δ-open sets. We also define the semi*δ-interior of a subset. Further, we study some fundamental properties of semi*δ-open sets and semi*δ-interior.

Keywords: δ-Semi-open set, δ-semi-interior, generalized closure, semi*δ-open set, semi*δ-interior.

[1]. D. Andrijevi´c, Semi-preopen sets, Mat. Vesnik38 (1986), no. 1, 24–32.
[2]. Dunham. W., A New Closure Operator for Non-T1 Topologies, Kyungpook Math. J. 22 (1982), 55-60.
[3]. Levine. N., Semi-Open Sets and Semi-Continuity in Topological Space, Amer. Math. Monthly. 70 (1963), 36-41.
[4]. Levine. N., Generalized Closed Sets in Topology,Rend. Circ. Mat. Palermo.19 (2) (1970), 89-96.

Abstract: The purpose of this study is to offer a method for prediction the result of treatment of gingival recessions using coronally advanced flap (CAF) and platelet rich fibrin membrane (PRFm) with CAF and connective tissue graft (CTG). The reported work gets answers to the following open questions: Is the treatment of mucogingival defects a predictable procedure? Is the jaw a factor affecting the outcome of coronally advanced flap root coverage procedure? To achieve this goal the authors followed the Creeping Attachment clinical parameter six months postoperatively

Keywords: Biostatistics, split mouth randomized controlled study, ANOVA-like model, Bayesian analysis, heterogeneous-variance model, two-way interactions.

[1] K. Anilkumar, A. Geetha, Umasudhakar et al., Platelet-rich fibrin: A novel root coverage approach, Journal of Indian Society of Periodontology, 13 (1), 2009, 50-54.
[2] S. Aroca, T. Keglevich, B. Barbieri, I. Gera, D. Etienne, Clinical Evaluation of a Modified Coronally Advanced Flap Alone or in Combination With A Platelet-Rich Fibrin Membrane for the Treatment of Adjacent Multiple Gingival Recessions: A 6-Month Study, J Periodontol, Feb, 2009, 80(2):244-52.
[3] Iv. Chenchev, D. Atanasov, D. Vicheva, The treatment of gingival recessions - Our experience, Romanian Journal of Rhinology, Vol. 6, No. 22, April-June, 2016, pp 85-91.
[4] Iv. Chenchev, D. Atanasov, D. Vicheva, V. Noncheva, Comparative Evaluation of the Subjective Results from the Treatment of Gingival Recessions with Connective Tissue Graft and Platelet Rich Fibrin Membrane, IOSR Journal of Dental and Medical Sciences, Vol. 15, Issue 5, Ver. 05 May, 2016, pp 73-78.

Abstract: A graph labeling is an assignment of integers to the vertices or edges or both subject to certain conditions. In this paper, we introduce the new concept, an absolute difference of cubic and square sum labeling of a graph. The graph for which every edge label is the absolute difference of the sum of the cubes of the end vertices and the sum of the squares of the end vertices. It is also observed that the weights of the edges are found to be multiples of 2. Here we characterize 2-tuple graphs of middle graph of paths and cycles, crown graph ,star graphs , the triangular snake graph, quadrilateral snake graph for adcss labelings is determined.

Keywords: Graph labeling, sum square graph, square sum graphs, cubic graphs, middle graphs, 2-tuple graph.

[1] Danuta Michalak , "On middle and Total Graphs with coarseness number equal 1". Springer Verlag Graph Theory, Lagow (1981) proceedings. Berlin Heidelberg, New York, Tokyo pp 139-150
[2] F Harary, Graph Theory, Addison-Wesley,Reading, Mass, (1972)
[3] Joseph A Gallian, A Dynamic Survey of Graph Labeling, The Electronic Journal of Combinatorics(2015), #DS6, Pages 1-389.
[4] P.L Vihol & P.H Shah, Difference Cordial Labeling of 2-tuple graphs of some graphs, International Journal of Mathematics and its Applications, Volume 4, Issue 2-A (2016), 111-119
[5] T K Mathew Varkey, Some Graph Theoretic Generations Associated with Graph Labeling, PhD Thesis, University of Kerala 2000.

Abstract: Survival analysis is the analysis of statistical data in which the outcome variable of interest is time until an event occurs. In this paper, attempt has been made to find the best fitted model for studying the survival time of esophagus cancer patients of Assam. The present retrospective study is conducted on medical records of 178 patients. Akaike Information Criterion(AIC) and Baysian Information Criteria (BIC) and 𝑅2 are used to identify the best fitted model. From the study it is found that Cox PH model is better than the other parametric counterparts for the esophagus cancer patients data.

Keywords: Cox PH model, AIC, BIC, esophagus cancer patients, 𝑅2 .

[1]. Akaike H.: A New Look at the Statistical Model Identification. IEEE. Transaction and Automatic Control AC-19. 1974, 716-23.
[2]. Austin PC, Rothwell DM, TU JV.:A Comparison of Statistical Modeling Stratigies for Analyzing Length of Stay after CABG surgery, Health Services and Outcomes Research Methodology, . 2002; 3(2):107-133.
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Abstract: In this paper we present a characteristic of a factorial state space with C* - algebra and von – Neumann algebra. We also discuss some theorems on C* - algebra and von – Neumann algebra.

[1]. Archbold, R.J.: On factorial states of operator algebra; J. Fuc. Ana., 55 (1984) No. 1, PP. 25-38.
[2]. Baty, C.J.K. : Nuctear faces of state spaces of c* - algebra, Proc, Amer. Math. Soc., 86 (1982), No. 2, PP. 273-278.
[3]. Sze-kai, Tsui : Factor state extension on nuclear C* - algebra, yokohoma Math. J., 29 (1981) No. 2, PP. 157-160.
[4]. Archbold, R.J.: Extension of factorial states of C*- algebra, J. Funct. Ana., 63(1985) Pp. 86-100.
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Abstract: An analysis has been carried out to study the effects of Hall current and radiation of MHD free convective heat and mass transfer flow past an accelerated inclined plate with temperature and concentration in a porous medium in presence of thermal diffusion and heat source. The solutions for velocity field, temperature field and concentration distribution are obtained using Laplace transform technique. The expressions for skin friction, Nusselt number and Sherwood number are also derived. The variations in fluid velocity, fluid temperature and species concentration are shown graphically, whereas numerical values of skin friction, Nusselt number and Sherwood number are presented in tabular form for various values of physical parameters

Keywords: Hall Current, Thermal Radiation, Heat and Mass Transfer, Thermal Diffusion, Accelerated inclined porous plate.

[1]. Raptis, A., Singh, A.K., "MHD free convection flow past an accelerated vertical plate". International Communications in Heat and Mass Transfer, Vol.10(4), p313-321, 1983.
[2]. Duwairi, H.M., Al-Kahlawi, Y., "MHD cojugate mixed convection heat transfer over avertical hollow cylinder embedded in a porous medium". International Journal of Heat and Technology, Vol.24(1), p123-128, 2006.
[3]. Seddeek, M.A., "The effect of variable voscosity on hydromagnetic flow and heat transfer past a contnuously moving porous boundary with radiation" Int. Commun Heat Mass, Vol.27(7), p1037-1046, 2000.
[4]. Abdelkhalek, M.M., "The skin friction in the MHD mixed convection stagnation point with mass transfer" ,Int. commun Heat Mass, Vol.33, 249-258, 2006.
[5]. Chowdhury, M. K., Islam, M.N., MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate. Heat Mass transfer 36, 439-447, 2000.

Abstract: In the initial stage we proposed the concept of Total Strong (Weak) domination in Fuzzy graph. It deal with the real time application that helps a individual person in crossing a road traffic signal. We will be giving a single value for vertices and edges. Enhancing the same concept, the Total Strong (Weak) domination in Intuitionistic Fuzzy graph was proposed. Here we will be giving a double value for the vertices and edges. Now in this paper, we demonstrate the concept of Total Semi- μ Strong (Weak) domination in Intuitionistic.........

Keywords: ntuitionistic Fuzzy graph, Strong (Weak) intuitionistic fuzzy graph, Total Strong (Weak) IFG, Total Semi - μ Strong (Weak) Domination in IFG, Fuzzy domination number

[1]. A Rosenfeild Fuzzy Graphs; ; in ; L.A. Zadeh, K.S. Fu, M. Shimura(Eds.), Fuzzy sets and Their Applications to Cognitive and Decision processes, Academic Press, New York, 1975, 77 – 95.
[2]. M.G. Karunambigai and R. Parvathi and R. Bhuvaneswari, Constant intuitionistic Fuzzy Graphs, NIFS 17 (2011), 1, 37 – 47.
[3]. A. Somasundaram and S. Somasundaram, Domination in Fuzzy Graphs – I, Pattern Recognition Letters, 19 (1998), 787 – 791.
[4]. Ayyasamy. S and Natarajan. C Strong (weak) domination in Fuzzy graphs, International Journal of Computational and Mathematical Science, 2010.
[5]. P.J. Jayalakshmi and C.V.R. Harinarayanan, Independent and Total strong (weak) domination in Fuzzy Graph, International Journal of Computational Engineering Research. / Vol. 04 / Issue, 1, (71 – 74).

Abstract: In this paper, after using Picard's method, the existence and uniqueness solution of the nonlocal Hammerstein-Volterra integral equation (H-VIE) of the second kind with continuous kernels are considered. Using two different numerical methods Trapezoidal rule and Simpson's rule, the nonlocal H-VIE, in each method, is conformal to a nonlocal nonlinear algebraic system (nonlocal NAS). Some numerical results are calculated, when the nonlocal term is neglected, in the linear case and in the nonlinear case. Moreover, the error estimate, in each case, is computed. Many special cases are derived from the work when the memory takes different cases. In addition, the HI termand VI term take the linear and nonlinear cases.

Keywords: Nonlocal Hammerstein-Volterra integral equation, Picard's method,Trapezoidal rule, Simpson's rule, nonlocal nonlinear algebraic system.

[1] A. Shidfar et al, A series solution of the nonlinear Volterra and Fredholmintegrodifferentialequations, Commun Nonlinear SciNumerSimulat 15 (2010) 205-215.
[2] A. Aky¨uz, M. Sezer, A Taylor polymial approach for solving high-order linear Fredholm integro differential equations in the most general form, International Journal of Computer Mathematics (2007)527-539.
[3] N. Lungu, I. A. Rus, On a functional Volterra- Fredholm integral equation viaPicard operator, Journal of Mathematical Inequalities, 3, (4) (2009), 519–527.
[4] M. A. Abdou, M. M. EL-Borai, M. M. El-Kojok, Toeplitz matrix method and nonlinear integral equation of Hammerstein type, J. Comp. Appl. Math.Vol. 223, (2009) 765 – 776.

Abstract: In this paper we study the additive properties of generalized Drazin inverse of two Drazin invertible operators in Minkowski spaceM in terms of PQ = QP: Further we have derived the explicit representations of generalized Drazin inverse (P + Q)yG interms of P; Q; PyG and QyG in Minkowski space M .

Keywords: Generalized Drazin Inverse, Minkowski Inverse. AMS subject classification 15A09.

[1]. A. Ben-Israel, T.N.E, Greville, Generalized Inverses: Theory and Applica- tions, Wiley-lnterscience, New York, 1974, second ed. Springer. New York, 2002.
[2]. N. Castro-Gonzalez, Additive perturbation results for the Drazin inverse, Linear Algebra Appl. 397 (2005) 279-297.
[3]. N. Castro-Gonzalez, JJ. Koliha, Perturbation of the Drazin inverse for closed linear operators, Integral Equations Operator Theory 36 (2000) 92- 106.
[4]. N. Castro-Gonzalez, J.J. Koliha, New additive results for the-Drazin in- verse, Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 1085-1097.

Abstract: In this research, we present the basic concepts of Tabu search method for optimizing problem such as Traveling Salesman Problem (TSP). The main purpose of this work is to understand the symmetric TSP, solve this problem by using Tabu search method to find the shortest distance with small search space and computational needs and then using a computer program (using MATLAB software) to solve large scale Symmetric TSP. Finally, we find the shortest distance to visit 64 district headquarters of Bangladesh.

Keywords: Traveling Salesman Problem (TSP), Hamiltonian Cycle, Tabu Search

[1]. Applegate David L. , Bixby Robert E., Vasek Chvatal, Cook William J., "The Traveling Salesman Problem A Computational study", Princeton university press, Princeton and oxford [2006].
[2]. Der-San Chen, Robert G. Batson, Yu Dang, "Applied Integer Programming", John Wiley & sons, inc, publication [2010].
[3]. TahaH. A., "Operations Research An Introduction", 8th edition, Pearson Prentice Hall, Pearson Education Inc. [2007].
[4]. Donald Davendra, "Traveling salesman problem, Theory and Applications", JanezaTrdine 9, 51000 Rijeka, Croatia, ISBN 978-953-307-426-9.
[5]. Fred Glover, Manuel Laguna, "Tabu search", Kluwer Academic publishers, 1997

Abstract: In this paper we introduce a new approach to solve fuzzy assignment problem namely, ones assignment method. Considering each fuzzy cost as a triangular fuzzy numbers the fuzzy assignment problem has been transformed into crisp values by using linguistic variables and ranking techniques and then it is solved by ones assignment method. The proposed method is a systematic procedure, easy to apply and can be utilized for all types of assignment problem with maximize or minimize objective functions. At the end, this method is illustrated with some numerical example

Keywords: Ranking of fuzzy numbers, triangular fuzzy numbers, Fuzzy Assignment problem, ones method

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