007683   Novlekar A A;Khobragade N W (Mathematics Dep, MJP Educational Campus, RTM Nagpur Univ, Nagpur-440 033) : Deflection of transient thermoelastic problem of a thin circular plate-I. J Indian Acad Math 2009, 31(2), 477-86.

This paper is concerned with the direct transient thermoelastic problem in which we need to determine the temperature distribution, displacement, stress functions and deflection of a thin circular plate with the stated boundary conditions. The finite Hankel transform and Laplace transform techniques are used.

9 ref

007682   Nalina V;Jeeva M (Mathematics Dep, Ethiraj College for Women, Chennai-600 114) : K-release inventory model in manpower planning. Indian J Sci Technol 2010, 3(7), 727-32.

A deterministic inventory model is developed to investigate the optimum number of persons to be trained by the organization; here we assume the replenishment rate is infinite with no shortages. In our model, we consider an organization with two centres; one is the training centre for the beginners and the other for the experienced which is treated as inventory house. Our aim is to obtain the optimal number of recruits Q for the organization and the optimal number of K employees trained and sent from the training centre to inventory house. The solution of the model is illustrated with the help of sensitivity analysis on the optimal average cost and the batch width. Also the effect of change in demand parameter on the optimal average cost is graphically presented.

4 illus, 2 tables, 3 ref

007681   Nair D H;Bandrji P K (Mathematics Dep, Faculty of Science, J.N.V. Univ, Jodhpur-342 005, Email: banerjipk@yahoo.com) : Roumieu type tempered ultradistributional Hartley transform. J Indian Acad Math 2009, 31(2), 637-48.

In this paper, authors have extended the hartley transformation to the Roumieu type space of ultradifferentiable function of rapid descent and the corresponding dual space. Mapping properties of the testing function space and its dual for the Hartley transform are also obtained.

12 ref

007680   Mukesh Kumar;Tripathi R P;Singh S R (Mathematics Dep, Dehradun Institute of Technology, Dehradun, Uttarakhand, Email: mukeshkumar_rke@yahoo.co.in) : Optimal ordering policy and pricing with variable demand rate under trade credits. J Natn Acad Math India 2008, 22, 111-23.

In this paper, we develop an EOQ model by considering the difference between the selling price and the purchase cost with variable demand rate when the supplier offers a permissible delay in payments.

15 ref

007679   Mohurley I S;Jumale J K;Thengane K D (Physics Dep, Shri Dnyanesh Mahavidyalaya, Nawargaon-441 223) : Wave solutions of field equations in generalized space-time of Adhao and Karade. J Indian Acad Math 2009, 31(2), 445-53.

Five dimensional (t/z)-type plane wave solution of the field equations containing electromagnetic field has been obtained in the generalized space-time of Adhao and Karade (1994) on the lines of Warade and Thengane (2006) in the present paper.

5 ref

007678   Mehta V;Gehlot K S (Mathematics & Statistics Dep, Jai Narain Vyas Univ, Jodhpur-342 001, Email: karan.gehlot@gmail.com ) : Instability in dusty plasma and effect of charge fluctuation. J Indian Acad Math 2010, 32(1), 139-46.

In this paper the radiative condensation instability has been analyzed in the presence of dust charge fluctuation. System is analyzed in normal mode technique and a dispersion relation has been derived and analyzed numerically. It has been found that the effect of dust dynamics enters to the charge fluctuation in dusty plasma and the charge fluctuations on the dust particles stabilize the system.

2 illus, 9 ref

007677   Mandal P K (Math Dep, A.M. college, Purulia, Email: pravat3112@yahoo.co.in) : Note on non-convective instability in a magnetostatic piezoelectric semiconducting medium. J Indian Acad Math 2009, 31(2), 455-64.

An attempt has been made to investigate numerically the possible instability and the parametric amplification of acoustic wave when laser beam interacts nonlinearly with a low frequency transverse acoustic wave in presence of transverse magnetostatic field in a heavily doped n-type piezoelectric semiconductor. The instability results in the parametric amplification of the acoustic wave. Using a hydrodynamic model of a homogeneous plasma, the possible instability has been studied for an Insb crystal at 77K.

11 ref

007676   Lukose S;Rajan A R (Mathematics Dep, Government College for Women, Thiruvananthapuram-695 014, Email: nunny.sunny@gmail.com) : Ring of normal cones. Indian J pure appl Math 2010, 41(5), 663-81.

Normal categories were introduced by Nambooripad, who proved that the set of normal cones in such a category forms a regular semigroup. In this paper, specialize normal categories to what we call RR-categories and prove that the set of normal cones in such a category forms a regular ring. As an example, we analyze the regular ring of finite-rank operators on an infinite-dimensional vector space in terms of RR-categories. This example can be realised as the characterisation of a regular ring in terms of its left ideals.

5 ref

007675   Kuo M K (Center for General Education, Jen-Tech Junior College of Medicine, Nursing and Management, oNo 79-9 Sha-Luen Hu Si-Zhou Li Hou-Loung Town, Miaoli County, Republic of China, Email: kuo53@seed.net.tw) : Bounds for matrices with monotonic rows. Indian J pure appl Math 2010, 41(6), 737-44.

The bounds L_x,y(A) and ||A||_x,y of an operator A = (a_n,k)_n,k ≥ 0 with monotonic rows are evaluated, where X and Y are quasi-normed real valued sequence spaces. In particular, in the case where X - 1_p and Y = 1_q, the results give the results when part 0 <60> p ≤ 1 and 0 <60> q <60> ∞ to complement the other results with range p ≥ 1 and 0 <60> q <60> ∞. Moreover, authors give a partial answer to a problem which was posed by Bennett.

6 ref

007674   Kulkarni S H;Ramesh G (Mathematics Dep, I.I.T. Madras, Chennai-600 036) : Projection methods for computing moore-penrose inverses of unbounded operatiors. Indian J pure appl Math 2010, 41(5), 647-62.

In this article authors give a characterization of the convergence of projection methods which are useful for approximating the Moore-Penrose inverse of a closed densely defined operator between Hilbert spaces. We illustrate the main theorem with an example. Also a procedure for constructing the admissible sequence of projections is discussed.

14 ref

007673   Krishna Gandhi B;Upender Reddy G (JNT Univ, Anantapur, Anantapur-515 055) : On square numbers in the generalized lucas sequence and generalized associated lucas sequence. J Indian Acad Math 2010, 32(1), 97-105.

The Lucas Sequence {U_n} and the Companion Lucas Sequence {V_n} with parameters P and Q are defined by U₀ = 0, {U₁ = 1 and U_n = PU_n-1 -QU_n-2 for n≥2 and V₀ = 2, V₁ = P and V_n= PV_n-1-QV_n-2 for n ≥ 2. Authors defines for a fixed integer α <62> 0, two sequences are called Generalized Lucas Sequence {U^(α)_n} defined by U^(α)₀ =0, U^(α)₁ = 1, U^(α)_n) = α(α + 1)/2 U^(α)_n-1-(α + 1) V^(α)_n=2 for n ≥ 2, and Generalized Associated Lucas sequence {V^(α)_n} defined by V^(α)₀ =2, V^(α)₁ = α(α + 1)/2, V^(α)_n = α(α+1)/2 V(^(α)_n-1 - (α + 1) V^(α)_n-2 for n ≥ 2. Authors proved that the theorems for possible square numbers in these sequences.

1 table, 9 ref

007672   Khobragade N W (Mathematics Dep, MJP Educational Campus, Nagpur Univ, Nagpur-440 033) : Thermoelastic problem of a thin annular disc-I. J Indian Acad Math 2009, 31(2), 465-76.

In this paper, an attempt is made to solve two problems of thermoelasticity. In both the problems, an attempt is made to determine the temperature distribution, displacement and stress functions of a thin annular disc by applying finite Marchi-Fasulo transform and Laplace transform techniques using stated boundary conditions.

7 ref

007671   Katkar L N;Chougule G (Mathematics Dep, Shivaji Univ, Kolhapur-416 004) : Electric and magnetic parts of weyl tensor in Kerr-Newman space-time. J Indian Acad Math 2009, 31(2), 565-72.

The Newman-Penrose (NP) formation is exploited to study the electric and magnetic parts of the Weyl tensor in the Kerr-Newman space-time. It has been shown that both the angular momentum per unit mass 'a' and the electric charge 'e' of the gravitating body are the sources of the electric part E_ij and magnetic part H_ij of the Weyl tensor. It has been seen that if a = 0 then magnetic part H_ij ceases to be zero in Kerr-Newman space-time, while electric part E_ij exists and at very far distance from the gravitating object i.e. r ∏ ∞ both the parts vanish.

9 ref

007670   Johari A K;Singh N K;Ashutosh (Mathematies Dep, Agra College, Agra) : MHD Fluctuating Flow with Mas transfer of Rivlin-Ericksen viscoelastic fluid past an impulsively started infinite porous plate with variable suction. J Natn Acad Math India 2008, 22, 23-40.

This paper deals with the two dimensional flow of an incompressible second-order Rivlin-Ericksen viscoelastic fluid with mass transfer past an infinite porous non-conducting plate with time dependent suction under the influence of a transverse magnetic field. It has been assumed here that (i) the free stream oscillates in magnitude about a non-zero constant mean (ii) the suction velocity at the plate also oscillates in magnitude about a non-zero constant mean suction velocity (iii) the plate is moved impulsively with a constant velocity (iv) there is no heat transfer between the fluid and the plate, i.e. the heated fluid flows past a themally isolated plate. The mean velocity, mean temperature and mean skin-fricªtion are shown graphically followed by discussion.

7 illus, 15 ref

007669   Jain V C (Math Dep, Govt. Engineering College, Ajmer, Rajasthan) : Magenetized bianchi type-I inflationary cosmological model in general relativity. J Indian Acad Math 2009, 31(2), 369-76.

In this paper, Bianchi type I inflationary cosmological model presence of magnetic field is investigated. To get an inflationary model, we have considered a flat region in which potential V is constant, the various physical and geometrical aspects of the model are also discussed.

10 ref

007668   Jain S;Mukesh Kumar;Advani P (Mathematics Dep, Government College, Ajmer, Email: drjainsanjay@gmail.com) : Comment on Sahu et al. (2007): an inventory model with on-hand inventory dependent demand rate without shortage. J Indian Acad Math 2009, 31(2), 539-44.

In the present article, the model already established by Sahu et al [1] has been rediscussed as there are some flaws in calculating the values of π₁ and dπ₁/dS.

1 ref

007667   Jain S;Aske S;Gujetiya R K (NO, Govt College, Badnagar, Ujjain, Madhya Pradesh) : Related fixed point theorem for two pairs of mapping fuzzy metric space. J Indian Acad Math 2009, 31(2), 545-52.

The aim of this paper is to introduced a new fixed point theorem on Fuzzy metric space.

6 ref

007666   Jain R;Nahar R (Mathematics Dep, Malviya National Institute of Technology, Jaipur-302 017) : Integrals involving product of H-functions. J Indian Acad Math 2009, 31(2), s385-400.

In this paper two integrals involving product of H-function, single and multivariable general polynomials and a general sequence of functions have been established under more general conditions for the existent of the defining Mellin-Barnes type contour integral of H-function than those given earlier. Both the integrals are believed to be new and a very large number of new and known integrals involving simpler functions and polynomials follow as their special cases. We work out integrals that involve Riemann Zeta function, Reduced Green function, Mittag Leffler function, Bessel function, generalized Hypergeometric function generalized Bessel function, Shively'.s function, multivariable Ja-cobi polynomial and multivariable Bessel polynomial which follow as special cases of our main integrals. These integrals may find applications in Science and Engineering Several basic integrals obtained earlier by Gupta and Soni [4], Jain [8], Kilbas and Saigo [9] also follow as special of our findings.

22 ref

007665   Jaimini B B;Saxena H (Mathematics Dep, Government P.G. College, Kota, Email: bbjaimini_67@rediffmail.com) : Certain class of generalized integro-differential equations. J Indian Acad Math 2010, 32(1), 209-18.

In this paper, solutions of certain generalized integro - differential equations are obtained. Two Cauchy type generalized integro-differential equations, with generalized Mittag-Leffler function in the Kernels, are considered. Solutions of the equations are obtained by invoking the method of reduction to integral equations and successive approximations. Section 4 deals with the derivations of some integro-differential equations under specific substitutions and some results as special cases of the equations considered.

13 ref

007664   Indrajeet Singh (Mathematics Dep, Jawahar Lal Nehru College, Pasighat-791 103) : Non-singular cosmological model with shear and rotation. J Natn Acad Math India 2008, 22, 94-8.

Investigated a non-static and rotating model of the universe with an imperfect fluid distribution. It is found that the model is free from singularity and represents an ever expanding universe with shear and rotation vanishing for large values of time.

4 ref

007663   Hemant Kumar;Srivastava S (Mathematics Dep, D. A. V. P. G. College, Kanpur, Uttar Pradesh, Email: palhemant2007rediffmail.com) : On certain extensions of the theorems on biliner and bilateral generating functions. J Indian Acad Math 2009, (Spl), 106-119.

In the present paper, authors derive certain extensions of the theorems related to the theorem on bilinear and bilateral generating functions stated already due to Srivastava and Yeh, then make their applications to obtain bilinear and bilateral generating functions of multiple hypergeometric functions of Srivastava and Daoust in terms of Whittaker and Watson type double loop integrals. Finally, discuss some of their particular cases.

14 ref

007662   Hemant Kumar;Shilesh Kumari (Mathematics Dep, D. A. V. P. G. College, Kanpur, Uttar Pradesh, Email: palhemant2007@rediffmai.com) : Some extensions of the theorems on bilinear and bilateral generating functions. J Indian Acad Math 2009, (Spl), 19-32.

Author stated and proved some extensions of the theorems related to the theorem stated already due to Srivastava and Yeh on bilinear and bilateral generating functions and then, make their applications to obtain bilinear and bilateral generating functions of Srivastava and Daoust multiple hypergemetric function in form of an Erdelyi et al. type single loop-contour integrals. Finally, discussed some of their known and unknown particular cases.

17 ref

007661   Hazarika D;Mitra D K (Mathematical Sciences Dep, Tezpur Univ, Napaam-784 028, Email: debajit@tezu.ernet.in) : L-locally quasi-uniform spaces. J Indian Acad Math 2009, 31(2), 317-24.

Authors have introduced L-local quasi-uniformity by localization of Hutton's quasi-uniformity. The compatibility of L-local quasi-uniformity and L-topology is examined and L-pseudo quasi-metrizability conditions of L-local quasi-uniformity are obtained. Further, L-weakly quasi-uniformly continuity is introduced as a generalization of L-quasi-uniform continuity.

15 ref

007660   Gyanendra Kumar;Sinha S K;Srivastava R S (Statistics Dep, R.K. (P.G.) College, Shamli, Muzaffar Nagar) : Bayesian estimation of parameters of length biased Weibull distribution. J Indian Acad Math 2009, (Spl), 65-72.

Length biased distribution arise when the probability of inclusion of population unit in sample is related to the value of the variable measured. For example textile sampling Cox (1969). In this paper Bayesian estimation of parameters of length biased Weibull distribution have been obtained under various loss functions and different prior distribution.

1 table, 9 ref

007659   Gupta M K (Mathematics Dep, M.S.J. Govt. P.G. College, Bharatpur-321 001, Email: mk_bhp@rediffmail.com) : Evaluation of certain finite integrals with H-function and fractional integration. J Indian Acad Math 2010, 32(1), 195-207.

Evaluates two finite integrals involving the product of a generalized hypergeometric function, general class of multivariable polynomials and H-function. Since the integrals obtained here involve general class of polynomials and functions they have potential to yield a large number of new and known integrals on specialization. We have obtained two new particular cases which may have sufficient basic in nature. At the end, we give an application of our integral formulas by connecting them with the Riemann-Liouville type of fractional integral operator.

21 ref

007658   Gupta K;Agrawal Y (NO, National Institute of Technology, Jaipur-302 017, Email: kantesh_gindiatimes.com) : Applications of unified integral formulae involving the product of I-function and general polynomials. J Indian Acad Math 2010, 32(1), 121-30.

Two unified finite integrals involving the product of I-function, general class of polynomial S^U_V and the multivariable polynomial S^U₁,..., U_kV are evaluated. The theorems of Orr and Bailey are applied to establish certain results. Certain expansion formulae are also evaluated. Certain results, established earlier, have been shown to be the particular cases of the results given.

10 ref

007657   Goyal A K (Mathematics Dep, Govt. R. D. Girls P.G. College, Bharatpur-321 001) : Relative asymptotic regularity and common fixed points. J Indian Acad Math 2010, 32(1), 89-95.

Authors proves a common fixed point theorem for three weakly commuting mappings by using the concept of relative asymptotic regularity of a sequence in 2-metris spaces. Our work generalizes some earlier results of Nesic Singh and Virendra and others.

8 ref

007656   Ferrara M;Stoka M I (Mediterranea Reggio Calabria Univ, Faculty of Law, Degree Course on Economics Via dei Bianchi, 2, Palazzo Zani, 89100 Reggio Calabria, Italy, Email: massimiliano.ferrara@unirc.it) : On 3-killing almost contact structue on a Riemannian manifold. J Indian Acad Math 2009, 31(2), 377-83.

The authors study 3-killing contact structure on a (2m + 3)-dimensional Riemannion manifold. Some new properties are introduced in the frame of this type of distinguished vector field elaborated by Rosca.

5 ref

007655   Elangovan K;Ratchagar N P (Mathematics Secton, Faculty of Engineering and Technology, Annamalai Univ Annamalainagar, Chidambaram-608 002) : MHD steady flow through porous medium. J Indian Acad Math 2010, 32(1), 131-8.

In order to determine the characteristics of magnetohydrodynamic flow through porous medium, the motion of a hydromagnetic, viscous and incompressible fluid in a channel with permeable slip boundaries is investigated. We have obtained an explicit form for the velocity in terms of Reynolds number, Hartmann number and Permeability parameter. The effects of all parameters of the problem are discussed and graphically explained.

7 illus, 12 ref

007654   Duraisamym C;Dhavmani M;Rajesh N (Mathematics Dep, Kongu Engineering College, Perundurai, Erode-638 052, Email: dhavamanim@yahoo.co.in) : Weak and strong forms of intuitionistic continuous functions. J Indian Acad Math 2010, 32(1), 219-26.

In this paper the concepts of intuitionistic strongly θ-continuous, intuitionistic weakly θ-continuous and intuitionistic θ-continuous functions are introduced and discussed in intuitionistic topological spaces.

4 ref

007653   Dubey S N (Engineering Mathematics Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur) : Approximation by Fejer operator. Int Rev pure appl Math 2008, 4(2), 175-8.

The present paper embodies the notion of the approximation of a 2π-periodic continuous function satisfying a Lipschitz condition of order a with constant M, i.e. LiP_M α for 0 <60> α <60> 1 by Fejer operator. As a matter of course, result may be deemed to be a quantitative version of Fejer's Theorem. Constants of approximation have inter alia been taken into notice quite meticulously.

8 ref

007652   Dubey S N (Engineering Mathematics Dep, Gyan Ganga Institute of Technology & Sciences, Jabalpur) : Modulus of continuity & approximation. Int Rev pure appl Math 2008, 4(2), 171-4.

The present paper altogether concentrates upon the study of the quantitative version of convergence of the partial sums S_n(f, x) of the Fourier series to f(x). Determined the rate at which S_n(f, x) converge to f(x) in terms of modulus of continuity.

7 ref

007651   Dubey R P;Singh N K (Mathematics Dep, Bhilai Institute of Technology, Bhilai House, Durg, Chhattishgarh-491 001, Email: nirmalsingh_1971@yahoo.co.in) : Extiensions of a fixed point theorem of Rhoades. J Indian Acad Math 2009, 31(2), 577-80.

A common fixed point theorem is established for a pair of mappings in normed space which extends a result of Rhoades[1] with the use of the G-iterative process.

3 ref

007650   Dube K K;Namdeo B L (Purviyau hills, Janta School Campus Sagar, Madhya Pradesh-470 002) : Note on D₁, R₁ topological spaces. J Indian Acad Math 2009, 31(2), 325-33.

In an R₁-topological space X, for any points x, y ∈ X with cl{x} ≠ cl{y} there exist disjoint open sets U and V such that x ∈ U and y ∈ V. In a D₁-space, every closed set has a countable open base for open sets containing it. In the present note, it is shown that every D₁, R₁-space is regular. Consequently, various results of C.E. Aull [2] for regular spaces can be restated more precisely for D₁, R₁-space. Also, several results for A.R. Singal and S. P. Arua [6] for D₁, T₂ - spaces are shown to be derived as a particular case of corresponding results of C.E. Aull [2] for D₁, regular spaces. Further, it is also shown that every countably paracompact. first countable, R₁-space is regular.

7 ref

007649   Dhagat V B;Sharma A (NO, Jai Narain College of Technology, Bairasia Road, Bhopal, Madhya Pradesh, Email: vanital_dhagat@yahoo.co.in) : Random fixed point theorem for multivalued inward random operator. J Indian Acad Math 2010, 32(1), 291-4.

In this paper authors prove the random fixed point theorems in banach space for multivalued asymptotically regular random operator under inward condition.

2 ref

007648   Devi R;Muthukumaraswamy K;Sampathkumar S (Mathematics Dep, Kongunada Arts and Science College, Coimbatore-641 029) : Fuzzy supra semiopen sets and fuzzy s-semicontinuous functions. J Indian Acad Math 2010, 32(1), 311-22.

Introduces fuzzy supra semiopen set and discuss sonic of its properties. We also introduce fuzzy s-semicontinuous functions and investigate several properties of these functions.

8 ref

007647   De U C (Mathematics Dep, Calcutta Univ, 35, Ballygaunge Circular Road, Kolkata-700 019) : On three-dimensional quasi-sasakian manifolds. J Indian Acad Math 2009, (Spl), 1-6.

The notion of quasi-Sasakian structure was introduced by Blair [1] in 1967 to unify Sasakian and cosympletic structures. In 1971 Tanno [2] added some remarks on quasi-Sasakian structures. The properties of quasi-Sasakian manifolds have been studied by several authors. In 1990 B. H. Kim [3] proved that fibred Riemannian spaces with invariant fibres normal to the structure vector field do not admit nearly Sasakian structure but a quasi-Sasakian or cosympletic structure. Recently some authors found significant applications of quasi-Sasakian manifolds to Physics, in particular, to supergravity and magnetic theory. Also quasi-Sasakian structures have wide applications in the mathematical analysis of string theory.

12 ref

007646   Chouhan U;Pardasani K R (Mathematics Dep, MANIT, Bhopal-462 051, Email: ycchouhan@gmail.com) : Spanning tree based model to study the evolutionary relationships and recombination detection of serially-sampled HIV quasispecies. J Indian Acad Math 2009, 31(2), 589-96.

A new computational model has been developed to study the evolution and pathogenesis of viruses. The traditional methods of generating phylogenetic trees are better suited for exploring relationships among sequences of different species, These sequences appear as leaves of phylogenetic tree. But viral sequences are often serially sampled from a single host species. Thus the data may be available at the leaves as well as nodes of phylogenetic tree. Further the recombination may also complicate this analysis. In view of above, a new model is proposed for multiple sequence alignment, which is based on Minimum Spanning Tree (MST). The model has been used to align the sequences and form a phylogenetic tree of HIV sequences data.

4 illus, 1 table, 13 ref

007645   Choksi H K;Shah D V (NO, Sir P.T. Sarvajanik College of Science Athwalines, Surat-395 001, Email: drdvshah@yahoo.com) : Golden proportions for the generalized fibonacci numbers. J Indian Acad Math 2010, 32(1), 281-9.

It is known fact that the ratios of consecutive terms of Fibonacci sequence converges to the fixed ratio - golden ratio. In this paper we generalize the recurrence relation of Fibonacci numbers to F_n + F_n+a = F_n+c for integers a and c. Considers the problem of finding the 'golden proportion' for the whole family of this generalized sequence. Using graphs, shows that lim _{n ← ∞} F_n+a+k/F_n+a = M^k; k = 1 2 3, ... unless when both a and c are even and k is odd.

4 illus, 1 table, 5 ref

007644   Chena Ram;Choudhary P (Mathematics and Statistics Dep, Jai Narain Vyas Univ, Jodhpur-342 005, Email: crc2007@redffmail.com) : Solutions of homogeneous and non-homogeneous Legender and Euler equations by fractional operator N". J Indian Acad Math 2009, 31(2), 581-8.

N-fractional calculus operator N^v is employed to solve homogeneous and non-homogeneous Legendre and Euler Equations.

2 ref

007643   Chaudhari N S (Computer Science & Engineering Dep, Indian Institute of Technology, Indore-452 017, Email: nsc183@gmail.com) : Improved polynomial algorithm for 3-SAT. J Indian Acad Math 2010, 32(1), 251-67.

Introduced an approach for polynomial solvability of 3-SAT problem. Represented a 3-clause as a conditional having a literal-pair as antecedent, and single literal as consequent. In this paper, authors study a few properties of this representation. These properties are: symmetry, contrapositivity, reduction, and transitivity. In the light of these properties, modify main algorithms for 3-SAT satisfiability in they are: W-Closure(A), and 3-SAT-satisfiability (ℑ). Further modify algorithm Truth-Value Assignments(ℑ) to use W-Closure(A) in an elegant way. In this paper, we report these modified algorithms and re-state a few related interesting properties.

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007642   Chaudhari N S (Computer Science and Engineering (CSE), Indian Institute of Technology (IIT), Indore-452 017) : Computationally hard problems: 3-sat and tes polynomial solvability. J Indian Acad Math 2009, 31(2), 407-44.

3-SAT problem is about the discovery of truth-value assignments of variables that result in the satisfaction of all clauses. To model this high level description of the problem, we first formulate the conditional with a clause (in a given 3-SAT formula) as the antecedent, and the literal(s) restricted by this clause as its consequent. We develop a framework for representing and analyzing these conditionals. To begin our discovery of restrictions on the truth values, we represent 3-Clause as a conditional having a literal-pair as antecedent, and single literal as consequent. In addition to the exploitation of this conditional, our framework involves the propagation of restricted literals (also called as stable literals). Discovery of the restricted literals makes use of the concept of the logical consequents of a literal pair, the concept central to our main formulation, and we give an algorithm to determine the same. The analysis used in our algorithm involves maximum three propagation levels of stable literals. In our formulation, at a particular propagation level, we do not allow the flipping the truth-value of a literal; this feature is important for us to demonstrate the polynomial bound on the number of operations. We give simplified analysis to demonstrate that our algorithm has a polynomial bound of O(n¹³) operations. Since 3-SAT is NP-Complete, our algorithm also implies the polynomial solvability of all NP-Complete problems.

7 illus, 5 ref

007641   Carbone A (Matematica Dep, Della Calabria Univ, 87036 Aracavacata di Rende (Cosenza), Italy, Email: carbonea@unical.it) : Commuting maps and fixed point theorems. J Indian Acad Math 2010, 32(1), 323-6.

Fixed points for commuting mappings have been of great interest and several researchers have worked on this topic. In the present paper we give a few results in metric spaces. The results proved extend earlier results. We derive a few interesting corollaries.

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007640   Borkar M S;Charjan S S (Post Graduate Mathematics Dep, Mahatma Jotiba Phule Educational Campus, R.T.M. Nagpur Univ, Amravati Road, Nagpur-440 033, Email: borkar.mukund@rediffmail.com) : Charged perfect fluid distribution in bimetric theory of relativity. J Indian Acad Math 2010, 32(1), 147-52.

The solution of Rosen's field equations of bimetric theory of relativity for the charged perfect fluid distribution have been derived. It is seen that the resulting model is expanding if (λ'-iλ) <62> (-4/3) (1/r). It is non-rotating but shearing.

6 ref

007639   Basu S (Mathematics Dep, Darjeeling Government College, Lebong Cart Road, Barjeeling, Email: basu_sanjib1964@yahoo.co.in) : Variant formulation of Dini's theorem. J Indian Acad Math 2009, 31(2), 573-6.

This paper endeavours to set forth a variant formulation of the classical Dini's theorem on sequences of functions. Here instead of a sequence, we have used a net of functions and in place of the real line, have chosen any compact topological space as domain and any general metric space as codomain.

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007638   Baskar Babujee J;Joshi A (Mathematics Dep, Anna University Chennai, Chennai, Email: baskarjee@yahoo.com) : Wiener polynomial for tensor product of graphs. Int Rev pure appl Math 2008, 4(2), 195-202.

Wiener Index is a graph invariant introduced originally for molecular graphs of alkanes. All structural formulas of chemical compounds are molecular graphs where vertices represent the set of atoms and edges represent chemical bonds. The construction and investigation of topological indices that could be used to describe molecular structures is one of the important directions of mathematical chemistry. The Wiener Index W(G) of a graph G is defined as the half of the minimum distances between every pair of vertices of G. As such there is no exact formula to determine the value of W(G) though there are some for particular classes of graphs. Determines Wiener index and polynomial for some Tensor product graphs.

3 illus, 4 ref

007637   Barakat H M;Nigm E M (Mathematics Dep, Faculty of Science, Zagazig Univ, Zagazing, Egypt, Email: hbarakat2@hotmail.com) : On the rate of convergence to asymptotic independence between order statistics under power normalization with extension to the generalized order statistics. Indian J pure appl Math 2010, 41(6), 703-14.

Based on the notion of the associated copula for order statistics and some L₁-distances, derive a symmetric nonparametric measure of asymptotic dependence between the order statistics under power normalization. This nonparametric criterion of dependence is extended to the generalized, as well as the dual generalized, order statistics.

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007636   Banerjee D;Jand S (Mathematics Dep, Visva-Bharati Santiniketan, West Bengal-731 235, Email: dibyendu192@yahoo.com) : Growth properties of iterated entire and composite entire and meromorphic functions. J Indian Acad Math 2010, 32(1), 295-309.

Considerd iteration of two entire functions and then study some growth properties of iterated entire functions and composition of entire and meromorphic functions to generalise some known results.

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007635   Banerjee d;Jana S (Mathematics Dep, Visva-Bharati Santiniketan, West Bengal-731 235, Email: dibyendu192@yahoo.com) : Comparative growth of maximum modulus and maximum term of iterated entire functions. J Indian Acad Math 2009, 31(2), 351-60.

Considered iteration of entire functions and then study the growth of iterated entire functions to improve some earlier results.

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007634   Bali R;Chandnani N K (Mathemtics Dep, Rajasthan Univ, Jaipur-302 004, Email: balir@5yahoo.co.in) : LRS bianchi type-II cosmological model for perfect fluid distribution in Lyra geometry. J Indian Acad Math 2009, 31(2), 553-64.

LRS Bianchi Type II cosmological model with time dependent gauge function β for perfect fluid distribution in Lyra geometry is discussed. To get the deterministic model of the universe, we have assumed that shear (a) is proportional to the expansion (θ). This leads to R = αSⁿ where R and S are metric potentials and α, n are constants. To get the deterministic model of the universe in terms of cosmic time t, we have assumed n = 3/2. The physical and geometrical aspects of the models are discussed in detail.

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