007964   Arumugam S;Sahul Hamid I (Core Group Research Facility National Centre for Advanced Research in, Kalasalingam Univ, Anand Nagar, Krishnankoil-626 190, Email: s_arumugam_akce@yahoo.com) : Graphs with unique minimum simple graphoidal cover. Indian J Math 2007, 49(2), 151-63.

Simple graphoidal cover of a graph G is a collection ψ of (not nec-essarily open) paths in G such that every path in ψ has at least two vertices, every vertex of G is an internal vertex of at most one path in ψ every edge of G is in exactly one path in ψ and any two paths in ψ have at most one vertex in common. The minimum cardinality of a simple graphoidal cover of G is called the simple graphoidal covering number of G and is denoted by ns (G). A simple graphoidal cover ψ of G with ψ = ns is called a minimum simple graphoidal cover of G. Two minimum simple graphoidal covers ψ and ψ 2 of G are said to be isomorphic if there exists an automorphism α of G such that ψ2 = {α(P) : P ∈ ψ. Trees, uni-cyclic graphs and complete graphs in which any two minimum simple graphoidal covers are isomorphic have been characterized.

8 ref

007963   Anichini G;Conti G (Facolta di Ingegneria, Univ di Firenze, Italy) : Some properties of the solution set for integral noncompact equations. Far East J mathl Sci 2007, 24(3), 415-23.

Existence of continuous solutions over noncompact intervals of some nonlinear integral equations have been studied. A special interest is devoted to the study of the solution sets of nonlinear Volterra equations.

20 ref

007962   Ambethkar V;Rai L (Mathematics Dep, Delhi Univ, Delhi-110 007) : Numerical solution of three dimensional viscous flow and heat transfer along a porous plate. Bull Calcutta Mathl Soc 2007, 99(2), 163-72.

Presents a numerical solution to the flow of an electrically conducting viscous incompressible fluid along an infinite porous plate with a finite difference technique. The velocity profiles, skin-friction and rate of heat transfer are obtained and have been displayed graphically. The effects of Reynolds number, Hartmann number, Prandtl number and Eckert number on the heat transfer at the plate are studied.

4 illus, 1 table, 7 ref

007961   Alzahary T C (Mathematics Dep, Harbin Engineering Univ, Harbin, Heilongjiang 150001, Peoples' Republic of China, Email: thammra@yahoo.com) : Small functions of meromorphic functions sharing three values with finite weights. Indian J pure appl Math 2007, 38(4), 305-16.

Authors study the problem of uniqueness of meromorphic functions with finite weighted sharing three values. The results improve some theorems of Ueda, Yi, Brosch and other authors.

13 ref

007960   Alegre P;Carriazo A;Kim Y H;Yoon D W (Geometry and Topology Dep, Faculty of Mathematics, Sevilla Univ, Apdo. Correos 1160, 41080 - Sevilla, Spain, Email: carriazo@us.es) : B.-Y. chen's inequality for submanifolds of generalized space forms. Indian J pure appl Math 2007, 38(3), 185-201.

Investigates sharp inequalities involving δ-invariants for submanifolds in both generalized complex space forms and generalized Sasakian space forms, with arbitrary codi-mension.

18 ref

007959   Ahmed S (Mathematics Dep, Govt. Degree College Thanna Mandi, Thanna Mandi, J & K, Email: shakeelar2002@yahoo.co.in) : On Q-finitistic spaces. Indian J Math mathl Sci 2007, 3(1), .

Concept of Q-finitislic space by using Q-open cover has been introduced and studied its various properties.

20 ref

007958   Adiga C;Mahadeva Naika M S;Han J H (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-560 006, Email: c_adiga@hotmail.com) : General modular transformations for theta-functions. Indian J Math 2007, 49(2), 239-51.

Four variable functions a'(q, ς, z, d), a(q, ς, z, d), b(q, ς, z, w, d) and c(q, ς, z, d), which are generalizations of the functions due to Hirschhorn et al. [8], Bhargava and Fathima [3]| The Main purpose is to establish the Laurent series expansions for Cubic, Quintic and Septic theta-functions and some new transformation formulas which generalizes the recent results of Bhargava and Fathima [3] and Cooper [7].

9 ref

007119   Yu H;Lv H;Liu Y (NO, Institute of Applied Mathematics, Academy of Mathematics and Systems S, Academia Sinica, Beijing, 100080, People's Republic of China, Email: hmyu@amss.ac.cn) : Existence and uniquencess of positive solution for sturm-liouville singular boundary value problem. Indian J pure appl Math 2007, 38(1), 3-15.

By constructing only a lower solution, this paper present a kind of sufficient and necessary condition of unique positive solution to Sturm-Liouville singular boundary value problem. Meanwhile, Two examples are worked. out to demonstrate the main results.

13 ref

007118   Yadav J D;Pawar Y S (Mathematics Dep, Shivaji University, Kolhapur-416 004) : Fuzzy pseudo ideals in near-rings. Bull pure appl Sci-Sect E 2006, 25(2), 461-9.

Introduce the fuzzy pseudo ideals, fuzzy weakly pseudo ideals of a near-ring and to investigate their properties Also obtained the correspondence theorem for fuzzy pseudo ideals of a near-ring.

19 ref

007117   Xu Z (School of Mathematical Sciences, South China Normal Univ, Guangzhou 510631, Peoples' Republic of China, Email: xztxhyyj@pub.guangzhou.gd.cn) : Oscillation criteria for even order delay differential equations with damping. Indian J pure appl Math 2006, 37(3), 167-77.

Oscillation criteria for even order delay differential equation with damping are established. The results are the extensions of the integral averaging technique and include earlier known results in existing literature.

13 ref

007116   Xu R;Ma Z;Hao F;Yang P (NO, Institute of Applied Mathematics, Shijiazhuang Mechanical Engineering, Shijiazhuang 050003, Peoples'Republic of China, Email: rxu88@yahoo.com.cn) : Global stability of a delayed predator-prey model with stage structure for the prey. Indian J pure appl Math 2006, 37(5), 273-89.

A predator-prey model with stage structure for the prey and time delays due to gestation of the predators is investigated. By means of appropriate Lyapunov functionals, sufficient conditions are derived for the global asymptotic stability of each of the nonnegative equilibria of the model. Numerical simulations are presented to illustrate the main results.

4 illus, 20 ref

007115   Vijayabalaji S;Thillaigovindan N (Mathematics Dep, Annamalai Univ, Annamalainagar-608 002, Email: balaji_nandini@rediffmail.com) : Intuitionistic fuzzy n-inner product space. Bull pure appl Sci-Sect E 2006, 25(2), 281-94.

Introduce the notion of intuitionistic fuzzy n-inner product space as a natural generalization of fuzzy n-inner product space. Results interrelating intuitionistic fuzzy n-inner product space and intuitionistic fuzzy n-normed linear space are estblished.

23 ref

007114   Venkata Ramana S;Basha S S (Mathematics Dep, S.V.U. Coll of Arts & Sci, S.V. Univ, Tirupati-517 502) : Reverse super vertex magic strength of a graph. Bull pure appl Sci-Sect E 2006, 25(2), 325-30.

Graph G is said to be reverse vertex magic if there exists a bijection f:VUE → {1,2,3..... V + ε} such that for all vertices u, f(u) - f[N(u)] is a constant. Such a bijection is called a reverse super vertex magic labelling. In this paper, the concept of the reverse super vertrex magic strength of a graph G is denoted by rs'm and is defined as the minimum of all constants where the minimum is taken over all reverse super vertex magic labellings of G. The reverse super vertex-magic strength of some well-known graphs P_2n+1, C_2n+1 and mC_n are obtained in this paper.

3 illus, 3 ref

007113   Thillaigovindan N;Kalyanaraman R;Manoharan P (Mathematics Section, Faculty of Engng and Technology, Annamalai University, Annamalainagar-608 002) : M<. Bull pure appl Sci-Sect E 2006, 25(2), 259-64.

M^K/G/1 queue with fixed number of arrivals and with second optional service is studied using supplementary variables technique. The transient and steady state solutions are obtained. Some particular cases are also deduced.

4 ref

007112   Thilagavathi K;Akbar Ali M M (Mathematics Dep, Kongunadu Arts and Science Coll, Coimbatore-641 029) : Edge face graph and vertexs face graph. Bull pure appl Sci-Sect E 2006, 25(2), 317-23.

Authors define the new concepts edge face graph and vertex face graph for the plane graph of a planar graph. Classify the faces of a plane graph as edge rudder, edge frame, vertex rudder and vertex frame. Prove some theorems to find the number of edges in the edge and vertex face graphs and also prove some results relating with the dual and edge face graph of a plane graph.

5 illus, 5 ref

007111   Tao Y;Yoshida N (Applied Mathematics Dep, Dong Hua University, Shanghai-200051, Peoples' Republic of China) : Oscillation criteria for hyperbolic equations with distributed deviating arguments. Indian J pure appl Math 2006, 37(5), 291-305.

Hyperbolic equations with continuous distributed deviating arguments are studied, and oscillaªtions of solutions of boundary value problems are investigated. Our approach is to reduce the multi-dimensional oscillation problems to one-dimensional oscillation problems by employing some integral means of solutions.

15 ref

007110   Subbiah M;Ganesh V (Mathematics Dep, Pondicherry Univ, Kalpet, Pondicheery-605 014) : On the stability of homogeneous shear flows in sea straits of arbitrary cross section. Indian J pure appl Math 2007, 38(1), 43-50.

For the stability problem of homogeneous shear flows in sea straits of arbitrary cross section considered in Deng et at. Authors prove the boundedness of the wave yelocity of neutral modes and the Howard's conjecture, namely, the growth rate tends to zero as the wave length tends to zero. Further we obtain two estimates for the growth rates and two parabolic instability regions which in conjunction with the semicircular region of Deng et at. reduce the latter instability region further. Finally we show that the plane Couette flow has no normal modes under some conditions.

8 ref

007109   Sthanummoorthy N;Lilly P L (NO, Ramanujan Inst for Advancded Study in Mathematics, University of Madr, Chennai-600 005, Email: sthanun@yahoo.com) : Root multiplicity of some generalized Kac-Moody algebras. Indian J pure appl Math 2007, 38(2), 55-78.

Determine explicitly the root multiplicities of all roots of generalized Kacª Moody algebras associated with Borcherds-Cartan matrices (of order 3) which are extensions of finite A₃, affine A₂⁽¹⁾) and hyperbolic H A₁. We also compute the root multiplicities of some generalized Kac-Moody algebras with more than one imaginary simple root.

37 ref

007108   Srivastava S M (Stat-Math Unit, Indian Statistical Institute, 203, BT Road, Kolkata-700 108, Email: smohan@isical.ac.in) : Godel's proof. 1. An introduction to mathematical logic. Resonance 2007, 12(2), 59-70.

4 ref

007107   Somasundaram R;Rajasekar M (Mathematics Dep, Faculty of Engineering, Annamalai University, Annamalai Nagar-608 002) : Labeling semi group of an automaton and road coloring conjecture. Bull pure appl Sci-Sect E 2006, 25(2), 341-6.

Concept of labeling semi group of an automation is used to define some relations on the set of states and a new conjecture is stated. The main result shows that the new conjecture is equivalent to road coloring conjecture.

5 ref

007106   Sitaramaiah V;Subbarao M V (Mathematics Dep, Pondicherry Engineering College, Pondichery-605 014, Email: ramaiahpec@yahoo.co.in) : Characterization of unitary convolution through its non-trivial identical equation. Indian J pure appl Math 2006, 37(3), 141-50.

Nicolas and Sitaramaih [4J recently proved a very interesting result characterizing the Dirichlet convolution. They proved that the only ψ-convolution with Z+ x Z+ as its domain that preserves multiplicativity and satisfies ψ(x, y) ψ max {x, y} for all x, y in the domain and with respect to which the ψ-extension of the Vaidyanathaswamy identity holds is the Dirichlet convolution. Author prove an analogous result that characterizes the Unitary convolution in terms of the extended Subbarao-Gioia identical equation, for ψ-products.

13 ref

007105   Singh R N;Yadav N S (Math Dep, Ranchi Univ, Ranchi, Jharkhand) : Homomorphic structure of accessible subrings. Bull pure appl Sci-Sect E 2006, 25(2), 483-5.

Analyse the results due to Kurosh chanin in the class of accessible subring, derived chain stability for first limit ordinal. Authors derive its accessibile structures and extend its homorphic characterization.

4 ref

007104   Singh K J (Mathematics Dep, University of Jammu, Jammu-180 006) : Weighted composition operators on hardy spaces of unit ball in C. Bull pure appl Sci-Sect E 2006, 25(2), 425-32.

Authors study the boundedness and compactness of weighted composition operation between Hardy spaces of unit ball in C.

13 ref

007103   Sharma P R;Yadav G R (Mathematics Dep, Rajasthan Univ, Jaipur-302 004) : Pulsatile MHD flow and heat transfer through a porous channel with ohmic effect. Bull pure appl Sci-Sect E 2006, 25(2), 499-509.

Investigate pulsatile MHD laminar flow and heat transfer of an incompressible viscous electrically conducting fluid throgh non-conducting porous channel in the presence of uniform transverse magnetic field when fluid is being injected through lower plate and the fluid is sucked off through the upper plate with the same rate. The governing equations of motion and energy are solved by the regular perturbation technique. The velocity and temperature distributions are derived, discussed numerically and presented through graphs. Skin-friction coefficient and the Nusselt number at both the plates were derived, discussed numerically and their numerical values for various values of physitcal parameters are presented through tables.

7 illus, 2 tables, 21 ref

007102   Sharma P R;Agarwal B (Mathematics Dep, Univ of Rajasthan, Jaipur-302 004) : Steady three-dimensional MHD flow along an infinite hot vertical porous surface bounded by a porous medium. Bull pure appl Sci-Sect E 2006, 25(2), 303-15.

Steady three-dimensional flow of an incompressible viscous electrically conducting fluid past an infinite hot porous vertical non-conducting surface bounded by a porous medium in the presence of heat source and transverse magnetic field is invesigated. The governing equations of motion and energy are solved by successive perturbation and separation of variables techniques. The velocity and temperature distributions are derived. discussed numerically and presented through graphs. The skin-friction coefficient and the Nusselt number at the surface are derived, discussed numerically and their numerical values for various valves of physical parameters are presented through Table.

7 illus, 1 table, 15 ref

007101   Sharma A K;Gupta M (Mathematics Dep, Raj Rishi Govt P. G. College, Alwar-301 001) : Deteriorating inventory model with power pattern demand. Bull pure appl Sci-Sect E 2006, 25(2), 407-13.

Deals with a mathematical model for deteriorating items. The demand is assumed to occur according to power pattern deman. Deteriorating is asumed to begin after a time interval, which may be called life period of the items in inventory. Shortages are completely backlogged. A numerical example is also given.

1 illus, 8 ref

007100   Sangalli L M (Dipartimento di Matematica, Universita Degli Studi di Pavia, Via Ferrata 1, 27100 Pavia, Italy, Email: laura.sangalli@unipv.it) : Some developments of the normalized random measures with independent increments. Sankhya 2006, 68(Pt 3), 461-87.

Deal with sequences of exchangeable observations, which are conditionally independent and identically distributed with a common (random) distribution T, where T is defined by the conditioning of a normalized random measure with independent increments. By application of a multidimensional version of the Faa di Bruno formula, authors derive explicit closed form expressions for the finite dimensional distributions and the predictive distributions of the sequence. The results are illustrated through suitable examples.

31 ref

007099   Saikia H K;Barthakur L K;Kalita M C (Mathematics Dep, Gauhati Univ, Guwahati-781 014) : On fuzzy prime and fuzzy semiprime n-subgroups. Bull pure appl Sci-Sect E 2006, 25(2), 375-84.

Investigate certain characteristics of fuzzy prime N-sbgroups and fuzzy semiprime N-subgroups of a near-ring N. Necessary and sufficient conditions to be a fuzzy prime N-subgroup of N are obtained. Various results on the nature of fuzzy prime N-subgroups under homorphism are established. Analogous results are also derived for fuzzy semiprime N-subgroups of N.

14 ref

007098   Sachithanantham S;Ganesan V;Sathiyamoorthy R (Statistics Dep, St. Joseph's College of Arts and Science, Cuddalore, Tamil Nadu) : Optimal reserve between two machines with repair time having SCBZ property. Bull pure appl Sci-Sect E 2006, 25(2), 487-97.

Optimal reserves between machines have been determined using standard optimization techniques. In this paper the optimal reserve inventory is obtained under the assumption that the repair time of machine M₁ is a random variable satisfying the so called Setting Clock back to Zero (SCBZ) property.

7 illus, 7 tables, 5 ref

007097   Rangamma M;Umamaheshwar Rao R;Srinivas V (Mathematics Dep, Osmania University, Hyderabad-500 007) : Fixed point theorem of compatible mappings of type (P). Bull pure appl Sci-Sect E 2006, 25(2), 231-6.

Aim of this paper is to prove a common fixed point theorem which generalizes the result of Das and Naik by using weaker conditions such as comppatible mappingsof type (P) and associated sequence.

4 ref

007096   Prasad S K (NO, College of Commerce (M.U.), Kankarbagh, Patna-20) : On non-archimecean structure of banach algebre. Bull pure appl Sci-Sect E 2006, 25(2), 421-4.

Concept of non-Archimedean metric was introducecd by Monna which satisfy stronger type of triangular inequality. Structue of Non-archimedian banach algebra by introducing the concept of Non-Archimedean seminorm has been discussed. The main purpose here is to examine that in the non-archimedean theory of Banach algebra, the Gelfan theory is essentialy trivial.

5 ref

007095   Pathak R S;Prasad A (Mathematics Dep, Banaras Hindu Univ, Varanasi-221 005) : Generalized pseudo-differential operator on Gel'fand-Shilov space and sobolev space. Indian J pure appl Math 2006, 37(4), 223-35.

A generalized pseudo-differential operator involving the symbol a(x, ξ) whose derivatives satisfy certain growth conditions is studied on Gel'fand-Shilov space S^β,B_{α, A}. It is shown that the generalized pseudo-differential operator is a well defined mapping of S^β,B_{α, A} (R) into another space of the same type on R². A Sobolev space boundedness result is obtained. The product of two generalized pseudo-differential operator is shown to be a pseudo-differential operator.

11 ref

007094   Nagoor Gani A;Maragatham M (P.G. and Research Mathematics Dep, Jamal Mohammed Coll, 295-301) : Economic production quantity in fuzzy sense. Bull pure appl Sci-Sect E 2006, 25(2), 295-301.

Two production inventory models with fuzzy parameters have been discussed. Production rate and demand are considered as triangular fuzzy numbers. Function Principle is used to calculate total fuzzy inventory cost and Graded Mean Integration representation method is used for defuzzification. Economic Production quantity (EPQ) is derived for these two models.

7 ref

007093   Nagoor Gani A;Edward Samuel A (P.G. & Research Dep of Mathematics, Jamal Mohamed College (Autonomous), Trichy-20) : Transportation problem in fuzzy environment. Bull pure appl Sci-Sect E 2006, 25(2), 415-20.

Solution for solving the fuzzy transportation problem in which supplies and demands are triangular fuzzy numbers has been presented. An efficient computational procedure is given for solving such model. The solution procedure is illustrated with a numerical example. A better transportation cost is also kept to the minimum.

5 ref

007092   Mukhopadhyay S (Applied Mathematics Dep, Inst of Technol, Banaras Hindu Univ, Varanasi-221 005, Email: mukho@banaras.ernet.in) : One dimensional state space approach to thermoelastic interactions without energy dissipation. Indian J pure appl Math 2006, 37(3), 151-66.

Work is concerned with the formulation of state space approach to the problems of thermoelastic interactions without energy dissipation in a thermoelastic medium. The formulation together with the Laplace transform procedure is applied for the problem of a half space whose boundary is subjected to ramp type increase in temperature and zero stress and ramp type increase in load and zero temperature change. Closed form solutions are obªtained for both the problems for the distributions of the displacement, temperature and stress of the medium. The results are compared with the earlier findings. Numerical works are also performed for a suitable material with the aim of illustrating the results.

6 illus, 24 ref

007091   Madan S K (Civil Engng Dep, National Institute of Technology, Kurukshetra-136 119) : Fatigue reliability of steel fiber reinforced concrete in flexure. Bull pure appl Sci-Sect E 2006, 25(2), 249-57.

Attempt has been made to implement the probablistic analysis for predicing the fatigue reliability of steel fiber reinforced concrete (SFRC) subjected to flexural bending. This type of loading is of concern in the design of concrete bridges and concrete pavement slabs. Experiments were conducted to obtain fatigue life of SFRC at various stress levels. A probabilistic approach is introduced to account for the large variability at a given stress level. The distribution of fatigue life of SFRC under a given stress level was found to approximately follow the Weibull distribution. The S-N curves are generated from the test results and an equation is obtained to predict the flexural fatigue strength of SFRC for different survival probabilities.

6 illus, 4 tables, 12 ref

007090   Lu X;Qi Y (Mathematics and Statistics Dep, Calgary Univ, 2500 University Drive NW Calgary, Alberta, T2N 1N4, Canada, Email: iux@math.ucalgary.ca) : Chover's law of the iteratecd logarithm for trimmed sums. Sankhya 2006, 68(Pt 3), 488-502.

Consider a sequence of independent and identically distributed random variªables with the underlying distribution in the domain of attraction of a stable distribution with an exponent in (0, 2). Define the trimmed sums as the parªtial sums excluding r largest observations in magnitude, where r is a fixed integer. This paper proves that Chover's law of the iterated logarithm holds for the trimmed sums.

20 ref

007089   Kim M O (Statistics Dep, University of Kentucky, Kentucky Univ, Lexsisngton, Ky 40506, USA, Email: miokkim@ms.uky.edu) : Quantile regression with shape-constrained varying coeflicients. Sankhya 2006, 68(Pt 3), 369-91.

Authors consider quantile regression with shape constrained coefficient functions. B-splines are used to approximate the unknown coefficient functions, and shape constraints are imposed on the spline coefficients. The method can be implemented with any existing linear program and knot selection algorithm. They show that the method does not compromise smoothness of the estimators, flexibility of the model or computational efficiency. Asymptotic results show that the conªstrained B-spline estimators have the same rate of convergence and the same normal limiting distribution as the unconstrained estimators. The method can accommodate a general class of linearizable shape constraints such as convexity/concavity, monotonicity, periodicity and pointwise constraints.

5 illus, 31 ref

007088   Kim J S;Choi J;Ozgur C;Tripathi M M (Mathematics Education Dep, Sunchon National Univ, Sunchon 540-742, Korea, Email: jskim315@hotmail.com) : On the contact conformal curvature tensor of a contact metric manifold. Indian J pure appl Math 2006, 37(4), 199-207.

Contact conformal curvature tensor of an N(k)-contact metric manifolds is studied. Proves that an N(k)-contact metric manifold with vanishing extended contact conformal curvature tensor is a Sasakian manifold. It is proved that a (2n + 1)-dimensional N(k)-contact metric manifold with non-vanishing contact conformal curvature tensor Co satisfies R(ξ, X) C₀ = 0 if and only if it is locally isometric to Eⁿ⁺¹ x Sⁿ(4) for n <62> 1 and flat for n = 1. Also proves that the Ricci tensor 5 of an N(k)-contact metric manifold satisfies the condition C₀(ξ, X). S = 0 if and only if the manifold is 3-dimensional and flat.

14 ref

007087   Khashyarmanesh K (Mathematics Dep, Mashhad Ferdowsi Univ, P.O. Box 1159-91775, Mashhad, Iran, Email: khashyar@ipm.ir ) : On the coassociated primes of generalized local cohomology modules. Indian J pure appl Math 2006, 37(4), 247-53.

Let α denote an ideal of a complete Noetherian local ring (R, m) and M and N two R-modules. For a positive integer t, shows that Hom_R(R/α, Hom_R(H^t_a(M, N),E_R(R/1a))), is finitely generated whenever M is finitely generated of finite projective dimension and (a) H^j_a(M, N) is Artinian for all j <62> t; and, (b) t <62> Pd_R(M) where Pd_R(M) is the projective dimension of M. Hence, the set Coass-H^t_a(M, N) ∩ V(a) is finite where V(a) denotes the set of all prime ideals of R containing a. This implies that if d = dim N <62> 1 and N is finitely generated i then the set Coass H^d-1_a(N) ∩ V(a) is finite.

26 ref

007086   Khan V A;Khan M A (Mathematics Dep, Aligarh muslim University, Aligarh-202 002) : Pseudo slant submanifolds of a sasakian manifold. Indian J pure appl Math 2007, 38(1), 31-42.

Study the pseudo slant sub manifolds of a Sasakian manifold. Authors work out integrability conditions of distributions on these submanifolds and also, obtain a few interesting results of this setting.

10 ref

007085   Katoe S D;Rane R S;Thakare S V (Mathematics Dep, Rajasthan Aryan Science College, Washim-445 505, Email: s_d_katoe@rediffmail.com) : Plane gravitational waves in bimetric theory of relativity in 4dimensional space-time. Bull pure appl Sci-Sect E 2006, 25(2), 439-46.

In Rosen's bimetric theory of gravitation, the form of the plane gravitational waves dedduced by Takeno (1961) can be retained. Furthermore, the existence of plane gravitational waves in bimetric theory has been investigated.

7 ref

007084   Kataria H R (Mathematics Dep, Faculty of Science, The M.S. University of Baroda, Vadodara-390 002) : General solution for fingero imbibiion in double phase flow through prous medium with capillary pressure. Bull pure appl Sci-Sect E 2006, 25(2), 243-7.

Discusses a theoretical model for fingero-imbibition phenomona of ground water replenishment in double phase flow through homogeneous porous medium with capillary pressure. The basic assumptions underlying the present investigation are that `Oil" and "Water" form two immiscible liquid phases and the later represents preferentially wetting phase. A mathematical formulation leads to a non-linear differential equation, which has been reduced to an ordinary differential equation. A formal mathematical solution has been obtained in terms of definite integral.

6 ref

007083   Kalita B (Computer application Dep, Assam Engg College, Guwahati-781 013, Email: bichitral_kalita@rediff.com) : Proof of goldbach conjecture and related conjectures of prime. Bull pure appl Sci-Sect E 2006, 25(2), 451-9.

Paper forwards a theoretical proof of Goldbach Conjecture. A theorem relating to the existence of consecutive primes ≥ 13 have been formulated. In addition to this, two new conjectures for existence and non existence of perfect numbers have also been proposed.

12 ref

007082   Jain P K;Kaushik S K;Vashisht L K (Mathematics Dep, University of Delhi, Delhi-110 007, Email: Shikk2003@yahoo.co.in) : On banach frames. Indian J pure appl Math 2006, 37(5), 265-72.

Examples and counter examples to distinguish various types of Banach frames have been given. It has been proved that if a Banach space has a Banach frame, then it also has a normalized tight as well as a normalized tight and exact Banach frame. In particular, it has been proved that a Banach space with a weak. separable dual has a normalized tight and exact Banach frame. A condition for the stability of a Banach frame has been given. Authors consider finite sum of Banach frames and give a condition under which finite sum of Banach frames is a Banach frame.

9 ref

007081   Ilyasov M (Faculty of Sci, Mathematics Dep, Istanbul Univ, 34118 Vezneciler-Istanbul, Turkey, Email: mhan@istanbul.edu.tr) : Mixed problems for a class of pseudoparabolic equations. Indian J pure appl Math 2007, 38(2), 97-103.

Integral operator method has been used for the solution of mixed problems for a class of pseudoparabolic equations. The obtained solutions are constructed on the basis of the solutions of corresponding problems for the parabolic equations and are represented by the integral of the multiplication of these solutions by a generalized functions, which are the generalized solutions of specific differential equation of hyperbolic type.

10 ref

007080   Hallan P P;Mangang K B (Mathematics Dep, Zakir Husain College, (Univ of Delhi), Jawahar Lal Nehru Marg, New Delhi-110 002, Email: pphallan@yahoo.com) : Non linear stability of equilibrium point in the robe's restricted circular three body problem. Indian J pure appl Math 2007, 38(1), 17-30.

Non-linear stability of the equilibrium point of the Robe's restricted circular three body problem has been studied when the density parameter K is zero. By applying Kolmogorov-Arnold Moser (KAM) theory. It has been found that the equilibrium point is stable for all mass ratios 8/9 μ in the range, <60> μ <60> 1, of linear stability except for five mass ratios μ₁ = 0.93711086..., = 0.9672922...,μ₃ = 0.9459503... μ₄ = 0.9660792..., μ₅ =0893981..., where the theory is not applicable.

2 illus, 14 ref

007079   Gulhane P A;Gudadhe A S (Maths Dep, Govt Coll of Engng, Amravati-444 604) : On LS-spaces of gelfand-shilov technique. Bull pure appl Sci-Sect E 2006, 25(2), 351-4.

Different testing function spaces are defined for distributional Laplace-Stieltjes transform bhy using Gelfaand-shilov technique of S_α spaces, some properties of the spaces are proved. At the end generalized Laplace-Stiltjes transformation is defined and some examples are solved.

5 ref