017109   Grigoryev I;Miftakhov E;Mustafina S (Physics and Mathematics Dep, Bashkir State Univ, Lenin Avenue, 37, Sterlitamak City, Postal Index-453 103, Republic of Bashkortostan, Russian Federation, Email: grigoryevigor@mail.ru) : Mathematical modelling of the copolymerization of styrene with maleic anhydride in a homogeneous environment. Int J chem Sci 2016, 14(1), 381-6.

In this paper, a mathematical model based on the kinetic scheme of the copolymerization of styrene and maleic anhydride was built. The mathematical model is a system of ordinary differential equations whose dimension tends to infinity, because of the infinite number of the reaction components. Applying the method of statistical moments, infinite system of ordinary differential equations is reduced to a system with a finite number of equations and becomes solvable. Numerical solution of the target system to determine the average molecular properties such as number average and weight average molecular weights and polydispersity index.

1 illus, 6 ref

017108   Bandari S R;Aleti S;Perati M R (Mathematics Dep, Kakatiya Univ, Warangal-506 009, Email: sandhyarani.bandari@gmail.com) : Flexural vibrations of finite composite poroelastic cylinders. Sadhana 2015, 40(2), 591-604.

This paper deals with the flexural vibrations of composite poroelastic solid cylinder consisting of two cylinders that are bonded end to end. Poroelastic materials of the two cylinders are different. The frequency equations for pervious and impervious surfaces are obtained in the framework of Biot's theory of wave propagation in poroelastic solids. The gauge invariance property is used to eliminate one arbitrary constant in the solution of the problem. This would lower the number of boundary conditions actually required. If the wavelength is infinite, frequency equations are degenerated as product of two determinants pertaining to extensional vibrations and shear vibrations. In this case, it is seen that the nature of the surface does not have any influence over shear vibrations unlike in the case of extensional vibrations. For illustration purpose, three composite cylinders are considered and then discussed. Of the three, two are sandstone cylinders and the third one is resulted when a cylindrical bone is implanted with Titanium. In either case, phase velocity is computed against aspect ratios.

5 illus, 1 table, 18 ref

017107   Alkan N;Terzi Y;Alkan B B (Faculty of Science and Arts, Statistics Dep, Sinop Univ, 57000 Sinop, Turkey) : Determining the sample size and power for cox regression analysis. Int J Med Hlth Sci 2015, 4(4), 414-20.

Statistical power is the probability of rejecting a false null hypothesis and a larger sample size will increase the power of test. In the process of computing power, the sample size is determined. Therefore, the power of the study should be determined before starting to work. Cox regression analysis is a popular method of survival analysis and it examines the relationship between survival times and one or more covariates. In this study, power and sample size of cox regression analysis is determined for different situations of parameters by creating of study designs. As results of calculation, the practical tables and suggestions about determining the appropriate sample size were presented to the researches for clinical study.

4 illus, 4 tables, 11 ref

016131   Vijaya Laxmi P;Jyothsna K;Seleshi D (Applied Mathematics Dep, Andhra Univ, Visakhaptnam-530 003, Email: vijaya_iit2003@yahoo.co.in) : Analysis of a discrete- time working vacation queue with balking. Opsearch 2015, 52(1), 562-81.

This paper investigates a discrete-time single server finite buffer queue with single working vacation wherein the customers decide either to join the queue or balk. The inter-arrival times, service times and vacation times are assumed to be independent and geometrically distributed. Using matrix method, the steady-state probabilities are obtained. Various performance measures of the model and average sojourn time are presented. An optimization problem is considered using particle swarm optimization (PSO) through a cost function. Further, maximum likelihood estimate (MLE) for the balking parameter is obtained. Numerical results are presented in the form of tables and graphs to show the effect of parameters on the system performance.

8 illus, 4 tables, 27 ref

016130   Upmanyu M;Saxena R R (Mathematics Dep, Delhi Univ, Delhi, Email: muditapmanyu@gmail.com) : Linearization approach to multi objective set covering problem with imprecise nonlinear fractional objectives. Opsearch 2015, 52(1), 597-615.

Set Covering Problem is one of most important NP-complete 0-1 integer programming problems as it serves as a model for many real world problems, like crew scheduling problems, facility location problems, vehicle routing etc. This paper develops an enumerative technique for solving the multiobjective set covering problem with fuzzy nonlinear fractional objectives, under certain convexity conditions. To mirror real life situations in the covering problem we have taken the objective functions in a nonlinear fractional form. In addition to that, the coefficients of the objective functions are of a fuzzy nature, as in most cases the decision maker is unable to provide information of a precise nature. The algorithm provided in this paper aims to not only solve this covering problem to obtain a set of efficient cover solutions, but also to provide the decision maker with a fuzzy solution for the same. It is based on a linearization technique with the subsequent application of the cutting plane approach, but it employs a more generalized and much deeper form of the Dantzig cut. An example to illustrate the technique is presented, and a few applications of this problem are also described.

5 tables, 28 ref

016129   Sangeetha N;Sivakumar B;Arivarignan G (School of Mathematics, Madurai Kamaraj Univ, Madurai-625 021, Email: sivabkumar@yahoo.com) : Optimal control of production time of pershable inventory system with finite source of customers. Opsearch 2015, 52(1), 412-31.

Authors consider a continuous-review inventory system with perishable items and make-to-stock production facility. The customers are assumed to be generated by a finite number of sources. Each customer demands a single item. The life time of each item is assumed to be exponential. Customers demand is met from stock, if available, otherwise the customer enters into an orbit. The orbiting customer sends out signal to get his demand satisfied and the duration between two successive retrials is assumed to be distributed as exponential. In order to replenish stock, a production facility is switched on when the inventory level drops to s and items are produced one by one until the stock level reaches a maximum capacity S(<62> s). The production facility is dynamic in the sense that the rate, at which the item is produced, can be selected from a pre-fixed set of positive values. In other words, the successive production time is assumed to follow an exponential distribution whose parameter is chosen from a given set of positive values. The purpose of this paper is to investigate the optimal set of production rates that minimizes the total expected cost per unit time. We formulate this problem as a semi Markov decision problem. The stationary optimal policy is computed using linear programming algorithm and the results are illustrated numerically.

7 illus, 2 tables, 19 ref

016128   Patra K;Mondal S K (Applied Mathematics with Oceanology and Computer Progr amming Dep, Vidyasagar Univ, Midnapore-721 102, Email: kpatrakp@gmail.com) : Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependent selling price. Opsearch 2015, 52(1), 505-29.

In this paper a production inventory model of a single item with a variable production rate and production time dependent selling price has been introduced. Realistically it is seen that for any business concern, demand is always uncertain. Henceforth, in this model, demand of an item has been assumed to be fuzzy but its membership function is not known in prior. It is also considered that the production rate is a decreasing function of the inverse efficiency of the system. Under these circumstances, a profit function of the model has been formulated. As demand is fuzzy with unknown membership function, hence to get expected maximum profit, the diffusion method including possibility probability distribution has been used and the risk estimation values for failure to attain different profit levels have been evaluated. Finally the proposed model has been demonstrated taking a numerical example and a comparison among different types of demand such as crisp, fuzzy with triangular and trapezoidal membership value and fuzzy with unknown membership value have been shown.

5 illus, 9 tables, 17 ref

016127   Maity A;Gupta U C (Mathematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: arnavamath@gmail.com) : Analysis and optimal control of a queue with infinite buffer under batch-size dependent versatile bulk-service rule. Opsearch 2015, 52(1), 472-89.

This article studies an infinite-buffer single server queue with versatile bulk service policy, where the service rates depend on the service batch sizes. Such queueing systems have potential applications in manufacturing, computer and telecommunication systems, semiconductor industry, group testing etc. Also from our present analysis, the results for several batch-service models can be derived. We use the matrix-geometric method to obtain joint distribution of the number of customers in the queue and the number of customers undergoing service, in steady-state. Based on these limiting probabilities, we present various performance measures, which are useful in determining optimal service policy and controlling congestion in the system. Some optimal policies has also been suggested based on a cost structure and the threshold values of the sensitive parameters.

3 illus, 4 tables, 72 ref

016126   Kar S;Basu K;Mukherjee S (NO, NIT, Durgapur, West Bengal, Email: supriyakar1234@gmail.com) : Generalized fuzzy assignment problem with restriction on the cost of job under hesitant fuzzy environment. Opsearch 2015, 52(1), 401-11.

As a generalization of fuzzy set, Hesitant Fuzzy Set (HFS) is very useful to express people's hesitancy in daily life. But there are some disadvantages in traditional HFS, as it expresses the membership degrees of an element to a given set only by several crisp numbers. In this paper, we extend the traditional HFS to Triangular Fuzzy Hesitant Fuzzy Set (TFHFS) in which the membership degree of an element to a given set is represented by several possible triangular fuzzy numbers. We have applied this TFHFS on solving Hesitant Fuzzy Generalized Assignment Problem (HFGAP). For this, we formulate the mathematical model of Generalized Assignment Problem (GAP) based on Triangular Fuzzy Hesitant Fuzzy Elements (TFHFEs) and with the help of well known TOPSIS method we have found the Relative Closeness Coefficient Matrix (RCCM). Using the above matrix as the initial data for a GAP in the minimization form we have solved the problem by Extremum Difference Method (EDM). To verify the result we have transformed the problem into LPP form and solved it by LINGO 9.0.

6 tables, 12 ref

016125   Jayswal A;Stancu Minasian I M;Choudhury S (Applied Mathematics Dep, Indian School of Mines, Dhanbad-826 004, Email: saritachoudhury09@yahoo.com) : Second order duality for variational problems involving generalized convexity. Opsearch 2015, 52(1), 582-96.

Aim of this paper is to introduce the concept of second-order (F, α, ρ, θ)-convexity for variational problems. An example is constructed to examine the existence of the introduced class of functions, which is more general than previously defined functions. In order to relate the primal variational problem and its second order dual, several duality results, viz., weak, strong and strict converse duality results are established.

27 ref

016124   How K Y;Sheng K Y;Chan K G (Genetics and Molecular Biology Div, Institute of Biological Sciences, Faculty of Science, Univ of Malaya, Kuala Lumpur-50603, Malaysia, Email: kokgan@um.edu.my) : Pantoea sp.strain A4, a new plant-associated bacterium exhibiting quorum sensing activity. Curr Sci 2015, 109(9), 1709-14.

Quorum sensing (QS) is a method of bacterial cell-tocell communication to coordinate adaptive behaviour. N-Acyl homoserine lactone (AHL) is the most studied signalling molecule among proteobacteria. In the present study, we characterize QS activity in Pantoea sp. A4, a new Rafflesia-associated bacterium. Results show the production of purple violacein by reporter bioassay Chromobacterium violaceum CV026 and bioluminescence activation in Escherichia coli [pSB401], indicating AHL production. Using liquid chromatography-mass spectrometry, Pantoea sp. was found to excrete four types of AHL, namely N-hexanoylhomoserine lactone, 3-oxo-N-hexanoylhomoserine lactone, N-octanoylhomoserine lactone and N-dodecanoylhomoserine lactone. To our knowledge, there is no previous documentation of Rafflesia-associated bacterium that produces long chain AHL.

5 illus, 24 ref

016123   Chakraborty D;Jana D K;Roy T K (Mathematics Dep, Heeritage Institute of Technology, Anandapur, Kolkata-700 107, Email: dipankar1920@gmail.com) : Arithmetic operations on generalized intuitionistic fuzzy number and its applications to transportation problem. Opsearch 2015, 52(1), 432-71.

Intuitionistic fuzzy has always been a subject of keen interest, and a rigorous research has also been done on it. However, those research works were mainly based on normal intuitionistic fuzzy- a generalized approach to it could hardly be seen. So in this paper, we have developed a generalized intuitionistic fuzzy number and its arithmetic operations. It is a unique attempt made by us in which for the first time two basic generalized intuitionistic fuzzy numbers namely generalized trapezoidal and generalized triangular intuitionistic fuzzy numbers have been considered to serve the purpose. All arithmetic operations have been formulated on the basis of (α, β)-cut method, vertex method and extension principle method. Comparison among those three methods using an example is given and numerical results have been presented graphically. A new method is proposed to solve generalized intuitionistic fuzzy transportation problem (GIFTP) using ranking function. To validate the proposed method we have solved a GIFTP by assuming transportation cost, supply and demand of the product in generalized intuitionistic fuzzy numbers and the optimum results have been compared with the results of normal intuitionistic fuzzy transportation problem.

8 illus, 32 ref

016122   Basu S;Sharma M;Ghosh P S (NO, Indian Institute of Management Calcutta, Jaoka, D.H. Road-700 104, Email: sumanta@iimcal.ac.in) : Metaheuristic applications on discreate facility location problems: a survey. Opsearch 2015, 52(1), 530-61.

This paper provides a detailed review of metaheuristic applications on discrete facility location problems. The objective of this paper is to provide a concise summary of solution approaches based on four commonly used metaheuristics: genetic algorithm, tabu search, particle swarm optimization and scatter search for different variants of the discrete facility location problem. Such a concise summary is expected to be useful for researchers interested in any of the major variants of discrete facility location problem as for each metaheuristic the paper provides a comprehensive review of different variants on which this metaheuristic has been applied, and the details of its implementation. Therefore, a research can exploit a method developed for another variant to solve the problem variant at hand. Based on our review of these papers, we also report some interesting observations, identify research gaps and highlight directions for future research.

19 tables, 102 ref

016121   Atash A A (Mathematics Dep, Aden Univ, Aden, Yemen) : Extension formulas for the first kind of Lauricell's function of three variables. Int J pure appl Sci Technol 2015, 28(2), 88-94.

Aim of this paper is to establish an extension formulas for the first kind of Lauricella's functions of three variables. The results are obtained with the help of two interesting special cases of the generalizations of Watson's summation theorem given by Lavoie et al.[5]. Some interesting special cases are also presented.

6 ref

015068   Vasuki R;Venkateswari J;Pooranam G (Mathematics Dep, Dr. Sivanthi Aditanar College of Engineering, Tiruchendur-628 215) : Skolem difference odd mean labelling for some simple graphs. Int J mathl Combinatorics 2015, 3, 88-98.

Graph G with p vertices and q edges is said to have skolem difference odd mean labeling if there exists an injective function f : V (G) → {1, 2, 3, ..., 4q - 1} such that the induced map f* : E(G) → {1, 3, 5, ..., 2q - 1} defined by f* (uv) = {|f(u) - f(v)|/2 if |f(u) - f(v)| is even and {|f(u) - f(v)| + 1/2 if |f(u) - f(v)| is odd, is a bijection. A graph that admits skolem difference odd mean labeling is called a skolem difference odd mean graph. Here we investigate skolem difference odd mean behaviour of some standard graphs.

10 illus, 10 ref

015067   Vadiraja Bhatta G R; (Mathematics Dep, Manipal Univ, Manipal, Karnataka-576 104) : Variations of orthogonality of latin squares. Int J mathl Combinatorics 2015, 3, 55-61.

Orthogonal properties of Latin squares represented by permutation polynomials are discussed. Pairs of bivariate polynomials over small rings are considered.

4 ref

015066   Sudev N K;Germina K A (NO, Vidya Academy of Science & Technology, Thalakottukara, Thrissur-680 501, Email: sudevnk@gmail.com) : On integer additive set-sequential graphs. Int J mathl Combinatorics 2015, 3, 125-33.

A set-labeling of a graph G is an injective function f : V (G) → P(X), where X is a finite set of non-negative integers and a set-indexer of G is a set-labeling such that the induced function f ^{⊕ : E(G) → P(X) - {∅} defined by f⊕(uv) = f(u)⊕f(v) for every uv<128><174><255>E(G) is also injective. A set-indexer f : V (G) → P(X) is called a set-sequential labeling of G if f ⊕(V (G) ∪ E(G)) = P(X) - {∅}. A graph G which admits a set-sequential labeling is called a set-sequential graph. An integer additive set-labeling is an injective function f : V (G) → P(N₀), N₀ is the set of all non-negative integers and an integer additive setindexer is an integer additive set-labeling such that the induced function f+ : E(G) → P(N₀) defined by f+(uv) = f(u) + f(v) is also injective. In this paper, we extend the concepts of set-sequential labeling to integer additive set-labelings of graphs and provide some results on them.}

2 illus, 15 ref

015065   Shahbazpour K;Nouri M (Mathematics Dep, Urmia Univ, Urima, I.R. Iran, P.O. Box, 57135-165, Email: shahbazpour@hotmail.com) : Calculus and algebra derived from directed graph algebras. Int J mathl Combinatorics 2015, 3, 1-32.

Shallon invented a means of deriving algebras from graphs, yielding numerous examples of so-called graph algebras with interesting equational properties. Here we study directed graph algebras, derived from directed graphs in the same way that Shallon's undirected graph algebras are derived from graphs. Also we will define a new map, that obtained by Cartesian product of two simple graphs p_n, that we will say from now the mah-graph. Next we will discuss algebraic operations on mah-graphs. Finally we suggest a new algebra, the mah-graph algebra (Mah-Algebra), which is derived from directed graph algebras.

21 illus, 6 tables, 26 ref

015064   Rajendra P;Rangarajan R (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-570 006) : Minimum equitable domination energy of a graph. Int J mathl Combinatorics 2015, 3, 62-72.

A subset D of V is called an equitable dominating set [8] if for every v ∈ V -D there exists a vertex u ∈ D such that uv ∈ E(G) and |deg(u) - deg(v)| ≤ 1, where deg(u) denotes the degree of vertex u and deg(v) denotes the degree of vertex v. Recently, The minimum covering energy E_c(G) of a graph is introduced by Prof. C. Adiga, and co-authors [1]. Motivated by [1], in this paper we define energy of minimum equitable domination E_ED(G) of some graphs and we obtain bounds on E_ED(G). We also obtain the minimum equitable domination determinant of some graph G given by det_ED(G) = μ₁μ₂ ... μ_n where μ₁, μ₂, ..., μ_n are eigenvalues of A_ED(G).

9 ref

015063   Narayankar K P;Lokesh S B;Mathad V (Mathematics Dep, Mangalore Univ, Mangalagangothri-574 199, Email: kishori_pn@yahoo.co.in) : Vertex-to-edge-set distance neighborhood pattern matrices. Int J mathl Combinatorics 2015, 3, 105-115.

The vertex to edge set (VTES) distance d₁(u, e) from a vertex u ∈ V (G) to an edge e ∈ E(G) is the number of edges on (u - e) path. For each u ∈ V (G) define N_M^{j [u] = {e ∈ M ⊆ V (G) : d(u, e) = j, where 0 ≤ j ≤ d₁(G)} and a non-negative integer matrix DM1 (G) = (|NM_j [u]|) of order V (G) x ((d₁(G) + 1) called the VTES-M-distance neighborhood pattern (M-dnp) matrix of G. If fM : u → fM (u) is an injective function, where f_M (u) = {j : NM_j [u] 6 = ∅}, then the set M is a VTES-distance pattern distinguishing (M-dpd) set of G and G is a VTES-dpd-graph. This paper is a study of VTES M-dnpmatrices of a VTES-dpd-graph.}

2 illus, 9 ref

015062   Muthammai S;Vidhya P (NO, Government Arts College for Women (Autonomous), Pudukkotai-622 001, Email: muthammai.sivakami@gmail.com) : Extended results on complementary tree domination number and chromatic number of graphs. Int J mathl Combinatorics 2015, 3, 116-24.

For any graph G = (V, E) a subset D ⊆ V is a dominating set if every vertex in V -D is adjacent to at least one vertex in D. A dominating set is said to be a complementary tree dominating set if the induced subgraph <60> V - D <62> is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number and is denoted by γ_ctd(G). In this paper, we find an upper bound for γ_ctd(G)+μ(G) = 2p-5 and γ_ctd(G) + χ(G) = 2p - 6, p is the number of vertices in G.

3 illus, 4 tables

015061   Murugan M (School of Science, Tamil Nadu Open Univ, 577, Anna Salai, Chennai-600 015, Email: muruganganesan@yahoo.in) : Radio number for special family of graphs with diameter 2, 3 and 4. Int J mathl Combinatorics 2015, 3, 99-104.

Radio labeling of a graph G is an injective function [4] f : V (G) → N ∪ {0} such that for every u, v ∈ V (G), |f(u) - f(v)| ≥ diam(G) - d(u, v) + 1. The span of f is the difference of the largest and the smallest channels used, that is, max u, v ∈ V (G) {f(u) - f(v)}. The radio number of G is defined as the minimum span of a radio labeling of G and denoted as rn(G). In this paper, we present algorithms to get the radio labeling of special family of graphs like double cones, books and nC₄ with a common vertex whose diameters are 2,3 and 4 respectively.

8 ref

015060   Maheswari V;Ramesh D S T;Balaji V (Mathematics Dep, KCG College of Engineering and Technology, Chennai-600 095, Email: pulibala70@gmail.com) : Some results on relaxed mean labelling. Int J mathl Combinatorics 2015, 3, 73-80.

In this paper, we investigate relaxed mean labeling of some standard graphs. We prove, any cycle is a relaxed mean graph; if n <62> 4, K_n is not a relaxed mean graph; K_2,n is a relaxed mean graph for all n; any Triangular snake is a relaxed mean graph; any Quadrilateral snake is a relaxed mean graph; the graph P₂^{n is a relaxed mean graph; L_n Θ K₁ is a relaxed mean graph. Also, we prove K_cn + 2K₂ is a relaxed mean graph for all n; W₄ is a relaxed mean graph; K₂ + mK₁ is a relaxed mean graph for all m; if G₁ and G₂ are tree, then G = G₁ ∪ G₂ is a relaxed mean graph; the planar grid P_m x P_n is a relaxed mean graph for m ≥ 2, n ≥ 2 and the prism P_m x C_n is a relaxed mean graph for m ≥ 2 and for all n ≥ 3.}

1 illus, 7 ref

015059   Jagadesh R;Babujee J B (Mathematics Dep, Easwari Engineering College, Chennai-6000 089, Email: jagadesh_rajagopal@yahoo.com) : Superior edge bimagic labelling. Int J mathl Combinatorics 2015, 3, 33-42.

A graph G(p, q) is said to be edge bimagic total labeling with two common edge counts k₁ and k₂ if there exists a bijection f : V ∪ E → {1, 2, ..., p + q} such that for each edge uv ∈ E, f(u) + f(v) + f(e) = k₁ or k₂. A total edge bimagic graph is called superior edge bimagic if f(E(G)) = {1, 2, ..., q}. In this paper we have proved superior edge bimagic labeling for certain class of graphs arising from graph operations.

5 illus, 10 ref

015058   Goudar V M;Ashalatha K S (Mathematics Dep, Sri Siddhartha Institute of Technology, Tumkur, Karnataka, Email: vmgouda@gmail.com) : Split geodetic number of a line graph. Int J mathl Combinatorics 2015, 3, 81-7.

A set S ⊆ V [L(G)] is a split geodetic set of L(G), if S is a geodetic set and hV - Si is disconnected. The split geodetic number of a line graph L(G), denoted by g_s[L(G)] is the minimum cardinality of a split geodetic set of L(G). In this paper we obtain the split geodetic number of line graph of any graph. Also obtain many bounds on split geodetic number in terms of elements of G and covering number of G. We also investigate the relationship between split geodetic number and geodetic number.

5 ref

015057   Bulut V;Caliskan A (Mathematics Dep, Ege Univ, Izmir, 35100, Turkey, Email: vahidebulut@mail.ege.edu.tr) : Spherical images of special smarandache curves in E₃. Int J mathl Combinatorics 2015, 3, 43-54.

In this study, we introduce the spherical images of some special Smarandache curves according to Frenet frame and Darboux frame in E^{3. Besides, we give some differential geometric properties of Smarandache curves and their spherical images.}

7 illus, 7 ref

014082   Rusanov V A;Daneev A V;Lakeev A V;Linke Y E (Institute of System Dyanamics and Control Theory, Siberian Branch of Russian Academy of Sciences, Russia, Email: v.rusanov@mail.ru) : On the differential realization theory of non-linear dynamic process in Hilbert space. Far East J mathl Sci 2015, 97(4), 495-532.

Paper presents different analytical criteria for realization of the continuous non-linear infinite-dimensional dynamic system defined by its input-output behavior (a "black box" model) in the separable Hilbert space in the class of controllable quasilinear time-invariant/variable differential models with program-positioning control.

36 ref

014081   Rana S;John A H;Midi H;Imon A H M R (Mathematics Dep, Institute for Mathematical Research Univ, Putra Malaysia-43400 UPM Serdang Selangor, Malaysia) : Robust regression imputation for missing data in the presence of outliers. Far East J mathl Sci 2015, 97(2), 183-95.

Missing value is a very common feature in a data which frequently occurs in many fields. Due to the missing value in a data set it is often difficult to apply the commonly used statistical techniques unless the missing values be estimated or discarded from an analysis. This article focuses on single imputations in conjunction to the regression data. It is now evident that the Random Regression Imputation (RRI) method is a very conventional approach to analyse missing data in regression. However, the RRI method is easily affected by some unusual observations that we often call outliers. Thus, author propose a robust version of RRI that we call Robust random Regression Imputation (RRRI). Results from the real life data and simulation approach are in favour of the RRRI than the RRI in the presence of outliers.

2 illus, 4 tables, 12 ref

014080   Rachmawati R N;Sufon (Mathametics and Statistics Dep, Bina Nusantara Univ, Jakarta, Indonesia) : Linear approximation of option pricing in incomplete market. Far East J mathl Sci 2015, 97(2), 139-81.

Skewness factor of underlying assets cannot be separated from the option pricing accuracy. Unfortunately, the Black-Scholes formula generally used in determining option price does not involve skewness. To calculate European option price, incomplete market model is chosen as a research instrument to determine the price using the Esscher transform and then convert it into the form of a linear approximation to the calculation of the option price. The aims of this study are to construct a linear approximation in option pricing with skewness effect and compare it to Black-Scholes option price. The result is linear approximation can predict the underlying assets on skewness effect accurately.

2 illus, 5 tables, 11 ref

014079   Pueon P (Mathametics Dep, Faculty of Science Mahasarkham Univ, Mahasarakham-44150, Thailand, Email: prapart.p@msu.ac.th) : Application of laplace adomian decomposition method to the Fornbrg-Whitham equations. Far East J mathl Sci 2015, 97(3), 377-87.

In this paper, Laplace Adomian decomposition method (LADM) is presented to solve Fornberg-Whitham equation. The powerful method can also be applied to modified Fornberg-Whitham equation. The solution reveals the efficiency and reliability of the method. Exact solutions can also be found from the known forms of the series solutions.

2 illus, 9 ref

014078   Payakkarak S;Sukawat D;Humphries U (Mathematics Dep, Faculty of Science King Mongkut's Univ of Technology Thonburi 126 Pach, Bangmod Tungkru, Bangkok.Pay@gmail.com) : Regional weather downscaling using ensemble Kalman filter with singular vector. Far East J mathl Sci 2015, 97(3), 347-76.

Modified ensemble Kalman filter (modified EnKF) is developed by using singular vector to generate the ensemble members instead of random generation as in the original EnKF. To test the performance of the modified EnKF, the outputs from weather downscaling by a shallow water model for wind speeds associated with two cold surges that reach Thailand are adjusted by the original EnKF and the modified EnKF. Result shows that the modified EnKF provides more realistic wind speed than the original EnKF.

10 illus, 10 tables, 12 ref

014077   Monsi M;Hassan N;Rusli S F M (Mathematics Dep, Faculty of Science Univ Putra Malaysia, 43400 UPM Serdang Selngor DE, Malaysia, Email: nas@ukm.edu.my) : Midpoint zoro symmetric single-step procedure for polynomial zeros. Far East J mathl Sci 2015, 97(2), 231-40.

The point symmetric single-step procedure l^ZSSl has R-order of convergence at least 4. This method is modified so that a better rate of convergence is achieved. The modified method is called the midpoint zoro symmetric single-step procedure PMZSS1 which has a faster convergence rate at least 8. In this paper, the convergence analysis of PMZSS1 is shown.

16 ref

014076   Kuntari S;Kusmayadi T A;Utomo L P H;Sudibyo N A (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Sebelas Maret Univ, Surakarta-57126, Indonesia, Email: kuntari.uns@gmail.com) : Eccentric digraph of corona of path graph with any graph H. Far East J mathl Sci 2015, 97(1), 45-52.

Distance d(u, v) from vertex u to vertex v in a graph G is the length of the shortest path from vertex u to v. The eccentricity of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to the eccentricity of u. The eccentric digraph ED(G) of a graph G is the digraph that has the same set of vertices as G, and there is an arc (directed edge) from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we determine the eccentric digraph of corona of path graph with any graph H.

14 ref

014075   Kuamayadi T A;Kuswardi Y;Usodo B;Sudibyo N A (Mathematics Dep, Faculty of Mathematics and Natural Sciences Sebelas Maret Univ, Surakarta-57126, Indonesia, Email: tri.atmojo.kusmayadi@gmail.com) : Eccentric digraph of corona of cycle with any graph H. Far East J mathl Sci 2015, 97(4), 407-16.

Let G be a graph with a set of vertices V(G) and a set of edges E(G). The distance from vertex u to vertex v in G is the length of the shortest path from vertex u to v. The eccentricity e(u) of a vertex a is the maximum distance of u to any other vertices of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph G is the digraph having the same set of vertices as G, and an arc (directed edge) from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we determine the eccentric digraph of corona of cycle with any graph H.

3 illus, 9 ref

014074   Kim M;Hahm N (Mathematics Dep, Incheon National Univ, Incheon-406 772, Korea, Email: mira@incheon.ac.kr) : Efficient LU factorization for non-square matrices. Far East J mathl Sci 2015, 97(1), 121-30.

In this paper, we suggest an efficient LU factorization for non-square matrices using the transpose of a matrix. We compute the total number of multiplications/divisions for LU factorization of non-square matrices and suggest an efficient LU factorization along with the numbers of rows and columns of a matrix.

2 illus, 7 ref

014073   Jun C (Mathematics Dep, Yuxi Normal Univ Yoxi-653 100, P.R. China, Email: caoj@yxnu.net) : Traveling wave solution for the modified benfmin-bona-mahony equation. Far East J mathl Sci 2015, 97(3), 337-46.

Bifurcation method of dynamical systems is employed to investigate exact solutions of the modified Benjamin-Bona-Mahony equation. Under some parameter conditions, their explicit expressions are obtained. These solutions contain solitary wave solutions, kink wave solutions, blow-up solutions and periodic blow-up solutions. Some previous results are extended.

12 ref

014072   Joshi L K;Joshi M C;Mathpal P C (Applied Mathematics Dep, Faculty of Engineering and Technology Gurukula Kangri Vishwavidyalaya, Haridwar-249 404) : Coincidence and fixed point theroems for multivalued mappings in symmetric spaces. Far East J mathl Sci 2015, 97(4), 397-406.

Aim of this paper is to establish some fixed point theorems for multivalued mapping using the multivalued analogous of the contractive condition introduced by Khan [4] in the setting of symmetric spaces generalizing some well-known results in metric spaces.

8 ref

014071   Jamaludin N A A;Monsi M;Hassan N (Mathematics Dep, Faculty of Science Univ, Putra, Malaysia-43400 Serdang) : Newton's method interval single-step procedure for bounding polynomial zeros simultaneously. Far East J mathl Sci 2015, 97(2), 241-52.

Existing interval symmetric single-step procedure IMW established in 1988 has a rate of convergence at least three. In this paper, the rate of convergence of this procedure is increased by introducing a Newton's method (NM) at the beginning of the procedure. It is used only once in the first iteration. The rate of convergence of NM is two. Based on the numerical results, this new procedure called INMW performed better than does IMW, with the rate of convergence possibly higher than three.

1 table, 21 ref

014070   Jaharuddin (Mathematics Dep, Bogor Agricultural Univ Jalan Meranti, Kampus IPB Dramaga Bogor-16680, Indonesia, Email: jaharipb@yahoo.com) : Approximate analytical solution of a higher order wave equation of KdV type. Far East J mathl Sci 2015, 97(2), 197-207.

Authors consider a higher order of Korteweg-de Vries (KdV) equation which is an important water wave model. We find the approximate analytical solution of the proposed model by Exponential Homotopy Analysis Method (EHAM). By using this method, we solve the problem analytically and then compare the numerical result with exact solution. Numerical results reveal that the EHAM provides * highly accurate numerical solutions for higher order KdV equation. The EHAM solution includes an auxiliary parameter. This parameter provides a convenient way of adjusting and controlling the convergence region of solution series.

2 illus, 13 ref

014069   Im M (Mathematics Education Dep, Han Nam Univ, Daejon-306 791, Korea, Email: mki@hannam.ac.kr) : Generalized conditional fourier-wiener transform and convolution product. Far East J mathl Sci 2015, 97(4), 417-41.

In this paper, we define a generalized conditional Fourier-Wiener transform and convolution product. Also, we investigate formulas for the generalized conditional Fourier-Wiener transform and convolution product. Moreover, we find the relationships of the generalized conditional Fourier-Wiener transform and convolution product.

19 ref

014068   Hwang J (Mathematics Education Dep, College of Education Daegu Univ, Jillyang, Gyeongsan, Gyeongbuk, Republic of Korea, Email: jshwang@daegu.ac.kr) : Frechet differentiability of solution mappings for semilinear second order Volterra integro-differential equations. Far East J mathl Sci 2015, 97(4), 457-80.

In this paper, we study the Frechet differentiability of the solution map from the set of parameters, which are composed of initial values and forcing terms, to the set of solutions for semilinear second order Volterra integro-differential equations. Also, we establish the strong Gateaux differentiability of the solution maps under the weaker conditions of nonlinear term. An application to the equation of nonlinear viscoelastic material with long memory is given.

11 ref

014067   Hermosillo O (NO, , Ciudad de la Cultura "Amado Nervo", Area de Ciencias Basicas e Ingenireia, Universidad Autonoma de Nayarit, Tepic, Nayar) : Presentation of links as n-Cucas. Far East J mathl Sci 2015, 97(1), 53-68.

Montesinos in [9] presented a way to form links from orbifolds. Hermosillo [6] defined the n-cuca as an alternative to Montesino's ideas. In fact, most of the results presented there are about 3-cucas and it is worked on a particular diagram. Hilden et al. [7] give a construction of these concepts referring to the structure as n-butterfly. Their results are independent from the diagram and they allow solvable arcs with 1 and 2 Riedemestier moves, but a 1-manifold is not always obtained. In this work, the definition of the n-cuca is perfectionated to ensure that we always obtain a 1 -manifold using only one type of diagram and we generalize the main result of [6], where it is guaranteed that the n-cuca generates an n-bridge link.

14 illus, 11 ref

014066   Dengyin J;Lisheng H;Shi P (Automation Dep, Shanghai Jiao Tong Univ Shanghai, 200 240, P.R. China, Email: 1shu@adelaide.edu.cn) : Tensor-based performance assessment of protection systems for safety-important process. Far East J mathl Sci 2015, 97(3), 283-324.

This paper considers the problem of performance assessment for protection systems based on tensor space approach. As a deep-defense measure for safety-important process, the protection system will let the systems behavior stop as soon as possible or refresh into the safety state when the control system fails to maintain the plant in a certain safety range. The protection system performance is highly coupled with that of control systems, which cannot, assess the protection system performance individually without considering the control systems performance. Moreover, unsuitable logical switching sequence caused by the protection setting points can potentially generate undesired switching dynamical behavior resulting. This study aims to clarify the effects of logical switching sequence between control systems and protection systems on the process safety performance. Specifically, the tensor space approach is proposed to develop the model of protection systems, which can synthetically describe the logical relation between control systems and protection systems. Furthermore, we employ the minimum variance criterion being as controller performance benchmark that characterizes the effect of logical switching sequence on protection systems performance, which is a measure of the effects commonly used to characterize the entire resulting. The procedures based on tensor space approach for computing the performance indices for the quantity are also provided. Finally, two illustrative examples are given to show the usefulness of the proposed tensor space approach for protection systems performance assessment by comparing with multiple model approach.

7 illus, 2 tables, 42 ref

014065   Ciurdariu L (Mathematics Dep, "Politechnia" Univ ov Timisoara P-ta. Victoriei, No.2 300 006-Timisoara, Romania) : About some inequalities for positive operators on Hilbert space. Far East J mathl Sci 2015, 97(3), 267-82.

In this paper, several inequalities for positive definite operators defined on Hilbert spaces will be presented under suitable assumptions, which improves the well-known inequality of Young. These inequalities will be rewritten then using norms, and other particular important case of these inequalities will be presented as consequences.

7 ref

014064   Choi S;Goo Y H (Mathematics Dep, Hanseo Univ, Seosan Chungnam-356706, Republic of Korea, Email: schoi@hanseo.ac.kr ) : h-Stability and boundedness in perturbed functional differential systems. Far East J mathl Sci 2015, 97(1), 69-93.

In this paper, we investigate h-stability and bounds for solutions of the perturbed functional differential systems using the notion of t_∞ -similarity.

18 ref

014063   Choi S;Goo Y H (Mathematics Dep, Hanseo Univ Seosan, Chungnam-356 706, Republic of Korea) : Lipschitz and asymptotic stability for perturbed nonlinear functional differential systems. Far East J mathl Sci 2015, 97(2), 209-230.

In this paper, we investigate Lipschitz and asymptotic stability for perturbed nonlinear functional differential systems.

15 ref

014062   Cai X (School of Information Science and Technology, Chuxiong Normal Univ, Chuxiong-675 000, P.R. China) : structural theory about right-eliminable BCI-algebras. Far East J mathl Sci 2015, 97(3), 389-95.

In this paper, the definition of right-eliminable BCI-algebra is given and some characters about its structure are studied. At last, the theory about decomposition is given.

1 table, 4 ref

014061   Brambilla C;Gurny M;Lozza S O (Management Dep, Economics and Quantitative Methods, Bergamo Univ, Via Dei Caniana 2, 24127 Bergamo (BG), Italy, Email: chiara.brambilla@unibg.it) : Structural credit risk models with levy process: the VG and NIG cases. Far East J mathl Sci 2015, 97(1), 101-19.

We propose alternative structural credit risk models for determining probabilities of default (PDs) based on two well-known Levy processes - the Variance Gamma (VG) process and the Normal Inverse Gaussian (NIG) process, respectively. In particular, using Levy processes, we propose a methodology to overcome the distributional drawbacks of the classical Merton model. Therefore, we discuss an empirical comparison of estimated PDs obtained from the VG and the NIG models on a dataset of 24 companies with strong capitalization in the US market. The empirical evidence suggests that both the models are able to capture the situation of instability that effects each company in considered period and, in fact, are very sensitive to the periods of the financial crisis.

4 illus, 1 table, 22 ref

014060   Bivin M R;Saivaraju N;Subramanian N (Mathematics Dep, Care Group of Institutions, Trichirappalli-620 009, Email: mrbivin@gmail.com) : Class of χ<. Far East J mathl Sci 2015, 97(1), 1-18.

In this paper, we introduce and study of the concepts of strongly χ^{2λ - convergence and statistically % -convergence for interval numbers. We give some relations involving these double sequences.}

42 ref

014059   Asawasamrit S (Mathematics Dep, Faculty of Applied Science King Mongkut's Univ of Technology North Ban, Bangkok-10800, Thailand, Email: suphawata@kmutnb.ac.th) : On derivations of KK-algebras. Far East J mathl Sci 2015, 97(3), 325-35.

In the present paper, we introduce the notions of derivations of KK-algebras and investigated some related properties. This paper also considers regular derivations and the d-invariant of KK-algebras.

6 ref