022242   Coelho C A;Mexia J T (Mathematics Dep Faculty of Science and Technology, The New Univ of Lisbon, 2829-516 caparica, Portugal, Email: cmac@fct.unl.pt) : On the distribution of the product and ratio of independent generalized gamma-ratio random variables. Sankhya 2007, 69(2), 221-55.

Using a decomposition of the characteristic function of the logarithm of the product of independent generalized gamma-ratio random variables (r.v.'s), authors obtain explicit expressions for both the probability density and cumulative distribution functions of the product of independent r.v.'s with generalized F or generalized gamma-ratio distributions in the form of particular mixtures of generalized Pareto and inverted Pareto distributions. The expressions obtained do not involve any unsolved integrals and are convenient for computer implementation. By considering power parameters which are not required to be positive, we were able to obtain, as particular cases, not only the distributions for the product of folded T and folded Cauchy r.v.'s but also for the ratio of two independent products of generalized gamma-ratio r.v.'s. Theoretical applications of the results as well as simulations are presented.

14 ref

022241   Clozel L (Paris-Sud Orsay Univ, Mathematiques Bat 425, 1405 Orsay, France, Email: Laurent.Clozel@math.u-psud.fr) : Equivariant embeddings of hermitian symmetric spaces. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 317-23.

Prove that equivariant, holomorphic embeddings of Hermitian symmetric spaces are totally geodesic (when the image is not of exceptional type).

8 ref

022240   Chanillo S (Mathematics Dep, Rutgers Univ, 110 Frelinghuysen Rd, Piscataway, NJ 08854, USA, Email: chanillo@math.rutgers.edu) : Uniqueness of solutions to schrodinger equations on complex semi-simple lie groups. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 325-31.

Time-dependent Schrodinger equation on complex semi-simple Lie groups.Show that if the initial data is a bi-invariant function that has sufficient decay and the solution has sufficient decay at another fixed value of time, then the solution has to be identically zero for all time. We also derive Strichartz and decay estimates for the Schrodinger equation. Our methods also extend to the wave equation. On the Heisenberg group we show that the failure to obtain a parametrix for our Schrodinger equation is related to the fact that geodesies project to circles on the contact plane at the identity.

10 ref

022239   Chang Y H;Hong C H (Mathematics Dep, National Taiwan Normal Univ, 88 Sec. 4, Ting Chou Road, Taipei, Taiwan, Republic of China, Email: changyh@math.ntnu.edu.tw) : Generalization of d' alembert formula. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 411-27.

Closed form of the solution for the factored inhomo-geneous linear equation Πⁿ_{j = 1} (d/dt - A_j) u(t) = f(t). Under the hypothesis A ₁, A₂, ..., A_n are infinitesimal generators of mutually commuting strongly continuous semigroups of bounded linear operators on a Banach space X. Here that A_js are distinct and the computational method to get explicit solutions ofcertain partial differential equations are assumed.

8 ref

022238   Chander S;Nandal P (Statistics Dep, M.D. Univ, Rohtak-124 001) : Mtsf and profit analysis of a system of three reliability models with the provision of spare unit. Pure appl Math Sci 2008, 67(1-2), 83-98.

Three reliability models are developed to study the effect of a spare unit on reliability and profit of a system. In model I system has one unit whereas one more identical unit is provided to the system models II & III in cold standby and parallel respectively. There is a single server who appears and disappears randomly from the system. The distribution of repair time is taken as general while the failure time distribution follows negative exponential. Some reliability and economic measures are obtained by using semi-Markov process and regenerative-point technique. Graphs are plotted to compare the mean time to system failure (MTSF) and profit of the models for a particular case.

9 illus, 7 ref

022237   Chakraborty S (Mathematics Dep Univ of Texas - Pan American 1201 West Univ Drive Edin, Texas 78539-2999, USA, Email: schakraborty@upta.edu) : Cyclicity and weak convergence for convolution of measures on Non-negative matrices. Sankhya 2007, 69(2), 304-13.

Let μ be a probability measure on Borel subsets of d x d non-negative matrices. Let S be the closed (multiplicative) semigroup generated by the support of μ, S_μ. Let the minimal rank of the matrices in S be 2. Then, author obtained necessary and sufficient conditions for weak convergence of μⁿ in terms of cyclicity of S_μ - a concept first introduced in the work of Chakraborty and Rao (1998, Sankhya A).

4 ref

022236   Cencelj M;Repovs D;Skopenkov M B (NO, Institute of Mathematics, Physics and Mechanics, P.O.Box 2964, 1001 Ljubljana Slovenia, Email: matija.cencelj@guest.arnes.si) : Classification of framed links in 3-manifolds. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 301-6.

Short and complete proof of the following Pontryagin theorem whose original proof was complicated and has never been published in detail. Let M be a connected oriented closed smooth 3-manifold, L₁(M) be the set of framed links in M up to a framed cobordism, and deg: L₁(M) → H₁(M: Z) be the map taking a framed link to its homology class. Then for each a ∈ H₁(M; Z) there is a one-to-one correspondence between the set deg^-1 a and the group Z_z2d, where d(α) is the divisibility of the projection of a to the free pan of H₁ (M; Z).

022235   Cai J;Xie S;Qiu W (Mathematics Dep, Yuxi Normal College Yuxi, Yunnan-653 100 P.R. China, Email: caijionghui@yxtc.net) : The solitary wave solutions of a generalized improved boussinesq four-order equation. Indian J Math 2008, 50(1), 163-75.

The qualitative theory of ordinary differential equations and numerical simulation methods are employed to investigate the solitary waves of a nonlinear four-ordered equation. Under the condition r <62> 0, the wave equation can be changed to a planar system, the properties of the singular points are studied, and the bifurcation phase portraits arc drew. The parameter conditions that the existence of solitary waves to be found, and their solutions are obtained. The planar graphs of the travelling wave equation are simulated using the mathematical software Maple. The numerical simulation and qualitative results are identical.

3 illus, 8 ref

022234   Byungbae Kim (Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, Korea, Email: bkim@hongik.ac.kr) : Icosahedron preserving mappings. Far East J mathl Sci 2007, 27(2), 443-51.

It has been shown that if a one-to-one mapping f: R³ →+ R³ preserves regular icosahedrons, then f is a linear isometry up to translation.

4 illus, 12 ref

022233   Bouzkoura K;Misane D (Mathematics Dep, Faculty of Science, , Agdal P.O. Box 1014, Rabat, Morocco) : T-lattice and hyperconvexity. Far East J mathl Sci 2007, 27(2), 373-80.

Hyperconvex in metric spaces is introduced. Obtained Sine-Soardi's theorem in these spaces for contracting or nonexpansive mappings, while using T-Iattice structure.

1 illus, 15 ref

022232   Boules A N (Mathematics and Statistics Dep, North Florida Univ, 4567 St. Johns Bluff Road S., Jacksonville, FL 32224) : New method for approximating solutions of high order linear boundary value problems. Indian J pure appl Math 2007, 38(6), 589-602.

A new method for approximating high order linear boundary value problems is presented. The proposed method is essentially a second order finite difference scheme that, when combined with extrapolation, produces approximations of any desired accuracy within machine precision. The method is derived and illustrated by a fourth order equation and an outline of the general form of the scheme is discussed in the appendix. Examples include eighth and fourth order equations, including applications to plate deflection problems. A useful byproduct of the method is that, for an equation of order p, it produces accurate approximations of the derivatives of the solution up to order p-1. This feature too, is illustrated in the examples.

2 illus, 6 tables, 8 ref

022231   Boccuto A;Rieca B;Sambucini A R (NO, Fakulta Prirodnych Vied Univerzita Mateja Bela Tajovskeho, 40 SK-97401 Banska Bystrica (Slovakia)) : Some properties of an improper Gh_k integral in riesz spaces. Indian J Math 2008, 50(1), 21-51.

GHk integral for [unctions defined on (possibly) unbounded subintervals of the extended real line and with values in Riesz spaces Some convergence theorems are proved, together with a version of the Fundamental Formula of Calculus.

34 ref

022230   Biswas I;Raghavendra N (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: indrani@math.tifr.res.in) : Atiyah-Well criterion for holomorphic connections. Indian J pure appl Math 2008, 39(1), 3-47.

Describes a criterion due to Atiyah and Weil for a holomorphic vector bundle over a compact Riemann surface to admit a holomorphic connection. Also contains a similar result for vector bundles on a smooth projective algebraic curve defined over an arbitrary perfect base field.

16 ref

022229   Bilombo R;Doliatovski V A (Normal School Superior (E.N.S.), University Marien Ngouabi, Boite Postale: 1664 Brazzaville, Republique du congo) : On models and methods of dynamic optimal management, model 17. Far East J mathl Sci 2007, 27(2), 401-14.

Model built allows to calculate optimal orders of a mechanical system in movement for variable regimes and succession of its moment of commutation. For example, in the case of management of the train, the used method puts in an obvious way the dependence between energy consumed E, the mass M, the slope Q, and the power of the engine u.

9 illus, 2 tables, 5 ref

022228   Berti P;Regazzini E;Rigo P (Matematica Dep, Pura Ed Applicata "G. Vitali" Univ' di Modena e Reggio-Emilia Via Cam, 1100 Modena, Email: patrizia.berti@unimore.it) : Modes of convergence in the coherent framework. Sankhya 2007, 69(2), 314-29.

Convergence in distribution is investigated in a finitely additive setting. Let X_n's be maps, from any set Ω into a metric space S, and P a finitely additive probability (f.a.p.) on the field F = U_n σ(X₁, ..., X_n). Fix H ⊂ Ω and X : Ω → S. Conditions for Q(H) = 1 and X_n → X under Q, for some f.a.p. Q extending P, are provided. In particular, one can let H = {ω ∈ Ω : X_n(ω) converges} and X = lim_n X_n on H. Connections between convergence in probability and that in distribution are also exploited. A general criterion for weak convergence of a sequence (μ_n) of f.a.p.'s is given. Such a criterion grants a σ-additive limit provided each μ_n is σ-additive. Some extension results are proved as well. As an example, let X and Y be maps on Ω. Necessary and sufficient conditions for the existence of a f.a.p. on σ(X,Y), which makes X and Y independent with assigned distributions, are given. As a consequence, a question posed by de Finetti in 1930 is answered.

20 ref

022227   Bai D;Xu Y (School of Mathematics and Information Science, Guangzhou Univ, Guangzhou-510006, China, Email: baidingyong@tom.com) : Positive solutions for semipositine BVPs of second-order difference equations. Indian J pure appl Math 2008, 39(1), 59-68.

Deals with the existence of positive solutions for superlinear semipositone Sturm-Liouville-like boundary value problems of second order difference equations. The main tool is the fixed point theorem in cones due to Guo-Krasnosel'skii.

21 ref

022226   Azziz A;Rather N A (Post Graduate Mathematics Dep, Kashmir Univ, Hazratbal, Srinagar-190 006, Email: nisararather@yahoo.co.in) : On an inequality concerning the polar derivative of a polynomial. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 349-57.

Correct proof of an L_p-inequality concerning the polar derivative of a polynomial with restricted zeros. Also extend Zygmund's inequality to the polar derivative of a polynomial.

13 ref

022225   Atshan W G;Kulkarni S R (Mathematics Dep, Univ of Pune, Pune-411 007, Email: waggashnd@yahoo.com) : Application of fractional derivatives and hypergeometric functions to multivalent analytic functions. Far East J mathl Sci 2007, 27(2), 277-94.

Application of fractional derivatives, hypergeometric functions to multivalent starlike and convex functions have been studies. Here authors have also attempted coefficient bounds, radii of starlikeness, convexity and distortion bounds. Several results about integral representation extreme points and convex linear combination on the class T_p^δ (α, β) are given.

7 ref

022224   Aouf M K;Darwish H E (Mathematics Dep, Faculty of Science, Mansoura Univ, Mansoura, Egypt, Email: mkaouf27@yahoo.com) : Certain subclass of p-valent meromorphically starlike functions with alternating coefficients. Indian J pure appl Math 2008, 39(2), 157-66.

Coefficient inequalites and distortion theorems are obtained for certain subclass of meromor-phically p-valent starlike functions with alternating coefficients. Further preserving integral operators are obtained.

7 ref

022223   Angerer W P (Universidad Autonoma Metropolitana Unidad Cuajimalpa Artificios 40, Col. Miguel Hidalgo, Delegacion Alvaro Obregon Mexico D.F., C.P. 01120, Mexico, Email: wolfgang.angerer@hotmail.com) : On seneta's constants for the supercritical bellman-harris process with E(Z+logZ+) = 8. Sankhya 2007, 69(2), 256-64.

For a finite mean supercriticial Bellman-Harris process, let Z_t be the number of particles at time t. There exist numbers X_t (the Seneta constants) such that X_tZ_t converges almost surely to a non-degenerate limit. Furthermore, X_t ∝ e^-βt L(e^-βt), where β is the Malthusian parameter, and œ is slowly varying at zero. We obtain a characterization of the slowly varying part of the Seneta constants under the assumption that the life-time distribution of particles is strongly non-lattice.

6 ref

022222   Altun I;Turkoglu D (Mathematics Dep, Faculty of Science and Arts Kirikkale Univ, 71450-Yahsihan, Kirikkale Turkey, Email: ialtun@kku.edu.tr) : Fixed point theorem on general topological spaces with a _T-distance. Indian J Math 2008, 50(1), 219-28.

Some fixed point theorem for mappings satisfying contractive condition of integral type on general topological spaces using a r-distance which is given by Aamri and El Moutawakil in [1]. Results extend and generalize the results of Aamri and El Moutawakil [1], Branciari [4] and some others.

15 ref

022221   Altinok H;Altin Y;Isik M (Mathematics Dep, Firat Univ, 23119, Elazig -Turkey, Email: hifsialtinok@yahoo.com) : Sequence space BV_o (M,p,q,s) on seminormed spaces. Indian J pure appl Math 2008, 39(1), 49-58.

Defines the sequence space BV(M,p,q,s) on a seminormed complex linear space, by using an Orlicz function. Gives various properties and some inclusion relations on this space.

14 ref

022220   Al-Kasasbeh F;Darus M (School of Mathematics Science, Faculty of Science and Technology, Univ Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan, Malaysia, Email: Alkasasbeh@yahoo.com) : Classes of univalent functions symmetric with respect to points defined on the open disc D<. Far East J mathl Sci 2007, 27(2), 355-71.

New differential operator ∇^k_af(z) = f^k-1)(z) + β(z - a) f^(k)(z) is introduced for analytic function f that is defined on the open disc D^(a) = {z : <157> z - a <157> <60> 1}. Subclasses within the differential operator ∇^k_(a) are obtained with respect to points, and the coefficient bounds of functions are calculated.

5 ref

022219   Afendras G;Papadatos N;Papathanasiou V (Mathematics Dep Section of Statistics and Operations Research Univ of, , Athens Panepistemiopolis-157 84 Athens, Greece, Email: g_afendras@math.uoa.gr) : Discrete Mohr and Noll inequality with applications to variance bounds. Sankhya 2007, 69(2), 162-89.

In this paper, authors provide Poincare-type upper and lower variance bounds for a function g(X) of a discrete integer-valued random variable (r.v.) X, in terms of the (forward) differences of g up to some order. Investigated a discrete analogue of the Mohr and Noll inequality (1952, Math. Nachr., vol. 7, pp. 55-59), which may be of some independent interest in itself. It has been shown by Johnson that for the commonly used absolutely continuous distributions that belong to the Pearson family, the somewhat complicated variance bounds take a very pleasant and simple form. It is shown here that this is also true for the commonly used discrete distributions. As an application of the proposed inequalities, variance behaviour of the UMVU estimator of log p in Geometric distributions has also been studied.

2 tables, 26 ref

021206   Yang Y;Kim C J (Mathematics Dep, Cheju National Univ,, Jeju 690-756, Korea, Email: yangyo@cheju.ac.kr) : Contractions of class Q*. Far East J mathl Sci 2007, 27(3), 649-57.

Hilbert space operator T is of class Q* if T*² T² - 2TT^* + I is nonnegative. Every * -paranormal operator is of class Q* , but class Q* operators are not necessarily normaloid. Several properties of class Q* are studied.

8 ref

021205   Srivastava R;Srivastava M (Applied Mathematics Dep, Institute of Technology, Banaras Hindu Univ, Varanasi) : On certain separation axioms in fuzzy bitopological spaces. Far East J mathl Sci 2007, 27(3), 579-87.

Main purpose of this work is to introduce and study the fuzzy bitopological counterparts of certain separation axioms introduced/ studied in [1] and [6] for bitopological spaces.

11 ref

021204   Siripitukdet M;Iampan A (Mathematics Dep, Naresuan Univ, Phitsanulok-65000, Thailand, Email: manojs@nu.ac.th) : On the n-prime ideals in Γ-semigroups. Far East J mathl Sci 2007, 27(3), 659-68.

Any semigroup can be considered as a Γ-semigroup. The concept of ideal extensions in Γ-semigroups was introduced in 2007 by Siripitukdct and Iarapan. The relationship between the n-prime ideals and ideal extensions are characterized in Γ-semigroups and give some characterizations of n-prime ideals and ideal extensions in Γ-semigroups and prove that for a Γ-semigroup M, n-prime ideals are a generalization of prime ideals for all integers n ≥ 2 and for all integers n ≥ 3, an ideal I of M is an n-prime ideal of M if and only if any extension of I is an (n - 1) -prime ideal of M.

8 ref

021203   Selvaraj C;Petchimuthu S;George R (Mathematics Dep, Periyar Univ, Salem-636 011, Email: spmuthuss@yshoo.co.in) : Strongly prime radicals of Γ-Rings. Far East J mathl Sci 2007, 27(3), 777-84.

Right (left) strongly prime radical P_rs(M) (P_ls(M)) of a Γ-ring M coincides with the P_rs(L)⁺ (P_ls(R)^*), where P_rs(L) (P_ls(R)) is right (left) strongly prime radical of left (right) operator ring L(R) of M are proved.

13 ref

021202   Raghavendra R;Padmavathamma;Rajeshkanna M R (Mathematics Dep, Reva Institute of Technology and Management, Kattigenahalli, Jala Hobli, Yelahanka Bangalore-560 064, Email: raghu_maths@yahoo.co.in) : New partition identity A<. Far East J mathl Sci 2007, 27(3), 720-40.

Object of this paper is to give a bijective proof of the new partition identity A⁰_{11, 2, 2} (n) = B⁰_{11, 2, 2} (n), where A⁰_{11, 2, 2}(n) counts the number of partitions of n subject to certain restrictions (too long to be stated in the abstract) and B⁰11, 2, 2 (n) counts the number of partitions of n = b₁ + ... + b_s into distinct parts with parts ≠ 2,3, ..., 10 and b_i - b_i+1 ≥ S 12 with strict inequality if b_i is a multiple of 12, f₁ + f₁₁ + f₁₂ ≥ 1, where f_i is the number of appearances of i in the partition and no part is ≡ 6 (mod 12).

9 ref

021201   Prasad T V S R K (Mechanical Engg Dep, Vignan's Engng Coll, Vadlamudi, Via Tenali, Guntur, Andhra Pradesh) : Determination of optimal product mix for a pump manufacturing industry. Mfg Technol Today 2007, 6(11), 19-23.

Determination of optimal product-mix for a pump manufacturing industry has been done for a small scale industry manufacturing hand pumps and centrifugal pumps in South India, in order to get the maximum profits with the available resources. The above company has been manufacturing eight models of hand pumps and centrifugal pumps. The unit profit of each model are different. These pumps contain several parts which have to be processed on various machines. The processing times of each part on each machine are studied. From this information, the processing time of each model of pump on each machine is obtained. The maximum available time of each machine is determined. The above information is used to formulate the linear programming model for maximizing the profits. The LPP is solved using the TORA software. The product mix for getting the maximum profits with the available resources is obtained. The maximum profit is found to be Rs. 128.55 Lakhs per annum.

10 tables, 4 ref

021200   Piotrowski Z;Vallin R W (Mathematics Statistics Dep, Youngstown State Univ, Youngstown, OH 44555, U.S.A., Email: zpiotr@math.ysu.edu) : On planar approximations and convergence. Far East J mathl Sci 2007, 27(3), 539-48.

Planar approximations are introduced in the study of separately continuous functions f : [0, 1] x [0, 1] → R. In Section 2. It is shown that how, when dealing with continuity in the ordinary sense, the convergence which was pointwise for separately continuous functions, becomes uniform. In Section 3, we look at sequences of planar approximable functions and their limits under various notions of convergence.

16 ref

021199   Papadopoulos B K;Georgiou D N (Mathematics Dep, Democritus Univ of Thrace-67100 Xanthi, Greece) : Note on oscillation in fuzzy topological spaces. Far East J mathl Sci 2007, 27(3), 589-606.

Theorems concerning the uniform convergence of sequences of continuous maps in the field of fuzzy sets are generalized. Notions of fuzzy uniform convergence of fuzzy oscillation and of fuzzy uniform oscillation are introduced.

8 ref

021198   Nozari K (Physics Dep, Faculty of Basic Sciences Mazandaran Univ, P.O. Box 47416-1467, Babolsar, Iran, Email: knozari@umz.ac.ir) : On the relation between generalized uncertainty principle and space noncommutativity. Far East J mathl Sci 2007, 27(3), 607-17.

Quantum correction of black hole temperature using two fundamental concepts: the generalized uncertainty principle (GUP) motivated by string theory and noncommutative geometry (NCG) is considered. Maximum temperature of black hole computed in these two approaches to find a relation between fundamental scales of string theory and noncommutative geometry is compared.

30 ref

021197   Lee I Y (Mathematics Dep, Kyungsung Univ, Busan 608-736, Korea) : On equations of A geodesic with respect to an infinite series (a, B)-metric. Far East J mathl Sci 2007, 27(3), 669-83.

Condtion that a Finsler space with an (a, (3) -metric be a geodesic is obtained. Conditions that a Finsler space with an infinite series (α, β) -metric be equations of a geodesic are found.

14 ref

021196   Kulkarni V S;Deshmukh K C (Mathematics Dep, Govt. College of Engineering, Chandrapur-442 401, Email: vinayakskulkarni1@rediffmail.com) : Quasi-static transient thermal stresses in a thick annular disc. Sadhana 2007, 32(5), 561-75.

The paper deals with the determination of transient thermal stresses in a thick annular disc. A thick annular disc is considered having zero initial temperature and subjected to arbitrary heat flux on the upper and lower surfaces where as the fixed circular edges are at zero temperature. The governing heat conduction equation have been solved by using integral transform technique. The results are obtained in series form in terms of Bessel's functions. The results for displacement and stresses have been computed numerically and are illustrated graphically.

12 illus, 10 ref

021195   Jaha Y (Mathematics Dep, Umm Al-Qura Univ Makkah, Saudi Arabia, Email: yousif@uqu.edu.sa) : On numerical solution for integral equations. Far East J mathl Sci 2007, 27(3), 549-57.

Existence and uniqueness solution for a mixed integral equation of type Volterra-Fredholm is discussed. The kernel of Volterra is considered in time while Fredholm in position. Using a numerical method, we have a linear system of Fredholm integral equation. Then using Torplitz matrix method we have a linear system of algebraic equation. The existence and uniqueness of this system is obtained. Also the convergence of the method is discussed. The error estimate when the kernel takes a logarithmic and Carleman forms is calculated.

4 illus, 2 tables, 12 ref

021194   Hiremath G R (Mathematics Computer Science Dep, Univ of North Carolina Pembroke Pembroke, NC 28372, USA) : New generalizations of developable spaces. Far East J mathl Sci 2007, 27(3), 517-37.

Generalizations of quasi-developable spaces and semi-developable spaces are introduced. Developable spaces are characterized as quasi-developable semi-developable spaces. Semi-metrizable spaces are characterized as T0 quasi semi-developable semi-stratifiable spaces. Semi-developable spaces are characterized as quasi semi-developable semi-stratifiable spaces, and are symmetrizable spaces.

13 ref

021193   Guangshi X (Mathematics Dep, Nanjing Univ of Aeronautics and Astronautics, Nanjing 210016, P.R. China, Email: xgs01cn@yahoo.com.cn) : On strongly regular rings and SF-Rings. Far East J mathl Sci 2007, 27(3), 693-9.

Some new properties of rings whose every simple singular left -R-module is flat are given. Some characterizations of strongly regular rings are proved. A ring R is strongly regular if and only if R is a ring whose every simple singular left .R-module is flat and every maximal right ideal is a GW-ideal if and only if R is a normal ring whose every simple singular left R-module is flat and every maximal essential right ideal of R is a GW-ideal. In particular, If R is a ring whose every simple singular left .R-module is flat and every maximal essential right ideal is a GTV-ideal, then R is regular.

10 ref

021192   Fu H P;Li Z Q (Center of Mathematical Sciences, Zhejiang Univ, Hangzhou 310027, P.R. China, Email: mathfu@126.com) : Spectrum of the laplacian on the cartan's minimal hypersurface in S<. Far East J mathl Sci 2007, 27(3), 701-15.

Spectrum of the Laplacian on the compact minimal isoparametric hypersurface M in S⁴ with three distinct principal curvatures are presented. The set of the spectrum of the Laplacian on M is spec (M) = {μ(m, k)|m = 0,1, ...; 0 ≤ k ≤ m} U {v(m, k) |m = 1, 2, ...; 1 ≤ k ≤ m}, where μ(m, k) = 2m(2m + 1) - 3k² and v(m, k) = 2(m + 1) (2m + 1) - 3k².

7 ref

021191   Fisher B (Mathematics Dep, Univ of Leicester, Leicester, Le1 7RH, U.K.) : Result on the composition of distributions. Far East J mathl Sci 2007, 27(3), 769-76.

Let F be a distribution in V and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {F_n(f(x))} is equal to h(x), where F_n(x) = F(x)* δ_n(x) for n = 1, 2, ... and {δ_n(x)} is a certain regular sequence converging to the Dirac delta function. It is proved that the composition of x^-2s+1 and sgn x |x|^μ exists and is equal to sgn x|x|^-μ(2s-1) for s = 1, 2, ... and 0 <60> μ (2s - 1) <60> 2.

12 ref

021190   Dawood S;Ahmed A G B;Saif A (School of Mathematical Sciences, Univ Kebangsaan Malaysia, Bangi-43600, Selangor D. Ehsan, Malaysia, Email: sul_dawood@yahoo.com) : On the classification problem in the theory for fibrations. Far East J mathl Sci 2007, 27(3), 569-77.

Some results have been given about the classification problem in the theory of H-fibration. That is under which conditions two H-fibrations over a common base will be fiber homotopy equivalent.

7 ref

021189   Dawood S;Ahmed A G B;Saif A (School of Mathematical Sciences Univ Kebangsaan Malaysia Bangi-43600, Selangor D. Ehsan, Malaysia, Email: sul-dawood@yahoo.com) : Conjugate Sf -functions . Far East J mathl Sci 2007, 27(3), 559-67.

Relation between the Sf-functions and, fiber homotopy equivalence for two Hurewicz fibrations , (H-fibrations) with a common base is given.

4 ref

021188   Biswas D (Mathematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: d_priya05@yahoo.co.in) : Geometry of EPH homogeneous spaces using clifford algebras and the isotropy subgroups. Far East J mathl Sci 2007, 27(3), 741-58.

Concept of homogeneous spaces and described the elliptic, parabolic and hyperbolic (EPH) cases arising from them are explained. Then we have proved the invariance of the upper half plane in the elliptic and parabolic cases whereas in the hyperbolic case the upper half plane is not preserved. We have also shown that vectors are preserved under Mobius transformation where defined, transitivity condition for SL₂(R) on the upper half plane in R^a is also proved. Lastly, the isotropy subgroups for the three EPH cases, are also obtained.

3 illus, 15 ref

021187   Bassey U N;Babalola V A (Mathematics Dep, Univ of Ibadan, Ibadan, Nigeria, Email: unbassey@yahoo.com) : Factoring compact elements of banach algebras. Far East J mathl Sci 2007, 27(3), 717-28.

It is shown that a compact element of a C* -algebra factors compactly; a compact normal element of a C* -algebra is the composition of two compact normal elements; and for any Banach algebra A with a bounded approximate identity every left compact element factors as a product of an element of A and a left compact one.

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021186   Baruah A K;Changmai J (Mathematics Dep, Dibrugarh Univ, Dibrugarh-786 004, Email: akb213@hotmail.com) : Quadratic triangular element approximation of multi-parameter eigenvalue problems. Far East J mathl Sci 2007, 27(3), 619-47.

In steady-state and dynamic analysis, the idealization of mathematical systems into desired forms with optimal discretization and condensation of parameters are generally treated under special eigenvalue problems and often applied to certain boundary value problems as well containing spectral parameters. The eigenvalues of interest are then extracted efficiently in closed form using various techniques of integration, separation of parameters and so on. The numerical treatment of a two-parameter eigenvalue problem in ordinary differential equations constraint under pre-imposed boundary conditions is considered. While dealing with the problem, a finite element procedure for a quadratic triangular element is considered in the process of finding the rough estimates of the values of the eigen pair rather than trial and error method. The actual values of the pair of the eigenvalues are then obtained by using the rough estimates as the starting approximation in the corresponding shooting method.

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021185   Al-Mahameed M M (Mathematics Dep, Irbid National Univ, Irbid, Jordan) : Maximum principles for some hyperbolic equations. Far East J mathl Sci 2007, 27(3), 685-92.

Maximum principles of the Cauchy problem hyperbolic equations in the 3-dimensional space-time is established.

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021184   Abe S (Mathematical Information Science Dep, Tokyo Univ of Science 1-3 Kagurazaka, Shinjuku-ku Tokyo 162-8601, Japan, Email: j1105701@ed.kagu.tus.ac.jp) : Actions of A5 on 2-groups. Far East J mathl Sci 2007, 27(3), 759-68.

Proved several properties of actions of the alternating group of degree 5 on 2-groups.

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020184   Zhe D;Jiang H Y (Mathematics Dep, Zhejiang Univ, Hangzhou 310027, People's Republic of China, Email: dongzhe@zju.edu.cn) : Compact solutions to the equation Tx = y in a weakly closed T(N)-module. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 495-503.

Given two vectors x, y in a Hilbert space and a weakly closed T(N)-module U, we provide a necessary and sufficient condition for the existence of a compact operator T in U satisfying Tx = y.

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020183   Sazeedeh R (Mathematics Dep, Urmia Univ, Urmia, Iran, Email: rsazeedeh@ipm.ir) : Bounds for regularity and coregularity of graded modules. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 429-41.

Let M be a finitely generated graded module over a Noetherian homogeneous ring R with local base ring (Ro, m_o). If RO is of dimension one, then we show that reg^l+1 (M) and coreg_i+1 (M) are bounded for all NO. Improves these bounds, if in addition, RO is either regular or analytically irreducible of unequal characteristic.

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020182   Parthasarathy K R (NO, Indian Statistical Institute, Delhi Centre, 7, S.J.S. Sansanwal Marg, New Delhi 110 016, Email: krp@isid.ac.in) : Extreme points of the convex set of joint probability distributions with fixed marginals. Proc Indian Acad Sci-Mathl Sci 2007, 117(4), 505-15.

By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.

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