008319   Salim T O;Shenan J M (Mathematics Dep, Al-Azhar Univ, Gaza P.O. Box 1277, Gaza, Pleastine, Email: trsalim@yahoo.com) : Certain class of multidimensional convolution integral equations involving a modified sequence of functions. Bull pure appl Math 2009, 3(2), 192-205.

Obtains a solution of a certain multidimensional convolution integral equation of Fredholm type whose kernel involves a modified sequence of functions. A number of results follow as special cases from the main theorem by specifying the parameters of the modified sequence of functions.

14 ref

008318   Sahu L (Stat-Math Unit, Indian Statistical Institute, Bangalore Centre, 8th Mile, Mysore Road, Bangalore 560 059, Email: lingaraj@isibang.ac.in) : Quantum random wlks and their convergence to Evans-Hudson flows. Proc Indian Acad Sci-Mathl Sci 2008, 118(3), 443-65.

Using coordinate-free basic operators on toy Fock spaces, quantum random walks are defined following the ideas of Attai and Pautrat. Extending the result for one dimensional noise, strong convergence of quantum random walks associated with bounded structure maps to Evans-Hudson flow is proved under suitable assumptions. Starting from the bounded generator of a given uniformly continuous quantum dynamical semigroup on a von Neumann algebra, we have constructed quantum random walks which converges strongly and the strong limit gives an Evans-Hudson dilation for the semigroup.

22 ref

008317   Sahoo N K;Sahoo C K;Sahoo S K (NO, Maharaja Institute of Technology (M.I.T.), Khurda, Bhubaneswar-752 055) : EOQ model with two-parameter constant deteriorration and price dependent demand. Ultra Scient phys Sci 2009, 21(2M), 515-20.

Inventory replenishment policy is developed for constant deteriorating item and price-dependent demand. The rate of deterioration is taken to be time proportional. A power law form of the price dependence of demand is considered and the numerical example is taken up to illustrate the solution procedure and sensitivity analysis is also carried out.

1 table, 12 ref

008316   Sahin B (Deparment of Mathematics, Inonu University, 44280 Malatya, Turkey, Email: bsahin@inonu.edu.tr) : Harmonic Riemannian maps on locally conformal kaehler manifolds. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 573-81.

Study harmonic Riemannian maps on locally conformal Kaehler manifolds (IcK manifolds). We show that if a Riemannian holomorphic map between IcK manifolds is harmonic, then the Lee vector field of the domain belongs to the kernel of the Riemannian map under a condition. When the domain is Kaehler, we prove that a Riemannian holomorphic map is harmonic if and only if the IcK manifold is Kaehler. Then we find similar results for Riemannian maps between IcK manifolds and Sasakian manifolds. Finally, we check the constancy of some maps between almost complex (or almost contact) manifolds and almost product manifolds.

11 ref

008315   Richhariya M;Mathur P K;Narain K (Mathematics Dep, Hindustan College of Science & Technology, Farah, Mathura Utter Pradesh) : Solution of certain simultaneous quadruple series equations involving generalized Bateman-k functions. Ultra Scient phys Sci 2009, 21(2M), 419-22.

Studies a closed form solution is obtained for the simultaneous quadruple series equation using generalized Bateman-k functions by multiplying factor method.

6 ref

008314   Ravindra Kumar;Singh K K;Sharma A K (NO, , 616, Pal Colony, Near Shesh Cold Store, Ashok Nagar, Etawah Utter Pradesh-206 001, Email: rkpal.maths@gmail.com) : Unsteady flow of rivlin-ericksen visco-elastic fluid through porous medium in a confocal elliptical duct. Ultra Scient phys Sci 2009, 21(2M), 571-5.

Purpose is to study the unsteady flow of visco-elastic Rivlin-Ericksen type fluid through porous medium in a long uniform confocal elliptical duct under the influence of an arbitrary time dependent pressure gradient. Mathieu functions have been used to obtain the exact solution of flow problem. Some particular cases for different pressure gradients have also been discussed in detail. Used the notations of Mc Lachlan^{7 as regard to Malhieu functions.}

20 ref

008313   Rama Krishna K;Sobha V V;Kondragunta R K (NO, , 10-171, Near Indane Gas Godown, Varalakshmipuram, Ashok Nagar, Kanuru, Vijayawada-07, Andhra Pradesh,-520 007, Email: kondraguntark@yahoo.com) : Mixed convective flow over a non-isothermal radiative vertical surface embedded in a porous medium with applied magnetic field. Ultra Scient phys Sci 2009, 21(2M), 405-14.

Deals with magneto hydrodynamic mixed convection heal transfer analysis over a vertical surface embedded in saturated porous medium with variable wall temperature. The effects of transverse magnetic field, radiation heat transfer and dissipation are examined. The plate temperature in excess of constant temperature of the ambient fluid is assumed to be proportional to x^{λ. The ratio of Rayleigh to Peclet number is taken as mixed convective parameter (∈) and the effect of ∈ <62> 0 and ∈ <60> 0 on the boundary layer solution is studied and presented in the graphical form. The boundary layer solutions are obtained by using similarity variables for ∈ <62> 0 and ∈ <60> 0. It is found that with the increase in λ value and radiation parameter (F), the rate of heat transfer increases through medium. Different velocity and temperature profiles and Nusselt number variation for both buoyancy aiding flow and opposing flow are also presented.}

8 illus, 9 ref

008312   Ram Reddy T Ram;Thirupathi Reddy P (Mathematics Dep, Kakatiya Univ, Warangal-506 009, Email: reddypt2@yahoo.com) : Meromorphic P-valent starlike functions with alternating coefficients. Bull pure appl Math 2009, 3(2), 254-62.

Introduces a new subclass σ_p (n, α) of meromorphic starlike functions with alternating coefficients in E = {z : 0 <60> |z| <60> 1} and investigate coefficient estimates, distortion theorem, radius of convexity and closed under convex linear combinations.

6 ref

008311   Rajesh V;Sridevi C;Verma S Vijaya Kumar (Mathematics Dep, Narayana Engineering College, Nellore-524 004, Email: v.rajesh.30@gmail.com) : Chemical reaction effects on transient MHD free convection and Mass trasfer flow of dissipative fluid with heat generation and thermal diffusion past an infinite vertical plate. Ultra Scient phys Sci 2009, 21(2), 285-94.

The effects of chemical reaction on transient MHD free convection and mass transfer flow of dissipative fluid past an infinite vertical porous isothermal plate in the presence of heat generation, thermal diffusion and viscous dissipation is studied numerically. The Problem is governed by a coupled nonlinear system of partial differential equations. This system is solved numerically by applying explicit finite difference method. The effect of chemical reaction parameter (K) in the presence of Heat generation parameter (H) and Soret number (So) is examined on Velocity, Temperature and Concentration. The numerical values of the skin friction, the rate of heat transfer and the rate of mass transfer are entered in tables. It is found that chemical reaction parameter K decreases velocity and concentration in the presence or no presence of Heat source parameter H and Soret number S₀. Further, it has no effect on temperature.

9 illus, 3 tables, 18 ref

008310   Rajabikafshgar G;Latha S (NO, DOS in Mathematics Univ, Mysore Manasagangotri, Mysore, Email: ghorban677@yahoo.com) : Investigation of the process of working on bieberbach conjecture. Ultra Scient phys Sci 2009, 21(2M), 509-14.

Study of complex functions theory is one of the most fascinating subjects in complex analysis. The most interesting shape of this theory is the interplay of analysis and geometric. The theory of univalent functions is concerned primarily with such relations between analytic structure and geometric behavior, born around the turn of the century. The serious study of univalent functions theory began in 1907. This theory was given a powerful impetus by the conjecture of Bieberbach. Investigates the process of studying this conjecture during approximately seven decades and attempts to prove of it.

6 ref

008309   Radul Taras;Repovs Dusan (Mechanics Dep, Mathematics, Lviv National Univ, Universytetska st., 1, Lviv, Ukraine 79602, Email: tarasradul@yahoo.co.uk) : Hartman-Mycielski functor of non-metrizable compacta. Proc Indian Acad Sci-Mathl Sci 2008, 118(3), 467-72.

Investigates certain topological properties of the normal functor H, introduced by the first author, which is a certain functorial compactification of the Hartman-Mycielski construction HM. We prove that H is always open and we also find the condition when HX is an absolute retract, homeomorphic to the Tychonov cube.

9 ref

008308   Prasad R;Yadav S P (Mathematics and Astronomy Dep, Lucknow Univ, Lucknow-226 007, Email: rp_manpur@rediffmail.com) : Some conharmonically flat manifold. Ultra Scient phys Sci 2009, 21(2M), 543-52.

Systematic study of conharmonically flat generalized Sasakian space form and conharmonically flat (k,μ)- manifold. Find the eigenvalues and eigenvectors of Ricci-operator Q. Further, established the relations between f1, f2 and f3 for three dimensional conharmonically Hat generalized Sasakian space form and proved that curvature tensorofthree dimensional conharmonically flat generalized Sasakian space form is zero. We have find the condition that a (k,μ)- manifold becbmes an η-Einstein manifold and Einstein manifold. It is also proved that only three dimensional (k,μ)- manifold may be Einstein manifold iff k = 0.

14 ref

008307   Prajapat J K (Mathematics Dep, Sohbasaria Engineering College, NH-11, Gokulpura, Sikar-332 001, Email: jkp_0007@rediffmail.com) : Inclusion and neighborhood properties for certains subclasses of analytic functions involving fractional calculus operators. Bull pure appl Math 2009, 3(2), 170-4.

A known fractional calculus operator is used to define some new subclasses of analytic functions in the unit open disc U. For each of these new function classes several inclusion relationships associated with the (q, δ)-neighborhoods are established.

11 ref

008306   Patel U;Choudhury S (Mathematics Dep, Government Autonomous College, Bhawani, Patna) : Weaker version of zeeman's conjecture on space topology. Ultra Scient phys Sci 2009, 21(2M), 531-42.

Zeeman, in his paper 'Topology of Minkowski Space' made two conjectures: (1) the topology in Minkowski Space that induces the 3-dimensional Euclidean topology on every space- like hyperplane (S-topology) has G as its group of homeomorphisms, where G is the smallest group generated by the inhomogeneous Lorentz group and dilatation (multiplication by +ve scalars); (2) the topology on Minkowski space that induces the one-dimensional Euclidean topology on every time-like line (T-topology) also has G as its homeomorphism group. Since it is known that G is precisely the set of < - automorphism (where <60> is the causality relation on Minkowski space), we have made an alternative formulation of the second conjecture as follows: every homeomorphism of the T-topology is a <60> - automorphism. Here we have dealt with a weaker version of Zecman's conjecture on space topology.

3 illus, 13 ref

008305   Parida P K;Sahoo S K (NO, Eastern Academy of Science & Technology, Andharua, Bhubaneswar-3, Orissa, Email: prashanta_math@yahoo.co.in) : Optimization of fuzzy expert systems using neural network in decision-making in competitive situation. Ultra Scient phys Sci 2009, 21(2M), 521-30.

Many decision making problems may be solved with Heuristic search algorithms. Expert systems taking decisions in competitive situation in uncertain environment/fuzzy environment may take a graph-search algorithm to tackle the situation. To improve the performance of the overall system, a set of important parameters of the decision making system is identified. Optimization methods such as Neural Network (N.N.) is used for the learning of the optimum parameters and also for an improvement of the performance.

4 illus, 19 ref

008304   Nadarajah S (School of Mathematics, University of Manchester, Manchester M13 9PL, UK) : On the distribution for the contract forces. Natn Acad Sci Lett 2008, 31(9-10), 285-8.

Discusses one of the most recent distributions proposed for contact force magnitudes. Expressions and simple computer programs are given for computing various statistical properties associated with this distribution. The programs are written in R: a freely downloadable statistical software

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008303   Muthaiyan A;Sathiyamoorthi R (Mathematics Dep, Roever Engineering College, Perambalur-621 212) : Stochastic model for estimation of expected time to recruitment under correlated wastage. Ultra Scient phys Sci 2009, 21(2M), 433-8.

In Business and Industrial organization the leaving of personnel is a common phenomenon. This is called wastage. The estimate of the size of wastage and the likely important aspect of study in manpower planning models. The wastage on successive occasions of policy decision regarding, promotion pay, perquisites and targets, are allowed to cumulate since recruitment can not be done alter every decision epoch. An estimate of the expected time to recruitment, is discussed, taking the time to recruitment as a random, variable. Its variance is also obtained and Numerical illustration provided.

1 illus, 1 table, 3 ref

008302   Mewomo O T (Department of Mathematics, University of Agriculture, P.M.B. 2240, Abeokuta, Nageria, Email: tosinmewomo@yahoo.com) : On n - weak amenability of Ress semigroup algebras. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 547-55.

Let S be a Rees matrix semigroup. It is shown that l^{1 (S) is (2k + l)-weakly amenable for k ∈ Z+.}

11 ref

008301   Meenakshi A R;Krishnamoorthy S;Vasudevan B (Mathematics and Computer Applications Dep, Karpagam Univ, Coimbatore-641 021, Email: arm_meenakshi@yahoo.co.in) : On conjugate k-EP matrices. Ultra Scient phys Sci 2009, 21(2M), 399-404.

The concept of Conjugate k-EP (Con-k-EP) matrix is introduced. Relations between Con-k-EP. Con-EP, k-EP and EP matrices are discussed.

6 ref

008300   Meenakshi A R;Krishnamoorthy S;Gunasekaran K (Mathematics and Computer applications Dep, Karpagam Univ, Coimbatore, Tamil Nadu) : On secondary range Hermitian matrices. Ultra Scient phys Sci 2009, 21(2M), 371-6.

Concept of secondary range Hermitian (s-EP) matrices is introduced as a generalization of s-Hermitian and EP matrices. Necessary and sufficient conditions are determined for a matrix to be s-EP_r (s-EP and rank r) Equivalent characterizations of a s-EP matrix are discussed. As an application, it is shown that the class of all EP matrices having the same range space form a group under multiplication.

6 ref

008299   Mathur P K;Gupta M (Mathematics Dep, Saifia P.G. College of Science & Education, Bhopal, M.P.) : Triple series equations involving the product of 'r' generalized bateman-K functions. Ultra Scient phys Sci 2009, 21(2M), 580-2.

Solution for the series equations is obtained by using the multiplying factor technique.

6 ref

008298   Mao L X (Insatitute of Mathematics, Nanjing Institute of Technology, Nanjing 211167, Email: maolx2@hotmail.com) : On P-Coherent endomorphism rings. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 557-67.

Ring is called right P -coherent if every principal right ideal is finitely presented. Let M_R be a right R-module. We study the P-coherence of the endomorphism ring S of M_R It is shown that S is a right P-coherent ring if and only if every endomor-phism of M_R has a pseudokernel in add M_R; S is a left P -coherent ring if and only if every endomorphism of M_R has a pseudocokernel in add M_R. Some applications are given.

14 ref

008297   Malviya N;Magarde D;Jhade P K (Mathematics Dep, R.K.D.F. Institute of Science and Technology, Bhopal, M.P.) : Some fixed point theoems for asymptotically regular maps in hilbert space. Ultra Scient phys Sci 2009, 21(2M), 357-60.

Aim of the paper is to prove fixed-point theorems for asymptotically T-regular sequences and asymptotically regular maps using parallelogram law in Hilbert space, which give proper generalization of recent results due to Engle Browder and Petryshyn, Hardy and Rogers.

4 ref

008296   Malgonde S P (Mathematics Dep, Bract's Vishwakarma Institute of Technology, Bidwewadi, Pune-411 037, Email: spmalgonde@rediffmail.com) : On a distributional finite integral transform with q-Dimensional bessel function as kernel. Bull pure appl Math 2009, 3(2), 175-91.

In this paper, the finite integral transform with q-dimensional Bessel function, as kernel, is extended to certain spaces of generalized functions by modifying the method developed by Zemanian in his research on variety of distributional series expansions in such a way that the theory of Sneddon in relation with finite Hankel transformation appears as a particular case. An inversion formula is established in the distributional sense. The operational calculus thus generated is used in solving certain partial differential equation of generalized Dirichlet's problem and of heat conduction in a long solid cylinder containing heat source of a particular type.

7 ref

008295   Lateef D;Sayyed S A;Bhattacharyya A (Mathematics Dep, Jadavpur Univ, Kokata-700 032) : Common fixed point for multivalued and compatible maps. Ultra Scient phys Sci 2009, 21(2M), 503-8.

Generalization of multivalued hybrid contraction and Meir- Keeler type multivalued maps are obtained in a metric space. Result is a generalize concept of commuting and compatible mappings under some conditions and corresponding results of ^{1,2,3,4,5,6,7,8,9,10,11,12, and many others.}

15 ref

008294   Lahiri B K;Chakrabarty M K;Sen A A (NO, , B-1/146, Kalyani, West Bengal-741 235) : Star operation in product spaces. Natn Acad Sci Lett 2008, 31(1-2), 27-9.

Completeness of the product space of two given metric spaces are studied by considering an operation suitably defined between two non-negative real numbers.

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008293   Kulkarni S H;Nair M T;Ramesh G (Mathematics Dep, Indian Institute of Technology Madras, Chennai-600 036, Email: shk@iitm.ac.in) : Some properties of unbounded operators with closed range. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 613-25.

Let H₁, H₂ be Hilbert spaces and T be a closed linear operator defined on a dense subspace D(T) in H₁ and taking values in H₂. In this article we prove the following results: (i) Range of T is closed if and only if 0 is not an accumulation point of the spectrum σ(T*T) of T*T, In addition, if H₁ = H₂ and T is self-adjoint, then (ii) inf {||Tx||: x ∈ D(T) ∩ N(T)^⊥ ||x|| = 1} = inf {|λ|: 0 ≠ λ ∈ σ(T)}, (iii) Every isolated spectral value of T is an eigenvalue of T, (iv) Range of T is closed if and only if 0 is not an accumulation point of the spectrum σT of T, (v) σ(T) bounded implies T is bounded. Authors prove all the above results without using the spectral theorem. Also, we give examples to illustrate all the above results.

16 ref

008292   Krishnamoorthy S;Gunasekaran K;Bkn Muthugobal (NO, Mathematics Government Arts College, Kumbakonam-621 001) : On 4 - inverses of GM matrix. Ultra Scient phys Sci 2009, 21(2M), 465-8.

Initiates to fine the 4 - inverse of GM matrix on a set of two distinct integers. The eigen value and eigen vectors are determined for the GM matrix.

7 ref

008291   Krishnamoorthy S;Gunasekaran K;Bkn Muthugobal (NO, Mathematics Government Arts College, Kumbakonam-612 001) : On 3 - inverses of GM matrix. Ultra Scient phys Sci 2009, 21(2M), 451-4.

Initiate to fine the 3 - inverse of GM matrix on a set of two distinct positive integers. The eigen value and eigen vectors are determined for the GM matrix.

7 ref

008290   Jiajin W;Jun Y;Shufeng Y (Mathematics and Computer Science, Chengdu University, 610106 Chengdu, China, Email: wenjiajin623@163.com) : Optimal version of an inequality involving the third symmetric means. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 505-16.

Let (GA)^[k]_n (a), A_n(a), G_n(a) be the third symmetric mean of k degree, the arithmetic and geometric means of a₁, ..., a_n (a_i <62> 0, i = 1, ..., n), respectively. By means of descending dimension method, proves that the maximum of p is (k-1)/(n-1) and the minimum of q is n/(n-1) (k-1/k)^k/n so that the inequalities (G_n(a))^1-p (A_n(a))^p ≤ (GA)^[k]_n (a) ≤ (1 - q) G_n(a) + qA_n(a) (2 ≤ k ≤ n -1) hold.

16 ref

008289   Jain M K;Dalela A K;Tiwari S K (School of Studies in Mathematics, Vikram Univ, Ujjain, M.P., Email: Manoj.kumarjain@gmail.com) : Fuzzy mathematical solution's of customer relationship management (financial sector for current economic era). Ultra Scient phys Sci 2009, 21(2M), 477-84.

Exploring issues that put in the fundamentals of CRM for franchise's network optimization and discuss mathematical solution for that. financial Institution's management team could use the findings of this study, in order to determine specific component in designing financial services and products, which would add in customers' satisfaction and reliability. The proposed approach could have significant implications for enlarging the duration of the relationship among customer and financial institution and for maximizing their franchise performance. There are different issues relating to the reorganization of financial industry are examined. Specifically the performance of a franchise network, the online service's as an alternative distribution channel and the duration of the relationship among customers (individuals or enterprises) are the three interrelated parties. fuzzy optimization techniques and generalized linear models are used in order to determine financial products and services which are offered to financial clients through traditional and Internet channels, forecasting customers' attitudes (adoption or rejection) to the new products and the time horizon of their cooperation with their sector.

14 ref

008288   Huang M;Ponnusamy S (Mathematics Dep, Hunan Naormal Univ, Changsha, Hunan 710081, People's Republic of China, Email: mzhuang79@yahoo.com.cn) : Decomposition and removability properties of John domains. Proc Indian Acad Sci-Mathl Sci 2008, 118(3), 357-70.

Characterize John domains in terms of John domain decom-position property. In addition, we also show that a domain D in R^{n is a John domain if and only if DP is a John domain, where P is a subset of D containing finitely many points of D. The best possibility and an application of the second result are also discussed.}

15 ref

008287   Hakeem A;Lata S;Navalagi G (Studies in Mathematics University of Mysore Dep, Manasagangotyri, Mysore-570 006, Email: hakim_albdoie@yahoo.com) : On fuzzy semi α-open sets and fuzzy semiα-continuous mappings. Bull pure appl Math 2009, 3(2), 158-69.

Extends the notion of semi α-open sets of General topology to fuzzy topology, and study some notions based on this new concept in fuzzy topology. Also, we study the relations between fuzzy semi α-open sets and other types of fuzzy open sets. Also introduced the concept of fuzzy semi α-continuous mapping and other weaker forms of fuzzy semi α-continuous mapping and discuss their relations with fuzzy continuous mappings and other weaker forms of fuzzy continuous mappings. Counter examples are given to show the non-coincidence of these mappings.

4 illus, 9 ref

008286   Gupta V P (Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: vpgupta@imsc.res.in) : Planar algebra of the subroup-subfactor. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 583-612.

Authors gives an identification between the planar algebra of the subgroup-subfactor R x H ⊂ R x G and the G-invariant planar 0subalgebra of the planar algebra of the bipartite graph *_n, where n = [G : H]. The crucial step in this identification is an exhibition of a model for the basic construction tower, and thereafter of the standard invariant of R x H ⊂ R x G in terms of operator matrices. Also obtain an identification between the planar algebra of the fixed algebra sub-factor R^G ⊂ R^H and the G-invariant planar subalgebra of the planar algebra of the 'flip' of *_n.

11 ref

008285   Gupta O P;Badshah V H (School of Studes in Mathematics, Vikram Univ, Ujjain-456 010) : Common fixed point theorems in Hilbert spaces. Ultra Scient phys Sci 2009, 21(2M), 439-42.

Proves a unique common fixed point theorem on a subset of a Hilbert space. The result presented generalizeses and extended some previously know result.

4 ref

008284   Gumber D K;Ram Karan;Pal I (School of Mathematics and Computer Applications, Thapar Univ, Patiala-147 004, Email: dkgumber@yahoo.com) : Some augmentation quotients of integral group rings. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 537-46.

Let G be a group and H be a subgroup of G. A complete description of Δ(G)Δ^{n (H)/Δn+1 (H) is given, and as a consequence the structures of Δ(G)/Δ(H) and Δ2(G)/Δ2(H) are determined. Also, the structure of Δn(G)/Δn (H) for all n ≥ 1 is determined when G is a free group.}

17 ref

008283   Garg A (Mathematics Dep, S.M.L. (PG) College, Jhunjhunu-333 011, Email: atuljjn@yahoo.co.in) : Some new relations of generalized VOIGT-function involving partial derivatives. Ultra Scient phys Sci 2009, 21(2M), 415-18.

Aim of the paper is to present multivariable and multiindices study of the generalized Voigt- function which plays an important role in the several diverse fields of physics such as astrophysical spectroscopy and the theory of neutron reactions. Derivative of Voigt function is introduced first time here. Some important recurrence relations involving derivative are also given in terms of generalized Voigt function.

14 ref

008282   Ganapathy Raman R;Sattanathan R (Maths. Dep, D.G. Vaishnav College, Chennai) : Circular chromatic number of lexicographic product. Ultra Scient phys Sci 2009, 21(2M), 583-4.

Of interest in this theory is the question of determining the circular chromatic number of product graphs. There are four kinds of graph products: (i) Cartesian Product (G x H), (ii) Categorical Product (G x H), (iii) Lexicographic Product (G, H) and (iv) Strong product (GO H). Discusses some theorems on circular chromatic number of lexicographic products.

9 ref

008281   Galewski M (Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland, Email: galewski@math.uni.lodz.pl) : On existence and stability of solutions for higher order semilinear dirichlet problems. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 627-35.

Provides existence and stability results for semilinear Dirichlet problems with nonlinearity, satisfying general growth conditions.Consider the case when both the coefficients of the differential operator and the nonlinear term depend on the numerical parameter. Show applications for the fourth order semilinear Dirichlet problem.

11 ref

008280   El-Alem M;El-Sobky B;El-Aziz M A (Mathematics and Computer Science Faculty of Science, Kuwait Univ, Safat-13060, Email: mr_azizmona@yahoo.com) : Extending Goodman's method to general nonlinear programming. Bull pure appl Math 2009, 3(2), 135-41.

A new algorithm for solving the general nonlinear programming problem is introduced. The algorithm uses the Coleman-Li scaling matrix together with a formulation for Newton's interior point method and can be viewed as a generalization of Goodman's method to general nonlinear programming.

6 ref

008279   Draouil B (Departement de Mathematiques, Faculte des Svciences de Bizxerte, 7021 Jarzouna, Tunisia, Email: Belgacem.Draouil@fsb.rnu.tn) : Local duality for 2-dimensional local ring. Proc Indian Acad Sci-Mathl Sci 2008, 118(4), 525-36.

Proves a local duality for some schemes associated to a 2-dimensional complete localfring whose residue field is an n-dimensional local field in the sense of Kato-Parshin, Our results generalize the Saito works in the case n = 0 and are applied to study the Bloch-Ogus complex for such rings in various cases.

19 ref

008278   Dorsett C (Mathematics Dep, Texas A&M Univ Commerce, Texas 75429 (USA)) : New characterizations of semi-T₂, semi-T₁, and semi-T₀ speces. Ultra Scient phys Sci 2009, 21(2M), 491-4.

Studay shown that semi-T_i reduces to T_i, i = 0, 1, 2, when an appropriate change of topology is invoked.

13 ref

008277   Das T;Mukherjee R N;Chaudhuri K S (Mathematics Dep, U.I.T., Burdwan Univ, Burdwan-713 104, Email: tapasi_10000@yahoo.co.in) : Combined harvesting of two competing fish species affected by toxicity. Bull pure appl Math 2009, 3(2), 276-96.

Bioeconomic exploitation of two competing fish species, each of which obeys the law of logistic growth and releases a substance toxic to the other, is discussed by using a reasonable catch-rate function instead of the usual 'catch-per-unit-effort hypothesis'. Here both the species are harvested. The dynamical behaviour of the exploited system is examined. The possibility of existence of a bionomic equilibrium is considered. The optimal harvesting policy is studied by using Pontryagin's maximum principle. Finally, some examples are carried out to illustrate the results of the model both numerically and graphically.

4 illus, 15 ref

008276   Chenna Kesavulu K;Nagarajan A S;Ramakrishna S (Mathematics Dep, S V Univ, Tirupati, Email: kondari_chennakesavulu@yahoo.co.in) : Radiation and mass transfer effects on unsteady MHD free natural convection flow past and inclined surface - A numerical study. Ultra Scient phys Sci 2009, 21(2M), 343-52.

Study is performed to analyze the radiation effects on MHD unsteady natural free convection flow past an inclined surface with variable surface temperature in the presence of transversal uniform magnetic field. The governing equations are transformed into a linear algebraic system and the solution is obtained by employing implicit finite-difference scheme of Crank-Nicolson type. A parametric study is performed to illustrate the influence of radiation parameter, magnetic parameter, Prandtl number and Schmidt number on velocity profile, temperature profile and concentration profiles. The numerical results reveal that the radiation has significant influences on the velocity and temperature profiles. The profiles of the dimensionless velocity, temperature and concentration distributions are shown graphically for various values of the parameters entering into the problem.

12 illus, 5 tables, 10 ref

008275   Chenna Kesavulu K;Nagarajan A S;Ramakrishna S (Mathematics Dep, S V Univ, Tirupati, Email: kondari_chennakesavulu@yahoo.co.in) : Heat and mass transfer effects on MHD free convection flow of dissipative fluid past an infinite vertical porous isothermal plate. Ultra Scient phys Sci 2009, 21(2M), 319-26.

Numerical study is performed to analyze the effect of mass transfer on unsteady MUD free convection flow of dissipative fluid past an infinite vertical porous isothermal plate taking into account viscous dissipative heat under the influence of transverse magnetic field. The governing equations are solved numerically by applying finite difference method. The velocity, the temperature and the concentration are studied for different parameters like magnetic field parameter M, suction parameter λ, Schmidt number Sc, Eckert number E, Grashof number Gr and modified Grashof number Gm. The numerical results are presented graphically for different parameters. The numerical values of Skin-frictions are presented in tabular form.

11 illus, 6 tables, 11 ref

008274   Chena Ram;Mathur N (Mathematics & Statistics Dep, Jai Narain Vyas Univ, Jodhpur-342 005, Email: crc2007@rediffmail.com ) : Application of fractional integral operators to generalized subclasses of certain geometric functions. Bull pure appl Math 2009, 3(2), 242-53.

Certain generalized subclasses M_n(b,p,A,B,η) and M_n' (b,p,A,B,η) of meromorphic starlike and convex functions, respectively, related to complex order have been introduced. Some results for the same subclasses studied in this paper, have been established on a class of analytic functions generated by two functions. Particular cases of the main results are mentioned.

9 ref

008273   Chawla M M;Kalla S L (Mathematics & Computer Science Dep, Kuwait University, P.O.Box 5969, Safat 13060, Kuwait, Email: drmmchawla@yahoo.com) : Simpson-type scheme for the valuations of European and American options. Bull pure appl Math 2009, 3(2), 212-18.

Presents a new Simpson-type scheme for the time integration of the Black-Scholes equation of option pricing. An existing scheme based on the trapezoidal rule, called the Crank-Nicolson scheme, often produces unwanted oscillations in the computed solution especially for large time steps taken. In contrast, since our present Simpson-type scheme is L-stable, it provides quite stable approximations without oscillations. With the obtained Simpson-type scheme, we consider the valuation of European options and the American options via the linear complementarity formulation. Computational and graphical comparison of the performance of the present Simpson-type scheme with the Crank-Nicolson scheme are provided for the valuation of both European and American options.

2 illus, 16 ref

008272   Chaudhary R C;Jain P (Mathematics Dep, Rajashtan Univ, Jaipur-302 055, Email: jainpreeti28@rediffmail.com) : Unified approach to analytical solution of hydromagnetic flow of a radiating fluid over an oscillating plate with variable temperature and mass diffusion. Bull pure appl Math 2009, 3(2), 297-321.

The problem of magnetohydrodynamic free-convection flow past an infinite vertical oscillating plate in the presence of chemical species concentration and thermal radiation effects has been solved. The plate temperature and concentration level near the plate is raised linearly with time and the fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The governing equations are non-dimensionalized and their solutions are obtained in closed form using Laplace-transform technique. A parametric study is performed to illustrate the influence of the radiation parameter, magnetic parameter, thermal Grashof number, modified Grashof number, time, Schmidt number and frequency parameter on the velocity, temperature and concentration profiles.

10 illus, 23 ref

008271   Chaudhary R C;Jain A (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: rcchaudhary@rediffmail.com) : Free convection in boundary layer flow of a dissipative magneto-micropolar fluid from radiating surface. Bull pure appl Math 2009, 3(2), 219-41.

A boundary layer analysis is presented to study the flow of magneto-micropolar fluid past a radiate vertical surface in the presence of viscous dissipation. The plate moves with a constant velocity and heat is supplied to it at a constant rate (CHF). A uniform magnetic field acts in transverse direction to the plate which absorbs the micropolar fluid with constant suction velocity. Cogley approximation is used to describe the radiative heat flux in the energy equation. Numerical result of velocity distribution of micropolar fluid is compared with the corresponding flow problem for a Newtonian fluid. The flow variables are presented graphically with various values of fluid properties and flow conditions. The physical aspects of the problem are also discussed.

10 illus, 26 ref

008270   Chandrasekhara Rao K;Kannan K;Narasimhan D (Mathematics Dep, Srinivasa Ramanujan Centre, Sastra University, Kumbakonam-612 001, Email: k.chandrasekhara@redifmail.com) : Generalized star star regular closed sets in bitopological spaces. Natn Acad Sci Lett 2008, 31(1-2), 31-3.

Aim of the communication is to introduce the concepts of τ₁ τ₂ - generalized star star regular closed sets, μ₁ τ₂ -generalized star star regular open sets and study their basic properties in bitopological spaces.

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