024055   Crnkovic D;Held D (Mathematics Dep, Faculty of Philosophy, , Omladinska 14, 51000 Rijeka, Croatia, Email: deanc@mapef.ffri.hr) : On some Menon designs with parameters (324, 153, 72). J appl Algebra Discrete Structs 2006, 4(1), 23-33.

There are exactly 10 symmetric (324, 153, 72) designs admitting an automorphism group isomorphic to Frob_19.9 x Z₂ acting with orbit size distribution (1, 19, 38, 38, 38, 38, 38, 38, 38, 38) for blocks and points. For eight of these designs, the full automorphyism group has order 342 and is isomorphic to Frob_19.9 x Z₂, one design has Frob_19.9 x Z₄ an the remaining design Frob_19.9 x Z₈ as full automorphism group. All 10 designs are self-dual. The derived design (with respect to the fixed block) of the design with full automorphism group of order 1368 is 1 rotational.

8 ref

024054   Chen H (Mathematics Dep, Zhejiang Normal University, Jinhua 321004, Email: chyzxl@hunnu.edu.cn) : Note on quasi-injective modules. J appl Algebra Discrete Structs 2006, 4(1), 13-21.

Let A be a quasi-injective right R-module. It is shown that for any R-monomorphisms f, g : M → A, there exist a split R-epimorphism h₁ ∈ End_R (A) and a split R-monomorphism h₂ ∈ End_R (A). x

10 ref

024053   Chakraborty P S;Pal A (NO, Institute of Mathematical Sciences, CIT Campus, Taramani, Chennai-600 113, Email: parthac@msc.res.in) : On equivariant dirac operators for SV_q(2). Proc Indian Acad Sci-Mathl Sci 2006, 116(4), 531-41.

12 ref

024052   Bhaumik R N;Bhattacharya J (Mathematics Dep, Tripura University, Suryamaninagar-799 130) : Nearly isocompactness in L-fuzzy topological spaces. Acta Cienc Indica-Math 2005, 31(4), 1063-6.

Bhaumik and Bhattacharya introduced the concept of isocompactness in L-fuzzy topological spaces. Introduces a weaker form of L-fuzzy isocompactness, namely, nearly L-fuzzy isocompactness and to study some of the basic properties of these spaces.

10 ref

024051   Bhatia R;Choi M D (Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, New Delhi-110 016, Email: rbh@isid.ac.in) : Corners of normal matrices. Proc Indian Acad Sci-Mathl Sci 2006, 116(4), 393-9.

Various conditions on matrices B and C under which they can he the off-diagonal blocks of a partitioned normal matrix have been studied.

2 ref

024050   Bhagtani M (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Multivalent analytic functions and Gaussian hypergeometric functions. Acta Cienc Indica-Math 2005, 31(4), 1305-12.

Role of the Gaussian hypergeometric function in geometric function theory is studied. Obtained the conditions on a, b and c so that z^p F(a, b; c; z) is certain subclasses of multivalent functions which represents some parbolic domain. Operators related to the hypergeometric functions are also examined. Follows the methods given by Silverman (1993) and Swaminathan (2004) to establish the results.

7 ref

024049   Belavkin V P;Gregory L (School of Mathematical Sciences, Nottingham Univ, Nottingham NG7 2RD, Email: viacheslav.belavkin@nottingham.ac.uk) : Representations of homogeneous quantum levy fields. Proc Indian Acad Sci-Mathl Sci 2006, 116(4), 477-88.

Authors study homogeneous quantum Levy processes and fields with independent additive increments over a noncommutative *-monoid. These are described by infinitely divisible generating state functional, invariant with respect to an endomorphic injective action of a symmetry semigroup. A strongly covariant GNS representation for the conditionally positive logarithmic functionals of these states is constructed in the complex Minkowski space in terms of canonical quadruples and isometric representations on the underlying pre-Hilbert field space. This is of much use in constructing quantum stochastic representations of homogeneous quantum Levy fields on Ito monoids, which is a natural algebraic way of defining dimension free, covariant quantum stochastic integration over a space-time indexing set.

8 ref

024048   Bean D (Mathematics and Computer Science Dep, University of San Diego, San Diego, CA 92110-2492, USA, Email: dbean@sandiego.edu) : Restricted transmit scheduling. J Computnl Math optimiz 2006, 2(2), 65-80.

Limiting scheduling of a satellite communictions network to the transmit side only, necessary and sufficient conditions for scheduling transmitters and some scheduling algorithms are obtained when available channels vary over time, transmitters have different restrictions on times when they can transmit, and when different transmitter types access different sets of channels.

16 ref

024047   Bathul S (Mathematics Dep, JNTU College of Engineering, Kukatpally, Hyderabad, Andhra Pradesh) : Three dimensional flow and heat transfer along a plane wall with varying suction. Acta Cienc Indica-Math 2005, 31(4), 1067-78.

Flow and heat transfer along a plane wall are analysed when transverse varying suction velocity distribution is introduced. The flow is three dimensional due to the periodic suction velocity transverse to the potential flow. Two particular cases of weak disturbances in suction velocity are considered and obtained analytic expressions for skin friction and heat transfer coefficient. It is found that in both the cases magnitude of skin friction along the man and perpendicular to the direction of main flow increases with R. The coefficient of heat transfer also increases with R as well as with σ in both the cases.

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024046   Baskar Babujee J (Mathematics Dep, Easwari Engineering College, Ramapuram, Chennai-600 089) : Antimagic labeling on certain classes of graphs. Acta Cienc Indica-Math 2005, 31(4), 1027-30.

Ringel [1] conjectured that every connected graph ∇ K₂ is antimagic. Introduces the concept of edge label and prove that every complete graphs, cycle graphs and wheel graphs are antimagic.

4 illus, 2 ref

024045   Balasubramanian S (P.G. Mathematics Dep, Sri Subbaraya Narayana College, Narasaraopet-522 601) : Semi-lindel of Bitopological spaces. Acta Cienc Indica-Math 2005, 31(4), 973-80.

Introduces a new class of Bitopological spaces, namely, weak-and strong-semi-Lindel of Bitopotogical spaces.

7 ref

024044   Bagwan A;Sharma S (Tidal Hydraulics Div, Central Water and Power Research Station, Khadakwasla, Pune-24) : Gregus type common fixed point theorems on normed space. Acta Cienc Indica-Math 2005, 31(4), 1135-40.

Proves a common fixed point theorem of Gregus type under the condition of compatible mappings of type (α), which is a generalization of various common fixed theorems on normed space and Banach space.

14 ref

024043   Artiras Dubickas (Mathematics and Informatics Dep, Vilnius University, Naugarduko 24, LT-03225 Vilninus, Lithuania, Email: arturas.dubickas@maf.vu.lt) : Conjugate dimension of a field extension. J appl Algebra Discrete Structs 2006, 4(1), 57-63.

Studied conjugate dimension n of a separable extension K / k defined as the dimension of the k-vector space spanned by all conjugate fields of K over k as linear spaces. Sharp bounds for n are given in terms of d=[K:k]. The cases for which these bounds are attained are also described.

10 ref

024042   Anitha M;Thangavelu P (Mathematics Dep, Govindammal Aditanar College for Women, Tiruchendur-628 215) : Pre-generalized pre-regular-closed sets. Acta Cienc Indica-Math 2005, 31(4), 1035-40.

In 2002, Veerakumar defined pre-semi-closed sets in topological spaces and investigated their properties. The purpose of this is to introduce pre-generalized pre-regular closed (briefly pre-gpr closed) sets and to study their properties. This class of sets is properly placed between the class of pre-closed sets and the class of pre-semi-closed sets. Characterizes pre-gpr-T_1/2 spaces and gpr-T_1/2 spaces and discuss their properties.

11 ref

024041   Alagar R (Mathematics Dep, Asian Memorial College of Engineering and Technology, Chengalpattu-603 105) : Finite product topologies with respect to ideals. Acta Cienc Indica-Math 2005, 31(4), 1125-8.

Given a topological space (X, τ) and an ideal ℑ in X, a finer topology τ^* in X can be associated with τ and ℑ. Given two topological spaces (X, τ₁), (Y, τ₂) and ideals ℑ, υ in X, Y respectively, an ideal ℑ x υ in X x Y, called the product ideal of ℑ and υ, in X x Y. Investigates inclusion relations between τ₁^* x τ₂^* and (τ₁ x τ₂^* and all the conditions under which τ₁^* x τ₂^* = (τ₁ x τ₂)^*.

5 ref

023078   Zaharescu A;Zaki M (Mathematics Dep, Illinois Univ at Urbana-Champaign, 409 W. Green Street, Urbana, Il-61801, USA, Email: zaharesc@math.uiuc.edu) : Derivations and generating degrees in the ring of arithmetical functions. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 167-75.

Studied a family of derivations in the ring of arithmetical functions of several variables over an integral domain, and compute the generating degrees of the ring of arithmetical functions over the kernel of these derivations.

10 ref

023077   Yuksel S;Acikgoz A;Gursel E (Mathematics of Dep, Selcuk Univ, 42031 Campus-Konya Turkey, Email: syuksel@selcuk.edu.tr ) : New classes of functions in some ideal topological spaces. Bull Calcutta Mathl Soc 2006, 98(5), 417-28.

Gives a new class of functions called θ-I-somewhat open functions in some ideal topological space. Some characterizations and several fundamental properties of this class of functions are obtained. Also, its relationship with other types of functions is investigated.

9 ref

023076   Xiong W;Lin W (Information and Computing Science Dep, Guangxi Institute of Technology, Liuzhou, Guangxi-545 006 P.R. China, Email: xiongwl@163.com) : Uniqueness of meromorphic functions concerning differential polynomials. J Analysis Applic 2006, 4(1), 51-63.

Deals with the uniqueness problems on meromorphic functions concerning differential polynomials that share one small function.

7 ref

023075   Udriste C;Udriste A (Mathematics Dep, University Politehnica of Bucharest Splaiul Independentei 313, 77206, , Email: udriste@mathem.pub.ro) : From flows and meteries to dynamics and winds. Bull Calcutta Mathl Soc 2006, 98(5), 389-400.

Shows that any flow can be enveloped by a conservative dynamics using a semi-Riemann metric g on M. This kind of dynamics was called geometric dynamics (Udriste and Udriste 1996, Udriste and Udriste 2000). The given vector field, the initial semi-Riemann metric, the Levi-Civita connection, and an associated (1, 1)-tensor field are used to build a new geometric structure (e.g., semi-Riemann-Jacobi, semi-Riemann-Jacobi-Lagrange, semi-Finsler-Jacobi, etc.) on the manifold M ensuring that all the trajectories of a geometric dynamics are pre-geodesics (Lorentz-Udriste world-force law). Implicitly, author solved a problem rised fiist by Poincare: find a suitable geometric structure that converts the trajectories of a given vector field into geodesics. The first two Sections are the same with those in (Udriste and Udriste 2000). Also refers to geometric dynamics and winds produced by three canonical flows and metrics on 3-dimenslonal manifolds.

13 ref

023074   Tiwari B (Mathematics of Dep, B.R.D.P.G. Coll, Deoria-274 001, Email: banktesh76@yahoo.com) : On Four dimensional semi-C-reducible Finsler space without Kikuchi condition. Bull Calcutta Mathl Soc 2006, 98(5), 481-6.

Purpose of is to represent Kikuchi condition for conformal flatness in terms of main scalars of a four dimensional Finsler space and to study a four dimensional semi-C-reducible Finsler space without Kikuchi condition.

9 ref

023073   Thangadurai R (NO, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad-211 019, Email: thanga@hri.res.in) : Variant of Davenport's constant. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 147-58.

Let p be a prime number. Let G be a finite abelian p-group of exponent n (written additively) and A be a non-empty subset of ]n[:={1,2,...,n} such that elements of A are incongruent modulo p and non-zero modulo p. Let k ≥ D(G)/|A| be any integer where D(G) denotes the well-known Davenport's constant. Proved that for an sequence g₁, g₂,...,g_k (not necessrily distinct) in G, one can always extract a subsequence g_i1, g_i2,...,g_i1 with 1≤l≤ k such that ∑^l_j1 a_jg_ij=0 in G, where a_j ∈ A for all j. Also provided examples where this bound cannot be improved. Furthermore, for the cyclic groups, Prove some sharp results in the direction. Explored the relation between this problem and a similar problem with prescribed length. The proof of Theorem 1 uses group-algebra techniques, while for the other theorems, used elementary number theory techniques.

8 ref

023072   Thakur C;Manoj Kumar;Mahan M K (Math Dep, B.I.T., Sindri 828 123) : Exct solutions of steady othogonal plane MHD flows through porous media. Bull Calcutta Mathl Soc 2006, 98(6), 583-96.

The two-dimensional motion of steady orthogonal MHD flows of an incompressible electrically conducting fluid through porous media has been considered. System of equations in the velocity field that the flow must satisfy has been determined and stream function has been introduced. This stream function is required to satisfy a system of two equations for this flow problem. Complex variable technique has been employed and exact solutions for three different flow problems have been determined. Finally, flows with isometric geometry have been studied.

9 ref

023071   Tascu I (Mathematics & Computer Sci Dep, North Univ of Baia Mare, Victoriei 76, 43012 Baia Mare, Romania, Email: itascu@yahoo.com) : Construction of the quadratures by the method of parameters. J Approximation Theor Applic 2006, 2(1), 5-10.

Uses a method of parameters given by D. D. Stancu in and for construction of quadratures formulas of gauss-Christoffel type. Presents the algorithm for finding the Gaussian nodes, the coefficients and the remainder of the quadrature formulae.

10 ref

023070   Takahiro Sudo (Mathematical Sciences Dep, Faculty of Science, Ryukyus Univ, Nishihara, Okinawa-903 0213, Email: sudo@math.u-ryukyu.ac.jp) : Defining the locally tracial rank for continuous field C-algebras. Int Rev pure appl Math 2006, 2(1), 45-8.

Introduces a notion (that is the locally tracial rank) for continuous field (Calgebras as a modification of the tracial rank of Lin. Also consider its basic properties.

3 ref

023069   Sundar P;Sadhasivam V (Mathematics of Dep, Kandaswami Kandar's College, Paramathi Velur-638 182, Email: abdella-77@yahoo.com) : Oscillation of bounded solutions of second order neutral difference equations with positive and negatie coefficients. Bull Calcutta Mathl Soc 2006, 98(5), 455-64.

Sufficient conditions have been obtained for the oscillation of bounded solutions of a class of homogeneous and non-homogeneous linear second .order neutral difference equations with positive and negative coefficients. Several examples are inserted into the text to illustrate the results.

19 ref

023068   Su Y;Qin X (Mathematics Dep, Tianjin Polytechnic Univ, Tianjin-300 160, Email: qxlxajh@163.com) : Strong convergence of modified Ishikawa iterations for nonlinear mappings. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 97-107.

Proved a strong convergence theorem of modified Ishikawa iterations for relatively asymptotically nonexpansive mappings in Banach space. The results extend and improve the recent results by Nakajo, Takahashi, Kim, Xu, Matsushita and some others.

19 ref

023067   Singh R N;Pandey M K (Mathematics Sci of Dep, A.P.S. Univ, Rewa-486 003) : Some properties of a semi symmetric non-metric connection on a Riemannian manifold. Bull Calcutta Mathl Soc 2006, 98(5), 443-54.

Deals with Riemannian manifold admitting a semi-symmetric non-metric connection with recurrent torsion tensor and obtained conditions for symmetry of Ricci tensor of semi-symmetric non-metric connection and existence of the gradient vector field. Among others it is shown that if the curvature tensor of the semi-symmetric non-metric connection vanishes and torsion tensor is recurrent, then manifold becomes a pseudo Ricci symmetric manifold.

6 ref

023066   Singh B B (Mathematics Dep, Dr. Babasaheb Ambedkar Technol Univ, Lonere-402 103) : Asymptotic behaviour of the steady laminar incompressible boundary layer flows. Bull Calcutta Mathl Soc 2006, 98(6), 607-12.

This paper deals with the asymptotic behaviours, as the similarly variable 'n' tends to infinity, of the solutions of equations governing the steady laminar incompressible boundary layer flows over a rotating disk in the presence of magnetic field; the discussion being based on the asymptotic integration of second order linear differential equations. It has been found that the principal and linearity independent solutions will exhibit asymptotic nature only under certain extra physical conditions.

15 ref

023065   Sharma S D;Sharma A K;Ahmed S (Mathematics Dep, Jammu Univ, Jammu-180 006, Email: somdatt_jammu@yahoo.co.in) : Carleson measures in a vector-valued Bergman space. J Analysis Applic 2006, 4(1), 65-76.

Vector-valued Bergman spaces of the upper half-plane are introduced and their reproducing kernel functions are obtained. Finally, authors prove Carleson Theorem for these spaces and use it to characterize composition operators.

13 ref

023064   Shanmugam T N;Singaravelu A;Sivasubramanian S (Mathematics Dep, Anna Univ, Chennai-600 025, Email: shan@annauniv.edu ) : Linear operators associated with parabolic starlike functions. Int Rev pure appl Math 2006, 2(1), 65-75.

7 ref

023063   Shaiju A J;Dharmatti S (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: shaiju@math.tifrbng.res.in) : Infinite dimensional differential games with hybrid controls. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 233-57.

Two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott-Kalton, proved the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.

8 ref

023062   Sengadir T (Mathematics Dep, SSN College of Engineering, Old Mahabalipuram Road, Kalavakkam-603 110) : Semigroups on Frechet spaces and equations with infinite delays. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 71-84.

Authors show existence and uniqueness of a solution to a functional differential equation with infinite delay. Authors choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

14 ref

023061   Sanyal D C;Karak A K (Mathematics of Dep, , Kalyani-741 235, Email: dcs_klyuniv@yahoo.com) : Heat transfer in steady laminar flow and blood oxygenation in channels with boundary irregularities. Bull Calcutta Mathl Soc 2006, 98(6), 613-26.

Analytical solution is obtained for heat transfer in steady laminar flow of blood in a channel with irregular surfaces to understand the abnormal flow conditions caused by the boundary irregularities in diseased vessels. The solution is then used to find the effects of wall roughness upon blood oxygenation in a membrane oxygenator. For sinusoidal variation, the effects of various pertinent parameters upon the flow field, energy loss and oxygen concentration and possible occurrence of separation and reattachment are examined. The secondary flows induced by the cell-plasma and cell-cell interactions are found to be more likely the primary mechanism for a vast increase in oxygenation efficiency.

6 illus, 17 ref

023060   Sanyal D C;Adhikari A (Mathematics of Dep, Univ of Kalyani, Kalyani-741 235, Email: dcs_klyuniv@yahoo.com) : Effect of radiation on MHD vertical channel flow. Bull Calcutta Mathl Soc 2006, 98(5), 487-96.

Effect of radiation on the combined free and forced convection flow of a viscous fluid permeated by a uniform transverse magnetic field through an open-ended conducting vertical channel in slip-flow regime, the walls of the channel being subjected to zero heat flux, is considered. The expressions for velocity, induced magnetic field, temperature, flow rate and the heat transfer coefficient are obtained on the assumption of optically thin limit and the influence of radiation on these entities are shown graphically.

13 ref

023059   Sanjay Kumar;Singh K J (Mathematics Dep, Jammu Univ, Jammu-180 006, Email: sks_jam@yahoo.co.in) : Weighted composition operators in weighted Bergman spaces of bounded symmetric domains. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 185-96.

Studied the weighted composition operators on weighted Bergman spaces of bounded symmetric domains. The necessary and sufficient conditions for a weighted composition operator Wψ to be bounded and compact are studied by using the Carleson measure techniques. In the last section, studied the Schatten p-class weighted composition operators.

18 ref

023058   Sai Sundara Krishnan G;Balachandran K (Math Dep, PSG Coll of Technol, Coimbatore-641 004) : On γ-semi-open sets in topological spaces. Bull Calcutta Mathl Soc 2006, 98(6), 517-30.

In this paper author introduced the concept of γ -semi-open sets in a topological space together with its corresponding γ-semi-closure and γ-semi-interior operators. Also introduced the concept of γ-semi-T_i spaces (i = 0, 1/2, 1,2) and study the relationship between them. Further introduced (γ, β)-semi-continuous maps and (γ, β)-semi- homeomorphism and investigate some of its properties. Finally, introduced the concept of 1γ - T_b and γ - T_d spaces using the concept of γ - gs. closed sets in a topological space and investigate the relationship between them.

9 ref

023057   Sahleh H (Mathematics Dep, Guilan Univ, P.O. Box. 1914, Rasht-Iran, Email: sahleh@guilan.ac.ir) : On the non-abelian tensor square and nilpotency class of a topological group. Int Rev pure appl Math 2006, 2(1), 77-84.

Let G be a topological group. The non-abelian tensor product, G ⊗ G is defined. The aim paper is to give a bound on the nilpotency class of G ⊗ G provided such information is given for G = [G, G]. Also Authors will show that, for G nilpotent of class 2 (i.e. [G, G] in the center of G ), G ⊗ G is abelian.

19 ref

023056   Saez E;Szanto I (Mathematica de Dep, Tecnica Federico Santa Maria Univ, Casilla-110-V, Valparaiso, Chile, Email: esaez@mat.utfsm.cl) : Polycycle and limit cycles in a non-differentiable predator-prey model. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 219-31.

For a non-differentiable predator-prey model, establish conditions for the existence of a heteroclinic orbit which is part of one contractive polycycle and for some values of the parameters, proved that the heteroclinic orbit is broken and generates a stable limit cycle. In addition, in the parameter space, proved that there exists a curve such that the unique singularity in the realistic quadrant of the predator-prey model is a weak focus of order two and by Hopf bifurcations can have at most two small amplitude limit cycles.

10 illus, 11 ref

023055   Ravi Shankar M;Hemantha Kumar G;Anami B S (NO, , ) : Linear predictive coefficient based algorithmic approach for the generation of pitman shorthand language symbols for consonants and vowels. J Analysis Computn 2006, 2(1), 9-17.

Pitman Shorthand Language (PSD) is a widely practiced medium for transcribing/recording Speech To Text (STT) in English Language. This recording medium continues to exist inspite of considerable development in Speech Processing Systems (SPS), because of its ability to record the spoken/dictated text at high speeds of more than 120 words per minute. Hence, the scope exists for exploiting this potential of PSL in the present SPS. In this paper, Linear Predictive Coefficients (LPC) Technique and Euclidean Distance method for generating Consonants and Vowels, of Pitman Shorthand Language from spoken English Language are proposed. LPC analysis is a set of coefficients that describe a digital filter. The features are derived from Linear Predictive Coding (LPC), a technique that attempts to derive the coefficients of a filter that would produce the utterance that is being studied. LPC is useful in speech processing because of its ability to extract and store time varying formant information. The process is divided into two stages. The first stage involves feature extraction wherein short temporal or spectral parameters of speech are extracted. The second stage involves classification of speech parameters wherein the obtained parameters are compared with reference parameters and decision is made based on minimum distortion rule. The features are extracted using LPC technique and classified using Euclidean Distance method. The proposed method is tested on large number of samples, drawn from different speakers and the results are found encouraging.

7 tables, 6 ref

023054   Ravi K;Arun Kumar M (Mathematics Dep, Sacared Heart College, Tirupattur-635 601) : On the generalized Hyers-Ulam-Rassias stability of a cubic functional equation. Int Rev pure appl Math 2006, 2(1), 13-23.

Authors etablish the generalized Hyers-Ulam-Rassias stability for a cubic functional equation f(3x + y) + f(3x-y) = 3f(x + y)+3f(x-y)+48f(x).

17 ref

023053   Popa D (Mathematics Dep, Constanta Univ, 8700 Constanta, Romania, Email: dpopa@univ-ovidius.ro) : Khinchin's inequality, Dunford-Pettis and compact operators on the space C ([0, 1], X). Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 13-30.

It has been proved that if X, Y are Banach spaces, Ω a compact Hausdorff space and U: C(Ω, X) → Y is a bounded linear operator, and if U is a Dunford-Pettis operator the range of the representing measure G (∑) ⊆ DP(X, Y) is an uniformly Dunford-Pettis family of operators and ||G|| is continuous at 0. As applications of this result we give necessary and/or sufficient conditions that some bounded linear operators on the space C([0, 1], X) with values in C_o or l_p (1 ≤ p <60> ∞) be Dunford-Pettis and/or compact operators, in which, Khinchin's inequality plays an important role.

11 ref

023052   Phukan D K (Math Dep, Moran Coll, P.O. Moranhat Assam-785 670) : Hydromagnetic flow and heat transfer past a stretching porous plate with a power-low velocity distribution. Bull Calcutta Mathl Soc 2006, 98(6), 627-36.

The boundary layer flow and heat transfer of an incompressible, viscous, electrically conducting fluid due to a porous plate stretching with a power-law velocity distribution in the presence of a transverse magnetic field, is studied. A special form of magnetic field is chosen so as to yield the similarity equations. A direct numerical solutions of the resulting non-linear ordinary differential equation viz., momentum boundary layer and thermal boundary layer equations are determined using Runge-Kutta shooting algorithm with Newton iterative method for the existing non-dimensional parameters, namely magnetic parameter, suction parameters, and Prandtl number. The effects of the magnetic parameter and suction parameter on the velocity and temperature of the conducting fluid are analysed. It is observed that the effects of the magnetic field are to decrease the dimensionless velocity across the boundary layer and to make rise the dimensionless temperature of the conducting fluid across the boundary layer for fixed Prandtl number. Moreover, the influences of suction are observed to decrease the velocity and temperature of the conducting fluid for constant Prandtl number. Furthermore, the effects of magnetic field are seen to decrease the heat transfer co-efficients at the wall but the effects of suction are seen to increase heat transfer coefficient at the wall for fixed magnetic parameter.

5 illus, 11 ref

023051   Pescar V;Owa S (Mathematics Dep, Transilvania Univ of Brasov, 22000 Brasov, Romania, Email: virgilpescar@unitbv.ro) : Univalence of certain integral operators. J Approximation Theor Applic 2006, 2(1), 11-16.

In view of some integral operators G_α,β f(z), J_γ f(z), and Hγ f(z) for analytic functions f(z) in the open unit disk U, suficient conditions for univalence of the integral operators are discussed.

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023050   Pal P C (Applied Mathematics Dep, ISM, Dhanbad-826 004, Email: pcpal.ism@yahoo.co.in) : On shear wave propagation in a multilayer medium including a fluid - saturated porous solid stratum. Bull Calcutta Mathl Soc 2006, 98(6), 597-606.

The propagation of SH-type waves in a double surface layered medium with an intermediate transverse isotropic fluid saturated porous stratum has been studied. The topmost layer is assumed to be impermeable, elastic, homogeneous and isotropic, where as the lower half space is an inhomogeneous one. The dispersion equation has been derived using the Biot's theory for the porous layer and the theory of elasticity for both the upper and the subjacent half-space. The corresponding dispersion equation has been obtained when both the layer and the semi-infinite medium are assumed to be homogeneous and isotropic. The numerical results obtained for this simplified case have been shown graphically.

3 illus, 11 ref

023049   Oros G I (Faculty of Mathematics & Computer Sci, Babes-Bolyai Univ, 3400 Cluj-Napoca, Romania) : On a nonlinear differential subordination. J Approximation Theor Applic 2006, 2(1), 43-8.

Finds conditions on the complex-valued functions A, B, C, D in the unit disc U such that the differential inequality <157>A(z)z²p"(z) + B(z)zp'(z) + C(z)p²<157> <60> M implies <157>p(z)<157> <60> N, where p is analytic in U, with p(0) = 0.

2 ref

023048   Niranjan K M (Mathematics Dep, Sri Venketeshwara College of Engineering, Vidyanagar, Email: niru_km@yahoo.com ) : Forbidden subgraphs for planar and outerplanar interms of blict graphs. J Analysis Computn 2006, 2(1), 19-22.

Authors characterize trees whose blict graphs are planar in terms of forbidden subgraphs and also present characterization of graphs whose blict graphs are outerplanar in terms of forbidden subgraphs.

4 illus, 5 ref

023047   Najafzadeh S;Kulkarni S R (Mathematics Dep, Fergusson College, Pune-411 004, Email: najafzadeh1234@yahoo.ie) : On a certain class of multivalently harmonic functions. Int Rev pure appl Math 2006, 2(1), 53-65.

New classes of multivalent harmonic functions in terms of linear combination are introuduced. Authors find sufficient coefficient conditions for those classes. Also these estimates are proved to be necessary for HC_p,n (λ, t, α, m). Extreme points, distortion bounds, convex combinations and integral operator for these functions has been found.

023046   Najafzadeh S;Kulkarni S R (Mathematics Dep, Fergusson College, Pune-411 004, Email: najafzadeh1234@yahoo.ie) : On a class of p-valent analytic functions with complex order defined by subordination. Int Rev pure appl Math 2006, 2(1), 35-44.

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023045   Najafzadeh S;Kulkarni S R (Mathematics Dep, Fergusson College, Pune-411 004, Email: najafzadeh1234@yahoo.ie) : Convex subclass of starlike functions in terms of combination of integral operators. Int Rev pure appl Math 2006, 2(1), 25-34.

Let T be the class of functions of the formes f (z)=z-<197>^∞_n=2 (a_n zⁿan≥ 0) that are univalent and analytic in Δ= (z : |z| <60> 1}. In this paper by using integral operators L_c(f) and Iσ (f) Authors define subclasses of T and prove some theorems about this classes.

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023044   Nadarajan S;Kotz S (Statistics Dep, Nebraska Univ, Lincoln, NE-685 83, USA) : Products of random variables with bessel kernel. Natn Acad Sci Lett 2006, 29(3-4), 117-24.

Distribution of the product XY of random variables X and Y is of interest in many applied problems. The existing literature deals with cases when X and Y arise from the same family of distributions. In this communication, Authors study the distribution of XY when X and Y arise from different but similar distributions. In particular, Authors take X to come from the Bessel family and Y to be from one of normal, t Laplace, logistic or Bessel families.

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