011450   Seal B;Sengupta A (NO, , Burdwan Univ) : On the foundations of dependency models and parameters for random variables on cylinder R<. Calcutta Statist Ass Bull 2012, 64(255-6), 151-65.

Directional data often deal with observations on circles, spheres, cylinders, torus, etc. The notion of dependency between the variables involved and the development of related models and dependency parameters are of fundamental importance in this area. Author developed a method of obtaining regression curves on manifold (cylinder) on R^{3 based on a differential geometric approach. With an aim to develop statistical inference procedures, proposed useful distribution on the cylinder for which the dependency parameter can be elegantly elucidated, and demonstrate how this parameter can be estimated in practice.}

13 ref

011449   Savariappan P R;Chandrasekar P;Selvam S; Vaidyanathan V S (Mathematics Dep, Luther College, Iowa, USA) : Statistical analysis of tandem queues with blocking. Calcutta Statist Ass Bull 2012, 64(255-6), 241-55.

A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected number of entities in the system (L_s) in a two service point tandem queue with at most one entity in between, the service points and busy service point 1 are obtained. Further, for a three service point tandem queue with busy service points 1 and 2 and at most one entity in between the last two service points, the MLE, CAN estimator and asymptotic confidence for Ls are obtained.

2 illus, 3 tables, 12 ref

011448   Ray P K;Kant S;Roy B;Basu A (Home (C & E) Dep, Government of West Bengal, Kolkata) : Classification of encryption algorithms using the Hidden Markov model. Calcutta Statist Ass Bull 2012, 64(255-6), 277-90.

The "Hidden Markov Model", HMM for short, represents a very rich class of stochastic models which is extensively used in modeling real data. In particular it has proved to be a strong and powerful tool for classification problems in some specific application areas including speech recognition and image analysis. The model involves a complex stochastic formulation of the underlying process and the implementation is numerically somewhat involved. In this article author presented some results involving the application of hidden Markov models in trying to classify a cipher text in terms of the source algorithm generating the cipher when it is known that the source algorithm belongs to a finite list of algorithms. This application is based on ten source algorithms, five each of the stream cipher and block cipher types. Performed a statistical analysis of each cipher text leading to the evaluation of me posterior chances of the cipher being generated by each of the competing source algorithms. Although there are some other instances of the use of the hidden Markov model in the area of cryptology there is little literature relating to the previous use of this model in the specific context of classification of encryption algorithms, which makes it hard to judge its performance or compare it against an existing standard. However on the basis of the limited study we feel that there is clear indication to suggest that further investigation of the hidden Markov model in the context of classification of encryption algorithms may be worthwhile as they appear to lead to classification results which are clearly better than random assignment.

14 ref

011447   Patil H S (Statistics Dep, S. B. Zadbuke Mahavidyalaya, Barsi, Maharashtra) : Two-stage estimation procedure for the parameter of U (θ, mθ) distribution. Calcutta Statist Ass Bull 2012, 64(255-6), 257-63.

In the literature, an extensive work on sequential fixed width confidence interval (CI) for the parameter of U(0, θ) model is available. In this article author proposed a two-stage fixed width (1 - a) level sequential CI for the parameter θ of U(θ, mθ) distribution, where m <62> 1 is known, based on the large-sample approximation of coverage probability.

1 table, 10 ref

011446   Liu Z (NO, College of Sciences, Hezhou Univ, Hezhou Guangxi, 542800 P.R. China, Email: gx_lzw@163.com) : On the exponential diophantine equation x<. Far East J mathl Sci 2014, 86(2), 129-38.

Let p be an odd prime, and let x, y, m, n be positive integers satisfying gcd(x, y) = 1 and n <62> 2. In this paper, we solve the equation x^{2 - p2m = yn in the following four cases: (i) 2| n; (ii) n <62> 3, 2|n 2|w and 2|y; (iii) n <62> 5, 2|n, 2|m and 2|y; (iv) n = 3 and 2|y. Moreover, we conjecture that the equation has only the solutions (p, x, y, m, n) = (11, 122, 3, 2, 5) and (43, 30042907, 96222, 4, 3) with 1/m + 2/n <60> 1.}

9 ref

011445   Lee G;Asci M (Mathematics Dep, Hanseo Univ, Seosan ChungNam 356-706, Korea, Email: gylee@hanseo.ac.kr) : On the factorizations of the Pascal matrices via Padovan matrices. Far East J mathl Sci 2014, 86(2), 165-81.

Riordan arrays are useful for solving the combinatorial sums by the help of generating functions. Many theorems can be easily proved by Riordan arrays. In this paper, we introduce the first kind of Padovan matrix and the second kind of Padovan matrix and we consider the factorizations of Pascal matrices involving the Padovan matrices.

9 ref

011444   Ku C Y;Wong K B (Mathematics Dep, National Univ of Singapore, Singapore 17543, Email: matkcy@nus.edu.sg) : On r-regular subgraphs with Hamiltonian cycles in graphs with many edges. Far East J mathl Sci 2014, 86(2), 221-32.

In this paper, authors prove that for 0 <60> β <60> l/(2r + 1) and sufficiently large n, every graph G with n vertices and at least n^{2β edges contains a subgraph G' with at least n2-2β /26 edges, such that any t disjoint edges in G lie together on an r-regular subgraph with at most 2rt vertices. Furthermore, the r-regular subgraph has a Hamiltonian cycle that contains all the t disjoint edges.}

11 ref

011443   Krishnamoorthy A;Nair S S;Narayanan V C (Mathematics Dep, Cochin Univ of Science and Technology, India) : An inventory model with server interruptions and positive lead time. Calcutta Statist Ass Bull 2012, 64(255-6), 219-39.

In this paper, authors considered a single server queuing system with inventory where customers arrive according to a Poisson process. The time required to meet a demand follows an exponential distribution. Replenishment of inventory is according to the (s, S) policy with lead-time following exponential distribution. The service process may be interrupted in-between, with interruption time following exponential distribution. More than one interruption is possible during a particular service and at each time, the repair time of an interrupted server follows an exponential distribution. It is assumed that during interruption, the customer being served waits there until his service is completed and that no inventory is lost due to interruption, Also assumed that, when the inventory level is.zero rio arrival is considered. Stability of the above system is analyzed and steady state vector is calculated using Matrix Analytic Methods. System performance measures such as expected number of customers in the system, expected inventory size, expected interruption rate, waiting time of a customer in the system etc are also obtained. A thorough numerical study of the dependence of the system performance measures on various system parameters has been carried out.

2 illus, 9 tables, 13 ref

011442   Kim Y K;Min W K (Mathematics Dep, MyongJi Univ, Youngin 449-728, Korea, Email: ykkim@mju.ac.kr) : Remarks of parameter sets for soft sets. Far East J mathl Sci 2014, 86(2), 211-20.

In order to investigate any operation and various types of subsets on a parameter set for a given soft set, we introduce the notions of A_{F, A^F and F^←} on a parameter subset A, and study some properties of such notions.

9 ref

011441   Karale M;Sharma H L (Mathematics and Statistics Dep, Jawaharlal Nehru Krishi Vishwa Vidhyalaya, Jabalpur-482 004, Email: mkarale@yahoo.co.in) : On probability models for describing population dynamics of major insect pests under rice potato okra cropping system. J Crop Weed 2014, 10(2), 451-6.

In the present investigation, trends in population dynamics of major insect pests under rice-potato-okra cropping system have been studied through probability models. Among the major insect pests climbing cutworms were observed on rice, whiteflies and jassids on potato and whiteflies, aphids and jassids on okra. The data have been taken from an experiment which was conducted by the staff of department of Agronomy during kharif, Rabi and summer season 2006-07 at the Krishi Nagar farm, Adhartal JNKVV, Jabalpur, following randomized complete block design (RCBD) with varying number of treatments under each crop. The variety pusa basmati was taken for rice, kufri jawahar for potato and ladies finger for summer okra. The occurrences of the insects were grouped in the form of frequency distribution according to the number of plants. The Poisson distribution is found to be adequate for describing the pattern of climbing cutworms on rice, white/lies andjassids on potato and aphids on okra. In addition to these, Polya-Aeppli distribution is well fitted for the number ofwhiteflies andjassids on okra. These distributions may be used for forecasting of the losses in these crops due to major insect pests considered here.

6 illus, 6 tables, 10 ref

011440   Guao M;Ghosh M (Statistics Dep, Florida Univ, USA) : Empirical bayes prediction in random effects models with covariates subject to measurement error. Calcutta Statist Ass Bull 2012, 64(255-6), 265-75.

The paper considers a nested error linear regression model with multiple covariates subject to measurement error. An efficient empirical Bayes (EB) predictor is obtained using the information on both the observed response variables and the observed covariates. We derive a correct second-order unbiased approximation to the mean squared error (MSE) of the EB predictor.

011439   Emami H;Rasekh A (Statistics Dep, Faculty of Science Zanjan Univ, Iran) : Influence diagnostics in linear regression under heteroscedasticity: a different approach. Calcutta Statist Ass Bull 2012, 64(255-6), 201-17.

Many procedures are available to identify a single outlier or an isolated influential point in linear regression model. But the detection of multiple outliers or subset of influential points is rarely considered under heteroscedasticity and not been studied from the point of direct procedure. In this paper, definition and properties of an influence statistic for one or a set of observations in linear regression under heteroscedasticity is generalized. Author expressed this influence statistic in terms of the residuals and the leverages. Proved that this statistic has asymptotically normal distribution and is able to detect a subset of high weighted leverage-outliers that will be undetected by Cook's distance. For illustration, a simulation study has been carried out and also a real data set has been analyzed.

3 illus, 2 tables, 11 ref

011438   Bo-Yao W;Shih-Hsiang N;Chia-Ying C;Shiang-You H (Applied Mathematics Dep, National Pingtung Univ of Education Pingtun 900, Taiwan, Email: justlovenpue@gmai.com) : Some equivalent relations among the weighted shapley value, the weighted potential approach and the weighted dividend approach. Far East J mathl Sci 2014, 86(2), 197-209.

Provide some equivalent relations to axiomatize the family of all solutions that admit a weighted potential. Based on these equivalent relations, several axiomatizations of the weighted Shapley value are also proposed. Further, we introduce the weighted dividend approach.

5 ref

011437   Banerjee K;Chattopadhyay G;Banerjee T (NO, St. Xavier's College, Kolkata, India) : A test for equality of marginals of FGM family of bivariate distributions using unordered pairs. Calcutta Statist Ass Bull 2012, 64(255-6), 181-99.

A test for equality of marginal distributions of Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions is proposed on the basis of a paired sample of size n, when the labels of the observations are not known. The test has desirable power properties and is an improvement over the test prescribed by Davies and Phillips [1988]. The test is illustrated with some interesting real-life applications.

5 illus, 2 tables, 27 ref

011436   Adiwijaya;Wisesty U N;Nhita Fx (NO, Telkom Univ, Jl. Telekomunikasi no. 1 Ters. Buah Batu Bandung 40257, Indonesia, Email: adiwijaya@telkomuniversity.ac.id) : Line search techniques on the modified backpropagation for forecasting of weather data in Indonesia. Far East J mathl Sci 2014, 86(2), 139-48.

Extreme alteration of weather condition in Indonesia at the last two decades is the main idea that encourages this research. Recently, we have been built an improvement system of backpropagation performance by using conjugate gradient on forecasting of air temperature and humidity in Indonesia [1]. Data of weather used in this research is derived from Indonesian Agency for Meteorology Climatology and Geophysics covering air temperature, rainfall, air humidity, length of sun radiation, air pressure, and wind velocity in Kemayoran Jakarta area along five years (2007-2012). In this paper, we examine a technique of line search on conjugate gradient for backpropagation training in the forecasting of temperature, humidity, and air pressure. The technique of line search plays a part in determining step size parameter on conjugate gradient to minimize the process of searching. Eventually, the proposed method provides good performance, in addition to the training needs of small epoch compared to the standard backpropagation.

4 illus, 2 tables, 9 ref

010452   Antony A;Nandagopal M S G;Rangabhashiyam S; Selvaraju N (Chemical Engineering Dep, National Institute of Technology Calicut, Kozhikode-673 601, Email: selvaraju@nitc.ac.in) : Probabilistic neural network prediction of liquid- liquid two phase flows in a circular microchannel. J scient ind Res 2014, 73(8), 525-9.

The present work proposes towards flow pattern prediction in a liquid- liquid microchannel flow through a circular channel. Mass transfer in a microchannel mainly depends on the flow regime inside the channel. The liquid-liquid two phase flow regime in a microchannel depends on the flow velocity and the junction characteristics. Hence, the prediction of patterns has a superior role for the characterisation of mass transfer rates. This paper experimentally investigates the flow pattern in an 800 micro meter diameter microchannel with T junction. The slug length variation corresponding to varying inlet flow rate for the aqueous (water) - organic (kerosene) liquids is visualised and measured. A model for the prediction of liquid- liquid flow patterns in a circular T-shaped microchannel is designed using Probabilistic Neural Network (PNN). The designed PNN algorithm is explicitly validated by comparing the predicted patterns with the experimentally observed data.

2 illus, 11 ref

009467   Yun J;Hahm N (NO, , Incheon Science High School, Incheon 400-831, Korea, Email: matheducation@hanmail.net) : Numbers of downward and upward creases in generalized paper folding sequences (X_pY_q)<. Far East J mathl Sci 2014, 84(1), 81-97.

In this paper, author compute the numbers of downward and upward creases in generalized paper folding sequences (X_pY_q)^{n, where X, Y ∈ {R, L, U, D} and n, p, q ∈ N with p, q ≥ 2. Using the classification in [9], we show the exact numbers of downward and upward in (X_pY_q)n by the recursion formula and successive elimination.}

9 ref

009466   Yoo J K;Rhee H J (Liberal Arts and Science Dep, Chodang Univ, 419 Sungnamri Muangun 534-701 Chonnam, Korea, Email: jkyoo@chodang.ac.kr) : On the stability of the localizable spectrum. Far East J mathl Sci 2013, 83(1), 113-26.

Suppose X is a complex Banach space and T ∈ L(X) is a bounded * linear operator. The localizable spectrum σ_loc (T) of an operator T ∈ L(X) defined as the set of all λ ∈ C for which χ_T(V) ≠ (0) for each open neighborhood V of λ, where χ_T-(V) denotes the space of all x ∈ X for which there exists an analytic function f : CV → X which satisfies (λI - T)f(λ) = x for all λ ∈ CV. This paper studies the basics of the localizable spectrum and relates it to local spectra. Moreover, we show that if the quasi-affinity A ∈ L(X, Y) intertwines S ∈ L(Y) and T ∈ L(X) asymptotically and S is decomposable and T has either property δ or the weak 2-SDP, then σ_loc(T) = σ_loc(S).

19 ref

009465   Yang M (Mathematics Dep, Incheon Univ, Yeonso-Gu Songdo-Dong 12-1 Incheon 406-772, Korea, Email: mhyang@incheon.ac.kr) : The extended space of a stationary multiscale system. Far East J mathl Sci 2013, 83(2), 167-83.

Let S be a Schur multiplier in a multiscale system. Then there is a quasi-coisometric linear system whose state space is the extension space D(S) of the de Branges-Rovnyak space H(S) and the transfer function is S.

9 ref

009464   Wen Y X;Wang T;Yao L (Mathematics Dep, Kunming Univ, Kunming, Yunnan 650214 P.R. China) : On the Δ-convergence of modified s-iteration schemes for total asymptotically nonexpansive non-self mappings in a cat(0) space. Far East J mathl Sci 2014, 86(1), 61-74.

In this paper, the modified S-iteration schemes are defined for approximating a fixed point of total asymptotically nonexpansive non-self mappings in CAT(O) spaces. Some Δ-convergence theorems are proved under suitable conditions in CAT(O) spaces.

22 ref

009463   Wareeprasirt N;Sukawat D (Mathematics Dep, King Mongkut's Univ of Technology Thonburi, Bangkok 10140, Thailand, Email: luecss@gmail.com) : A simplified model for chaotic behavior study of winter monsoon. Far East J mathl Sci 2014, 87(2), 149-72.

A simplified model for winter monsoon over Southeast Asia is developed from the atmospheric convection problem. The simplified model is two dimensions in the meridional-vertical plane. The approach in simplification from the convection model to the monsoon model is based on the technique used in Lorenz model. Chaotic behavior of the proposed model is investigated from the characteristic equation of the linearized version of the model using Routh-Hurwitz stability criteria. Out of five equilibrium points of the simplified model for winter monsoon, chaotic behavior can occur only at two equilibrium points.

9 illus, 17 ref

009462   Venetis J (NO, , Section of Mechanics, NTU Athens 5 Heroes of Polytechnion Avenue GR 15773, Athens Greece, Email: john24@otenet.gr) : A rephrased form of equations of conservation for incompressible flows in lagrangian coordinates. Far East J mathl Sci 2014, 87(2), 261-70.

In this paper, the author obtains a rephrased form of the equations of mass and momentum conservation for a generic type of a three dimensional, unsteady, isothermal viscous flow according to Lagrangian formalism for the fluid motion: In particular, the system of equations, of mass and momentum conservation is equivalently represented as a linear ordinary differential equation, which holds along any network of streamlines for incompressible flow patterns and has been derived without any distinction of the flow field as inviscid or viscous. Thus, it is valid for all types of unsteady, incompressible and isothermal flows.

8 ref

009461   Venetis J (NO, School of Civil Engineering NTUA, Greece, Email: john24@otenet.gr) : Approximate explicit solution to prandtl's system of equations. Far East J mathl Sci 2014, 84(1), 1-11.

Objective of this paper is the obtainment of an approximate explicit solution to Prandtl's system of equations for isothermal, incompressible and steady boundary layer flows of Newtonian fluids, in a coordinate free context. The basic novelty of this work is the modification of the corresponding boundary conditions. Particularly, we will not take into consideration the no - slip and kinematic wall conditions for velocity profile. Instead of these ones, we will complete Prandtl's equations of mass and momentum conservation with two generalized boundary conditions of Dirichlet and Neumann type, which evidently concern the governing velocity component. Besides, the condition of uniform flow at infinity will not be taken into consideration.

11 ref

009460   Udayabaskaran S;Murthy R;Viswanath J (Computer Applications Dep, Vel Tech Dr. RR & Dr. SR Technical Univ, Chennai-600 062, Email: udayabaskaran.s@gmail.com) : Optimal harvesting of a renewable resource whose growth rate moves stochastically with three finite velocities. Far East J mathl Sci 2013, 83(1), 1-20.

Natural renewable resource is considered in which the growth rate is assumed to fluctuate cyclically with three constant velocities at random time points. The resource is harvested continuously with rate E over a period 0 to T of time. We formulate an expression for the total profit based on which we adopt a numerical optimal search procedure and obtain an optimal harvesting policy E*.

5 illus, 7 tables, 24 ref

009459   Udayabaskaran S;Karthikeyan T;Viswanath J (Mathematics Dep, Vel Tech Dr RR & Dr SR Technical Univ Avadi, Chennai-600 062, Email: udayabaskaran.s@gmail.com) : A modified markov branching process with state-dependent immigration. Far East J mathl Sci 2014, 87(1), 113-32.

Parthasarathy [5] considered a modified Markov branching process in which each particle surviving at least up to a definite time T splits into several particles at a later time t (t <62> T) while all particles whose lifetime ends before the time T leave no descendants. He calls T as the maturity age of the particles. This type of maturity dependent branching has not been studied yet in Markov branching processes with immigration. To fill this gap, we investigate in the present paper the modified Markov branching processes which incorporate state-dependent immigration.

2 illus, 8 tables, 7 ref

009458   Tsukamoto I (NO, , 3-10-38 Higashi-kamagaya, Kamagaya-schi, Chiba, 273-0104 Japan, Email: ktkmt@k9.dion.ne.jp) : On asymptotic behaviour of positive solutions of x" = -t<. Far East J mathl Sci 2013, 83(2), 233-50.

May consider an initial value problem of the differential equation denoted in the title, and show the domain of its positive solution and the analytical expressions of this valid in the neighbourhoods of the ends of the domain. This is done for all initial conditions.

21 ref

009457   Tadikonda S;Bhagavan V S (Mathematics Dep, K.L. Univ, Guntur-522 502, Email: tsluguntur@gmail.com) : Irreducible representation of SL(2, C) and generating relations for the generalized hypergeometric functions. Far East J mathl Sci 2013, 83(2), 127-44.

The aim of the present paper is to obtain a new class of generating relations for the generalized hypergeometric functions Ψ_{α,β,γ ,.m}(x) by constructing a realization of the algebraic representation D(u, m₀) of SL(2, C) (a complex special linear group). Here the suitable interpretation to various parameters has been given simultaneously. These generating functions, in turn yield, us special cases, a number of linear generating functions to various important classical orthogonal polynomials of mathematical physics and statistics, namely, the Laguerre, Hermite (even and odd), Meixner, Gottlieb and Krawtchouk polynomials. Many results obtained as special cases are known but some of them are believed to be new in the theory of special functions.

15 ref

009456   Susilowati L;Zamrud M;Anggraeni D P F (Mathematics Dep, Faculty of Sciences and Technology, Universitas Airlangga, Surbaya Indonesia, Email: lilik_rofiudin@yahoo.co.id) : Super (a, d)-C_n-antimagic total labeling of grid graph P_n x P_m. Far East J mathl Sci 2014, 87(1), 53-73.

A graph G = (F(G), E(G)) admits an (H₁, H₂, ..., H_k) -covering if every edge in G belongs to at least one of the subgraphs H_i, I ≤ i <≤ k_o. If for every i, H_i isomorphic to a given graph H, then G is called having an H-covering. An (a, d) -H-antimagic total labeling of graph G is a bijection f : V(G) ΔE(G) → {1, 2,..., | V(G)! + E(G)} such that the set of weight of every subgraph H' which is isomorphic to H is a + (a + d) + ... -'- (a + (t - 1)d), where a and d are positive integers, and t is the number of subgraph of G isomorphic to H. If f : V(G) → {1, 2, ..., | F(G)|}, then G is called having a super (a, d) -H-antimagic total labeling. This project applying this labeling to the grid graph (P_n x P_m) with cover is H = C₄, C₆ for some value of d are possible and its application using computer programming.

1 illus, 5 ref

009455   Sungchasit R;Pongsumpun P;Tang I M (Mathematics Dep, Faculty of Science King Mongkut's Institute of Technology Ladkrabang C, Ladkrabang, Bangkok 10520, Thailand, Email: kppuntan@kmitl.ac.th) : Transmission model of dengue virus by Aedes aegypti and Aedes albopictus. Far East J mathl Sci 2013, 83(1), 85-112.

Mathematical models are used for describing many diseases. Dengue disease is occurred by biting of infected Aedes aegypti and Aedes albopictus mosquitoes. Dengue outbreak is found during the rainy season. Each Aedes mosquito has the different dengue outbreaks and they depend on the temperature and areas. The standard dynamical modeling method is used in this study. The SIR (susceptible-infected-recovered) model is modified to describe the transmission of dengue virus by two species of vectors. The transmission of dengue virus is varied with time. The dynamical analysis method is used for analyzing this model. We confirm these results by using numerical results.

9 illus, 19 ref

009454   Sriramachandran G V;Palanivel M (Mathematics Dep, Dr. Mahalingam College of Engineering and Technology, Pollachi-642 003, Email: gvsriramachandran@yahoo.com) : Acceptance sampling plan from truncated life tests based on exponentiated gamma distribution. Far East J mathl Sci 2014, 84(1), 47-64.

In this paper, an acceptance sampling plan is developed for a truncated life test when the life time of a product follows an exponentiated Gamma distribution. The minimum sample size required is determined for various acceptance numbers when the consumer's risk and the termination time are specified. The operating characteristic values and the minimum ratios of the true average life to the specified life at a specific producer's risk are obtained. The results obtained are compared with ordinary Gamma distribution.

10 tables, 9 ref

009453   Shin D H (Global Finance and Banking Dep, Inha Univ, 253 Yonghyun-dong Nam-gu Incheon, 402-751, Korea, Email: dhshin@inha.ac.kr) : European call options with singularly perturbed two time scale regime-switching model. Far East J mathl Sci 2014, 87(1), 37-52.

In this paper, we consider the European call option pricing on where the market of an underlying asset has two states and the price of the asset is perturbed singularly between the two states. We set up the European call option value function depending on the perturbation rate. The convergence of the value function is proved when the perturbation becomes singularly faster. Numerical examples follow to show the convergence.

1 illus, 1 table, 10 ref

009452   Samartkoon S;Jampachon P (Mathematics Dep, Faculty of Science Khon Kaen Univ, Khon Kaen 40002, Thailand, Email: samartkoon@hotmail.com) : Green's relations on the menger algebra (Pol_min<. Far East J mathl Sci 2013, 83(1), 75-84.

3 ref

009451   Roy S L;Biswas L;Chakravarty N (NO, Regional Meteorological Centre, Kolkata, Email: sukumarlala@gmail.com) : Statistical model for prediction of arial rainfall over barakar catchment. Mausam 2013, 64(2), 376-9.

3 tables, 4 ref

009450   Rosyida I;Widodo;Indrati C R;Sugeng K A (Mathematics Dep, GadjahMada Univ, Indonesia, Email: widodo_mathugm@yahoo.com) : New results on upper bounds for the chromatic number of fuzzy graphs and their complements. Far East J mathl Sci 2014, 87(1), 89-111.

Upper bounds for sum and product of chromatic number of complementary fuzzy graphs are given in [9]. We find that these bounds do not hold for fuzzy graphs which have certain properties. This problem motivates us to investigate upper bounds for sum and product of chromatic number of several classes of fuzzy graphs and their complements. We obtain new results on upper bounds for sum and product of complementary fuzzy graphs. Finally, we investigate these results related to the bounds given in [9]. We add a necessary condition to fuzzy graphs so that the upper bounds given in [9] can be improved.

2 illus, 1 table, 13 ref

009449   Rao T S;Suresh Kumar G;Murty M S N (Mathematics Dep, Koneru Lakshmaiah Univ, Vaddeswaram, Guntur dt., Email: drgsk006@kluniversity.in) : Ψ-asymptotic stability of nonlinear difference equations. Far East J mathl Sci 2013, 83(1), 21-39.

This paper deals with obtaining sufficient conditions for Ψ-asymptotic stability of trivial solution for the linear and nonlinear difference equations on N. And also we provide a way to construct asymptotically stable difference equation from the given equation using Y-asymptotic stability.

3 illus, 16 ref

009448   Ramesh R;Vengataasalam S (Mathematics Dep, K.S. Rangasamy College of Technology, Tiruchengode-637 215, Email: rameshrajappa@yahoo.com) : Existence of solutions of fuzzy impulsive delay integrodifferential equations with nonlocal condition. Far East J mathl Sci 2014, 86(1), 37-60.

In this paper, we prove the existence of solutions of fuzzy impulsive delay integrodifferential equations with nonlocal condition. The results are obtained by using the fixed point principles. An example is presented to illustrate the theory.

21 ref

009447   Park J S (Mathematics Education Dep, Institute of Mathematics Education, Chinju National Univ of Education, Jinju 600-756, Korea, Email: parkjs@cue.ac.kr) : Some common fixed point theorems for weakly compatible and property (EA) maps family without continuity. Far East J mathl Sci 2014, 87(2), 185-94.

In this paper, we obtain some common fixed point theorems for weakly compatible and property (EA) maps family in IFMS. The results are proved without the notion of continuity, and generalized several results in existing literature (see [6, 10]).

11 ref

009446   Park J S (Mathematics Education Dep, Institute of Mathematics Education, Chinju National Univ of Education Jinju 660-756, South Korea, Email: parkjs@cue.ac.kr) : On convergence theorems of the fixed points for pointwise convergent maps in an ifms. Far East J mathl Sci 2014, 84(1), 33-46.

Shen et al. [14] proved the convergence of the sequence of fixed points for some sequences of contraction mappings satisfying certain conditions in fuzzy metric space. In this paper, we define some properties and obtain the convergence of the fixed points sequence for pointwise convergent sequences of contraction mapping and IFM satisfying certain conditions in IFMS.

14 ref

009445   Ogata S (Mathematical Institute, Tohoku Univ, Sendai 980-8578, Japan, Email: ogata@math.tohoku.ac.jp) : Projective normality of toric 3-folds with non-big adjoint hyperplane sections, II. Far East J mathl Sci 2014, 84(1), 99-110.

Assuming (X, A) being a nonsingular polarized toric 3-fold. Authors show that if I the adjoint bundle of A has no global sections, then all ample line bundles on X are normally generated. Even if the adjoint bundle of A is effective, if it is not big, then it is also shown the normal generation. Especially, we show that all ample line bundles on a nonsingular toric Fano 3-fold are normally generated.

2 illus, 11 ref

009444   Nishimura H (Institute of Mathematics, Tsukuba Univ, Tsukuba, Ibaraki, 305-8571, Japan) : From the biot-savart law to ampere's magnetic circuital law via synthetic differential geometry. Far East J mathl Sci 2014, 87(2), 207-23.

It is well known in classical electrodynamics that the magnetic field given by a current loop and the electric field caused by the corresponding electric dipoles in sheets are very similar, as far as we are far away from the loop, which enables us to deduce Ampere's magnetic circuital law from the Biot-Savart law easily. The principal objective in this paper is to show that synthetic differential geometry, in which nilpotent infinitesimals are available in abundance, furnishes out a natural framework for the exquisite formulation of this similitude and its demonstration. This similitude in heaven enables us to transit from the Biot-Savart law to Ampere's magnetic circuital law like a shot on earth.

9 ref

009443   Muthulakshmi V;Vinodhini D (Mathematics Dep, Periyar Univ, Salem, Email: vmuthupu@gmail.com) : Oscillation criteria for forced second order differential equations with damping term and mixed nonlinearities. Far East J mathl Sci 2014, 86(1), 101-9.

In this paper, some new oscillation criteria are established for the forced second order differential equations with damping term and mixed nonlinearities by using Riccati technique. The results obtained here improve and generalize some results in the literature. An example is also given for illustration.

8 ref

009442   Muthulakshmi T;Subramanian M (NO, Anna Univ: Tirunelveli Region, Tirunelveli-627 007, Email: laxmemu@gmail.com) : Independence saturation number of some classes of graphs. Far East J mathl Sci 2014, 86(1), 11-21.

Let IS(v, G) denote the maximum cardinality among all independent sets of G containing v. Then IS(G) = mm{IS(v) : v ∈ V(G)} is called the independence saturation number of G. In this paper, we compute the independence saturation number of some classes of graphs such as central graph, total graph, line graph of star graph K_1,n and double star graph K_1,n,n' central graph of cycle graph, expansion graphs, corona graphs, Mycielskian graphs and maximal triangle free graphs.

2 illus, 19 ref

009441   Muthucumaraswamy R;Venkatesan J (Applied Mathematics Dep, Sri Venkateswara College of Engineering Irungattukottai, Sriperumbudur Taluk-602 117, Email: venkatesan.j@rajalakshmi.edu.in) : Thermal radiation effects on flow past a parabolic started vertical plate with variable temperature and uniform mass flux. Far East J mathl Sci 2013, 83(1), 49-63.

The objective of this paper is to investigate an unsteady flow of viscous incompressible fluid past a parabolic started infinite vertical plate with variable temperature and uniforrn mass flux, in the presence of thermal radiation. The plate temperature is raised linearly with time and the mass diffused from the plate to the fluid at a constant rate. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The dimensionless governing equations are solved using Laplace-transform technique. The effects of the velocity, the temperature and the concentration are studied for different physical parameters. It is observed that the velocity increases with decreasing values of the thermal radiation parameter. The trend is just reversed with respect to the thermal Grashof number or mass Grashof number.

6 illus, 15 tables

009440   Liu S;Zhang Q;Gao L (Mathematics and Information Science Dep, Binzhou Univ, Shandong 256603 P.R. China, Email: 13169207@163.com) : Oscillation theorems of the third-order nonlinear delay dynamic equations on time scale. Far East J mathl Sci 2014, 86(1), 75-100.

In this paper, a class of third-order nonlinear delay dynamic equations on time scales is studied. By using the generalized Riccati transformation and the inequality technique, two new sufficient conditions which ensure that every solution is oscillatory or converges to zero are established. The results obtained essentially generalize and improve earlier ones. Examples are given to illustrate our main results.

18 ref

009439   Lee D W;Lee S Y (Mathematics Dep, Institute of Pure and Applied Mathematics, Chonbuk National Univ, 567 Baekje-daero, Deokjin-gu, Jeonju-si Jeollabuk-do 561-756, Republic of Korea, Email: dwlee@jbnu.ac.kr) : Group structures and actions of an automorphism group on the set of lie algebra comultiplications. Far East J mathl Sci 2014, 87(1), 75-88.

In this note, we give a group structure on the set of Lie algebra comultiplications and study some actions of an automorphism group on the sets of comultiplications, associative comultiplications and commutative comultiplications of Lie algebras. We also investigate the dual notions of those topics to the topological points of view.

16 ref

009438   Lee D S;Kang S (NO, CNU Science Education Center for the Gifted Chonnam National Univ, Gwangju 500-757, Korea, Email: apig5942@naver.com) : On the complexity of finite sequences over a finite set. Far East J mathl Sci 2014, 87(2), 133-47.

There are various factors by which we recognize a sequence is complicated. Thus, it is very difficult to assign a real number representing the degree of complexity to a sequence by considering all factors. J.-P. Allouche says that the way of measuring complexity of a sequence is classified into two main classes, algorithmic complexity and combinatorial complexity, according to view of looking at sequences. In this paper, we will give two definitions of complexity functions focused on the amount of the repetition in a sequence. Then we prove the equivalence of two definitions and obtain the approximations to the maximum and the average of complexities of sequences over a finite set of the length n.

3 ref

009437   Lane J (NO, Winston-Salem State Univ, Winston-Salem, NC, U.S.A., Email: laneja@wssu.edu) : Uniqueness of solutions for n-dimensional degenerate parabolic equations. Far East J mathl Sci 2013, 83(2), 259-67.

In this paper, author proved that if models satisfy nonattainability conditions, then the final-value problem of general n-factor parabolic partial differential equations on rectangular domains has a unique solution. For such problems one can obtain numerical solutions without the use of artificial boundary conditions.

3 ref

009436   Kusmayadi T A;Sudibyo N A;Sri Kuntari (Mathematics Dep, Faculty of Mathematics and Natural Sciences Sebelas Maret Univ, Surakarta Indonesia, 57126, Email: trikusma@uns.ac.id) : The eccentric digraph of corona of K_1,n with any graph H. Far East J mathl Sci 2013, 83(2), 251-7.

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 u 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 w 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 K_1,n with any graph H.

8 ref

009435   Kulosman H;Miller A (Mathematics Dep, Louisville Univ, Louisville, KY 40292, U.S.A., Email: h0kulo01@louisville.edu) : A note about finite lower semilattices whose set of join-reducible elements is totally ordered. Far East J mathl Sci 2014, 87(2), 195-205.

In the previous papers [2] and [3], we have introduced the notion of special semigroups. They are commutative Boolean semigroups that can be built from a trivial semigroup in finitely or infinitely many steps, where in each step an idempotent is adjoined in one of the three allowed ways. In this paper, we show that finite special semigroups are precisely those finite commutative Boolean semigroups with a least element whose set of join-reducible elements is totally ordered.

5 illus, 3 ref

009434   Krakulli A;Pasku E (Departamenti i Matematikes, Fakulteti i Teknologjise dhe informacionit Universiteti Aleksander Moi, Albania, Email: anjezakrakulli@uamd.edu.al) : Completely prime ideals and bi-FP∞ condition. Far East J mathl Sci 2014, 84(1), 111-21.

Proved that if a monoid S contains a completely prime ideal I which is itself a monoid, then S is of type bi- FP_∞ if and only if / and the corresponding filter are of the same type. This makes bi-FP_∞ a better homological finiteness condition than one sided FP_∞conditions, since in contrast with the latter, one cannot expect to obtain a bi- FP_∞ monoid by simply adding a zero to a non bi- FP_∞ one.

15 ref