021482   Azad S I (General Studies Dep, Yanbu Industrial College, Yanbu, KSA, Email: dr.ismailazad@gmail.com) : Exact solution of perturbed harmonic oscillator by Hypergeometric approach. Int J latest Technol Engng Mgmt appl Sci 2014, 3(11), 4-8.

In classical mechanies, the problemof a simple harmonic oscillator, modified by the presence of a non harmonic term, is customarily solved by perturbative methods. These methods yield approximate solutions which may not be represented in a closed form. In the present study, it is shown that exact solutions of the problem may be obtained by the application of hypergeometric functions.

9 ref

021481   Ahmed N (Mathematics Dep, Gauhati University, Gauhati-781 014, Assam, Email: saheel_nazib@yahoo.com) : Soret and dufour effects in steady flow of a viscous conducting fluid through a circular cylinder. J Energy Heat Mass Transfer 2014, 36(2), 165-82.

This paper presents an exact solution to the problem of the steady laminar fully developed convective mass transfer flow of a viscous incompressible electrically conducting fluid through a circular cylinder under constant pressure gradient influenced by a magnetic field in the azimuthal direction in presence of constant heat source and chemical reaction. The Soret and Dufour effects are considered but the electrical and the induced magnetic fields are neglected. The effects of different physical parameters entering into the problem on the velocity, temperature and concentration fields and on the coefficient of the skin friction, the rates of heat and mass transfer at surface of the cylinder and mass flux across a normal section of the cylinder are discussed through graphs.

26 illus, 18 ref

020529   Yadav D S;Thakur S S;Thakur S S (Applied Mathematics Dep, Takshshila institute of Engineering & Technology, Jabalpur, Email: dinyadav1976@gmail.com) : Some common fixed point theorems of compatible mappings of type (A) in fuzzy metric spaces. J Indian Acad Math 2014, 36(2), 325-36.

11 ref

020528   Toure S D;Sanghare M;Mohamed S M O (Departement de Mathematiques et Informatique, Faculte des Sciences et Techniques, de l'Universite Cheikh Anta Diop d, Senegal, Email: sidydtoure@yahoo.fr) : On weakly FGI-duo rings and generalized FGS-duo rings. Far East J mathl Sci 2014, 88(2), 275-80.

Let R be a ring. A left R-module M is said to be weakly co-hopfian (resp. generalized hopfian) if every injective (resp. surjective) endomorphism of M is essential (resp. surperfluous). The ring R is called a weakly left FGI-ring (resp. generalized left FGS-ring) if every weakly left co-hopfian (resp. generalized hopfian) module is finitely generated. The purpose of this paper is to give a characterization of weakly FGI-duo-rings and generalized FGS-duo-rings.

10 ref

020527   Sundar P;Kishokkumar B (Mathematics Dep, Om Muruga College of Arts and Science, Mettur, Tamilnadu, Email: mydt972009@gmail.com) : Oscillation of nonlinear neutral difference equations of fourth order with several delays. J Indian Acad Math 2014, 36(2), 337-65.

27 ref

020526   Singh S N (Mathematics Dep, T.D.P.G. College, Jaunpur-222 002, Email: snsp39@gmail.com) : A Note on bailey transform and q-series transformation. J Indian Acad Math 2014, 36(2), 221-31.

In this paper certain transformation formulae for q-series have been established by using Bailey transform and some known summation formulae.

3 ref

020525   Singh S N (Mathematics Dep, T.D.P.G. College, Jaunpur-222 002, Email: snsp39@yahoo.com) : On certain results involving partial theta functions. J Indian Acad Math 2014, 36(2), 203-10.

In this paper, making use of some known results, we have established certain results involving partial theta functions.

4 ref

020524   Shrivastava S S;Sikarwar P (Mathematics Dep, Govt. P.G. College, Shahdol, Madhya Pradesh, Email: sss.math@yahoo.co.in) : Temperatures in the prism involving I-function of several variables. J Indian Acad Math 2014, 36(2), 233-8.

3 ref

020523   Sharma S C;Bairwa R K (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: sureshchand26@gmail.com) : Analytic study of the time fractional Klein-Gordon equation by adomian decomposition method. J Indian Acad Math 2014, 36(2), 259-69.

In the present paper, we use Adomian decomposition method (ADM) to derive analytic solution of linear and non-linear time- fractional Klein-Gordon equation. The fractional derivatives are considered in the Caputo sense. Some examples are given and it has been observed that the ADM is very effective and convenient for solving linear and non-linear time- fractional Klein-Gordon equation.

36 ref

020522   Parsa R A;Kim J J;Srinivasan M R (College of Business and Public Administration, Drake Univ, Des Moines, IA 50321, Email: rahul.parsa@drake.edu) : Characteristic function for the truncated triangular distribution. J Indian Acad Math 2014, 36(2), 297-305.

There are two types of procedures for masking microdata namely, adding independent noise and multiplying by independent noise. The triangular distribution is one of the options for incorporating multiplicative noise. The triangular distribution truncated around 1 is a better option than the untruncated triangular distribution and is of great practical relevance in areas like economics and finance. The distributional form of the truncated triangular distribution was developed and is available in the. literature. However, investigation of the statistical properties of data masked by using the truncated triangular distribution requires knowledge of the moments. In this paper, an attempt has been made to first develop the characteristic function for the truncated triangular distribution; then, the moments can be derived from the characteristic function. The general for the moments are also presented. This will be of immense practical help to data users in recovering the estimated moments of original data.

2 illus, 8 ref

020521   Oxman V;Stupel M (NO, Western Galilee College, P.O.B. 2125, Acre 24121, Israel, Email: victor.oxman@gmail.com) : Vector algebra as a tool for developing formulas in the trapezoid. Far East J mathl Sci 2014, 88(2), 241-556.

The paper presents a simple and elegant way for using vector algebra for the development of formulas linking different segments in the trapezoid. Each formula from among the formulas presented constitutes a necessary and sufficient condition for a quadrilateral to be a trapezoid. Several examples are given for tasks of calculations in the trapezoid. For the first example, the solutions are obtained by using the developed formulas and by an additional way which consists of combining trigonometry and Euclidean geometry, in order to emphasize the didactic advantage of using the prepared formulas.

4 illus, 8 ref

020520   Ounsrimuang P;Boonjing V (Software Engineering Laboratory, Computer Science Dep, Faculty of Science King Mongkut's Institute of Technology Ladkrabang, Bangkok 10520, Thailand, Email: s9062912@kmitl.ac.th) : Proposed algorithm for feature selection based on rough set and mutual information. Far East J mathl Sci 2014, 88(2), 199-216.

The feature selection approaches based on rough set theory aim to reduce the input data for improvement classification accuracy. Most existing approaches have concerned the discernibility relation to find the features, and have employed the dependency function for measuring the goodness of feature. The most relevant information cannot be visible by using information from discernibility relation only, so that neglecting indiscernibility relation, mostly relevant may be invisible. Moreover, their results are not tolerant to noisy or inconsistency data. Therefore, this paper proposes new algorithm based on rough set theory, which concerned both the discernibility and indiscernibility relations. The experimental results show that our approach gives higher classification accuracy than existing approaches.

1 illus, 4 tables, 23 ref

020519   Muslikh M (Faculty of Science, Brawijaya Univ, Jln. Veteran, Malang 65144, Indonesia, Email: mslk@ub.ac.id) : Existence of a continuous caristi selection of set-valued mappings. Far East J mathl Sci 2014, 88(2), 165-74.

In this paper, the existence of a continuous Caristi selection of compact set-valued mapping with values is shown.

10 ref

020518   Marin A M;Ortiz R D;Rodriguez J A (Grupo de Ondas Facultad de Ciencias Exactas y Naturales, Universidad de Cartagena Programa de Matematicas Sede San Pablo, Cartagena de Indias Bolivar, Colombia, Email: amarinr@unicartagena.edu.co) : Equation of heat subdiffusion with Neumann boundary condition. Far East J mathl Sci 2014, 88(2), 187-98.

In this paper, we consider a nonhomogeneous subdiffusion heat equation of fractional order with Neumann boundary conditions.

7 ref

020517   Lakshmi S;Durgadevi N (NO, Government Arts College, Peravurani-641 804, Email: lakshmi291082@yahoo.co.in) : A trivariate weibull model for contextual control over expression of fear in humans. J Indian Acad Math 2014, 36(2), 271-85.

The purpose of the present study is threefold: first, we aim at developing an experimental paradigm specifically capable of capturing contextual modulation of the expression of fear. Second, it tests whether cortisol will alter the contextualization of fear expression. Third, it is aimed at assessing whether alterations in contextualization due to cortisol are different for men and women. First of all, all subgroups showed significantly differential conditioning [A(CS1)+ vs B(CS2)-] in men or in women, as compared to their respective control groups. The survival functions for corresponding values of startle magnitude, skin conductance, probability density function and log-likelihood functions for placebo and cortisol have been found.

20 illus, 13 ref

020516   Lakshmi S;Agalya M (NO, Govt. Arts & Science College, Peravurani, Dist: Thanjavur, Email: lakshmi291082@yahoo.co.in) : A mathematical model for finding the moment generating function of multivariate normal distribution for the four variables luteinizing hormone, follicle stimulating hormone, estrone and pregnandiol. J Indian Acad Math 2014, 36(2), 307-23.

In many applications involving functions of random variables one may be interested in only the mean and variance of those functions. Furthermore, one may have available data from which the mean, variance and perhaps correlation coefficients among the variables can be calculated [3]. Here we express the statistics of a function of several random variables as a function of statistics on its component [8, 11]. In the discussion which follows, the joint density is assumed to be multivariate normal. The mean and Variance of the Product of two variables have been utilized in the application part. From a Clinical point of view menstrual irregularities due to secretion of the hormones LH, FSH, E₁ and PGd which are the first sign of underlying ovarian dysfunction. The; curves for the moment generating function of the above four variables are obtained here and explained by a figure in the mathematical result.

1 illus, 11 ref

020515   Koshy T (NO, Framingham State Univ, Framingham, MA 01701-9101, USA, Email: tkoshy@framingham.edu) : Pellnomial numbers. J Indian Acad Math 2014, 36(2), 189-201.

Introduces a new class of numbers, called Pellnomial numbers; they have a close relationship with binomial coefficients. We then explore some interesting properties, including their relationship with the well known Catalan numbers.

3 illus, 7 ref

020514   Kim C;Kang C (Mathematics Education Dep, Dankook Univ, 126, Jukjeon, Yongin Gyeonggi-do 448-701, Korea, Email: kci206@hanmail.net) : Generalized hyers-ulam stability of additive functional inequalities in non-archimedean space. Far East J mathl Sci 2014, 88(2), 233-40.

In this paper, we investigate the following additive functional inequality || f(x) + f(y) + f(2z) || ≤ || f(x + y)- f(-2z) || and prove the generalized Hyers-Ulam stability of it in non-Archimedean spaces.

11 ref

020513   Kim C I;Jung K H (Mathematics Education Dep, Dankook Univ, Yongin 448-701, Republic of Korea, Email: kci206@hanmail.net) : Stability of quadratic functional equations in non-archimedean spaces. Far East J mathl Sci 2014, 88(2), 217-24.

In this paper, using fixed point method, we prove the generalized Hyers-Ulam stability of the following functional equation: f(ax + by) + af(x - by) = a(a + l) f(x) + b^{2(a + 1) f(y) for some non-zero integers a, b with a2 ≠ b2 and a ≠-1.}

10 ref

020512   Kim B (Math-Physics Section, College of Science and Technology, Hong-Ik Univ, 339-701 Chochiwon, Sejong, Korea, Email: bkim@hongik.ac.kr) : Spinor representations and field equations. Far East J mathl Sci 2014, 88(2), 225-32.

Using left and right handed spinors, authors represent massive particles and find related field equations.

3 ref

020511   Khan Q H (Mathematics Dep, Z. H. (E) College, Delhi Univ, Email: qhkhan.ssitm@gmail.com) : Common fixed point theorem for six mappings in metric spaces. J Indian Acad Math 2014, 36(2), 287-95.

A common fixed point theorem for six mappings satisfying a rational inequality has been obtained, which generalized several previously known results given by Kannan, Fisher, Hardy-Rogers, Pande-Dubey and others. A related example is also furnished.

16 ref

020510   Kaushal N;Tiwari M;Parihar C L (Engineering Mathematics Dep, Indore Institute of Science and Technology, Indore-453 331, Email: nams0053@gmail.com) : Partial ordering on alternating sign matrices and its bijection. J Indian Acad Math 2014, 36(2), 367-76.

Out of several combinatorial objects like, alternating sign matrices (ASMs), totally symmetric self-complementary plane partitions (TSSCPPs), Catalan objects, tournaments, semistandard young tableaux, and totally symmetric plane partitions in order to put ASMs in larger context, they viewed as poset. In this paper we present two and three dimensional structure of pentagonal poset and sub-posets having certain ordering relations. Moreover by using ordered ideal of these sub-posets, a cover preserving bijection also will be presented.

4 illus, 6 ref

020509   Hong S P;Kim W K (Mathematics Education Dep, Chungbuk National Univ, Cheongju 361-763, Korea, Email: sph40@hanmail.net) : On the algorithm for generating pythagorean triples. Far East J mathl Sci 2014, 88(2), 175-85.

In this paper, authors first give a theorem for the Pythagorean triples with g-gap in the Pythagorean triangle, and next, investigate the new algorithm for generating Pythagorean triples with g-gap.

8 ref

020508   Hiwarkar R A;Jaiswal V K;Jumale J;Thengane K D (NO, Guru Nanak Institute of Engineering & Technology, Nagpur, Email: rhiwarkar@gmail.com) : Exact vacuum solutions of six dimensional bianchi type-V space-time in f(R) theory of gravity. J Indian Acad Math 2014, 36(2), 245-58.

This paper is dealt with the accelerating expansion of the universe in f(R) theory of gravity using metric approach in six dimensional Bianchi type-V space-time and obtained two exact vacuum solutions in V₆. Some physical properties of these solutions have also been studied.

3 ref

020507   Deo S D;Qureshi A A (Mathematics Dep, N.S. Science and Arts College, Bhadrawati, Dist. Chandrapur-442 902, Email: sdeo01@yahoo.in) : Spherically symmetric string cloud with strange quark matter in bimetric relativity. J Indian Acad Math 2014, 36(2), 239-44.

In this paper, spherically symmetric space-time is studied with the matter string cloud and Strange quark in the context of Rosen's Bimetric Theory of Relativity. Here it is observed that nonexistence nature of strange quark as well as string cloud in biometric relativity.

12 ref

020506   de Mattos J R L;Lopes E P (Institute of Mathematics and Statistics, Fluminense Federal Univ, Brazil, Email: jrlinhares@vm.uff.br) : Stability and uniqueness of the solution of an ill-posed elliptic problem. Far East J mathl Sci 2014, 88(2), 147-63.

In this work, authors consider an ill-posed Cauchy problem for an elliptic equation with variable coefficients. Authors assume the existence of a solution u(x, .) in H^{2(R) and we use a wavelet regularization method. Furthermore, we get the numerical estimates for the convergence of the method and prove the uniqueness of the solution for the problem.}

8 ref

020505   Changphas T (Mathematics Dep, Faculty of Science Khon Kaen Univ, Khon Kaen 40002, Thailand, Email: thacha@kku.ac.th ) : On (m,n)-ideals of an ordered semigroup. Far East J mathl Sci 2014, 88(2), 137-45.

A subsemigroup A of an ordered semigroup (S, ≤) is said to be an (m, n) -ideal (m, n are non-negative integers) if A^mSAn

11 ref

020504   Bansal M K;Jain R (Mathematics Dep, Malaviya National Institute of Technology, Jaipur-302 017, Email: bansalmanish443@gmail.com) : On unified finite integrals involving I₃ function, generalized mittag-leffler function and appell polynomials. J Indian Acad Math 2014, 36(2), 211-19.

In this paper, we evaluate unified finite integral whose integrand involves the product of generalized form of the astrophysical thermonuclear functions I₃, Appell polynomials and Generalized Mittag-Leffler Function. Further, its argument contains the factors of the form x ^{λ-1 (a-x)σ--1 (1-uxl) -p. On account of the most general nature of the functions occurring in the integrand, a large number of new integrals can easily be obtained from it merely by specializing the functions and parameters involved therein. For the sake of illustration, we obtain herein three new integrals involving the functions namely: Steady State Function Cesaro Polynomial, Laguerre Polynomial, Shively Polynomaial, Generalized Wrights Hypergeometric Function, Bessel Maitland Function, Generalization of the Mittag-Leffler Function.}

12 ref

019529   Yoo J K (Liberal Arts and Science Dep, Chodang Univ, 419 Sungnamri Muangun Chonnam, Korea, Email: jkyoo@cdu.ac.kr ) : Super-decomposable operators and invariant subspace. Far East J mathl Sci 2014, 90(2), 235-44.

15 ref

019528   Yadav S K;Mishra S S;Singh L;Shukla A K;Tyagi D (Mathematics and Statistics (A Centre of Excellence) Dep, Dr. RML Avadh Univ, Faizabad-224 001, Email: drsinghlakahan@gmail.com) : Efficient ratio type estimator of two population means in stratified random sampling. Int J agric statist Sci 2015, 11(1), 93-6.

In this manuscript, an efficient estimator of ratio of two population means using auxiliary variable under stratified random sampling has been proposed using kappa technique. The expressions for the bias and mean square error (MSE) have been obtained up to the first order of approximation. The minimum MSE of proposed estimator is also obtained for the optimum value of the constant kappa. A comparison has been made with the existing estimators and theoretical findings have been justified with the help of a numerical example.

10 ref

019527   Wang Q;Ruan H;Li J (Applied Mathematics Dep, Changzhou Univ, Jiangsu Province 213164, P. R. China) : Distributions about functions of inhomogeneous random variables. Far East J mathl Sci 2014, 90(2), 245-52.

There are often involving functional distribution problems in two or more mixed random variables, to solve practical problems by probability theory. Let X be a discrete random variable and Y be a continuous random variable. We discuss the distributions of aX + bY, aXY, aY/X and aX/Y, where a ≠ 0, b ≠ 0 are constants. When it is a continuous random variable, the density function is proposed. It is an extension of existing results.

6 ref

019526   Wang L;Ren L (School of Mathematics and Computation Science, Shanxi Normal Univ, Lifen 041004, P.R. China, Email: lfwang@163.com) : Generalization of minimal non-abelian p-groups. Far East J mathl Sci 2014, 91(1), 1-15.

6 ref

019525   Viriyapong R;Bunwong K;Moore E J (NO, Centre of Excellence in Mathematics CHE, Sri Ayuttahya Road, Bangkok 10400, Thailand, Email: ratchadapa@nu.ac.th) : The influence of light irradiance and rainfall patterns on phytoplankton dynamics. Far East J mathl Sci 2014, 91(2), 191-210.

The effects of light irradiance and nutrient availability on the dynamics of a phytoplankton model are studied for four species of phytoplankton, two with photoinhibition and two without photoinhibition. In particular, the dynamical effects of changes of nutrient availability and levels of irradiance associated with rainfall and storm conditions are examined. For constant nutrient input and light irradiance, it is proved analytically that the model has a trivial equilibrium point (zero phytoplankton population) which always exists and a nontrivial equilibrium point (positive phytoplankton population) which exists only if the trivial point is unstable. It is also proved analytically that if the nontrivial point exists, then it is locally and globally stable and that limit cycles cannot occur. Results of numerical simulations are presented showing the differing dynamics of species with and without photoinhibition under conditions of constant nutrient input and a range of values of constant irradiance. Results of numerical simulations are also presented showing the dynamics during and after periods of heavy rainfall and storms on the assumption that the heavy rainfall increases the nutrient input, the irradiance is reduced during the rainfall, and strong sunlight returns after the rain stops. The simulations show that increased phytoplankton densities and algal blooms can occur at the end of a period of heavy rainfall followed by a return of sunlight, and that a double algal bloom can occur in some phytoplankton species if the increase in nutrient flow lasts long enough during and after rainfall.

4 illus, 33 ref

019524   Vijay Kumar;Sinha A K (NO, Rajendra Memorial Research Institute of Medical Sciences (ICMR), Agamkuan, Patna-800 007, Email: vijay_stat2007@rediffmail.com) : Extimating underground farm produce by ranked set sampling with unequal allocations. Int J agric statist Sci 2015, 11(1), 47-52.

Ranked set sampling (RSS) performs better than simple random sampling (SRS) with the same sample size. Its performance improves when appropriate unequal allocation is used instead of equal allocation. For skewed distributions, the optimum gain in precision is obtained through an unequal allocation based on Neyman's approach. In this method, the sample size for each rank order is kept proportional to the standard deviation of that rank order. These procedures are illustrated using a real data set related to the yield of potato. The technique appears useful to those who look for observational economy for estimating farm produces that are grown under the land surface such as potato, ginger, turmeric, garlic, onion, beetroot, peanut, etc.

4 tables, 18 ref

019523   Unai A (Mathematical Information Science Dep, Tokyo Univ of Science 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan, Email: unai@rs.kagu.tus.ac.jp) : An elementary proof of the boundedness of eigenfunctions for the negative p-Laplacian operator under Dirichlet boundary conditions. Far East J mathl Sci 2014, 91(2), 247-57.

3 ref

019522   Udayabaskaran S;Dora Pravina C T (Mathematics Dep, Vel Tech Dr. RR & Dr. SR Technical Univ, Avadi, Chennai-600 062, Email: udayabaskaran.s@gmail.com) : Transient analysis of an M/M/1 queue in a random environment subject to disasters. Far East J mathl Sci 2014, 91(2), 157-67.

This paper obtains the transient behaviour of an M/ M/1 queue which operates in a random environment having n distinct phases. The queueing system is subject to randomly occurring catastrophes which wipe out all customers in the system instantaneously. Immediately after the occurrence of every disaster, the server goes for repair and during the repair time, customers are allowed to join the system. Immediately after the repair, the server is ready for offering service in phase i with probability q_i. We obtain time-dependent state probabilities and deduce the corresponding steady-state results.

9 ref

019521   Tiwari S K;Bhatt D K (School of Studies in Mathematics, Vikram Univ Ujjain, Madhya Pradesh, Email: skt_tiwari75@yahoo.co.in) : On the degree of approximation of function by almost riesz means of its fourier series. J Indian Acad Math 2014, 36(1), 59-69.

In the present paper, we have established the degree of approximation of functions belonging to weighted W(L^r, ξ(t)), r ≥ 1,class by almost Riesz means of its Fourier series.

13 ref

019520   Tiwari S K;Acharya S (School of studies in Mathematics, Vikram Univ, Ujjain, Madhya Pradesh, Email: skt_tiwari75@yahoo.co.in) : A mathematical optimization model for collection of medical waste. J Indian Acad Math 2014, 36(1), 129-38.

Small and medium-sized clinics and hospitals do not have on-site treatment facilities for their medicals and infectious wastes and must rely on outside agencies for its collection and treatment. In this paper the problem of optimally planning and scheduling the collection of medical wastes from a disperse group of facilities is formulated as a Periodic VRP. Special attention is given to the requirement that waste pickup be made on at least a weekly basis. Optimization model consist of two phase: first phase solves a standard VRP to determine the set of individual routes for the collection vehicles. Whereas second phase assigns routes to particular days of the week by mixed-integer programming.

14 ref

019519   Sung Y O (Applied Mathematics Dep, Kongju National Univ, 182 Sinkwandong, Kongju-city, 314-701, Korea) : Notes of fuzzy difunctional relations. Far East J mathl Sci 2014, 91(1), 123-31.

The images and preimages of fuzzy conformable relations and fuzzy difunctional relations are studied under the so-called semibalanced maps.

7 ref

019518   Sundar P;Kishokkumar B (Mathematics Dep, Om Muruga College of Arts and Science, Mettur, Tamilnadu, Email: mydt972009@gmail.com) : Nonoscillatory solution of even-order nonlinear neutral difference equation. J Indian Acad Math 2014, 36(1), 155-66.

In this article, the existence of non-oscillatory solutions of the even-order nonlinear neutral difference equations is studied. Sufficient conditions for the existence of a non-oscillatory solution of such equations are established. Our results generalize and extend some related results in the literature.

24 ref

019517   Sumi T;Sakata T;Miyazaki M (Faculty of Arts and Science, Kyushu Univ, 744 Motooka, Nishi-ku Fukuoka 819-0395, Japan, Email: sumi@artsci.kyushu-u.ac.jp) : Rank of n-tensors with size 2 x ... x 2. Far East J mathl Sci 2014, 90(2), 141-62.

We study an upper bound of ranks of n-tensors with size 2 x ... x 2 over the complex and real number field. We characterize a 2x2x2 tensor with rank 3 by using the Cayley's hyperdeterminant and some function. Then we see another proof of Brylinski's result that the maximal rank of 2x2x2x2 complex tensors is 4. We state supporting evidence of the claim that 5 is a typical rank of 2x2x2x2 real tensors. Recall that Kong and Jiang [9] showed that the maximal rank of 2x2x2x2 real tensors is less than or equal to 5. The maximal rank of 2x2x2x2 complex (resp. real) tensors gives an upper bound of the maximal rank of 2 x ... x 2 complex (resp. real) tensors.

12 ref

019516   Sudha S;Raja G M (Ramanujan Institute for Advanced Study in Mathematics, Madras Univ, Chepauk, Chennai-600 005, Email: ssudha50@sify.com) : Tripartite graphs of a semigraph. J Indian Acad Math 2014, 36(1), 1-11.

5 illus, 3 ref

019515   Sudha S;Kanniga V (Ramanujan Institute for Advanced Study in Mathematics, Madras Univ, Chepauk, Chennai-600 005, Email: ssudha50@sify.com) : Star-in-coloring of cycles, generalized petersen graphs and their middle graphs. J Indian Acad Math 2014, 36(1), 13-27.

In this paper, we have given the definition for star-in-coloring by combining together the definitions of star-coloring and in-coloring and showed that even cycles C_n and generalized Petersen graphs P(n, 1) (for even n) admit star-in-coloring. We have also found the star-in-coloring for the middle graphs of even cycles C_n and the generalized Petersen graphs P(n, 1) (for even n), and found the star-in-chromatic number of the above graphs.

12 illus, 4 ref

019514   Sripanya W (Faculty of Science and Technology, Nakhon Pathom Rajabhat Univ, Nakhon Pathom 73000, Thailand, Email: w.sripanya@windowslive.com) : Inverse problem of resistivity sounding for an exponential earth with buried electrodes. Far East J mathl Sci 2014, 90(2), 203-10.

An analytical solution of the electric potential is derived for the problem of a buried current source and a buried receiver. The model of a layered earth is developed for source and receiver electrodes buried anywhere within an exponentially varying conductive ground. Our variation in conductivity is realistic and can be generalized to all cases of exponential profiles. The Hankel transform is introduced to our problem and analytical result is obtained. Our solution is achieved by solving a boundary value problem in the wave number domain and then transforming the solution back to the spatial domain. An expression derived for the electric potential can be used to interpret hole-to-hole, hole-to-surface and conventional surface array data. An inverse problem via the use of the Levenberg-Marquardt optimization technique is introduced for finding the conductivity parameters of the ground. The optimal result of our model is close to the true value with percentage errors of our two conductivity parameters less than 2.8% and 3.5% after using only 5 iterations.

14 ref

019513   Sisodia B V S;Kaushal R P;Hukum Chandra (Agril. Statistics Dep, N.D. Univ of Agriculture & Technology, Faizabad-224 229, Email: bvssisodia@gmail.com) : Some shrunken predictors in stratified population. Int J agric statist Sci 2015, 11(1), 123-9.

Bouza (1990) and Bouza & Allende (1991) proposed shrunken predictors and analyzed their behavior in stratified sampling under super-population models ξ(0,1:1). Robustness of the shrunken predictors measured in terms of bias and mean squared error (MSE) was further studied by Bouza (1994) which depends on stratified balanced sample and difference between the common slope (β) and uncommon slopes (β_h) to strata. In this paper, we proposed a new set of predictors under same super population model ξ(0,1:1). The proposed predictors are compared with that of due to Bouza (1994) and they have been found more efficient under certain conditions. The robustness of the proposed predictor is also studied on the same lines as discussed by Bouza (1994), and it has been found that robustness of the proposed predictor depends upon the difference between β and βh. Simulation experiments also indicated superiority of the proposed predictor over the predictors due to Bouza.

1 table, 6 ref

019512   Singh B;Sisodia B V S (Basic Science Dep, College of Horticulture and Forestry, Jhalarapatan, Jhalawar-326 023) : A note on estimation of overall average for small domain. Int J agric statist Sci 2015, 11(1), 245-9.

In this article, methods of estimation of overall average for small domains between two points of time have been proposed by using small area statistical techniques. Direct and indirect estimators are proposed to estimate the overall average in successive sampling over occasions for small domain using small area estimation techniques. The expression for bias and variance/mean squared error of the proposed estimators are obtained. A comparison between variances of the estimates is studied. It was found that the indirect estimator has been more efficient than the direct estimator under certain conditions.

15 ref

019511   Singh A;Loonker D;Banerji P K (DST Centre for Interdisciplinary Mathematical Sciences Faculty of Scie, Banaras Hindu Univ, Varanasi-221 005, Email: abhijnvu@gmail.com) : On dunkl-plancherel theorem for vector valued boehmians. J Indian Acad Math 2014, 36(1), 41-58.

de Jeu studied the Dunkl transform and proved the inversion and plancherel theorem. In this paper the Dunkl-Plancherel theorem is introduced for vector-valued Boehmians and an isomorphism between L² (R) onto L²(R) has been established.

16 ref

019510   Shukla Y;Yadav A S (Mathematics Dep, AMITY Univ, Madhya Pradesh, Gwalior, Email: yshukla@gwa.amity.edu) : Mathematical approach to unstudy temperature regulation of human body due to arterial blood temperature. J Indian Acad Math 2014, 36(1), 119-28.

The study of temperature regulation of human body has great importance to understand the physiology of the human body. The outer surface of skin is assumed to be exposed to environment temperature (T_b) at 37°C. Any disturbance in the temperature regulation may cause lots of abnormality in the body. In the present paper an attempt has been made to unsteady temperature variations of dermal region of human body by changing arterial blood temperature for transient case. The nodal temperatures are noted at different time intervals.

2 tables, 16 ref

019509   Shelake G D;Joshi S B (Mathematics Dep, Willingdon College, Sangli-416 415, Email: shelakegd@gmail.com) : Subclasses of multivalent harmonic mappings defined by convolution. J Indian Acad Math 2014, 36(1), 139-53.

Two new subclasses of multivalent harmonic functions defined by using convolution and integral convolution are introduced in this paper. These subclasses generates several known and new-subclasses of multivalent harmonic functions as special cases and thus provide a unified treatment in the study of these classes. Sufficient coefficient condition are obtained that are also shown to be necessary when functions have negative coefficients. Distortion bounds, extreme points and convex combination are also determined.

24 ref

019508   Sharma V;Mukesh Kumar;Chauhan A (Mathematics Dep, Graphic Era Univ, Dehradun-248 002, Email: vikas.sharma0204@gmail.com) : An imperfect production model with preservation technology, fuzzy and variable holding cost under two storage capacity. Int J agric statist Sci 2015, 11(1), 225-31.

In this paper, we develop a two-warehouse production-inventory model with imperfect quality items. Shortages are allowed and partially backlogged with variable holding cost. The lot sizing problem is then to find the optimal production while minimizing the manufacturer's total cost over the planning horizon. Finally, numerical examples will be used to illustrate the results.

2 illus, 4 tables, 47 ref