002168   Kai-Shi S;Fa-Sheng L (College of Electrical Engineering and Automation, Shandong Univ of Science and Technology, Qingdao, 266590, P. R. China, Email: 343927567@qq.com) : Hamiltonian structure and integrable coupling to a system of liouville integrable. Far East J mathl Sci 2014, 93(2), 165-74.

Discrete Liouville integrable system is obtained by virtue of zero curvature equation. Then the bi-Hamiltornian structure of the obtained system is given by means of the trace identity. Finally, integrable coupling of the above system is presented based on the semi-direct sums of Lie algebras.

20 ref

002167   Jayachitra P;James Albert A (Mathematics Dep, Karpagam Univ, Coimabatore, Tamil Nadu, Email: jayaasasi_akshu@rediffmail.com) : Optimal control of an N-policy M/E_k/1 queueing system with server start UP and breakdowns. Far East J mathl Sci 2014, 94(1), 13-32.

This paper is concerned with the optimal control of -a non-reliable and removable server in an N-policy M/E_k/1 queueing system with server start up. When the queue length reaches N (N ≥ 1), the server is immediately turned on but is temporarily unavailable to serve the waiting units. The server needs a startup time before providing the service until there are no units in the system. It is assumed that server breakdowns according to a Poisson process and the repair time have an exponential distribution. Explicit expressions for the number of units in the system are obtained and also derived various system measures. The total expected cost function is developed to determine the optimal threshold N at a minimum cost. The sensitivity analysis is performed to examine the effect of various parameters in the system.

3 illus, 4 tables, 17 ref

002166   Irfan N (NO, Sharda Univ, School of Engineering and Technology, Knowledge Park III, Greater Noida-201 306, Email: nagmairfanmath@gmail.com) : Computational method based on operational matrices for special kind of Volterra integro-differential equation. Indian J ind appl Math 2015, 6(1), 95-104.

In this paper, authors presented the application of operational matrix in solving special kind of Volterra integro-differential equation. The operational matrix method converts Volterra integro-differential equations into the system of algebraic equations, which is a considerable complexity reduction. Since the operational matrix contains many zero entries, it shows lower computational complexity with respect to the other approximations. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive. A good agreement between the obtained solution and a well-known result has been obtained. The test function is provided to show high accuracy and efficiency of the proposed method. This method is capable of greatly reducing the size of calculations while still maintaining high accuracy of the numerical solution.

2 illus, 21 ref

002165   Im Y B;Lee J S;Cho Y D (College of Dharma, Dongguk Univ, Seoul 100-715, Korea, Email: philpen@dongguk.edu) : Fuzzy pairwise α-semi-irresolute continuous mappings. Far East J mathl Sci 2014, 93(2), 197-210.

Defined and characterize a fuzzy pairwise α-semi-irresolute continuous mapping and a fuzzy pairwise α-semiopen irresolute mapping on a fuzzy bitopological space.

8 ref

002164   Guo X;Lu L;Mo D (College of Sciences, Hezhou Univ, Hezhou, Guangxi, 542899, P. R. China, Email: quoxiufeng198282@126.com) : Travelling wave solutions of an integrable evolution equation for surface waves. Far East J mathl Sci 2014, 93(2), 175-84.

In this paper, authors study the exact parametric representations of V traveling wave solutions of an integrable evolution equation for surface waves in deep water. Authors apply the bifurcation method and qualitative theory of dynamical systems to analyze the phase portraits of the traveling wave systems, and obtain four types of traveling wave solutions such as smooth periodic wave solutions, periodic cusp wave solutions, loop soliton solutions and periodic loop solutions.

2 illus, 18 ref

002163   Garasym O;Taralova I;Lozi R (NO, , IRCCyN UMR CNRS 6597, Ecole Centrale de Nantes, Nantes, France, 44300, Email: rlozi@unice.fr) : Application of observer-based chaotic synchronization and identifiability to the original CSK model for secure information transmission. Indian J ind appl Math 2015, 6(1), 1-26.

Modified Lozi system is analyzed as chaotic PRNG and synchronized via observers. The objective of the study is to investigate chaotic-based encryption method that preserves CSK model advantages, but improves the security level. The CSK model have been discussed to message encryption because it implies better resistance against noise, but there are many evidences of the model weaknesses. The investigation provides the original CSK model analyses of secure message transmission over the communication channel by examining identifiability and observability; switched regimes detection; sensitivity to initial conditions and session key; NIST tests of the encrypted signal; correlation between wrong decrypted messages; system ergodicity. The proposed model has a significant effect on the security level of the transmitted signal that successfully passed chaotic and randomness tests. The results suggest that the original CSK model can be used for information security applications.

22 illus, 3 tables, 44 ref

002162   Fadail Z M;Ahmad A G B (School of Mathematical Sciences, Faculty of Science and Technology, Univ Kebangsaan Malaysia, 43600 UKM Bangi Selangor Darul Ehsan, Malaysia, Email: zaid_fatail@yahoo.com) : Common fixed point theorem of N-order for W_N-compatible mappings in cone metric spaces. Far East J mathl Sci 2015, 96(2), 133-66.

Existence and uniqueness of the common coupled and common triple fixed points in cone metric spaces have been studied. The concepts of coincidence point, point of coincidence and common fixed point of N-order for mappings F : X^{N → X and g : X → X have been introduced recently in 2012. In this paper, we establish coincidence point of N-order theorem and common fixed point of N-order theorem for W_N -compatible mappings in such spaces. The presented theorems extend and generalize several well-known comparable results in literature, in particular, the results of Fadail and Ahmad [6], Abbas et al. [13] and Aydi'et al. [19].}

21 ref

002161   Diallo A S;Hassirou M;Katambe I (NO, Universite Alioune Diop de Bambey UFR SATIC B.P. 30, Bambey, Senegal, Email: abdoulsalam.diallo@uadb.edu.sn) : Examples of affine osserman 3-manifolds. Far East J mathl Sci 2014, 94(1), 1-11.

An affine manifold (M, ∇) is affine Osserman if the eigenvalues of the affine Jacobi operators vanish. In the present paper, we exhibit examples of affine Osserman connections which are Ricci flat and which are not Ricci flat on R^3.

9 ref

002160   Creuse E;Farhloul M;Nicaise S;Paquet L (NO, Univ Lille 1 - Laboratoire Paul Painleve and E.P.I. SIMPAF - INRIA Li, 59655 Villeneuve d' Ascq Cedex France, Email: creuse@math.univ-lille1.fr) : Posteriori error estimates of the stabilized Crouzeix-Raviart finite element method for the lame-navier equations. Far East J mathl Sci 2015, 96(2), 167-92.

Obtained a posteriori error estimates for a variant of (non-locking) stabilized nonconforming methods based on the Crouzeix-Raviart element introduced by Hansbo and Larson in [21]. Authors derived upper and lower a posteriori error bounds which are robust with respect to the nearly incompressible matrials.

13 illus, 35 ref

002159   Canadas A M;Giraldo H;Vargas V C (Mathematics Dep, National Univ of Colombia, Colombia, Email: amorenoca@unal.edu.co) : Categorification of some integer sequences and higher dimensional partitions. Far East J mathl Sci 2014, 93(2), 133-49.

In this paper, authors prove that the number of some 3-dimensional partitions is given By the number of indecomposable objects of some posets of finite representation type.

2 illus, 11 ref

002158   Boulbrachene M (Mathematics and Statistics Dep, Sultan Qaboos Univ, P.O. Box, 36, Muscat 123, Oman, Email: boulbrac@squ.edu.com) : Algorithmic finite element approach for a class of non-linear quasi variationla inequalities. Indian J ind appl Math 2015, 6(1), 27-35.

In this paper, we introduce a new method to analyze the convergence of the standard finite element method for a class of elliptic quasi-variational inequalities (QVIs) with non-linear source terms. It consists of approximating the solution of the non-linear QV1 by a sequence of solutions of linear QVIs. Under a realistic assumption on the non-linearity, we first prove that the resulting iterative scheme is geometrically convergent to the solution of the QVI. Afterwards, we establish an error estimate in the maximum norm between the continuous iterative scheme and its finite element counterpart. Finally, combining this latter estimate with the geometrical convergence of the iterative scheme, we also derive an error estimate between the solution of the QVI and its finite element counterpart.

10 ref

002157   Bouchemella A;Benmostefa F Z (Commercial Sciences Dep, Univ of 08 May 1945 Guelma, Algeria, Email: abdelhalimgbs@yahoo.fr) : On random coefficient autoregressive models. Far East J mathl Sci 2014, 93(2), 151-63.

In this paper, authors study the class of bilinear GARCH models that are considered as random coefficient autoregressive models and widely used in modeling of financial time series like leverage effects and volatility clustering. We illustrate some probabilistic properties of this model, then we study the statistical inference in this class of models using the composite likelihood method to establish the consistency and the asymptotic normality properties.

15 ref

002156   Bhatnagar G (NO, Gaurav Bhatnagar Educomp Solutions Ltd, Delhi, Email: bhatnagarg@gmail.com) : How to discover the Rogers-Ramanujan identities. Resonance 2015, 20(5), 416-30.

We examine a method to conjecture two very famous identities that were conjectured by Ra-manujan, and later found to be known to Rogers.

10 ref

002155   Azaizeh A;Hasni R;Ahmad A;Gee-Choon L (School of Informatics and Applied Mathematics, Univ Malaysia Terengganu, 21030 UMT, Kuala Terengganu, Terengganu, Malaysia) : 3-total edge product cordial labeling of graphs. Far East J mathl Sci 2015, 96(2), 193-209.

For a graph G = (V(G), E(G)), an edge labeling function f : E(G) → {0, 1, ..., k - 1}, where k is an integer, 2≤ k ≤ |E(G)|, induces a vertex labeling function f* : V(G) → {0, 1, ..., k -1} such that f*(v) is the product of the labels of the edges incident to v (mod k). This function f is called a k-total edge product cordial (or simply k-TEPC) labeling of G if | (v_f(i) + e_f (i)) - (v_f(j) + e_f(j)) | ≤ 1 for all i, j ∈ {0, 1, ..., k-1}. In this paper, authors introduce this concept and investigate 3-TEPC labeling of some graphs.

8 illus, 9 ref

002154   Anamika Ranjan;Bhardwaj R (Univ School of Basic and Applied Science, Non-linear Dynamics Research Lab, Guru Gobind Singh Indraprastha Univ, Dwarka, New Delhi, Email: nonlineardynamicsrl_rb@ipu.ac.in) : Bifurcation analysis in economic system dynamics. Indian J ind appl Math 2015, 6(1), 49-56.

This paper discusses the role of investment on dynamics of micro-economic in nonlinear financial model. The interest rate, investment demand and price index are modeled with the help of saving amount, cost per investment and demand elasticity of commercial markets, all these parameters are considered as positive. Using bifurcation theory, bifurcation point and time period is studied for the financial system. Through numerical methods, it is observed that the value of time bifurcation decreases as investment demand decreases, further the time bifurcation decreases with the investment demand parameter and elasticity of commercial markets. It is concluded that the bifurcation analysis depends on the value of investment demand and also on the elasticity of commercial markets parameter.

4 illus, 4 tables, 7 ref

002153   Alkasbi N;Darus M (School of Mathematical Sciences, Faculty of Science and Technology, Univ Kebangsaan Malaysia Bangi, 43600, Selangor D. Ehsan, Malaysia, Email: nasserksb@yahoo.com) : Order of univalency of general integral operator. Far East J mathl Sci 2014, 93(2), 185-95.

10 ref

002152   Ahlem G;Ouannas A (Mathematics and Computer Science Dep, Constantine Univ, Algeria, Email: gasri.ahlem@yahoo.fr) : Synchronization analysis of quadratic chaotic systems in n-D. Far East J mathl Sci 2015, 96(2), 241-8.

In this paper, based on the Lyapunov stability theory, a simple criterion is derived for chaos synchronization between two arbitrary n-dimensional quadratic systems in continuous-time. To demonstrate the efficiency of the proposed synchronization scheme, the suggested approach is applied to some typical chaotic and hyperchaotic quadratic systems.

2 illus, 14 ref

002151   Abdul Razak K;Rajakumar K (Mathematics Dep, TRP Engineering College (SRM Group) Trichy, Tamil Nadu, Email: arrazak76@gmail.com) : Fuzzy system reliability with minimization of coefficient of variance for multistage series-parallel systems. Far East J mathl Sci 2015, 96(2), 249-64.

System reliability optimization models containing uncertainty are "expressed and a new formulation is proposed to maximize the reliability subject to the available cost of the system reliability estimate. The redundancy allocation problem can be defined as the selection of the system configuration and the type of the components to optimize some objective functions while satisfying some system related constraints. This paper proposes a solution for multistage series-parallel system with nonlinear function to evaluate the maximum reliability subject to available cost using triangular intuitionistic fuzzy number. In addition to that, we propose the coefficient of variance of the system reliability estimate for each membership function and non-membership function. These methods are utilized to identify minimum CV with high reliability estimate.

2 illus, 2 tables, 25 ref

001083   Yurko V (Mathematics Dep, Saratov State Univ, Astrakhanskaya 83, Saratov 410012 Russia, Email: yurkova@info.sgu.ru ) : Inverse spectral problem for integro-differential operators. Far East J mathl Sci 2014, 92(2), 247-61.

The uniqueness theorem is proved for the solution of the inverse spectral problem for second-order integro-differential operators on a finite interval. The main tool is an integral transform connected with solutions of integro-differential operators.

22 ref

001082   Titi Udjiani SRRM;Surodjo B;Wahyuni S (Mathematics Graduate Programme, Mathematics and Natural Sciences Dep, Gadjah Mada Univ, Indonesia, Email: surodjo_b@ugm.ac.id) : Generalized moore penrose inverse in rings with an involution. Far East J mathl Sci 2014, 92(1), 29-40.

Paper studies the generalized of the Moore Penrose inverse in rings with involution. Characteristics and existences of the inverse are discussed.

4 ref

001081   Sukparungsee S (Applied Statistics Dep, Faculty of Applied Sciences, King Mongkut's Univ of Technology, North Bangkok Bangkok 10800, Thailand, Email: swns@kmutnb.ac.th) : Martingale approach for closed-form expression of average run length of EWMA chart for detection of a change in number of defects. Far East J mathl Sci 2014, 92(2), 141-56.

The closed-form formula of average run length for exponentially weighted moving average (EWMA) control chart is proposed based on the martingale approach. Usually, the number of defective products is defined by binomial distribution. Based on this approach, we prove a martingale identity and apply it for obtaining the closed-form formula for the first passage times. Furthermore, the algorithms for obtaining the optimal parameter of EWMA control chart have been developed in order to design the optimal EWMA control chart for detecting of a change in number of defective products in process. The numerical results are compared with the algorithm which combined the results from the martingale and the Monte Carlo simulations, the proposed algorithm is very time saving.

4 tables, 17 ref

001080   Sugito H;Santoso D (Mathematics and Statistics Dep, School of Computer Science Bina Nusantara Univ, Jl. Kebon, Jeruk Raya No. 27 Jakarta 11530, Indonesia, Email: djunsan2002@yahoo.com) : Design optimization of distribution program application construction work on the auditorium search by Taboo Anzen Dezine. Far East J mathl Sci 2014, 93(1), 23-42.

CV Anzen Dezine is a contractor company in Indonesia and is able to do various types of development. In addition to receiving the construction of the auditorium, they also receive other types of development such as school, shop, shopping, and more. Workers are hired workers from outside this office because of the limitations of existing workers in this office. Therefore, they often slow down the construction work with a variety of reasons in order to obtain a larger payment. Also, at the applicant's development proposal development inaccurate data provided to the applicant's development, because the calculation is still based on a rough estimate only. The purpose of this thesis is to design a scheduling application program development using the theory of algorithms auditorium taboo search. Program design is done by applying the algorithm to create optimal work schedules through a mathematical approach. Through scheduling, we can calculate the cost of labor required. So that it can calculate the total cost required for development. The method used is the method of analysis and design. After implementation in the existing system, it can be concluded that the application of taboo search algorithm in scheduling the construction of the auditorium can assist decision-making and scheduling to win a development proposal to the applicant building.

1 illus, 3 tables, 9 ref

001079   Sornmee P;Sukawat D (Mathematics Dep, Faculty of Science King Mongkut's Univ of Technology Thonburi 126 Pra, Bang Mod Thung Khru, Bangkok 10140, Thailand, Email: spy2@hotmail.com) : Modified lyapunov exponent and predictability of global warming by EdGCM. Far East J mathl Sci 2014, 92(2), 215-31.

This study proposes a new technique for determination of atmospheric predictability, namely the modified Lyapunov exponent (MoLE). This method is based on the classical Lyapunov exponent (LE). It is established to apply to predictability measurement of global warming by the Educational Global Climate Model (EdGCM) from time series of monthly data over Southeast Asian region. The point of interest is an effect of small perturbations in the initial conditions which are generated by increasing of greenhouse gases level. The results show that carbon dioxide (CO₂) and chlorofluorocarbon-12 (CFC-12) cases provide the least predictability which indicates that they have the largest effects on predictability of global warming by EdGCM.

4 illus, 2 tables, 26 ref

001078   Siddiqi A H;Rahaman M;Ahmad R (School of Basic Sciences and Research, Sharda Univ, Greater Noida, NCR-201306, Uttar Pradesh, Email: mrahman96@yahoo.com) : Generalised mixed vector equilibrium problem with new relaxed monotonicity. Indian J ind appl Math 2014, 5(2), 77-86.

In this paper, we introduce a new notion of relaxed α - β - C- monotonicity for bi-mappings. It has been shown that the α - β - C -monotonicity is a proper generalisation of monotonicity. Using the KKM technique, we obtain the existence of solutions for generalised mixed vector equilibrium problem with relaxed α - β - C -monotonicity in reflexive Banach spaces. Some examples are also given.

21 ref

001077   Shaikh A;Thakar S (Mathematics Dep, Shivaji Univ, Kolhapur-416 004, Email: asmashaikh301@gmail.com) : Numerical solutions of non-linear fredholm integro-differential equations of second kind. Indian J ind appl Math 2014, 5(2), 131-40.

In this paper, authors propose a method that determines the approximate solution of nonlinear Fredholm integro-differential equations of second kind. The integro-differential equation is converted into an integral equation by using suitable transformation. The integral part is approximate by Newton Cote's method. The convergence of method is established. The theory is supported by some examples.

2 tables, 17 ref

001076   Ramli M;Munzir S;Khairuman T;Halfiani V (Mathematics Dep, Syiah Kuala Univ, Postal Code 23111, Banda Aceh, Indonesia, Email: marwan.math@unsyiah.ac.id) : Amplitude increasing formula of bichromatic wave propagation based on fifth order side band solution of Korteweg de Vries equation. Far East J mathl Sci 2014, 93(1), 97-117.

Previous analytical, numerical and experimental results show that surface waves which initially bichromatic signals deform during their propagation in hydrodynamic laboratories. The deformation is followed by the increase of the bichromatic wave amplitude. It has been investigated that the position where the bichromatic wave generates the highest amplitude is of order O (1/q^{2, 1/K2_lin), where q and K_lin are the amplitude and frequency of the bichromatic wave envelope, respectively. The result is based on the third order Korteweg de Vries (KdV) equation and the quantity obtained is called maximal temporal amplitude (MTA). However, the dependence of the increase in the maximum amplitude of the bichromatic wave over wave parameters is unknown. This paper describes the derivation of a formula that can be used to predict the increase of the maximum amplitude of bichromatic wave. Here, the bichromatic wave is defined as a superposition of two monochromatic waves with the same amplitude but slightly different of frequencies. The formula is derived using the approximation of fifth order KdV equation and MTA. It has been found that the increase of a bichromatic wave maximum amplitude is of orderO(q/k_lin)2. The result of the increase of maximum amplitude for bichromatic wave found using this formula is in accordance with the experimental results as well as the result of a numerical software HUBRIS.}

4 illus, 2 tables, 27 ref

001075   Rahman N A;Abdullah L (Mathematics Dep, Faculty of Science and Technology Univ Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu Malaysia, Email: hamikahrun@yahoo.com) : Review on solutions for fuzzy polynomials. Far East J mathl Sci 2014, 93(1), 65-87.

Fuzzy polynomials had attracted much interest for those in the field of mathematics, engineering and the social sciences. There are many numerical methods for solving fuzzy polynomials. However, these methods have their own algorithms that make it an efficient method to find the actual root of fuzzy polynomials; In this study, a current review on the solution for fuzzy polynomials in the form of A₁X + A₂X^{2 + + A_nxn = A0 will be presented. Related books and articles appearing in international journals from 1978-2011 were gathered and analyzed.}

1 illus, 31 ref

001074   Priya C;Saivaraju N;Subramanian N (Mathematics Dep, Sri Angalamman College of Engineering and Technology, Trichirappalli 621105, Email: priyasubu1980@gmail.com) : Ideal convergent sequence spaces over np-metric spaces defined by sequence of modulus. Far East J mathl Sci 2014, 92(2), 173-203.

In this paper, authors introduce the I- of x sequence spaces over np-metric spaces defined by Musielak function. We also examine some topological properties and prove some inclusion relation between these spaces.

49 ref

001073   Priya C;Saivaraju N;Subramanian N (Mathematics Dep, Sri Angalamman College of Engineering and Technology, Trichirappalli-621 105, Email: priyasubu1980@gmail.com) : Fibonacci numbers of χ<. Far East J mathl Sci 2014, 93(1), 1-21.

45 ref

001072   Pratikno B;Jajang;Zulfia R (Mathematics Dep, Univ of Jenderal Soedirman Purwokerto Jl. Dr. Suparno, Kampus Unsoed Karangwangkal Purwokerto 53122, Indonesia, Email: pbratikto@gmail.com) : Testing intercept with non-sample prior information for one-side hypothesis (maximum) on a multivariate simple regression model. Far East J mathl Sci 2014, 92(2), 157-71.

Testing the intercept with non-sample prior information (NSPI) on the slope on a multivariate (bivariate) simple regression model is discussed in this paper. Following previous work of Pratikno [15], we use different hypothesis test, one-side hypothesis (maximum), for testing the hypothesis using three tests, namely, the unrestricted test (UT), restricted test (RT), and preliminary-test test (PTT). Here, we consider a test which has a maximum power and minimum size. A simulation study and graphical analysis are given to compare the three tests. The PTT tends to have maximum power (and/or it lies between UT and RT) and smaller size than that RT for φ₂ <62> 2. Thus, we consider that the RT is a relevant choice for values of 0 <60> φ₂ <60> 2, and the PTT is the best choice for values of φ₂ <62> 2.

2 illus, 24 ref

001071   Park J W (Mathematics Education Dep, Sehan Univ, YoungAm-gun, Chunnam, 526-702 Republic of Korea, Email: a0417001@knu.ac.kr) : On the twisted q-daehee polynomials of higher order. Far East J mathl Sci 2014, 92(2), 233-45.

The Daehee polynomials and numbers are introduced by Kim et al. in [3]. Some interesting properties of those polynomials are derived from umbral calculus (see [6]). In this paper, we consider Witt-type formula for the nth twisted q-Daehee numbers and polynomials of higher order and derive some new interesting identities and properties of those polynomials and numbers from the Witt-type formula which are related to special polynomials and numbers.

11 ref

001070   Lekkoksung N;Jampachon P (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khon Kaen, 40002, Thailand) : On regular ordered ternary semigroups. Far East J mathl Sci 2014, 92(1), 67-84.

In this paper, authors introduce fuzzy quasi-ideal and characterize regular ordered ternary semigroups and characterize regular ordered ternary semigroups by means of their fuzzy generalized bi-ideals and fuzzy quasi-ideals, fuzzy generalized bi-ideals and fuzzy ideals, fuzzy bi-ideals and fuzzy ideals. Also, we characterize regular ordered ternary semigroups in terms of fuzzy generalized bi-ideals, fuzzy left ideals and fuzzy right ideals and fuzzy bi-ideals, fuzzy left ideals and fuzzy right ideals.

15 ref

001069   Kim Y K;Min W K (Mathematics Dep, MyongJi Univ, Yongin 449-728, Korea, Email: ykkim@mju.ac.kr) : Remarks on monotonic operations induced by a soft set. Far East J mathl Sci 2014, 92(1), 113-23.

The purpose of this paper is to introduce an operation F : P(U) → P(U) induced by F^{← and a given soft set (F, X) over a common universe set U, and to study some basic properties of the operation.}

11 ref

001068   Kim J (Mathematics Education Dep, Kangwon National Univ, Chunchon 200-701, Kangwon Do, Korea, Email: jaeman64@kangwon.ac.kr) : On extended birecurrent manifolds. Far East J mathl Sci 2014, 92(1), 41-54.

In this paper, authors introduce a type of Riemannian manifolds (namely, extended birecurrent manifold) and study its various geometric properties. Also the existence of such a manifold is ensured by a proper example.

14 ref

001067   Jong-Kwang Y (Liberal Arts and Science Dep, Chodang Univ, 419 Sungnamri Muangun Chonnam, Korea) : Hyponormal operators with property (δ) have invariant subspaces. Far East J mathl Sci 2014, 92(1), 101-12.

In this paper, authors show that if T ∈ L(H) is hyponormal, then H_T({λ}) = ker(λI - T) for all λ ∈ C and moreover, T is algebraic if and only if the spectrum σ(T) is finite. We also prove that if T ∈ L(H) is hyponormal with property (8), then T has a non-trivial invariant subspace. As a corollary, every subnormal (compact hyponormal) operator has a non-trivial invariant subspace. Finally, let T ∈ L(H) be a subnormal operator on a Hilbert space H. Suppose that T ∈ L(H) and S ∈ L(K) are quasi-similar and S has property (C). Then S has a non-trivial invariant subspace.

21 ref

001066   Im Y B;Lee J S;Cho Y D (College of Dharma, Dongguk Univ, Seoul 100-715, Korea, Email: philpen@dongguk.edu) : Fuzzy α-precontinuous mappings. Far East J mathl Sci 2014, 92(1), 55-65.

Defined and characterize a fuzzy α-precontinuous mapping and a fuzzy α-preopen mapping on a fuzzy topological space. Besides, some interesting properties of those mappings are given.

7 ref

001065   Hanumantha Rao S;Vasanta Kumar V;Srinivasa Rao T;Srinivasa Kumar B (NO, VFSTR Univ, Vadlamudi-522 213, Guntur (Dt.) Andhra Pradesh, Email: sama.hanumantharao@gmail.com) : Optimal control of an N-policy two-phase M/M/1 queueing system with server startup subject to breakdowns and different arrival rates. Far East J mathl Sci 2014, 92(1), 1-17.

In this paper, authors analyze a two-phase N-policy M/M/1 queueing system with server startup where service station is subject to breakdowns while in operation and arrival rate depends on the state of the system. Waiting customers receive batch service all at a time in the first phase and proceed to the second phase to receive individual service. The server needs a startup time before providing batch service in the first phase. Explicit expressions for the steady state distribution of the number of customers in the system and hence the expected system length are derived. The sensitivity analysis is carried out to examine the effect of the system parameters on the optimal threshold N.

3 tables, 12 ref

001064   Elizabeth S;Sujatha L (Mathematics Dep, Auxilium College (Autonomous) Vellore, Tamil Nadu, Email: elizafma@gmail.com) : Fuzzy shortest path problem based on level λ-LR type representation of fuzzy interval. Far East J mathl Sci 2014, 93(1), 43-63.

In this paper, authors have presented a new approach to obtain the shortest paths between a pair of specified vertices on an acyclic network whose edge weights are of imprecise in nature. In particular, we have considered the edge weights as level λ-LR trapezoidal fuzzy numbers. An example is illustrated to show that the proposed method is useful in solving the real-world problems. It is proved that the optimal solution obtained through the algorithms proposed in this paper coincides with the existing earlier results.

6 illus, 5 tables, 16 ref

001063   Debnath A;Dey J K;Kar S (Economics Dep, Vivekananda Mahavidyalaya (under the Univ of Burdwan), Sripally, Burdwan-713 103, Email: animesh2007.1813@rediffmail.com) : Fuzzy mathematical modelling in consequence of the framework of socially-responsible tea production system and the governance - a regional study in India. Indian J ind appl Math 2014, 5(2), 111-30.

Socially responsible investment or SRI was introduced in the earlier time in tea sectors of west Bengal to ensure the betterment of the labourers associated with the sectors but until date those hardworking persons living below the poverty line do not test the essence of the concept. In gradual course, the collaboration between tea sectors management and governance is forced to be decomposed and as an obvious result, social development is thwarted. In the following study, there is ample scope to throw light on the SR initiatives vide/through the fuzzy mathematical modelling and to give stress on the modelling on the system of tea production along with the problems interconnected. The result shows that the fallacy of extended alliance between the estate owners and government may jeopardize the SR activity.

5 illus, 3 tables, 46 ref

001062   Chawla M;Bhardwaj R (Non-linear Dynamics Research Lab, Univ School of Basic and Applied Sci, Guru Gobind Singh Indraprastha Univ, Dwarka, New Delhi-110 078, Email: rashmib22@gmail.com) : Surface roughness and slip velocity effect on magnetic lubricated porous pivoted slider bearings. Indian J ind appl Math 2014, 5(2), 87-95.

This paper describes the theoretical analysis of the surface roughness and slip velocity effect on magnetic fluid based porous-pivoted slider bearing. The bearing surface is defined by stochastic random variable with skewness, variance and non-zero mean. The concerned stochastically averaged Reynolds equation is solved numerically to get the pressure distribution. The expression for dimensionless centre of pressure is obtained in form of integrals. The value of centre of pressure is calculated and plotted numerically. It is observed that the value of centre of pressure depends on surface roughness, magnetic, slip and permeability parameters. It is concluded that slip and permeability parameters play a vital role for increasing the life of bearing system roughness.

4 illus, 3 tables, 11 ref

001061   Canadas A M;Giraldo H;Espinosa P F F (Mathematics Dep, National Univ of Colombia, Colombia, Email: amorenoca@unal.edu.co) : Categorification of some integer sequences. Far East J mathl Sci 2014, 92(2), 125-39.

k-linear representations of posets are used to define some partitions of multiples of polygonal numbers. Furthermore, the number of indecomposable representations of some posets of finite representation type is used to obtain a partition formula for elements of the sequence A002662 in the On-Line Encyclopedia of Integer Sequences (OEIS).

4 illus, 11 ref

001060   Binthiya R;Sarasija P B (Mathematics Dep, Noorul Islam Centre for Higher Education, Kumaracoil-629 175, Email: binthiya_r@yahoo.co.in) : Laplacian energy and Laplacian Estrada index of strongly quotient graphs. Far East J mathl Sci 2014, 93(1), 119-31.

16 ref

001059   Bhardwaj R;Manjeet Kaur (Non-Linear Dynamics Research Lab, School of Basic and Applied Sciences, Guru Gobind Singh Indraprastha U, Dwarka, New Delhi, Email: rashmib22@gmail.com) : Hamiltonian function for satellite motion in an elliptic orbit under the influence of aerodynamic torque. Indian J ind appl Math 2014, 5(2), 141-7.

This paper deals with the non-linear oscillation of a satellite in an elliptic orbit around the Earth under the influence of aerodynamic and gravitational torque. It is assumed that the orbital plane coincides with the equatorial plane of the Earth. Using Euler's dynamical equation of motion, the equation of motion and Hamiltonian function for the problem is derived. Taking aerodynamic torque of the order of eccentricity, it is observed that Hamiltonian function is dependent on aerodynamic torque. The equilibrium points and Double Asymptotic solutions related to the problem are calculated. It is concluded that in the phase space (0, 2) and (π, 2) are the equilibrium points, out of which (0, 2) is a stable and (π, 2) is an unstable equilibrium point.

1 illus, 10 ref

001058   Athreya K B (Mathematics Dep, Iowa State Univ, Ames, Iowa, USA, Email: kbathreya@gmail.com) : What is probability theory?. Resonance 2015, 20(4), 292-310.

This issue of Resonance features Joseph Leonard Doob, who played a critical role in the development of probability theory in the world from 1935 onwards. The goal of the present article is to explain to the readers of Resonance what probability theory is all about.

3 ref

001057   Asmiati (Mathematics Dep, Faculty of Mathematics and Natural Sciences Lampung Univ, Jl. Brojonegoro no. 1, Bandar Lampung, Indonesia, Email: asmiati308@yahoo.com) : Locating-chromatic number of non-homogeneous amalgamation of stars. Far East J mathl Sci 2014, 93(1), 89-96.

Let G be a connected graph and c be a proper coloring of G. The color code c_Π(v) of vertex v in G is the ordered k-tuple distance v to every color classes C_i for i ∈ [1, k]. If all distinct vertices of G have distinct color codes, then c is called a locating-coloring of G. The locating-chromatic number of graph G, denoted by χ_L(G) is the smallest k such that G has a locating-coloring with k colors. In this paper, we discuss the locating-chromatic number of non-homogeneous amalgamation of stars.

10 ref

001056   Asawasamrit S (Mathematics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Ba, Bangkok, 10800, Thailand, Email: suphawata@kmutnb.co.th) : On associative in KK-algebras. Far East J mathl Sci 2014, 92(1), 19-28.

In this paper, authors introduce the notions of associative and quasi-associative in KK-algebras and provide several characterizations and the results for the associative and quasi-associative. Moreover, we establish relation between a-ideal, p-ideal, g-ideal and associative in KK-algebras.

10 ref

001055   Arora S;Inderpreet Kaur;Amandeep Kaur (Mathematics Dep, Punjabi Univ, Patiala-147 002, Email: aroshelly@gmail.com) : 1D reaction diffusion problem using hermite collocation method. Indian J ind appl Math 2014, 5(2), 105-10.

Study of reaction diffusion problem has been carried out using Hermite collocation method with cubic Hermite basis. The numerical values have been compared with analytic values obtained from Laplace transforms and also from orthogonal collocation method.

4 illus, 7 ref

001054   Areepong Y (Applied Statistics Dep, Faculty of Applied Science King Mongkut's Univ of Technology North Ban, Bangkok 10800, Thailand, Email: yupaporna@kmutnb.ac.th) : Analytical explicit formula and optimal parameters for performance of exponentially weighted moving average procedure. Far East J mathl Sci 2014, 92(2), 205-14.

The main goal of this paper is to study statistical process control (SPC) with exponentially weighted moving average (EWMA) control chart for detecting changes in process mean. The characteristic of control chart is average run length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL₀). Otherwise, it should be small when, the process is out-of-control, so-called average of delay time (ARL₁) or a mean of true alarm. We obtain explicit formulas of ARL for EWMA chart for autoregressive and moving average (ARMA) processes with exponential white noise. The explicit formulas for ARL have been found to be accurate, fast and easy to calculate. In particular, the explicit analytical formulas for evaluating ARL₀ and ARL₁ be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of ARL₁.

4 tables, 15 ref

001053   Areepong Y (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Ba, Thailand, Email: yupaporna@kmutnb.ac.th) : Optimal parameters of control charts for zero-inflated process. Far East J mathl Sci 2014, 92(1), 85-100.

Objective of this paper is to show optimal parameters of moving average (MA) and double moving average control charts (DMA) when the probability of observing a defective product follows a zero-inflated Poisson (ZIP) distribution, i.e., a distribution that is similar to a Poisson distribution but with an excess number of zeros. The most popular characteristics of a control chart are average run length for in-control process (ARL₀) - the mean of observations that are taken before a system is signaled to be out-of-control when it is actually still in-control, and average delay time (ARL₁) which is mean delay of true alarm times. An important property required of ARL₀ is that it should be sufficiently large when the process is in-control to reduce a number of false alarms. On the other side, if the process is actually out-of-control, then ARL₁ should be small as possible. The explicit analytical formulas for evaluating ARL₀ and ARL₁ be able to get a set of optimal parameters which depend on a width of the moving average (w) and width of control limit (H) for designing MA_ZIP and DMA_ZIP charts with minimum of ARL₁.

4 tables, 14 ref

001052   Abdellaoui M A;Bedjaoui N;Dahmani Z (NO, , LPAM, Faculty SEI, UMAB Mostaganem, Algeria, France, Email: abdellaoui.amine13@yahoo.fr) : On a couple system of integro-differential equations of arbitrary orders. Indian J ind appl Math 2014, 5(2), 96-104.

This paper studies the existence and the uniqueness of solutions for a coupled system of nonlinear fractional integro-differential equations. New existence and uniqueness results are established using Banach theorem. Other results are obtained using Schaefer fixed point theorem. Some concrete examples are also presented.

13 ref