000074   Rajneesh Kumar;Ranjit Singh;Chadha T K (Math Dep, K U Kurukshetra, Kurukshetra) : Eigen value approach to second axisymmetric problem of micropolar elastic medium. Bull Calcutta Mathl Soc 2003, 95(4), 325-38.

The second axisymmetric problem in micropolar elastic medium has been investigated by employing eigen value approach after applying the Laplace and the Hankel transforms. An example of infinite space with concentrated force at the origin has been presented to illustrate the application of the approach. The integral transforms have been inversed by using a numerical technique to obtain the components of microrotation, displacement, force stress and couple stress in the physical domain. The results for these quantities are given and illustrated graphically.

12 illus, 13 ref

000073   Rajeev B;Thangavelu S (NO, Indian Statistical Institute, R.V. College Post, Bangalore-560 059) : Probabilistic representations of solutions to the heat equation. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 321-32.

Provides a new (probabilistic) proof of a classical result in partial diferential equations, viz. if φ is a tempered distribution, then the solution of the heat equation for the Laplacian, with initial condition φ, is given by the convolution of φ with the heat kernel (Gaussian density). The results also extend the probabilistic representation of solutions of the heat equation to initial conditions that are arbitrary tempered distributions.

12 ref

000072   Prasad A (NO, Max-Planck-Institut fur Mathematik, Postfach 7280, D-53072 Bonn, Germany) : Reduction theory for a rational function field. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 153-63.

If G be a split reductive group over a finite field F_q, if F = F_q (t) and if A denote the adeles of F, every double coset in G (F)G(A)/K has a representative in a maximal split torus of G. Here K is the set of integral adelic points of G. When G ranges over general linear groups this is equivalent to the assertion that any algebraic vector bundle over the projective line is isomorphic to a direct sum of line bundles.

15 ref

000071   Pati V (Stat-Math Unit, Indian Statistical Institute, R.V. College Post, Bangalore-560 059) : Subanalytic bundles and tubular neighbourhoods of zero-loci. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 251-79.

The natural and fairly general notion of a subanalytic bundle on a subanalytic subset X of a real analytic manifold M has been introduced and it has been proved that when M is compact, there is a Baire subset U of sections in P whose zero-locin in X have tubular neighbourhoods, homeomorphic to the restriction of the given bundle to these zero-loci.

6 ref

000070   Park D G (Mathematics Dep, Dong-A Univ, Pusan-604 714) : Existence and uniqueness of the solutions for the second order nonlinear Volterra integrodifferential equations of hyperbolic type. Far East J mathl Sci 2003, 9(3), 293-308.

By using the Schauder's fixed point theorem, the existence of solution by a similar method to that of M. L. Heard has been proved. The equation in the space H^-1(Ω) has been considered that is, H^-1(Ω) satisfies uniformly Lipschitz conditions. Then the uniqueness result (Hi(Ω) CL²(Ω)) has been obtained.

17 ref

000069   Pandey S N (Applied Sciences Dep, M M M Engineering College, Gorakhpur, U P) : Gravitational waves in a higher order theory of gravitation. Vikram mathl J 1999, 19, 1-13.

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000068   Panayappan S;Senthil Kumar D (Mathematics Dep, Govt Arts Coll, Coimbatore-641 018) : Spectral properties of p-hyponormal composition operators. Far East J mathl Sci 2003, 9(3), 287-92.

Spectral properties of p-hyponormal composition operators acting on an L² -space have been studied.

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000067   Padmavathamma;Ruby Salestina M (Studies in Mathematics Dep, University of Mysore, Manasagangotri, Mysore-570 006) : Simple proof of schur's 1926 theorem on partitions. Appl Sci Period 2003, 5(3), 135-8.

In 1926 I.J. Schur gave an analytical proof of a partition theorem with minimal difference 4. In 1980, D.M. Bressoud gave a combinatorial proof of this theorem. A different combinatorial proof of the same result has been given.

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000066   Ozarslan H S (Mathematics Dep, Erciyes University, 38039 Kayseri, Turkey) : Note on absolute summability factors. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 165-9.

By using an almost increasing and δ-quasi-monotone sequence, a general theorem on ϕ-<157>C, α<157>_k summability factors, which generalizes a result of Bor on ϕ - <157> 1<157>_k summability factors, has been proved under weaker and more general conditions.

8 ref

000065   Nakasuji M (Mathematics Dep, Keio University, 3-14-1 Hiyoshi, 223-8522,, Japan) : Prime geodesic theorem for some noncompact quotients of symmetric spaces of rank one. J Ramanujan Mathl Soc 2003, 18(3), 237-56.

For a noncompact connected semisimple Lie group G of real rank one with finite center, and a discrete subgroup Γ of G, when vol(G/Γ) <60> ∞ and the contribution of the continuous spectrum is small enough to be ignored, the lower bound of the error term of the prime geodesic theorem for higher dimensional manifolds has been obtained. This result is the generalization of that obtained earlier.

8 ref

000064   Mahurpawar V;Deo S D (NO, Govt. Auto. P.G. College, Chindwara-480 001) : Static plane symmetric space time with cosmic strings in bimetric relativity. Appl Sci Period 2003, 5(3), 148-51.

A four-dimensional static plane symmetric space-time studied in bimetric relativity taking the source as cosmic strings coupled with perfact fluid diostribution. The solution represents the non-existence of cosmic strings as well as perfect fluid distribution in this theory and it is observed that resulting space-time can be reduced to the conformal space-time.

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000063   Lee D W;Lee H J (Mathematics Dep, Myungshin Univ, Sunchon, Chonnam-540-871) : Homology theories and phantom maps. Far East J mathl Sci 2003, 9(3), 309-17.

It is shown that for an inverse system of chain complexes one can induce an epimorphism from a strong r-stage homology group to the Cech homology group. Also the phantom maps from a connected CW-complex X to a space Y with respect to a map g : X (F128><142>Y have been studied.

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000062   Kurokawa N;Wakayama M (Mathematics Dep, Tokyo Institute of Technology, Oh-Okayama, Tokyo, 152-8551 Japan) : Comparison between the sum over selbergs' zeroes and Riemann's zeroes. J Ramanujan Mathl Soc 2003, 18(3), 221-36.

The respective zeroes of the Selberg zeta function and the Riemann zeta function have been compared directly in the critical strip. A certain formula which expresses a difference between the sum over zeroes of the Selberg zeta function for the modular group and the Riemann zeta function relative to an explicit choice of a test function suitably has been established. A new type of the Selberg zeta function has been introduced by an infinite shifted product of the usual Selberg zeta function. A special value of the similarly defined infinite product of the Riemann zeta function also appear naturally.

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000061   Kim T S (Electronic Engng Dep, Kyungpook National Univ, Taegu-702-701, Korea) : On the wavelet transform defined on a fractal domain. Far East J mathl Sci 2003, 9(3), 261-71.

It is well known that conventional wavelet transform is very sensitive to the location of the signal. Two signals, though they differ only by temporal or spatial shift, may have quite different energy distribution on a wavelet space. This may have induced worse problems in pattern discrimination or recognition and low efficiency of data compression such as video image coding. In this sense, it may be efficient to take a fractal-wise wavelet transformation using their energy distribution as in sampling or digital conversion of data. Till now every conventional wavelet have assumed the uniform distribution in temporal domain. Here it has been generalized to the fractal domain and its properties investigated so that it can be utilized to design a useful digital filter.

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000060   Jung S M;Bae J H (Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, Korea) : Some functional equations originating from number theory. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 91-8.

Two new functional equations which are strongly related to two well-known formula of number theory have been introduced, and the solutions of the equations have been investgated. Some stability problems of those equations have been studied.

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000059   John L (Math Dep, Univ Kerala, Kariavattom-695581, Trivandrum, Kerala) : Regular subsemigroups of semigroup of Fredholm operators with a parameter. Bull Calcutta Mathl Soc 2003, 95(4), 291-300.

Let H be an infinite dimensional Hilbert space and X a compact Hausdroff space. Then C(X,F(H)), the set of all continuous maps from X to F(H) where F(H) denotes the set of all Fredholm operators on H; is a semigroup which is not regular. Some regular subsemigroups in terms of choice of two classes of vector bundles one containing vector bundles of finite dimensional subspaces of H and the other containing vector bundles of infinite dimentsional subspaces of H has been described. Also, several interesting subsemigroups of C(X,F(H)) which are regular have been described.

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000058   Jain S;Dolas U;Rathore M S (Govt College, , Badnagar M.P) : Common fixed point theorem for compatible mappings of type-P. Vikram mathl J 1999, 19, 70-9.

Results established on fixed points for compatible mappings of type (P) in have been extended.

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000057   Ikeda K I (Mathematics Dep, Istanbul Bilgi University, Inonu Caddesi No. 28, Kustepe, 80310 Sisli, Istanbul, Turkey) : On the local artin conductor ƒ_Artin (F128><99>) of a character χ of gal (E/K) = II. Main results for the metabelian case. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 99-137.

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000056   Holmes R R;Texier F (Mathematics Dep, Auburn Univ, AL 36849-5310, U.S.A.) : A generalization of the Deutsch-Jozsa quantum algorithm. Far East J mathl Sci 2003, 9(3), 319-26.

A quantum algorithm is presented that can be used to distinguish between certain classes of functions on a finite abelian group. The algorithm is patterned after and generalizes one due to Deutsch and Jozsa for distinguishing a constant function from a balanced function on a direct sum of copies of the integers modulo two.

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000055   Gupta V K;Gupta V;Gupta J K (Govt Girls P G College, , Ujjain) : Test function set for the convergence of double singular integral. Vikram mathl J 1999, 19, 18-22.

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000054   Gopalan M A;Venkatachalapathy M (Mathematics Dep, National College, Tiruchirappalli-620 001) : Note on the cubic diophantine equation. Appl Sci Period 2003, 5(3), 175-6.

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000053   Gon Y (Mathematics Dep, Faculty of Science, Saitama University, 255 Shimo-ookubo Sakura-ku, Saitama, 338-8570, Japan) : First variation of Selberg zeta functions and variational trace formulas. J Ramanujan Mathl Soc 2003, 18(3), 257-80.

An explicit formula for the first variation of Selberg zeta functions in Teichmuller spaces has been given. The variational formula is described by periods of automorphic forms, local Selberg zeta functions and local higher Selberg zeta functions. Also analytic properties of first variations for Selberg zeta functions have been studied by using variational trace formulas.

20 ref

000052   Gasinski L;Papageorgiou N S (NO, Institute of Computer Science, Jagiellonian University, Nawojki 11, 30072 Cracow, Poland) : Nonlinear second-order multivalued boundary value problems. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 293-319.

Nonlinear second-order differential inclusions involving the ordinary vector p-Laplacian, a multivalued maximal monotone operator and nonlinear multivalued boundary conditions have been studied. The framework is general and unifying and incorporates gradient systems, evolutionary variational inequalities and the classical boundary value problems, namely the Dirichlet, the Neumann and the periodic problems. Using notions and techniques from the nonlinear operator theory and from multivalued analysis, solutions of both the `convex' and nonconvex' problems have been obtained. Finally, the cases of special interest, which fit into the framework, illustrating the generality of the results have been presented.

26 ref

000051   Garg M;Mishra R (Math Dep, Univ Rajasthan, Jaipur-302 004, Rajasthan) : On product of hypergeometric functions, general class of multivariable polynomials and a generalized hypergeometric series associated with Feynman integrals. Bull Calcutta Mathl Soc 2003, 95(4), 313-24.

A finite integral has been established and three theorems have been obtained with the help of the integral and the results of Slater and further studied by Buschman and Srivastava. The H-function contains certain class of Feynman integrals, the exact partition function of the Gaussian model in statistical mechanics, the polylograrithm of order p and several other functions as its particular cases. The results obtained are quite general in nature due to the presence of two general classes of multivariable polynomials and the H-function, and from them a number of similar results involving simpler functions and polynomials have been obatined. For the same of illustration, three particular cases of the results have been memntioned which are new and of interest by themselves. References of some known results which follow from the main findings of the paper have also been given.

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000050   Gao C;Zhou S (Mathematics Dep, Changsha Communications Univ, Changsha, Hunan-410076) : A class of analytic functions and Hadamard product. Far East J mathl Sci 2003, 9(3), 273-85.

A class of analytic functions defined by Hadamard product has been defined. Some subordinations and some distortion estimates of this class have been obtained. Some applications of these conclusions for the univalency and starlikeness have been given. The results generalize some known work.

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000049   Ganguly A;Tapi U D (Appl Math Dep, Shri G S Inst of Technol and Sci, 23, Park Road Indore-452003 MP) : An iterative algorithm for generalized random strongly quasi-variational inequality problem and related complementarity problem. Bull Calcutta Mathl Soc 2003, 95(4), 273-80.

A random iterative algorithm for generalized random strongly quasivariational inequality problem has been proposed. Its related complementarity problem has been defined and an equivalence between them has been proposed. Finally, the existence and convergence of a random iterative sequence generated by an algorithm has been proved.

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000048   Douglas R G;Misra G (NO, Texas A & M University, College Station, Texas-77843, USA) : Equivalence of quotient hilbert modules. Proc Indian Acad Sci-Mathl Sci 2003, 113(3), 281-91.

If M be a Hilbert module of holomorphic functions over a natural function algebra A (Ω), where Ω ⊆ C^m is a bounded domain, and if M_o ⊆ M be the submodule of functions vanishing to order k on a hypersurface Z ⊆ Ω a method has been described, which in principle may be used, to construct a set of complete unitary invariants for quoteint modules Q = M Θ M_o. The invariants are given explicitly in the particular case of k = 2.

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000047   Dey R (Mathematics School, Harish-Chandra Research Institute, Allahabad-211 019) : The Wieierstrass-Enneper representation using hodographic coordinates on a minimal surface. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 189-93.

The general solution to the minimal surface equation, namely its local Weierstrass-Enneper representation, using a system of hodographic coordinates has been obtained. This is done by using the method of solving the Born-Infeld equations by Whitham. Conformal coordinates on the minimal surface which give the Weierstrass-Enneper representation have been directly computed. The hodographic coordinate p ∈ D ⊂ C and σ its complex conjugate has been derived enables to write the Weierstrass-Enneper representation in a new way.

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000046   Deo S D;Thengane K D (N S Sci Coll, , Bhadrawati) : Static plane symmetric space-time in bimetric relativity. Bull Calcutta Mathl Soc 2003, 95(4), 339-42.

Nil contribution of the perfect fluid distribution to the four-dimensional static plane symmetric space-time in bimetric relativity is obtained. And it is observed that the resulting space-time can be reduced to the conformal one.

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000045   Bhatt S J;Dedania H V (Mathematics Dep, Sardar Patel University, Vallabh Vidyanagar-388 120) : Beurling algebra analogues of the classical theorems of Wiener and Levy on absolutely convergent Fourier seies. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 179-82.

It ƒ be a continuous function on the unit circle Γ, whose Fourier series is ω-absolutely convergent for some weight ω on the set of integers Z and if ƒ is nowhere vanishing on Γ, then there exists a weight v on Z such that 1/ƒ had v-absolutely convergent Fourier series. This includes Wiener's classical theorem. As a corollary, it follows that if ϕ is holomorphic on a neighbourhood of the range of ƒ, then there exists a weight χ on Z such that ϕ o ƒ, has χ-absolutely convergent Fourier series. This is a weighted analogue of Levy's generalization of Wiener's theorem. In the theorems, v and ω are non-constant if and only if σ is non-constant. In general, the results fail if v or χ is required to be the same weight ω.

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000044   Bhati S S;Purohit M (Math Statists Dep, JNV University, Jodhpur) : Certain integral representation and transformation formulae for hypergeometric functions of four variables. Bull Calcutta Mathl Soc 2003, 95(4), 285-90.

Integral representation and transformation formulae for certain hypergeometric functions of four variables have which can be further reduced to some functions of three variables been obtained.

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000043   Behera B;Madan S (Mathematics Dep, Indian Institute of Technology, Kanpur-208 016) : Wavelet subspaces invariant under groups of translation operators. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 171-8.

The action of translation operators on wavelet subspaces have been studied. This action gives rise to an equivalence relation on the set of all wavelets. It has been shown by explicit construction that each of the associated equivalence classes is non-empty.

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000042   Bai S Z (Mathematics Dep, Wuyi Univ, Jiangmen, Guangdong-529 020, P. R. China) : Semi-precompactness in L-fuzzy topological spaces. Far East J mathl Sci 2003, 9(3), 343-58.

A good definition of semi-precompactness is introduced in L-fuzzy topological spaces, where L is a fuzzy lattice. Some of its properties are studied.

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000041   Badshah V H;Khan A (School of Studies in Mathematics, Vikram University, Ujjain-456010) : A common fixed point with six mappings. Vikram mathl J 1999, 19, 31-9.

A common fixed point theorem for six mappings satistying a retional inequality which unifies and improves earlier fixed point theorem due to Fisher, Kannan, Hardy-Rogers, Jeong-Rhodes, Imdad-Khad and others has been proved. Using notion of compatibility, weak compatibility and commutativity, weak commutativity mappings have been defined.

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000040   Ares-Gastesi P;Biswas I (School of Mathematics, Tata Institute of Fundamental Research, Mumbai-400 005) : Jacobian of a nonorientable klein surface. Proc Indian Acad Sci-Mathl Sci 2003, 113(2), 139-52.

Using divisors, an analog of the Jacobian for a compact connected nonorientable Klein surface Y is constructed. The Jacobian in identified with the dual of the space of all harmonic real one-forms on Y quotiented by the torsion-free part of the first integral homology of Y. Denote by X the double cover of Y given by orientation. The Jacobian of Y is identified with the space of all degree zero holomorphic line bundles L over X with the property that L is isomorphic to σ^* L^-, where σ is the involution of X.

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000039   Amardeep Singh;Rajpur A;Arya S (Govt Motilal Vigyan Mahavidayalaya, , Bhopal-462 003) : Coincidentally commuting maps in D-metric space for fixed point. Vikram mathl J 1999, 19, 40-7.

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017564   Upadhyaya L M;Dhami H S (Mathematics Dep, Municipal Post Graduate College, Mussoorie, Dehradun-248 179, Email: imupadhyaya@rediffmail.com) : On an exton's generalized quadruple hypergeometric function of matrix arguments. Panjab Univ Res J Sci 2009, 59(1-4), 227-35.

In continuation of our previous studies [7-10] we have defined the Exton's ^(k)_(I)E⁽ⁿ⁾_D function for the matrix arguments case in this paper and have established two integral representations for it along with a case of reducibility.

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017563   Talawar A S;Wali K S (NO, Karnatak University, Dharwad, Email: talwar_as@hotmail.com) : Model of HIV/AIDS epidemic in homosexual population. Arya Bhatta J Math Inf 2010, 2(2), 203-10.

In the present paper both Deterministic and Stochastic models for HIVIAIDS epidemic are developed Asymptotic behavior of the model is studied using Routh-Hurwitz criterion. The significance of variable infectiousness to the course of the epidemic is assessed through the basic reproductive rate of infection R_o Numerical illustration of the model gives a clear picture of development of epidemic after the introduction of HIV into a susceptible population. The solution for the stochastic model is obtained using the procedure provided by Billard and Zhao.

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017562   Taherkhani B;Iranmanesh A;Alizadeh Y (Mathematics Dep, Tarbiat Modares Univ, P.O. Box: 14115-137, Tehran, Iran, Email: iranmana@modares.ac.ir) : Computing the szeged and PI indices of HAC₅C₇[p.q] and HAC₅C₆C₇[p,q] nanotubes by GAP program. Asian J Chem 2009, 21(5), 3683-96.

Gives a GAP program for computing the Szeged and the PI indices of any graph. Also computes the Szeged and PI indices of HAC₅C₇ [p,q] and HAC₅C₆C₇[p.q] nanotubes by this program.

4 illus, 30 ref

017561   Sunita;Singh D A (MMEIT, , Ramba, Karnal, Email: suniguct@yahoo.co.in) : Analytical approach to satisfaction level of demand maker in 2 -stage scheduling under Fuzzy environment. Arya Bhatta J Math Inf 2010, 2(2), 235-40.

Authors had shown how non-fuzzy scheduling problems can be reformed in the frame work of fuzzy due time. The membership function of fuzzy due time assigned to each job shows the satisfaction level of demand maker. Authors first describe the concept of fuzzy processing time. Next we find the due time of each job and then by finding the & membership of fuzzy, satisfaction level of demand maker can be analyzed graphically. Combination of all these factors helps a company to face the huge demand of market. In one side we can control early expiry of the jobs, storage problem etc. and on the other hand the late jobs are not beneficial for the company The objective of the study is to get optimal or near optimal sequence of jobs in order to minimize the make span of jobs and the level of satisfaction of demand maker graphically, through a heuristic algorithm.

5 illus, 9 ref

017560   Sonika Kumari;Vinod Kumar (NO, J.V. Jain (P.G.) College, Saharanpur, Uttar Pradesh) : Aerodynamic forces acting on two square cylinders arranged horizontally to the direction of a uniform flow. Arya Bhatta J Math Inf 2010, 2(2), 241-50.

Authors presented a third-order upwind finite element method for solutions of a two-dimensional flow around two square cylinders arranged horizontally in the direction of a uniform flow and show validity of the method. It is well known that flow patterns around the two square cylinders are more complicated than flow pattern around one square cylinder because of interference between the Karman vortices behind the two square cylinders. In this paper the normalized gap size SID, between the surfaces of the two square cylinders is set in the range of 0.5-2.0. The Reynolds number given in the computations is 10000.

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017559   Solairaju A;Nagarajan R (PG&Research Dep of Mathemaics, Jamal Mohamed College, Trichirappalli-20, Email: solairama@yahoo.co.in) : Lattice valued Q-fuzzy left R-submodules of near rings with respect to T-norms. Adv Fuzzy Math 2009, 4(2), 137-45.

A Technique of generating of Q- fuzzy R- sub module by a given arbitrary Q-fuzzy set is provided. It is shown that (i) The sum of two Q- fuzzy R- sub module of a module M is the Q- fuzzy R- sub module generated by their union and (ii) The set of all Q- fuzzy sub module of a given module forms a complete lattice. Consequently it is established that the collection of all Q-fuzzy R- sub module, having the same values at zero, of M of the lattice of Q-fuzzy R- sub module of M. Interrelationship of these finite range sub lattices is established. Finally it is shown that the lattice of all Q- fuzzy R- sub module of M can be embedded into a lattice of Q- fuzzy R- sub module of M. Through out this paper, M denote as Q- fuzzy R- sub module where R is the commutative near ring with unity. Characterization of Q- fuzzy left R- sub modules with respect to t- norm are also given.

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017558   Solairaju A;Nagarajan R (PG & Research Dep of Mathematics, Jamal Mohamed College, Trichirappalli-20, Email: solairama@yahoo.co.in) : Charactarization of interval valued anti fuzzy left h - ideals over hemi rings. Adv Fuzzy Math 2009, 4(2), 129-36.

Introduces the concept of maxⁱ-interval valued anti fuzzy left h- ideals in a hemi rings and extension principle of interval valued fuzzy set. Investigates some of their properties and structural characteristics, some theorems for homomorphic image and its inverse image on max ⁱ - interval valued anti fuzzy left h- ideals of a hemi rings. Relationship between anti fuzzy left h- ideals in a hemi ring and fuzzy left h- ideals is also given. Using lower level set, we give a characterization of interval value anti fuzzy left h ideals.

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017557   Singh T;Jain S K;Mahajan p (NO, , 121, Mahashweta Nagar, Ujjain-456 010, Email: pravin_mahajan75@yahoo.com) : Error bound of function (signal) in a normed space. Proc Natn Acad Sci India-Sect A 2009, 79(4), 333-6.

A theorem has been established to measure the degree of approximation of function associated with HL-series in H_ω-space.

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017556   Singh T;Chaubey R (Applied Mathematics Dep, Institute of Technology, Banaras Hindu Univ, Varanasi, Email: drtrilokisingh@yahoo.co.in) : Bianchi type-III, V, VIo and Kantowski-Sachs universes with varying A,G and σ<. Proc Natn Acad Sci India-Sect A 2009, 79(4), 337-54.

The solution of Einstein's equation with variable A and G, in which A, C and the shear parameter σ² all are coupled have been obtained for Bianchi type - III, V, VIo and Kantowski-Sachs (KS) universes in the quadrature form. Some physically interesting cases have been studied in detail. Some of the models isotropize for large time t.

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017555   Singh R P;Tomar V P (NO, , 7/33 Rajendra Nagar, Sector-e Sahibabad, Ghaziabad-201 005, Email: drrpsingh@mail.com) : Refinement of inequalities among fuzzy means difference. Adv Fuzzy Math 2009, 4(2), 113-27.

Establishes interesting inequalities among fuzzy mean difference measures which are given by authors [ ] in previous communication. Fuzzy f-divergence property has been exploited to establish inequalities among these fuzzy mean difference measures. Section 2 presents fuzzy mean difference measures and their calculus to apply fuzzy f-divergence theorem. Section 3 correlates these fuzzy means difference in the form of inequalities.

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017554   Singh R K (Applied Science Dep, S.D. Institute of Technology & Management, Israna-Panipat Haryana) : Pre normal, semi normal, pre C-normal and semi C-normal spaces. Arya Bhatta J Math Inf 2010, 2(2), 319-22.

In this research paper, -We have presented the study of pre normal, semi normal, pre c-normal and semi c-normal spaces. The concepts have been developed in terms of p-open, s-open, g-open and some weakly generalized open sets. Concepts like p-T₄, s-T₄, *(p-T₄) *(s-T₄), (p-T₄)*, (s-T₄)*, (p-T₄)** and (s-T₄)** have also been studied alongwith their interconnections and properties. C- Type normal spaces in terms of p-open, s-open sets have been studied which include characteristic properties.

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017553   Singh A K;Aggrwal D C;Singh N P (Mathematics Dep, C. L. Jain (P.G.) College, Firozabad-283 203, Email: drnpsingh2008@rediffmail.com) : Hydromagnetic natural convection and mass transfer of a dusty non-Newtonian liquid (Walters B'-modle). Proc Natn Acad Sci India-Sect A 2009, 79(4), 359-66.

Deals with natural convection and mass transfer in oscillatory, laminar flow of a dusty, incompressible, electrically conducting, non-Newtonian liquid (Walters B' model) past an infinite porous plate in porous medium under the action of transverse uniform magnetic field. The velocity of the liquid and dust particles, temperature field, concentration field, skin-friction, rate of heat transfer and rate of mass transfer coefficient are obtained. The effects of magnetic parameter, permeability, Grashof number and modified Grashof number on the velocity field are observed and discussed. The effects of Prandtl number on temperature distribution and the effects of Schmidt number on concentration field are also discussed.

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017552   Sharma J P;Jayapandian D P;Thomaa S (Physics Dep, College of Basic Science, Allahabad Agricultural Institute of Deemed U, Naini, Allahabad-211 007) : Very massive stellar models in Ni's theory of gravity. Proc Natn Acad Sci India-Sect A 2009, 79(4), 375-80.

The equations of stellar structures of massive stars with locally isotropic pressure are derived from the field equations of Ni's theory of gravity, using γ-law equation P=(γ-1)∈, Approximate analytical solutions of the coupled first and second order differential equations have been given. P/p_gc and p_g/p_gc in terms of the solutions of structure equations have been obtained for γ = 4/3, 5/3 and 2 configurations and values of physical parameters θ, -θ' and ξ₁ are discussed.

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017551   Setiya R;Arora S (CSE Department, N.C. College of Engineering, Israna Panipat, Email: shakti.nagpl@gmail.com) : Skeletonization technique with parallel and robust algorithms. Arya Bhatta J Math Inf 2010, 2(2), 323-8.

A number of image processing & pattern reorganization applications require that the raw data should be minimized. I am presenting an algorithm that is providing the connectivity of pixels & two pixel wide line property means the junction points & strong curves should be clearly seen. The proposed thinning algorithm is giving the one pixel wide skeleton of the image as well as maintaining the original structure of the object.

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