024208   Cho Y U (Mathematics Dep, College of Education Silla Univ, Pusan 617-736, Korea, Email: yucho@silla.ac.kr) : Semidirect sum of right substructures in near-rings. Far East J mathl Sci 2011, 55(1), 85-90.

In this paper, authors begin with some right substructures of near-rings, may define the right semidirect sum of near-rings. Investigated that every near-ring can be decomposed with right semidirect sum of right ideal by right R-subgroup, and then give some examples.

5 ref

024207   Cho Y U (Mathematics Dep, College of Education, Silla Univ, Pusan-617 736, Korea, Email: yucho@silla.ac.kr) : Centralizer near-ring from groups. Far East J mathl Sci 2011, 54(2), 217-23.

In this paper, we denote that R is a near-ring and G is an R-group. We initiate the study of faithful R-group, the substructures of R and G. Next, we investigate some properties of centralizer near-ring from groups.

5 ref

024206   Bordoloi R (Mathematics Dep, Bilasipara College, Bilasipara-783 348, Email: rajubordoloi@yahoo.co.in) : Square root of a few class of p-adic integers. Far East J mathl Sci 2011, 56(1), 7-21.

In this paper, an expository study has been carried over to a few class of recurred p-adic integers, which exhibits the same squares. In particular, we have shown that it is really the contributions from the sequential structure of p-adic integers that help us to determine the square root of a good number of p-adic integers.

8 ref

024205   Bian X;Yun Z (Fundamental Sciences Dep, Yancheng Institute of Technology, Yancheng, Jiangsu-224 051, P.R. China, Email: xiaoxiabian@yahoo.com.cn) : Metrizability of stratifiable spaces. Far East J mathl Sci 2011, 56(1), 83-94.

In the present paper, authors prove that a regular space (or a regular k-space) X is metrizable if and only if X is a stratifiable space with (NF) property (or (CF) property), and a regular space X is an ℵ-space (or a σ-space) if and only if X is a k-semistratifiable space (or a semistratifiable space) with (NF) property. Some applications of the characterizations of metrizable spaces are given.

12 ref

024204   Bao Z;Zhang Y;Liu Z (School of Mathematics, Liaoning Normal Univ, Dalian-116 029, P.R. China, Email: zhhbao@126.com) : Note on a class of discrete time delayed renewal risk processes. Far East J mathl Sci 2011, 54(2), 193-200.

The discounted penalty function, introduced by Gerber and Shiu [2], is considered for a class of discrete time delayed renewal risk processes, where it is expressed in terms of the same discounted penalty function in the ordinary discrete time renewal risk model. The result obtained in the present paper generalizes known special case.

7 ref

024203   Anichini G;Conti G (NO, Firenze Univ, Facolta di Ingegneria, Italy, Email: giuseppe.anichini@unifi.it) : Existence of solutions for quadratic integral equations on unbounded intervals. Far East J mathl Sci 2011, 56(2), 113-22.

In this paper, authors investigate the existence of a solution on a semi-infinite interval for a quadratic integral equation of Urysohn or Volterra type in Frechet spaces using a fixed point theorem due to Petryshyn and Fitzpatrick.

22 ref

024202   Amir A K;Astuti P;Muchtadi Alamsyah I;Irawati (NO, Algebra Research Group Faculty of Mathematics and Natural Sciences Ins, 40132, Indonesia, Email: s301_amir@students.itb.ac.id) : On maximal orders and factor rings of ore extension over a commutative dedekind domain. Far East J mathl Sci 2011, 55(1), 21-30.

Let R = d[x; σ, δ] be an Ore extension over a commutative Dedekind domain D, where σ is an automorphism on D. Chamarie [2] implicitly proved that R is a maximal order. In this paper, authors give an explicit and simpler proof. Then we use that result to study the prime factor ring of d[x; σ, δ] over the prime ideals.

6 ref

024201   Alattass A (Mathematics Dep, Faculty of Science Hadramout Science and Technology Univ, P.O. Box 50663, Mukalla, Yemen, Email: alattassali@yahoo.com) : (Amply) δ_M-supplemented modules. Far East J mathl Sci 2011, 56(2), 123-35.

Let M be a right module over a ring R. In the present paper, several properties of (amply) δ_M -supplemented modules are proved. It is shown, among others, that The class of (amply) δ_M-supplemented modules is closed under taking homomorphic images; Every π-projective module in σ[M] is an amply δ_M -supplemented module; Every module in σ[M] is an amply δ_M -supplemented module if and only if every module in σ[M] is a δ_M-supplemented module; and A projective module in σ[M] is an amply δ_M -supplemented module if and only if it is a δ_M -supplemented module and also investigate the interconnections between δ_M -supplemented modules and δ_M -semiperfect modules.

8 ref

024200   Al-Saidi N M G;Said M R M;Ahmed A M (Applied Sciences Dep, Applied Mathematics, Technology Univ, Baghdad, Iraq, Email: nadia_alsaidi@hotmail.com) : About fuzzy fixed point theorem in the generaized fuzzy fractal space. Far East J mathl Sci 2011, 53(1), 53-64.

Balanch fixed point theorem has applications in several branches of science. Many authors prove this theorem in different types of fuzzy metric spaces and fuzzy fractal spaces. The aim of this paper is to prove the Banach fixed point theorem in a new generalized space called multi fuzzy fractal space.

2 illus, 16 ref

024199   Akinfenwa O;Jator S;Yao N (College of Coputer Science and Technology, Harbin Engineering Univ, Harbin 15001, P.R. China, Email: akinolu35@yahoo.com) : Seventh-order hybrid multistep integrator for second order ordinary differential equations. Far East J mathl Sci 2011, 56(1), 43-66.

Presented a new block hybrid linear multistep method with four off-step points of order m = (7, 7, 7, 7, 7, 8)ⁿ (T is the transpose) for the direct solution of second order ordinary differential equations of the forms y" = f(t, y) and y" = f(t, y,y'), y(t₀) = y₀ = y'ⁿ (t₀) = y'₀. The block method is obtained from a single hybrid linear multistep method with continuous coefficients derived via interpolation and collocation procedures. The stability properties of the block method are discussed. Numerical results obtained using the proposed method reveal that it compares favorably with existing methods in the literature.

11 tables, 48 ref

024198   Akinfenwa A O;Jator S N;Yao N M (College of Computer Science and Technology, Harbin Engineering Univ, Harbin 15001, P.R. China, Email: akinolu35@yahoo.com) : On the 7-step backward differentiation formula with continuous coefficients for stiff systems. Far East J mathl Sci 2011, 56(1), 23-41.

Seven-step Backward Differentiation Formula (BDF) with continuous coefficients is constructed and used to generate the standard BDF and additional methods; which are combined as a Block Backward Differentiation Formula (BBDF) for solving stiff Initial Value Problems (IVPs). It is well known that the BDFs are zero-stable for 1 ≤ k ≤ 6 and unstable for k ≥ 1, where k is the step number. We show that the instability of the 7-step BDF is improved to L0 -stability in the sense of Cash [4] via its block form; hence the BBDF can be extended to solve very large systems of Ordinary Differential Equations (ODEs) resulting from the semi-discretization of parabolic Partial Differential Equations (PDEs). The BBDF has order 7 in time and self-starting. The method numerical results produced by the BBDF show that the method is accurate and efficient.

8 tables, 25 ref

024197   Abel M (Institute of Mathematics, Tartu Univ, 2-615 J. Liivi Str., 50409 Tartu, Estonia, Email: mart.abel@ut.e) : (δ, ε)-double derivations on topological; algebras. Far East J mathl Sci 2011, 54(1), 87-95.

Several results about (δ, ε)-double derivations and δ-double derivations are generalized from the case of Banach algebras to the case of general topological algebras. Mainly, the problems concerning continuity of linear maps are considered.

2 ref

023123   Wang C Y;Guan J;Wang B Y (Mathematics Dep, Northeast Petroleum University, Daqing 163318, China, Email: chunyanmyra@163.com) : The classification of single travelling wave solutions to the Camassa-Holm-Degasperis-Procesi equation for some values of the convective parameter. Pramana J Phys 2011, 77(4), 759-64.

By the complete discrimination system for the polynomial, we give the classification of single travelling wave solutions to the Camassa-Holm-Degasperis-Procesi equation for some values of the convective parameter.

^ssc13 ref

023122   Vijaya Kumar A G;Rajashekara Goud Y;Nanda Gopal K;Varma S V K (Mathematics Dep, Sree Vidyanikethan Engineering College, Tirupati, A.P., Email: agvijaykumar1729@gmail.com) : Thermal diffusion and radiation effects on unsteady MHD free convection flow past an inclined plate with variable temperature and mass diffusion in the presence of heat source/sink. Ultra Scient phys Sci-Sect B 2012, 24(3), 517-28.

An analytical study is performed is to investigate thermal diffusion and radiation effects on unsteady MHD flow past an inclined plate with variable temperature and mass diffusion in the presence of heat source or sink under the influence of applied transverse magnetic field. The fluid considered here is a gray, absorbing/emitting radiation but a non-scattering medium. At time t<62>0, the plate is exponentially accelerated with a velocity u = u₀ exp(a't') in its own plane. And at the same time, the plate temperature and concentration levels near the plate raised linearly with time t. The dimensionless governing equations involved in the present analysis are solved using the Laplace transform technique. The velocity, temperature, concentration, the rate or heat transfer and the rate of mass transfer are studied through graphs and tables in terms of different physical parameters, like magnetic field parameter (M), radiation parameter (R), heat source parameter (H), Schmidt parameter (Sc), inclination parameter (α), soret number (So), Prandtl number (Pr), thermal Grashof number (Gr), mass Grashof number (Gm) and time (t).

12 illus, 4 tables, 15 ref

023121   Tripathi A;Ravindra Kumar;Singh K K (Mathematics Dep, K.K.P.G. College, Etawah (U.P.), Email: rkpal.maths@gmail.com) : Study of oscillatory flow of blood through porous medium in a stenosed artery in the presence of magnetic field. Ultra Scient phys Sci-Sect B 2012, 24(3), 439-44.

Purpose of this paper is to study the effect of magnetic field on oscillatory flow of blood through porous medium in a rigid tube with a mild stenosis. Here Authors assumed that the blood behaves as a Newtonian fluid and the maximum height of the roughness is very small compared with the radius of the unconstricted tube. The expression are given for the instantaneous flow rate, resistive impedance and wall shear stress.

2 illus, 13 ref

023120   Siswadi;Bakhtiar T (Mathematics Dep, Bogor Agricultural Univ, Jl. Raya Darmaga, Bogor 16880, Indonesia, Email: siswadi@inrr.org) : Goodness-of-fit of biplots via procrustes analysis. Far East J mathl Sci 2011, 52(2), 191-201.

This paper provides a direct derivation of the goodness-of-fit of biplots via Procrustes analysis. A series of transformations, namely, translation, rotation and dilation, is carried out preceding the calculation of Procrustes distance. It is validated that the goodness-of-fit measures of data and object matrices can be restored. Based on this concurrence, author suggested a new expression for goodness-of-fit measure of variable matrix to strengthen the accuracy of the current form. showed the association between goodness-of-fit coefficients of biplots analysis and principal component analysis.

1 illus, 5 ref

023119   Shukla D P;Tiwarib S K;Chetan (Mathematics Dep, Govt P G Science College, Rewa, Madhya Pradesh, Email: shukladpmp@gmail.com) : Fixed point theorem in Banach space. Indian J scient Res 2012, 3(1), 177-8.

Established fixed point theorem with help of self mapping which satisfying contractive type of condition in Banach space.

4 ref

023118   Sharma G K;Varshney N K (Mathematics Dep, S.V. College, Aligarh, U.P.) : Effect of heat transfer on MHD flow of visco-elastic fluid of an arbitrary inclined plane. Ultra Scient phys Sci-Sect B 2012, 24(3), 505-10.

Effect of heat transfer on the flow of visco-elastic conducting fluid of Rivlin - Ericksen type flowing down an inclined plane in presence of a transverse magnetic field is investigated. This type of problem finds application in many technological and engineering fields such as rocket propulsion systems, space craft re-entry aerothermody-namics, cosmical flight aerodynamics, plasma physics, Glass production and furnace engineering. Velocity of the flow has been presented for various parameters. In this study velocity of fluid increases with the increase in G_r (Grashof number), but it decreases with the increase in H (Hartmann number) and P_r (Prandtl number).

3 illus, 3 tables, 7 ref

023117   Sanjeev Kumar;Diwakar C S (Mathematics Dep, (Dr. B.R. Ambedkar Univ, Agra, Email: sanjeevibs@yahoo.co.in) : Biomagentic fluid dynamic model for the MHD couette flow between two infinite horizontal parallel porous plates. Ultra Scient phys Sci-Sect B 2012, 24(3), 483-8.

A model of biomagentic fluid dynamics, which is suitable for the description of the MHD Couette flow of a viscous-incompressible fluid, is discussed in this work. Take two infinite horizontal parallel porous flat plates. The upper plate is subjected to a constant suction while the lower plate is to a transverse sinusoidal injection along with the velocity distribution. In this work finite difference method is used for solving the non-linear partial differential equations and our results shows that the main flow component (U) decreases with the increase of Hartmann number (M) and the velocity decreases with the increases of the injection suction parameter (R). Here we also investigate the effects of Hartmann number (M) and suction parameter (R) along with the velocity and temperature distribution.

1 illus, 18 ref

023116   San H C;Majid Z A;Othman M;Suleiman M (Mathematics Dep, Faculty of Science & Institute of Mathematical Research, Putra Malaysi, 46400 UPM Serdang, Selangor Darul Ehsan, Malaysia, Email: chisan789@yahoo.com) : New technique of VSVO coupled block method for solving first order ODEs. Far East J mathl Sci 2011, 52(1), 9-23.

Coupled block method is developed for solving first order ordinary differential equations (DDEs) using variable step size and order (VSVO). The coupled block method will consist of two proposed block methods, i.e., the two point three step block method of order six and the three point four step block method of order eight. These methods will estimate the numerical solutions at two and three points simultaneously within a block. The changing of block in the interval will allow varying the order. The stability of the methods is also studied. The performance of the proposed code suggested a significant improvement of the code over the existing block method.

7 illus, 3 tables, 11 ref

023115   Prasad V;Nagaich M;Varshney N K (Mathematics Dep, D.S. College, Aligarh, U.P.) : Effect of porous medium on flow of dusty incompressible visco-elastic second order oldroyd fluid through rectangular channel. Ultra Scient phys Sci-Sect B 2012, 24(3), 511-16.

Purpose of present study is to analyze the effect of porous medium on unsteady flow of dusty visco-elastic second order Oldroyd fluid with transient pressure gradient through a rectangular. Here we considered the second order Oldroyd fluid and investigate the same problem in this new visco-elastic model. The numerical expressions of the liquid velocity and particle velocity have been given.

18 ref

023114   Patra B K;Biswal S;Mishra A P (NO, NM Institute of Engineering and Technology, Sijua, Bhubaneswar-19) : Heat and mass transfer effects on the marginal stability of rotating dusty ferro fluid flowing through a porous medium. Ultra Scient phys Sci-Sect B 2012, 24(3), 469-82.

Deals with the theoretical investigation of the heat and mass transfer effects on the marginal stability of a rotating ferrofluid heated below saturating a porous medium. For a flat fluid layer contained between two free boundaries, an exact solution is obtained using a linear stability analysis theory normal mode analysis method. For the case of stationary convection, the effect of various parameters like medium permeability, dust particle coupling parameter and conduction parameter has been analyzed. The critical thermal Raleigh number for the onset of instability is also determined numerically. Results are depicted graphically. It is observed that the critical thermal Rayleigh number is reduced because the heat capacity of clean fluid is supplemented by that of the dust particles. The principle of exchange of stabilities is found to hold true for the ferrofluid with internal angular momentum saturating porous medium in the absence of dust particles, coupling parameter and micro inertia. The oscillating modes are introduced due to the presence of dust particles, coupling parameter and micro inertia, which were nonexistent in their absence. The sufficient conditions for the non existence of stability are also obtained.

6 illus, 35 ref

023113   Park J (Mathematics Dep, Aanseo Univ, Seosan-si, Chungnam-do, 356-706, Korea, Email: jkpark@hanseo.ac.kr) : Hermite-hamdard type inequalities for differentiable (s,m)- convex mappings in the second sense. Far East J mathl Sci 2011, 52(1), 57-73.

In this paper, the author obtained some generalized properties of Hermite-Hadamard type inequalities for differentiable (s, m) -convex mappings in the second sense.

13 ref

023112   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do, 356-706 Korea, Email: jkpark@hanseo.ac.kr) : New generalization of Simpson's type inequalities for twice differentiable convex mappings. Far East J mathl Sci 2011, 52(1), 43-55.

In this paper, author obtained some generalizations and refinements of Simpson's type inequalities for twice differentiable convex mappings.

11 ref

023111   Park J (Mathematics Dep, Hanseo Univ, Seosan-si, Chungnam-do-356 706, Korea, Email: jkpark@hanseo.ac.kr) : Some inequalities of hermite-hadamard type via differentiable (s,m)- convex mappings. Far East J mathl Sci 2011, 52(2), 209-21.

In this article, the author obtains some properties of Hermite-Hadamard type inequalities for differentiable (s, m) -convex mappings in the second sense, and establishes some new integral inequalities analogous to the well-known classical Hadamard's inequalities.

12 ref

023110   Ostad K;Habibi M;Safari F (NO, Islamic Azad Univ, Branch of Dehdasht, P.O. Box 7571763111, Dehdasht, Iran, Email: ostad.k@iaudehdasht.ac.ir) : On n-tuples of weighted shifts to be topologically mixing. Far East J mathl Sci 2011, 52(2), 203-8.

In this paper, author characterized the topologically mixing to a tuple of unilateral backward weighted shifts on a Frechet space.

11 ref

023109   Nascimento K D;Grados L R (Mathematics and Statistics Dep, State Ponta Grossa Univ, 84030-900 Ponta Grossa, Brazil, Email: izaeldn@hotmail.com) : Boundaries for algebras of holomorphic functions on the preduals of the lorentz sequence spaces. Far East J mathl Sci 2011, 52(1), 25-42.

Let IB be a complex Banach space and let B_E be the closed unit ball of E. Consider the Banach algebra defined by A_b(B_E) = (↵ : B_E → C : ↵ is continuous and bounded in B_E and holomorphic in its interior) endowed with the usual operations and the usual sup norm. In this paper, And define a family (X_p) of preduals of Lorentz sequence spaces and we give a complete description of the Shilov boundary of A_b,(B_{p, F}), for every finite dimensional subspace X_{p, F} of X_p. Additionally, we present some sufficient conditions for a set to be a boundary for A_b(B_xp) and also we show that the Shilov boundary for this algebra does not exist.

16 ref

023108   Nakazi T;Yamamoto T (Mathematics Dep, Hokusei Gakuen Univ, Sapporo 004-8631, Japan, Email: z00547@hokusei.ac.jp ) : Three dimensional Q-algebras. Far East J mathl Sci 2011, 52(2), 121-48.

Describes the structure of a 3-dimensional commutative Banach algebra β with identity by the classification of β through the number of the elements of the maximal ideal space M_β. It is proved that β is isomorphic to a Q-algebra of a bidisc algebra. As an application, we study BQ-algebras and CQ-algebras which are generalizations of Q-algebras. A BQ-algebra (resp. CQ-algebra) is defined to be a commutative Banach algebra β with identity such that there exists a bounded (resp. contractive) isomorphism from a Q-algebra to B.

12 ref

023107   Iyigun E (Mathematics Dep, Faculty of Art and Sciences Uludag Univ, Gorukle 16059, Bursa, Turkey, Email: esen@uludag.edu.tr) : Some curves in the 3-dimensional lightlike cone Q<. Far East J mathl Sci 2011, 52(2), 223-32.

In this paper, author gave a Frenet curve and W-curves in the 3-dimensional lightlike cone Q³. Some results related to these curves are obtained.

6 ref

023106   Iswadi H;Baskoro E T;Simanjuntak R (MIPA Dep, Surabaya Univ, Gedung TG Lantai 6 Jalan Raya Kalirungkut Surabaya 60292 Indonesia, Email: hazrul_iswadi@yahoo.com) : On the metric dimension of corona product of graphs. Far East J mathl Sci 2011, 52(2), 155-70.

For an ordered set W = (w₁, w₂, ..., w_k) of vertices and a vertex v in a connected graph G, the representation of v with respect to W is the ordered k-tuple r(vW) = (d(v, w₁), d(v, w₂), ..., d(v, w_k)), where d(x, y) represents the distance between the vertices x and y. The set W is called a resolving set for G if every vertex of G has a distinct representation. A resolving set containing a minimum number of vertices is called a basis for G. The metric dimension of G, denoted by dim(G), is the number of vertices in a basis of G. A graph G corona H, GOH, is defined as a graph which is formed by taking n copies of graphs H₁, H₂, ..., H_n of H and connecting ith vertex of G to the vertices of H_i. In this paper, we determine the metric dimension of corona product graphs GOH, the lower bound of the metric dimension of K₁ + H and determine some exact values of the metric dimension of GOH for some particular graphs H.

19 ref

023105   Durrani I R (Faculty of Basic Sciences, Gujrat Univ, Pakistan) : KDV6: an integrable system. Bull pure appl Sci 2012, 31D(1), 89-101.

K²S²T[5] recently derived a new 6th-order wave equation KdV6: (ℵ_x² + 8u_x + 4u_xx) (u_t + u_xxx + 6u²_x) = 0, and thereby found a llnear problem and an auto-Backlund transformation for it, and conjectured its integrability in the usual sense. Proves this conjecture by constructing an infinite commuting hierarchy KdVn with a common infinite set of conserved densities. A general construction is presented applicable to any bi-Hamiltonian system (such as all standard Lax equations, continuous and discrete) providing a nonholonomic perturbation of it. This perturbation is conjectured to preserve integrability. That conjecture is verified in a few representative cases: the classical long-wave equations, the Toda lattice (both continuous and discrete), and the Euler top.

12 ref

023104   Dehghani Zadeh F (Mathematics Dep, Islamic Azad Univ, Yazd Branch, Yazd, Iran) : Finiteness properties of generalized local cohomology modules. Far East J mathl Sci 2011, 52(2), 149-54.

Membership of the generalized local cohomology modules H_αⁿ(M, N) of two R-modules M and N with respect to an ideal a in certain Serre subcategories of the category of modules is studied from below i <60> n.

8 ref

023103   Cristoforis M L D;Musolino P (Matematica Pura ed Applicata Dep, Degli Studi di Padova Univ, Via Trieste 63, Padova 35121, Italy) : Perturbation result for periodic layer potentials of general second order differential operators with constant coefficients. Far East J mathl Sci 2011, 52(1), 75-120.

It was shown that periodic layer potentials associated to parameter dependent analytic families of fundamental solutions of second order differential operators with constant coefficients, depend real-analytically upon the density (or moment) function and on a suitable parameterization of the supporting hypersurface and on the parameter.

29 ref

023102   Caragiu M;Risch A (Mathematics and Statistics Dep, Ohio Northern Univ, 525 S Main Street, Ada, Ohio, 45810, U.S.A, Email: m-caragiu.1@onu.edu) : Euler-fibonacci sequence. Far East J mathl Sci 2011, 52(1), 1-7.

Presented several computational results and conjectures involving an Euler-Fibonacci sequence (X_n)_n ≥0 defined as follows: X₀ = 0, X₁ = 1 and X_n = ϕ(X_n-1 + X_n-2 + 1) thereafter. The term X_n turns out to be even whenever n ≥ 3, while the inequality X_n ≤ F_n holds true for all n. The computation of the first 500 terms of the Euler-Fibonacci sequence, with X₅₀₀ having 91 digits, suggests a series of interesting questions concerning the congruence classes of X_n modulo 4, and the behavior of the consecutive quotients Q_n = X_n+1/X_n for n ≥ 1.

3 illus, 9 ref

023101   Beaula T;Partheeban (Mathematics Dep, T.B.M.L. College, Porayar-609 307) : Fuzzy analysis of the ravages and losses caused by Tsunami at Karaikal region. Ultra Scient phys Sci-Sect B 2012, 24(3), 497-504.

In this article the authors attempted to identify the part of the coastal area affected much and to ascertain the group of affected people (based on region) due to Tsunami in Karaikal district during the year 2004.

9 illus, 6 tables, 5 ref

023100   Barry M;Bazubwabo E;Diop P C (Mathematiques et Informatique Dep, Faculte des Sciences et Techniques, Cheikh Anta Diop de Dakar Univ, Senegal, Email: mansabadion1@hotmail.com) : On TFR-DUO rings. Far East J mathl Sci 2011, 52(2), 179-89.

Let R be a ring. Then a unital left R-module _RM is said to have property (7) if every injective endomorphism of _RM is an automorphism. The ring R is called a left (right) FGI-ring if every left (right). R-module with property (I) is finitely generated: R is called an FGI-ring if it is both a left and a right FGI-ring. A ring R is called duo-ring if every left (right) ideal of R is a two-sided ideal. If _RM is a left R-module, then author denote M_R⁸¹ = Hom(_RM, _RR) and _RM^81,81 = Hom(M⁸¹_R, R_R). The R-module _RM is called a reflexive module if the natural homomorphism _RM → _RM^81,81 x → x^81,81 : M_R⁸¹→ R ↵ → x⁸¹ (↵) = ↵(x) is an isomorphism. The ring R is called a left (resp. right) TFR-ring if every left (resp. right) R-module is reflexive if and only if it is finitely generated. The ring R is called a TFR-ring if R is both a left and a right TFR-ring. In this paper, we first give a characterization of a TFR-duo ring. Then we prove that a local duo-ring R is TFR if and only if R is an Artinian self-injective ring. Finally, if R is a local duo-ring with maximal ideal J such that J² = (0), then R is a TFR-ring if and only if R is an FGI-ring.

6 ref

023099   Ansari-Toroghy H;Keyvani S (Mathematics Dep, Faculty of Science, Guilan Univ, P.O. Box 41335-19141, Rasht, Iran, Email: ansari@guilan.ac.ir) : Dual notion of divisible modules. Far East J mathl Sci 2011, 52(2), 171-8.

In this paper, author introduced the dual notion of divisible (that is, codivisible) modules over a commutative ring and studied the some properties of this new class of modules.

6 ref

022031   Yadav V K (Mathematics Dep, V.S.S.D. (P.G.) College, Kanpur-208 002, Email: vinodkumaryadav3@gmail.com) : Note on the form of wave equation used in Harish-Chandra's paper 'motion of an electron in the field of a magnetic pole. Ultra Scient phys Sci-Sect A 2012, 24(1), 19-26.

Authors have tried to go through the research paper1 of Prof. Harish-Chandra with the intention of getting some idea of method of thinking and working of that great mathematician as well as of his Ph.D. thesis supervisor Prof. P.A.M. Dirac. The wave equation for the motion of an electron derived by Dirac has been transformed to the form suitable to the problem under consideration by Harish-Chandra. It is interesting and enjoying to clarify the steps directly written by him. For us it is a great job to fill the gaps to verify his steps. This paper is consequence of our effort in this direction.

5 ref

022030   Tripathi V N;Gupta A;Pathak Y (Mathematics Dep, SBPG College, Baragaon, Varanasi, Uttar Pradesh) : On the degree of approximation to a function by (N, p, q)_K (C,1) means of its fourier laguerre series. Ultra Scient phys Sci-Sect A 2012, 24(1), 165-70.

Superimposing the Nolund mean on Cesaro mean of order one, Singh and Khare have studied the degree of approximation to a function by Cesaro-Norlund mean of its Fourier Laguerre series under certain conditions.

5 ref

022029   Singh T (AMHD, SVNIT, Surat-395 007, Email: twinklerpatel@gmail.com) : Solution of longitudinal dispersion of miscible fluid flow through porous media by bender-schmidt method. Ultra Scient phys Sci-Sect A 2012, 24(1), 63-6.

Discusses the solution of longitudinal dispersion of miscible fluid flow in porous media by numerical method.

9 ref

022028   Singh J R;Kulkarni K (NO, School of Studies in Statistics Vikram Univ, Ujjain, M.P., Email: jrsingh@gmail.com) : Effect of Yule's process on the power of X-chart. Ultra Scient phys Sci-Sect A 2012, 24(1), 227-34.

Attempt has been made to study the effect of Yule's process on the Power of X-chart. Process measurements which are use in construction of X -chart involve several of errors. These include the inherent variability in the process and the error due to Yule's process.

2 illus, 2 tables, 8 ref

022027   Shrivastava K;Iyer V;Golhani A (Mathematics Dep, S.N.G.G.P.G. College, Bhopal, Email: kiranshri_1@rediffmail.com) : Order-dimensional topological spaces. Ultra Scient phys Sci-Sect A 2012, 24(1), 59-62.

Order - dimensional topological spaces are introduced. Several basic properties relating to order - dimension defined in terms of order of elements are established. The definitions of order of an element and of a set in a topological space are taken from and respectively.

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022026   Sahu G;Gupta B K;Aloney M R (NO, Babulal Tarabai Inst. of Research and Tech. Sagar and TIT, Bhopal) : Introduction of exact sequences and exact functor. Ultra Scient phys Sci-Sect A 2012, 24(1), 149-52.

Short exact sequence are fundamental objects in abelian categories, and one of the most basic ways to study an additive functor from one abelian category to another is to examine what it does to short exact sequences.

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022025   Rawat K S;Mukesh Kumar (Mathematics Dep, H.N.B. Garhwal Univ Campus Badshahi Thaul, Tehri, Garhwal-249 199, Email: mukesh.nautiyal2@gmail.com) : Motions in a Riemannian space and some integrability conditions. Ultra Scient phys Sci-Sect A 2012, 24(1), 9-14.

Author have studied Affine motion, Projective motion, Conformal motion, Integrability conditions of Killing equations also several theorems have been established and proved therein.

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022024   Rajputa Dwivedi P K;Aharwal R P;Jain A (CSA, Govt. P.G. College, Sehore, Email: dranilrajput@hotmail.com) : Weakly compatible maps of a complete metric space. Ultra Scient phys Sci-Sect A 2012, 24(1), 153-6.

The purpose of this paper is to prove a common fixed point theorem, from the class of compatible continuous maps to a larger class of maps having weakly compatible maps without appeal to continuity, which generalizes the results of Jungck, Fisher, Kang and Kim, Jachymski, and Rhoades.

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022023   Rajarajeswari P;Krishna Moorthy R (Mathematics Dep, Chikkanna Government Arts College, Tirupur-641 602, Email: p.rajarajeswari29@gmail.com) : Intuitionistic fuzzy weakly generalized irresolute mappings. Ultra Scient phys Sci-Sect A 2012, 24(1), 204-12.

The aim of this paper is to introduce and study the concepts of intuitionistic fuzzy weakly generalized irresolute mappings in intuitionistic fuzzy topological space. Investigates some of their properties.

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022022   Rabbani Q;Dixit S;Somvanshi T V S (Mathematics Dep, Integral Univ, Lucknow) : Applications of queueing process in economic literature with some models. Ultra Scient phys Sci-Sect A 2012, 24(1), 177-84.

In economic applications queuing processes as a subject that have been overlooked by researchers. The objective of this paper is to give economic insights of the queuing applications that have been tried over the years, as well as to propose some new ways of tackling the problem.

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022021   Pujar S S;Khairnar V J (Mathematics Dep, K. K. Wagh Institute of Engineering Education and Research, Panchavati, Nasik-422 003, Email: drsspujar@rediffmail.com) : On weak concircular symmetries of ε-trans Sasakian manifolds. Ultra Scient phys Sci-Sect A 2012, 24(1), 127-48.

The object is to study weakly concircular symmetric and weakly concircular Ricci symmetric ∈-Trans-Sasakian manifolds and the relationship among the 1 -forms A, B and D for locally symmetry in a weakly symmetric and Ricci symmetry of ∈ -Trans-Sasakian manifolds. Also the geometric meaning of 1-forms B and D for recurrency. Geometrical meaning for B and D for Ricci recurrency in a weakly Ricci symmetric ∈ -Trans-Sasakian manifolds.

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022020   Pujar S S;Khairnar V J (Mathematics Dep, K. K. Wagh Institute of Engineering Education and Research, Panchavati, Nasik-422 003, Email: drsspujar@rediffmail.com) : On weakly φ-Ricci symmetric Lorentzian Para (LP) α-Sasakian manifolds. Ultra Scient phys Sci-Sect A 2012, 24(1), 67-80.

Deals with weakly φ-Ricci Symmetric; locally φ-Ricci Symmetric and φ- Ricci recurrent Lorentzian Para (LP) α-Sasakian manifolds of dimension (M²ⁿ⁺¹,g) (n<62>1). The existence of weakly φ-Ricci Symmetric Lorentzian Para (LP) α-Sasakian manifolds is ensured by an example.

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022019   Perumal R;Balakrishnan R;Uma S (Mathematics Dep, Kumaraguru College of Technology, Coimbatore-641 049, Email: perumalnew_07@yahoo.co.in) : Some special seminear-ring structures II. Ultra Scient phys Sci-Sect A 2012, 24(1), 91-8.

Authors introduce the concepts of P_k and P_k seminear-rings where 'k' is a positive integer and study some of their properties. Also discuss certain properties of P₁ and P1 seminear-rings and also obtain their characterizations.

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