000040   Biswas D (Mathematics Dep, Indian Institute of Technology-Kharagpur, Kharagpur-721 302, Email: d_priya05@yahoo.co.in) : Realm of matrices exponential and logarithm functions. Resonance 2015, 20(2), 136-50.

In this article, we discuss the exponential and the logarithmic functions in the realm of matrices. These notions are very useful in the mathematical and the physical sciences [1,2]. We discuss some important results including the connections established between skew-symmetric and orthogonal matrices, etc., through the exponential map.

10 ref

023359   Sury B (Stat-Math Unit, Indian Statistical Institute 8th Mile Road, Bangalore-560 059, Email: sury@isibang.ac.in) : Multivariable chinese remainder theorem. Resonance 2015, 20(3), 206-16.

Sun-Tsu wrote the treatise Sunzi Suanjiing around the 3rd century. The problem of finding an integer x which is simultaneously 2 modulo 3, 3 modulo 5 and 2 modulo 7 was considered. The smallest solution was found to be 23 and such a result is now called the Chinese Remainder Theorem (CRT). From early times - perhaps, from the 1st century itself - the CRT was employed in the preparation of calendars. In India, Aryabhata's mathematics from the 5th century contains instances of the CRT. However, a mul-tivariable version of CRT does not seem to be well known and is not a part of textbooks. Qin Jiushao seems to have considered one such version in the 13th century. In this article, the basic CRT is recalled and some multivariable versions are studied using elementary linear algebra.

2 ref

023358   Patel R;Parekh R U;Patel S S (Statistics Dep, Veer Narmad South Gujarat Univ, Surat, Email: patelramanb@yahoo.co.in) : Deteriorating items production inventory models with two warehouses under shortages, inflation and permissible delay in payments. Int J latest Technol Engng Mgmt appl Sci 2015, 4(4), 55-66.

Production inventory model for deteriorating items with linear trend in demand, time varying holding cost, inflation and permissible delay in payments with two warehouses is developed. Shortages are allowed and completely backlogged. The excess units over the capacity of the own warehouse (OW) are stored in a rented warehouse (RW). Numerical examples are provided to illustrate the model.

1 illus, 5 tables, 24 ref

023357   Behera D;Chakraverty S (Mathematics Dep, National Institute of Technology Rourkela, Odisha-769 008, Email: diptiranjanb@gmail.com) : New approach to solve fully fuzzy system of linear equations using single and double parametric form of fuzzy numbers. Sadhana 2015, 40(1), 35-49.

This paper proposes two new methods to solve fully fuzzy system of linear equations. The fuzzy system has been converted to a crisp system of linear equations by using single and double parametric form of fuzzy numbers to obtain the non-negative solution. Double parametric form of fuzzy numbers is defined and applied for the first time in this paper for the present analysis. Using single parametric form, the n x n fully fuzzy system of linear equations have been converted to a 2n x 2n crisp system of linear equations. On the other hand, double parametric form of fuzzy numbers converts the n x n fully fuzzy system of linear equations to a crisp system of same order. Triangular and trapezoidal convex normalized fuzzy sets are used for the present analysis. Known example problems are solved to illustrate the efficacy and reliability of the proposed methods.

3 illus, 4 tables, 39 ref

023356   Barua B;Das J (NO, , Indian Society of Nonlinear Analysts (INSA) 248 B, B B Chatterjee Road, Kolkata-700 042, Email: baruabandana@yahoo.co.in) : Trigonometric characterization of some plane curves. Resonance 2015, 20(3), 235-44.

There is a way to describe a family of plane curves different from that using Cartesian or polar co-ordinates. This is a trigonometric equation involving two angles. In this article, we highlight the fact that trigonometric equations are convenient to describe certain one-parameter families of plane curves. In some cases, the trigonometric form makes it easier to characterize the family than if one were to use the equivalent Cartesian or polar representations.

9 illus, 2 ref

022474   Zhao C (Mathematics Dep, AnHui JianZhu Univ, HeFei, 230022, P.R. China, Email: chengbingzhao@163.com) : Gradient and complex hessian estimate on heat equation. Far East J mathl Sci 2014, 89(2), 185-90.

In this paper, let M be an n(n ≥ 2) dimension Rimannian manifold with nonnegative and bounded bisectional curvature. The gradient estimate and the complex Hessian estimate of positive solutions on heat equation are obtained with a less condition.

7 ref

022473   Yong U C (Mathematics Dep, College of Education Silla Univ, Pusan 617-736, Korea, Email: yucho@silla.ac.kr) : On corresponding properties in Γ-near-rings. Far East J mathl Sci 2014, 89(2), 177-83.

7 ref

022472   Yong U C (Mathematics Dep, College of Education Silla Univ, Pusan 617-736, Korea, Email: yucho@silla.ac.kr) : On isomorphic properties in GSA III. Far East J mathl Sci 2014, 89(2), 169-75.

In this paper, authors are concerned with some concepts of R-groups, where R is a near-ring, and their related algebraic structures such as group semiautomata: the first and second isomorphism theorems of group semiautomata have already been studied by us in earlier papers.

6 ref

022471   Yang Q (College of Information Management, Dezhou Univ, Dezhou 253023, P.R. China, Email: dlzxyanglixia@163.com) : Eigenvalues of higher-order regular Sturm-Liouville problems. Far East J mathl Sci 2014, 88(1), 65-88.

In this paper, we consider eigenvalues of higher-order regular Sturm-Liouville (SL) problems. We show that the eigenvalues depend not only continuously but smoothly on the problem and give an expression for the derivative of an eigenvalue with respect to a given parameter: an endpoint, a boundary condition, a coefficient or the weight function.

10 ref

022470   Sung Y O (Applied Mathematics Dep, Kongju National Univ, 182 Slnkwandong, Kongju-City, 314-701 Korea) : Fuzzy congruences on groups. Far East J mathl Sci 2014, 89(2), 227-37.

The purpose of this paper is to introduce some basic concepts of fuzzy congruence and to characterize fuzzy congruence relations on a group X. Authors also investigate some properties in connection with fuzzy difunctional relations.

7 ref

022469   Singh K D (NO, , Applied Mathematics Dep, Wexlow, Lower Kaithu, Shimla-171 005, Email: kdsinghshimla@gmail.com) : Oscillatory MHD convective flow of viscoelastic fluid through a porous medium in a rotating vertical channel in slip-flow regime with thermal radiation and hall current. J Energy Heat Mass Transfer 2013, 35(2), 109-32.

An exact solution of the magnetohydrodynamic (MHD) connective flow of a viscoelastic fluid through a porous medium filled in a vertical channel is obtained. One of the plates of the channel is subjected to a slip-flow condition and the other to a no-slip condition. The pressure gradient in the channel varies periodically with time. The entire system rotates in unison about an axis perpendicular to the planes of the channel plates. The fluid is electrically conducting and a magnetic field of uniform strength is applied along the axis of rotation. The non-uniform temperature difference of the plates is high enough to induce heat radiation. A closed form solution of the equations governing the flow is obtained. The effects of rotation, Hall current, slip-flow parameter, viscoelastic parameter, Grashof number, Reynolds number, permeability of the porous medium etc. are shown graphically on the velocity and skin friction and discussed in detail.

15 illus, 47 ref

022468   Shobana A;Jothimani S;Palaniammal S (Science and Humanities Dep, Sri Krishna College of Engineering and Technology, Coimbatore, Email: gsakhil@rediffmail.com) : Efficient 2-domination number in circulant graphs. Far East J mathl Sci 2014, 89(1), 21-30.

Cayley graphs are constructed out a finite group Γ and its generating set A, denoted by Cay(Γ, A). Circuital graphs are particular case of Cayley graphs when Γ = Z_n and denoted by Cir(n, A). In this paper, we find the 2-domination number of a class of circulant graphs. In that class of graphs, we find a necessary and sufficient condition for the existence of efficient 2-dominating set. Further, we prove that any subgroup of Z_n can be an efficient 2-dominating set of Cir(n, A) for some specific generating set A. We identify some 2-dominating 2-excellent circulant graphs and 2-dominating 2-restricted circulant graphs.

5 ref

022467   Revathi R;Rajeswari R (Mathematics Dep, Sathyabama Univ, Chennai-600 119, Email: revathi_kumaran@yahoo.com) : Structural properties of some families of modular multiplicative divisor graphs. Far East J mathl Sci 2014, 89(2), 217-25.

A graph G(V, E) with |V| = n is said to have modular multiplicative divisor (MMD) labeling if there exist a bijection f : V(G) → {1, 2, ..., n} and the induced function f* : E(G) → {0,1, 2, ..., n-1}, where f* (uv) = f(u)f(v)(mod n) such that n divides the sum of all edge labels of G. In this paper, we prove that the union of two MMD graphs of an arbitrary super subdivision graph and union of two MMD graphs of star graph are MMD graphs.

1 illus, 11 ref

022466   Reddy P R;Neelima A;Rama Rao K;Thiagarajan S (NO, ChaitanyaBharathi Institute of Technology, Gandipet, Hyderabad-500 075, Email: drrajpendyala@yahoo.com) : MHD and oscillatory flow of Rivlin-Ericksen fluid through an inclined channel. J Energy Heat Mass Transfer 2013, 35(2), 149-63.

The magneto hydrodynamic unsteady flow of a visco-elastic (Rivlin-Ericksen) fluid through an inclined channel with two parallel flat plates moving with oscillatory motion under the influence of magnetic field with heat transfer including heat generating sources or heat absorbing sinks, while one of these two plates is adiabatic is studied in this paper. Pertubation method is applied to obtain the expression for the velocity and temperature distribution in oscillatory motion. The effect of magnetic parameter, Prandtl number, source or sink, elastic parameter, Froude's number, Grasshoff number on velocity distribution is discussed with the aid of graphs. The effect of Prandtl number and source or sink term on the temperature distribution is observed.

18 illus

022465   Reddy M G (Mathematics Dep, Acharya Nagarjuna Univ, Ongole Campus, Ongole-523 001) : Lie group analysis of heat and mass transfer effects on steady MHD free convection dissipative flow past an inclined porous surface. J Energy Heat Mass Transfer 2013, 35(1), 69-86.

An analysis has been carried out to study heat and mass transfer effects on steady two-dimensional flow of an electrically conducting incompressible dissipating fluid past an inclined semi-infinite porous surface. The flow is permeated by a uniform transverse magnetic field. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation, and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The coupled ordinary differential equations along with the boundary conditions are solved numerically. Comparisons with previously published work are performed and the results are found to be in very good agreement. Many results are obtained and a representative set is displayed graphically to illustrate the influence of the various parameters on the dimensionless velocity, temperature and concentration profiles. It is observed that the velocity decreases with an increase in the magnetic field parameter and permeability parameter. It is found that the velocity increases with an increase in the thermal and solutal Grashof numbers. Also, the velocity and concentration of the fluid decreases with an increase in the Schmidt number. The results, thus, obtained are presented graphically and discussed.

13 illus, 21 ref

022464   Rao J A;Sivaiah S;Bibi S K N;Raju R S (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: anandrao_jakkula@yahoo.com) : Soret and radiation effects on unsteady MHD free convective fluid flow embedded in a porous medium with heat source. J Energy Heat Mass Transfer 2013, 35(1), 23-39.

The numerical solution of unsteady two-dimensional, laminar, boundary layer flow of viscous, incompressible, electrically conducting fluid along a semi-infinite vertical plate in the presence of thermal and concentration buoyancy effects under the influence of uniform magnetic field applied normal to the flow, has been obtained. Time-dependent suction is assumed and the radiative flux is described using the differential approximation for radiation. The Galerkin finet element method is used to sole the equations governing flow. The flow phenomenon has been characterized with the help of flow parameters such as velocity, temperature and concentration profiles for different parameters such as S_c P_Γ M O K N_Γ, K_Γ, G_m, S_o, E_c and G_Γ. Schmidt number, Prandtl number, Magnetic field, Heat source, Permeability parameter, Thermal radiation, Chemical reaction, Solutal Grashof number, Soret number, Eckert number and Grashof number. The velocity, temperature and concentration are shown graphically. The coefficient of skin-friction, Nusselt number and Sherwood number are shown in tables.

11 illus, 3 tables, 20 ref

022463   Rajotia D;Jat R N (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: rajotia.dinesh@gmail.com) : Unsteady three-dimensional boundary layer flow with diffusion and first-order chemical reaction due to a permeable axisymmetric shrinking sheet with suction. J Energy Heat Mass Transfer 2014, 36(3), 209-26.

In the present analysis, we are investigating the nature of dual solution of anunsteady three dimensional boundary layerflow of an incompressible viscous fluidwith diffusion of chemically reactive species undergoing first-order chemical reaction due to a permeableaxisymmetric shrinking sheet with suction and power-law variation in wall concentration. The similarity transformations are used to convert the governing partial differential equationsinto non-linear ordinary differential equations and then solved numerically by shooting technique. The conditions of the existence,non-existence and duality of the similarity solution are explored by theinvestigation where the solution depends not only on suction parameter but on unsteadiness parameter also. Further, it is emerged thatthe range of the suction parameter S, where the similarity solution exists, is increased with the increase of unsteadiness parameter λ. Also, the graphs of velocity profile, concentration profile, skin-friction coefficient and rate of solute transfer at the sheet are drawn with various values of the parameters and then discussed these characteristic features in detail.

13 illus, 38 ref

022462   Pendyala R R (Mathematics and Humanities Dep, Chaitanya Bharathi Institute of Technology Gandipet, Hyderabad-500 075, Email: drrajpendyala@yahoo.com) : Effects of heat and mass transfer on flow past an oscillating vertical plate with variable temperature by using finite element analysis. J Energy Heat Mass Transfer 2014, 36(3), 227-36.

In the present paper, a finite element analysis is made to study the variable temperature and mass diffusion effects on free convection flow of a viscous incompressible fluid past an oscillating infinite vertical plate. The governing coupled with non linear partial differential equations in dimensionless form are solved by Gelerken finite element method. The velocity, temperature and concentration profiles are discussed, analysed and graphically presented for various parameters such as phase-angle, Schmidt number, Prandtl number and time. The stuy found that an increase in the phase angle leads to an increase in the velocity of the fluid. It is also noted that the temperature and concentration of the fluid decrease for an increasing values of the Prandtl and Schmidt number respectively.

3 illus, 1 table, 11 ref

022461   Oladipo A T;Fadipe-Joseph A O;Moses B O (Pure and Applied Mathematics Dep, Ladoke Akintoal Univ of Technology, Ogbomoso P.M.B. 4000, Ogbomoso, Nigeria, Email: atlab_3@yahoo.com) : On a new class of uniformly analytic functions associated with q-analogue of Dziok-srivastava operator. Far East J mathl Sci 2014, 89(2), 153-67.

Authors study the new classes of uniformly ω-starlike and co-convex functions using a generalized operator involving basic hypergeometric function. Precisely, properties such as coefficient bounds, growth and distortion theorems are considered. Also, we try to have a look at the results involving radii of starlike, convexity and close-to-convexity.

20 ref

022460   Mukhopadhyay S;Bhattacharyya K;Chamkha A J (Mathematics Dep, The Univ of Burdwan, Burdwan-713 104, Email: swati_bumath@yahoo.co.in) : Effects of partial slip and variable fluid viscosity on stagnation point flow past a stretching sheet in the presence of a heat source/sink. J Energy Heat Mass Transfer 2013, 35(2), 87-108.

The boundary layer stagnation-point flow and heat transfer past a stretching sheet in the presence of partial slip and a heat source/sink is investigated. The fluid viscosity is assumed to vary as a linear function of temperature. With the help of the similarity transformations, the partial differential equations corresponding to momentum and the energy equations are transformed into highly non-linear ordinary differential equations. Numerical solutions of these equations are obtained by the shooting method. It is found that the horizontal velocity increases with increasing values of the ratio of the free stream velocity and the stretching velocity. The fluid velocity also increases with the increase in the temperature dependent fluid viscosity parameter when the free-stream velocity is less than the stretching velocity but the opposite behavior is noted when the free-stream velocity is greater than the stretching velocity. The momentum boundary layer thickness is found to increase with increasing values of the temperature dependent fluid viscosity parameter. With the increase in the velocity slip parameter, the fluid velocity is predicted to increase while the fluid temperature decreases when the free-stream velocity is greater than the stretching velocity. The opposite behavior of the velocity and temperature fields are noted for increasing values of the velocity slip when the free-stream velocity is less than the stretching velocity. It is also predicted that the fluid temperature decreases with increasing values of thermal slip parameter.

7 illus, 3 tables, 57 ref

022459   Moorthy M B K;Senthilvadivu K (Mathematics Dep, Institute of Road and Transport Technology, Erode-638 616) : Effect of thermal stratification on convective heat transfer past a vertical plate embedded in porous medium with an applied magnetic field. Int J Comp Applic 2014, 9(2), 215-31.

Free convection flow over a vertical plate embedded in a saturated porous medium in the presence of an Applied Magnetic field together with Thermal stratification effect is analyzed based on the boundary layer approximation. Similarity solutions are obtained for the case of power law variation in wall temperature. The resultant equations are solved numerically by using Runge - Kutta Gill method. Effects of porous parameter (K), Magnetic field parameter (N) and Thermal stratification parameter (M) on the behavior of nusselt number, velocity and temperature variations have been brought out. Velocity and temperature profiles are presented for different values of e -the power law index of the surface temperature, C- the parameter influences on the magnetic field and M-the thermal stratification parameter. The viscous boundary layer thickness and thermal boundary layer thickness are also obtained.

18 illus, 9 tables, 15 ref

022458   Marin A M;Ortiz R D;Rodriguez-Ceballos J A (Grupo de Ondas, Facultad de Ciencias Exactas y Naturales, Universidad de Cartagena Pro, Sede San Pablo Cartagena de Indias, Bolivar, Colombia, Email: amarinr@unicartagena.edu.co ) : On the nonexistence of periodic orbits of some quadratic systems. Far East J mathl Sci 2014, 89(1), 129-35.

3 ref

022457   Manyuen C;Jampachon P;Poomsaard T (Mathematics Dep, Faculty of Science Khonkaen Univ, Khonkaen 41000, Thailand, Email: chaowat_seed@hotmail.com) : Hyperidentities in graph variety generated by ((xx) ((yx)w))((zx)(zw) graph. Far East J mathl Sci 2014, 89(1), 31-50.

Graph algebras establish a connection between directed graphs without multiple edges and special universal algebras of type (2, 0). We say that a graph G satisfies a term equation's ≈ t if the corresponding graph algebra A(G) satisfies s ≈ t. The set of all term equations s ≈ t which the graph G satisfies denoted by Id({G}). The class of all graph algebras satisfy all term equations in Id({G}) is called the graph variety generated by G denoted by V_g({G}). A term equation s ≈ t is called an identity in V_g({G}) if A(G') satisfies s ≈ t for all G' ∈ V_g({G}). An identity s ≈ t of terms s and t of any type τ is called a hyperidentity of an algebra A if whenever the operation symbols occurring in s and t are replaced by any term operations of A of the appropriate arity, the resulting identities hold in A. In this paper, we characterize all identities, all graphs and all hyperidentities in V_g({G}), where G is the ((xx)((yx)w))((zx)(zw)) graph.

11 ref

022456   Manoj Kumar;Raman J;Raman P (NO, , International Engineering Services H.No.- 87A, RZI - Block West Sagarpur, New Delhi-110 046, Email: kumarm1968@rediffmail.com) : Novel approach for calculation of momentum, heat and mass transfer of gas-solid flow. J Energy Heat Mass Transfer 2014, 36(3), 183-208.

The Discrete Element Method (DEM) has been widely used as a mathematical tool for the study of flow characteristics involving paniculate solids. One distinct advantage of this Discrete Element Method (DEM) technique is the ability to compute trajectories of discrete particles. This provides the opportunity to evaluate the interactions between particle, fluid and boundary at the microscopic level using local gas parameters and properties, which is difficult to achieve using a continuum model. To date, most of these applications focus on the flow behaviour. This paper provides an overview of the application of Discrete Element Method (DEM) in gas-solids flow systems and discusses further development of this technique in the application of drying paniculate solids. A number of sub-models, including momentum, heat and mass transfer, have been evaluated to describe the various transport phenomena. A numerical model has been developed to calculate the heat transfer in a gas-solids pneumatic transport line. This implementation has shown advantages of this method over conventional continuum approaches.

7 illus, 63 ref

022455   Lee D W (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) : Digital singular homology groups of digital images. Far East J mathl Sci 2014, 88(1), 39-63.

In this article, we study the digital singular homology groups of digital images based on the singular homology groups of topological spaces in algebraic topology. More specifically, we define a digital standard n-simplex, a digital singular n-simplex, and the digital singular homology groups of digital images with k-adjacency relations. We then construct a covariant functor from a category of digital images and digitally continuous functions to the one of abelian groups and group homomorphisms, and investigate some fundamental and interesting properties of digital singular hornology groups of digital images such as the digital version of the dimension axiom which is one of the Eilenberg-Steenrod axioms.

18 ref

022454   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-semicontinuous mappings. Far East J mathl Sci 2014, 89(1), 7-19.

It defines and characterizes a fuzzy pairwise α-semicontinuous mapping and a fuzzy pairwise α-semiopen mapping on a fuzzy bitopological space.

7 ref

022453   Ibeh G J;Mshelia E D (Physics Dep, Nigerian Defence Academy Kaduna, Nigeria) : Energy dissipation in a model of coupled three-dimensional harmonic oscillators. Far East J mathl Sci 2014, 88(1), 107-36.

The three-dimensional model for the dissipation of energy from a collective degree of freedom represented by free motion into intrinsic excitations represented by three coupled oscillators is presented. It is shown that the quantum mechanical probability amplitude for the intrinsic excitations can be determined analytically exactly. The results of numerical computations of the probability distributions as functions of some quantities of physical interest are presented graphically.

13 illus, 42 ref

022452   Gaketem T (Mathematics Dep, School of Science, Phayao Univ, Phayao, 56000, Thailand, Email: newtonisaac41@yahoo.com) : Minimal bi-ideals in la-semigroup. Far East J mathl Sci 2014, 89(1), 1-5.

The purpose of this paper is to study on defined a minimal bi-ideal and 0-minimal bi-ideal in LA-semigroup. Also we introduce the concepts of a bi-simple and 0-bi-simple of LA-semigroup.

6 ref

022451   Feng D Y (Basic Teaching Dep, Liaoning Construction Vocational College, Liaoyang 111000, P.R. China, Email: 1f2d3y@163.com) : On geometric characterization and regular node configurations for bivariate lagrange interpolation. Far East J mathl Sci 2014, 89(2), 137-52.

An interpolation problem is determined by the space of interpolating functions and interpolation nodes. Geometric characterization (GC) for sets of interpolation nodes was introduced by Chung and Yao, such that for the interpolation nodes satisfying GC condition the associated Lagrange polynomials could be expressed in the form of first degree polynomials with real coefficients. A conjecture concerning GC condition presented by Gasca and Maeztu stated that any set in the plane satisfying GC_n condition must have n + 1 collinear points in it. The conjecture has been proved by some recent authors for degree <60> 4 and the relevant regular node configurations in the plane have been given. In this paper, regular node configurations of GC₅ sets are discussed and a description of defect for GC₅ sets is also made, which generalize the main conclusions of the previous study on this aspect.

5 illus, 24 ref

022450   Doku I (Mathematics Dep, Saitama Univ, Saitama 338-8570, Japan, Email: idoku@mail.saitama-u.ac.jp) : Star-product functional and unbiased estimator of solutions to nonlinear integral equations. Far East J mathl Sci 2014, 89(1), 69-128.

In this paper, authors consider a class of deterministic nonlinear integral equations. We begin with constructing a branching model, define a star-product and construct a tree-based star-product functional. By studying mathematical structure of the functional, we prove that the function given by expectation of the functional with respect to the law of a branching process satisfies the original integral equations. Moreover, we study other probabilistic solutions in terms of the notion of unbiased estimator. Finally, some generalization is discussed as well.

5 illus, 28 ref

022449   Deng Z (Mathematics Dep, Shanghai Univ, Shanghai 200444, P.R. China, Email: zdeng2007@126.com) : Solvability to some systems of matrix equations, and matrix inequalities. Far East J mathl Sci 2014, 89(2), 239-48.

In this paper, we derive necessary and sufficient conditions for the solvability to the systems of matrix equations and matrix inequalities A₁X = B₁, A₂Y = B₂, A₃Z = B₃, A <62> BXB* + CYC* + DZD*, A₁X = B₁, A₂Y = B₂, A₃Z = B₃, A <62> BXB* + CYC* + DZD*, A₁X = B₁, A₂Y = B₂, A₃Z = B₃, A <62> BXB* + CYC* + DZD*, A₁X = B₁, A₂Y = B₂, A₃Z = B₃ A <60> BXB* + CYC* + DZD**.

7 ref

022448   Cimpoiasu R (Research Center Frontier in Biology and Astrobiology, Craiova Univ, 13 A.I.Cuza, 200585 Craiova, Romania, Email: rodicimp@yahoo.com) : On symmetry groups of a 2D nonlinear diffusion equation with source. Pramana J Phys 2015, 84(4), 543-53.

Symmetry analysis of a 2D nonlinear evolutionary equation with mixed spatial derivative and general source term involving the dependent variable and its spatial derivatives is performed. The source terms for which the equation admits nontrivial Lie symmetries are identified for two different forms of the symmetry operator. In one of these cases, the symmetries do not depend on the form of nonlinearities and in the other case, nonlinearities of power, exponential and trigonometric forms are considered. There are no supplementary nonclassical symmetries for the investigated equation. The results reported here generalize the previous results on the 2D heat equation and the 2D Ricci model.

18 ref

022447   Chauhan S;Haq S;Alamgir Khan M (NO, Near Nehru Training Centre, H. No. 274, Nai Basti B-14, Bijnor-246 701, Email: sun.gkv@gmail.com) : A related fixed point theorem in two menger spaces employing an implicit relation. Far East J mathl Sci 2014, 88(1), 27-37.

In this manuscript, we prove a related fixed point theorem in two Menger spaces satisfying an implicit relation. An example, is also furnished, which demonstrates the validity of the hypothesis and degree of generality of our main result. Our results generalize several known results existing in the literature.

20 ref

022446   Cerin Z;Gianella G M;Junicic M (NO, , Kopernikova 7, 10020 Zagreb, Croatia, Email: cerin@math.hr) : Sums of (p, q)-Fibonacci and (p, q)-Lucas numbers. Far East J mathl Sci 2014, 88(1), 1-25.

This paper considers some sums of (p, q)-Fibonacci and (p, q)-Lucas numbers H_n and K_n when the indices n belong to one of the three residue classes of the number 3. We discover the explicit formulas for these sums and study their properties.

8 ref

022445   Canadas A M;Arcos A M S;Angarita M A O (Mathematics Dep, National Univ of Colombia, Bogota, Colombia, Email: amorenoca@unal.edu.co) : Entropy of a poset. Far East J mathl Sci 2014, 89(2), 191-215.

In this paper, authors define entropy of a partially ordered set (poset) and use it to establish the properties of endomorphism rings of posets of tame representation type.

4 illus, 16 ref

022444   Busababodhin P (Mathematics Dep, Faculty of Science Mahasarakham Univ, Mahasarakham 44150, Thailand, Email: piyapatr99@hotmail.com) : An analytical expression to cusum chart for seasonal AR(p) model. Far East J mathl Sci 2014, 88(1), 89-105.

The Cumulative Sum (CUSUM) chart provides good performance in detecting small shifts of process means compared to the traditional Shewhart chart. A common assumption of the control chart is the independent and identically distributed random variables, however, this assumption could be deviated from in practice such as chemical processes or if financial market is autocorrelated and trend stationary. In this paper, the explicit formulas of the Average Run Length (ARL) when observations form a pure seasonal autoregressive of order pth (seasonal AR(p)) models with exponential distribution white noise on CUSUM chart are derived. The numerical results from explicit formulas and the numerical integration approach are presented. Our results illustrate that the explicit formulas can reduce computational times to evaluate the ARL when compared with the results obtained from the numerical integration approach. According to the proposed explicit formulas for the ARL, it is very useful in practical applications in order to design an optimal CUSUM chart.

4 tables, 19 ref

022443   Azis M I;Clements D L (Jurusan Matematika, Universitas Hasanuddin, Makassar 90245, Indonesia) : Boundary element method for transient heat conduction problem of nonhomogeneous anisotropic materials. Far East J mathl Sci 2014, 89(1), 51-67.

A boundary element method (BEM) is obtained for the nonlinear transient heat conduction problem of inhomogeneous anisotropic media.

2 illus, 3 tables, 8 ref

022442   AnandRao J;Ramesh Babu P;Srinivasa Raju R; Sheri S R (Mathematics Dep, Univ College of Science, Osmania Univ, Hyderabad-500 007, Email: ramesh.patkar@yahoo.in) : Heat and mass transfer effects on an unsteady MHD free convective chemical reacting fluid flow past an infinite vertical accelerated plate with constant heat flux. J Energy Heat Mass Transfer 2014, 36(3), 237-57.

The study of this paper to investigate the effects of heat and mass transfer on an unsteady magnetohydrodynamicfree convective chemical reacting fluid flow of a viscous incompressible fluid past an infinitevertical accelerated plate embedded in porous medium with constant heat flux in the presence of transverse magnetic field. The governing equations are solved by Galerkin finite element method. The results are obtained for velocity, temperature, concentration, Skinfriction, Nusseltnumber and Sherwood number. The effects of different flow parameters on the flow variables are discussed and presented through graphs and tables. The numerical results for particular cases were compared with the available solution in the literature and the results are found to be in good agreement.

15 illus, 4 tables, 29 ref

022441   Alamoush A G;Darus M (School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia Bangi, 43600 Selangor D. Ehsan Malaysia, Email: adnan_omoush@yahoo.com) : On coefficient estimates for BI-univalent functions of fox-wright functions. Far East J mathl Sci 2014, 89(2), 249-62.

In this paper, we introduce and investigate a new subclass of the function class Σ of bi-univalent functions of the Fox-Wright function type denoted as hlΣ^{(α_i, (β_i) (k, β; h) in the open unit disk U. We estimate the coefficients | a₂ | and | a₃ | for the newly subclass of functions.}

18 ref

022440   Ahmed S;Kalita K (Heat Transfer and Fluid Mechanics Research, Mathematics Dep, Computing Rajiv Gandhi Univ, Rono Hills, Itanagar-791 112) : A sinusoidal fluid injection/suction on MHD three-dimensional couette flow through a porous medium in the presence of thermal radiation. J Energy Heat Mass Transfer 2013, 35(1), 41-67.

This work is focused on modeling of three-dimensional Couette flow of a viscous incompressible electrically conducting, Newtonian and radiating fluid between two long horizontal parallel flat plates filled with porous medium in the presence of a transverse magnetic field. The stationary plate is subjected to a transverse sinusoidal injection velocity distribution while the uniformly-moving plate is subjected to a constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The fluid is an optically-thick gray gas, absorbing-emitting but nonscattering medium and the Rosseland approximation is used to describe the radiative heat flux in the energy equation. The governing equations of the Couette fluid flow along with the boundary conditions are first converted into dimensionless form by a non-similar transformation, and then the resulting system of coupled non-linear partial differential equations is solved by series solution method. Comparisons with previously published works are performed and the results are found to be in excellent agreement. Numerical results for the velocity and temperature profiles as well as the skin-friction coefficients and the heat fluxes under various parametric conditions are reported and discussed. An increase in the permeability and suction/injection parameter is found to escalate the main flow velocity throughout the channel. Further, a growing thermal radiation or magnetic parameter decelerates the main flow velocity throughout the channel. In addition, the heat flux rate at the plate at rest is decreased as the thermal radiation increases. Increasing porosity enhances the x-component and reduces the z-component of the skin-friction coefficient at the wall at rest. The acquired knowledge in our study can be used by designers to control Magnetohydrodynamic (MHD) flow as suitable for certain applications. Possible applications of the present study include laminar magneto-aerodynamics, materials processing and MHD propulsion thermo-fluid dynamics.

9 illus, 2 tables, 49 ref

022439   Ahmed N;Das K K (Mathematics Dep, Gauhati Univ, Guwahati-781 014, Email: saheel_nazib@yahoo.com) : Soret effect on an MHD free convective mass transfer flow past an accelerated vertical plate with chemical reaction. J Energy Heat Mass Transfer 2013, 35(2), 133-47.

An exact solution to the problem of an MHD heat and mass transfer flow with Soret effect past an accelerated infinite vertical plate embedded in a porous medium in presence of chemical reaction is presented. A magnetic field of uniform strength is applied normal to the plate directed into the fluid region. The governing equations are solved by Laplace-Transform technique in closed form. The expressions for the velocity field, the temperature field, the concentration field, the coefficient of skin friction at theplate in the direction of flow and the coefficient of heat and mass transfer in terms of Nusselt number and Sherwood number at the plate are obtained and their nature are demonstrated graphically for different values of the parameters involved in the problem. It is found that the Soret effect or thermal diffusion effect has a significant role in controlling the flow and heat and mass transfer characteristics.

21 illus, 14 ref

021491   Wadi A S;Dimian M F;Ibrahim F N (Mathematics Dep, AinShams University, Cairo, 0020, Egypt, Email: ali.wadi4@gmail.com ) : Analytical solutions for one-dimensional advection-dispersion equation of the pollutant concentration. J Earth Syst Sci 2014, 123(6), 1317-24.

We present simple analytical solutions for the unsteady advection-dispersion equations describing the pollutant concentration C(χ, t) in one dimension. The solutions are obtained by using Laplace transformation technique. In this study we divided the river into two regions χ ≤ 0 and χ≥0 and the origin at χ = 0. The variation of C(χ, t) with the time t from t = 0 up to t → ∞ (the steady state case) is taken into account in our study. The special case for which the dispersion coefficient D = 0 is studied in detail. The parameters controlling the pollutant concentration along the river are determined.

5 illus, 24 ref

021490   Tiwari H;Sharma N (NO, , ) : Statistical study of turbulence near piano key weir. J expl appl Mech 2014, 5(3), 16-28.

Piano Key Weirs are more efficient than the traditional Labyrinth weir and Piano Key Weirs can be an interesting solution for increasing the active storage of reservoir or for improving the safety of dam during extreme flood. This technology helps to reduce the reservoir sedimentation. It will also help in minimizing the sub-mergence effect. Flushing is vital for the preservation of long-term storage in reservoirs. However, downstream impacts such as turbidity act as a constraint in the planning and operation of sediment flushing. Physics especially about turbulence phenomena will be helpful to decide the design criteria. Turbulent mixing is an important process controlling the descent rate, water mass modification and volume transport. Under stable conditions dissipation essentially balances shear production, while turbulent transport and buoyant production are of secondary importance. Under unstable conditions, dissipation slightly exceeds the total production, and energy is also lost at a substantial rate due to upward export by the turbulence. Theoretical analysis and prediction of turbulence has been problem of fluid dynamics due to random or chaotic nature of turbulence phenomena. Because of this unpredictability, it has been usual to work with the time averaged forms of the governing equations, which inevitably results in terms involving higher order correlations of fluctuating quantities of flow variables. Turbulence is a very complex phenomenon so near PKW occurrence need extensive laboratory experiment and analysis of these results through some statistics will be reliable. This paper deals with issues, gaps and scope of statistical turbulence study near PKW.

021489   Singh A K;Singh U;Singh R R;Singh A K;Tandon P K;Singh N P (Mathematics Dep, C L Jain (P G) College, Firozabad-283 203, Uttar Pradesh, Email: aksinghnpsingh@rediffmail.com) : Hydrodynamically and thermally fully developed MHD flow between two horizontal plates: analysis with viscous dissipation Joule heating and Constant Heat Flux Boundary Conditions. J Energy Heat Mass Transfer 2014, 36(2), 135-64.

In the present paper hydrodyn,mically and thermally fully developed laminar flow of viscous, incompressible, conducting, Newtonian fluid through two horizontal parallel plates is investigated under the influence of transversely applied uniform magnetic field. The effect of viscous dissipation, Joule heating and constant heat flux boundary conditions on the heat transfer and temperature distribution is taken into account, whereas axial heat conduction is neglected. The thermal boundary conditions are considered for three cases; (i) when the upper and the lower plates are kept at different constant heat fluxes, (ii) when the upper and the lower plates are at the same constant heat flux and (iii) the upper plate is at constant heat flux and the lower plate is insulated. Analytical solutions for the velocity field and the temperature distribution are obtained for all the three cases. The results of the study are evaluated numerically and discussed through graphs and tables for different numerical values of the parameters entered into the problem. The results of Francisca and Tso [15] are deduced as particular cases of the present study.

8 illus, 4 tables, 33 ref

021488   Sharma P R;Mehta T (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Oscillatory flow of a visco elastic electrically conducting fluid and heat transfer through porous medium filled in a vertical channel in the presence of chemical reaction and heat source. Int J latest Technol Engng Mgmt appl Sci 2014, 3(10), 138-50.

Aim of the paper is to investigate the effect of chemical reaction and heat source on oscillatory flow of a visco-elastic electrically conducting fluid and heat transfer through a channel filled with saturated porous medium. The visco-elastic fluid model suggests rheological liquids encountered in biotechnology (medical creams) and chemical engineering. The rheological model introduces additional terms into the momentum equation. It is assumed that one plate is moving, fluid has small electric conductivity and the electromagnetic force produced is very small. Numerical results for the velocity, temperature and concentration profiles for various physical parameters as well as the local skin' friction coefficient, local Nusselt number and Sherwood number are discussed numerically and presented graphically.

20 illus, 3 tables, 27 ref

021487   Sharma P R;Choudhary S (Mathematics Dep, University of Rajasthan, Rajasthan) : Radiation and chemical reaction effects on unsteady slip flow over a semi infinite vertical porous plate embedded in a porous medium in the presence of inclined magnetic field. Int J latest Technol Engng Mgmt appl Sci 2014, 3(12), 17-24.

Unsteady free convective viscous slip flow of an incompressible, electrically conducting and radiating fluid over a semi infinite vertical porous plate embedded in a porous medium in the presence of inclined magnetic field is investigated. The resulting. non-linear system of coupled partial differential equations is solved by using regular perturbation technique. The effects of various physical parameters on velocity, temperature and concentration profiles as well as on the skin friction coefficient, Nusselt number and Sherwood number are discussed numerically and shown through graphs and table.

13 illus, 1 table, 15 ref

021486   Parikh A K;Mehta M N;Pradhan V H (Mathematics Dep, C U Shah University, Wadhwan city-363 030) : Mathematical modeling and analysis of fingero-imbibition phenomenon in homogeneous porous medium with magnetic field effect in vertical downward direction. Int J latest Technol Engng Mgmt appl Sci 2014, 3(10), 17-23.

The present paper discusses the Fingero-Imbibition phenomenon arising in two immiscible phase (Inter with magnetic particles and oil) flow through homogeneous porous media with the effect of variable magnetic field in vertical downward direction which may arise during secondary oil recovery process on account of simultaneous occurrence of two important phenomenon viz., Instability (fingering) and Imbibition. The effect of variable magnetic field is chosen in such a way that it increases the velocity of injected conductive fluid by gradient of μH^{2/8π where μ is permeability of magnetic field H, Verma (1980). The hypothetical hydrological situation assumed here for the present investigated mathematical model describing fingero-imbibition phenomenon which, as great importance in secondary oil recovery process. Mathematical formulation leads to non linear partial differential e lion. The classical exact solution is obtained by using generalized separable method in terms of quadratic polynomial by using appropriate initial and boundary conditions and s physical interpretation is given with numerical tabulated values and graphical presentation.}

3 illus, 1 table, 15 ref

021485   Mukherji P (Gokhale Memorial Girls' College, , Kolkata) : A remarkable technique of solving linear ordinary differential equations using linear algebra. Sci Cult 2015, 81(1-2), 23-6.

4 ref

021484   Chena Ram;Choudhary P (Mathematics & Statistics Dep, J N V University, Jodhpur, Rajasthan) : r-fractional calculus and generalized k- wright type function. Int J latest Technol Engng Mgmt appl Sci 2014, 3(12), 99-102.

This paper is devoted to study of r- Fractional calculus of generalized k- Wright type function introduced by Ram et al (4).

6 ref

021483   Basavarajappa N S;Anil Kumar K N (Mathematics Dep, Bapuji Institute of Engineering & Technology, Davangere-577 004) : Conservative concircular curvature tensor with respect to semi-symmetric metric connection on k-contact and trans-sasakian manifolds. Int J latest Technol Engng Mgmt appl Sci 2015, 4(3), 104-9.

Obtain results on the vanishing of divergence of Concircular curvature tensor with respect to semi-symmetric metric connection on K-contact and trans-Sasakian manifolds.

18 ref