002058   Mukul Singh;Rai P N (Mathematics Dep, Dr. P.N. Singh Degree College, (J.P. University), Chapra (Bihar)) : Velocity profiles of non-Newtonian fluids and between flat parallel plates. Acta Cienc Indica-Math 2007, 33(2), 503-8.

Velocity profiles of Non-Newtonian fluids between flat parallel plates have been obtained in simplified form. These expressions are suitable to be used for any practical problems and industrial purposes easily.

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002057   Mukherjee B (Mathematics Dep, Indian School of Mines, Dhanbad-926 004) : Statistical study of gravitationallensing by galaxy without core-radies. Acta Cienc Indica-Math 2007, 33(2), 275-82.

After the discovery of the first multiply imaged quasar, gravitational arcs and arclets, gravitational lensing has rapidly become one of the most promising tools for cosmology. The effect of the cosmological constants on the statistical properties of gravitational lenses was studied on the basis of the fact that the logarithm of likelihood functions depend on the value of Schechter parameter a, cosmological parameter Ω_o and others parameters. The logarithm of likelihood as a function of Schechter parameter α for the SIS-model (without core-radius) were studied. The best fit seems to be the NS - 97 parameter.

4 illus, 4 tables, 15 ref

002056   Mishra B K;Verma N (Mathematics Groups, Birla Institute of Technology of Science, Pilani-333 031) : Bingham plastic fluid model of blood flow through an arterial stenosis. Acta Cienc Indica-Math 2007, 33(2), 303-10.

An attempt has been made to investigate the resistance to flow across mild stenosis situated symmetrically on steady blood flow through arteries with uniform or non-uniform cross-section by assuming the blood to be Non-Newtonian, incompressible and homogeneous fluid. An analytic solution for Bingham Plastic fluid has been obtained. For the physiological insight of the problem various parameters of pulmonary artery are taken and the study reveals that as the height of the stenosis increases in uniform or non-uniform or both portion of the artery, the resistance parameter also increases.

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002055   Mishra B K;Shekhawat S S (Mathematics Groups, Birla Institute of Technology of Science, Pilani-333 031) : Magnetic effect on blood flow through a tapered artery with stenosis. Acta Cienc Indica-Math 2007, 33(2), 295-301.

Mathematical model has been developed in order to examine the effect of shear stress on the blood flow under the action of an applied magnetic field in a single constricted blood vessel. This model is consistent with the principles of ferrohydrodynamics and magnetohydrodynamics (MHD). The effects of interaction between a magnetic field and the hemodynamics of arterial system have been studied. The blood flowing through the artery is considered to be Newtonian. The study reveals that as the Hartmann's number increases the wall shear stress decreases.

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002054   Mercy J;Arockiarani L (Mathematics Dep, Nirmala College for Women, Coimbatore (T.N.)) : On Ω-closed sets and Ωp-closed sets in topological spaces. Acta Cienc Indica-Math 2007, 33(2), 509-15.

In this paper author introduced new classes of sets called Ω^*-closed sets and Ωp-closed sets in topological spaces. Also author introduced and study Π^*-continuous functions and Ωp-continuous functions and prove pasting Lemma for these functions. Classes of topological spaces called Ω^* - T1/2 and Ω^* - Tp have also been introduced and obtained their characterizations.

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002053   Maralabhavi Y B;Venkanagouda;Goudar M (Mathematics Dep, Bangalore Univ, Central College Campus, Bangalore-560 001) : Block vertex graph of a graph with (0, 1) matrices. Acta Cienc Indica-Math 2007, 33(2), 389-94.

New type of a graph called block vertex graph BV(G) of a graph G with (0, 1) matrices has been introduced and obtained some properties on planar, outerplanar, minimally nonouterplanar, coverings, Eulerian and Hamiltonian.

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002052   Maralabhavi Y B;Goudar V M (Mathematics Dep, Bangalore Univ, Central College Campus, Bangalore-560 001) : Pathos middle graph of a tree. Acta Cienc Indica-Math 2007, 33(2), 499-02.

In this paper, author introduced the concept of the pathos middle graph of a tree. Its study is concentrated only on trees. Obtained some properties of this graph. In addition, presented characterization of graphs whose pathos middle graph are planar, outerplanar and maximal outerplanar. Further, author establish a characterization of graphs whose pathos middle graph have crossing number 1 or 2, further pathos middle graph is always non eulerian and non hamiltonian.

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002051   Maralabhavi Y B;Goudar V M (Mathematics Dep, Bangalore Univ, Central College Campus, Bangalore-560 001) : Block edge cutvertex graph. Acta Cienc Indica-Math 2007, 33(2), 493-7.

In this paper, author introduced the concept of the block edge cutvertex graph. Obtained some properties of these graphs. Author presented characterization of graphs whose block edge cutvertex graphs are planar outerplanar, minimally nonouterplanar, crossing number one and eulerian.

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002050   Maloo A K (Mathematics and Statistics Dep, IIT, Kanpur-208 016, Email: akmaloo@iitk.ac.in) : Maximally differential ideals in regular local rings. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 267-70.

It is shown that if A is a regular local ring and / is a maximally differential ideal in A, then / is generated by an A-sequence.

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002049   Maheswari V;Nagarajan A;Somasundaram S (Mathematics Dep, V.O. Chidambaram College, Tuticorin (T.N.)) : On randomly F-decomposable graphs. Acta Cienc Indica-Math 2007, 33(2), 395-407.

A graph G is said to be packable by the graph F or F-packable if its edges can be partitioned into copies of F. It is called randomly F-packable if what remains after deletion of the edges of a proper subgraph that is F-packable is also F-packable. Also characterize the class of graphs that are randomly F-packable where F = C₃.C₃, C₃.P₂ or C₃.P₃. Also observed some disconnected graphs that are randomly 2P_n+1-packable and also we establish some results on graphs that are randomly 2P_n+1-packable.

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002048   Madhukar J;Jha R (Mathematics Dep, S.K. College, G.T. Road, Etah) : MHD free convective flow of viscous fluid through a porous medium bounded by an oscllating porous plate in slip flow regme with heat source/sink. Acta Cienc Indica-Math 2007, 33(2), 581-8.

An exact solution of free convective flow of viscous, incompressible fluid of small electrical conductivity through a porous medium bounded by an oscillating infinite porous plate in slip flow regime with heat source/sink in presence of uniform magnetic field. The expressions for velocity, temperature, concentration profile, skin friction and rate of heat transfer and mass transfer are obtained. The effects of various different parameters are discussed graphically.

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002047   Lashkaripour R;Foroutannia D (Mathematics Dep, Sistan and Baluchestan Univ, Zahedan, Iran, Email: lashkari@hamoon.usb.ac.ir) : Inequalities involving upper bounds for certain matrix operators. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 325-36.

Considered the problem of finding the upper bound Hausdorff matrix operator from sequence spaces l_p(U) (or d(v, p)) into l_p(u') (or d(w, p)). Also author considered the upper bound problem for matrix operators from d( v, I) into d(w, I), and matrix operators from e(w, ∞) into e(v, ∞), and deduce upper bound for Cesaro. Copson and Hilbert matrix operators, which are recently considered in [5] and [6] and similar to that in [10].

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002046   Kulli V R;Biradar M S (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106) : Point-block graphs and crossing numbers. Acta Cienc Indica-Math 2007, 33(2), 637-40.

Established a necessary and sufficient condition for graphs whose point-block graphs have crossing number k, k = 1, 2, 3 or 4.

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002045   Kulli V R (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106) : Cycle nonsplit domination and path nonsplit domination in graphs. Acta Cienc Indica-Math 2007, 33(2), 641-4.

A domination set D of a connected graph G is a cycle nonsplit dominating set if the induced subgraph (V - D) is a cycle in G. The cycle nonsplit domination number y_cns (G) of G is the minimum cardinality of a cycle nonsplit dominating set. A dominating set D of a connected graph G is a path nonsplit dominating set if the induced subgraph (V-D) is a path in G. The path nonsplit domination number y_pns (G) of G is the minimum cardinality of a path nonsplit dominating set. Also initiate a study of these two new parameters.

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002044   Kubrusly C S (NO, Catholic Univ of Rio dde Janeiro, 22453-900, Rio de Janeiro, RJ, Brazil, Email: carlos@el.puc-rio.br) : Concise introduction to tensor product. Far East J mathl Sci 2006, 22(2), 137-74.

A brief introduction to tensor product in Hilbert space is organized into five sections. The inner product space H ⊗ IC of Hilbert spaces H and K, as well as the tenl'or product A ⊗ B of operators A and B is discussed. Their completion, leading to the concept of tensor product space, is the topic of Section 2. Kronecker product comprises the subject of Section 3, and commutativity of the tensor product of operators is focused in Section 4. Finally, tensor product for classes of operators closes this expository paper in Section 5.

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002043   Khelifa M;Ayache B (Departement de Mathematiques, Faculte des Sciences, Universite de Batna, 5000 Batna, Algeria) : Nonperiodic convex integral functionals and epiconvergence. Far East J mathl Sci 2006, 22(1), 25-42.

The limit analysis, by epiconvergence techniques, of the sequence of nonperiodic convex integral functionals, with time dependent case, is studied by a new approach. This approach allows to treat some cases more general than the ones considered in the previous literature. Generalizes the one obtained by Mascarenhas [Trans. Amer. Math. Soc. 81(1) (1984), 179-195], in the time independent case. An example of such sequence is presented.

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002042   Khan M A;Rouhi B (Applied Mathematics Dep, Faculty of Engineering, AMU, Aligarh-202 002) : Calculus for the T_k,x,y,z - operator. Acta Cienc Indica-Math 2007, 33(2), 559-66.

The present paper deals with the calculus of T_k,x,y,z-operator. The operator is a three variable analogue of the operator given earlier by W.A. Al-Salam [1] and H.B. Mittal [10]. The operator is useful for finding operational representations and generating functions of polynomials of three variables and will be dealt in a separate communication.

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002041   Khalsa L S;Khobragade N W (Mathematics Dep, MJP Educational Campus, RTM Nagpur Univ, Nagpur-440 033) : Inverse steady-state thermoelastic problem of a thick rectangular plate. Acta Cienc Indica-Math 2007, 33(2), 189-94.

This paper is concerned with the inverse steady-state thermoelastic state thermoelastic problem to determine the known temperature, displacement and thermal stresses on the lower plane surface of a thick rectangular plate occupying the space D:0≤x≤a; -b≤y≤b;O≤z<131>< F255>h with the known boundary conditions by applying finite integral transform, Marchi-Fasulo transform and Laplace transform techniques. Numerical estimate for temperature on the lower plane surface has been obtained and depicted graphically.

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002040   Kayathri K;Vijayan M S (Mathematics Dep, Thiagarajar College, Madurai (T.N.)) : Coloring of complete semigraphs. Acta Cienc Indica-Math 2007, 33(2), 605-14.

Let G⁽²⁾ denote the collection of all complete semigraphs in which all the vertices except two vertices u₁ and U₂, are strictly end vertices. In this paper, determine the chromatic number of semigraphs in G⁽²⁾ in which u₁ and u₂ lie on the same semiedge.

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002039   Kayathri K;Pethanachi Selvam S (Mathematics Dep, Thiagrarajar College, Madurai-625 009) : EDGE complete (p, 3) semigraphs. Acta Cienc Indica-Math 2007, 33(2), 621-31.

A semigraph G is an ordered pair (V, X) where Vis a nonempty set whose elements are called vertices of G and X is a set of n-tuples (n ≥ 2), called edges G, of distinct vertices satisfying the following conditions: (i) any edge (v₁, v₂, .... v_n) of G is the same as its reverse (v_n, v_n-1, -v₁), and ii) any two edges have at most one vertex in common. Two edges are adjacent if they have a common vertex. A semigraph is edge complete if any two edges in it are adjacent. In this paper, author categorize the edge complete (p, 3) semigraphs into 20 categories and prove that no two semigraphs of different categories are isomorphic.

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002038   Joshi N (Mathematics Dep, Govt. P.G. College, Pithoragarh-262 502) : On commuators and conjugates in rings. Acta Cienc Indica-Math 2007, 33(2), 251-4.

The purpose of this paper is to establish some results and theorems concerning the commutators and conjugates in rings.

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002037   Joshi N (Mathematics Dep, Govt. P.G. College, Pithoragarh-262 501) : On some notions concering random variates. Acta Cienc Indica-Math 2007, 33(2), 247-9.

Some theorems and results are established - concerning the expected values, characteristic functions, moment generating functions and cumulative functions of the random variates.

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002036   Jain A;Bijendra Singh (School of Studies in Mathematics, Vikram Univ, Ujjain-456 010) : Fixed point theorem for compatible mappings of type (A) in Fuzzy metric space. Acta Cienc Indica-Math 2007, 33(2), 339-46.

This paper contains a fixed point theorem for six self maps in Fuzzy metric space. Result generalizes and extends many results in Fuzzy metric spaces.

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002035   Jadon V K;Jha R;Yadav S S (Mathematics Dep, Narain College, Shikohabad) : MHD free convection and mass transfer flow of visco-elastic (Rivlin-Ericksen) fluid through porous medium. Acta Cienc Indica-Math 2007, 33(2), 575-9.

An exact solution to the problem of unsteady free convection flow of an incompressible, electrically conducting, visco-elastic (Rivlin-Ericksen) fluid through porous medium between two vertical parallel plates in the presence of uniform transverse magnetic field is obtained. The expressions for velocity profile, temperature & concentration profile are obtained by using perturbation technique. The effects of different parameters like as Magnetic field parameter M, Porosity parameter K, Visco-elastic parameter λ, Prandtl number Pr, and Schmidt number Sc are discussed and shown through graphically.

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002034   Huang Y (Mathematics Dep, Sanming Coll, Sanming, Fujian-365 004, P.R. Choma, Email: s,caohy@126.com) : Characterizations of weakly implicati BCI-algebras. Far East J mathl Sci 2006, 22(2), 263-72.

Gives four equivalent conditions of the weakly implicativity in BCI-algebras and two equivalent conditions of the condition (8) in weakly implicative BCI-algebras as well as two axiom systems of weakly implicative BCI-algebras.

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002033   Huang C (Mathematics dep, Wright State University, Dayton, OH 45066, U.S.A) : Global smooth nonconstant vortex patches in bounded domains. Far East J mathl Sci 2006, 22(2), 227-38.

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002032   Hansson A A;Reidys C M (Los Alamos National Laboratory, , CCS-5, 87545 New Mexico, U.S.A., Email: duck@santafe.edu) : Discrete dynamical systems framework for packet-flow on networks. Far East J mathl Sci 2006, 22(1), 43-67.

Introduces a certain class of network-routing protocols over arbitrary simple, undirected graphs. These protocols transmit data-packets between adjacent vertices and will be formally specified as local maps of a sequential dynamical system (SDS). An SDS consists of (a) a finite (labeled) graph Y with vertex set {v_i,., v_n}, where each v_i has a finite state, X_vi ε K, (b) a vertex labeled multi-set of Ly-local functions (F_vi, Y)_wi, where Ly is a mapping from Y-vertices into subgraphs of Y and (c) a word w, i.e., a multi-set (w_1k), where w_i as a function of the vertices contained in the subgraph Ly(w_i) and simultaneously updates all states of the Ly(w_i)-vertices other than w_i. The SDS is then the product of the local maps: [vy, w] = Π^k_i=1 F_wi : Kⁿ → Kⁿ. Also specify generic, parameterized data transmission protocols as Ly(v) -local maps. where Ly(v) is a subgraph of Y. The protocols will facilitate Retyhe the transmission of unlabeled packets from a fixed source S to a fixed destination D and route using the distance to D. the actual load of the neighbors and their total capacities as base parameters. The state of a vertex willl be the vector of queue-sizes of their respective next-hop-destinations. Presented several instances of the system dynamics produced by these protocols and utilize the SDS-framework in order to study which update schedules induce equal or equivalent systems. Finally author investigated further system symmetries that arise from automorphisms of the base graph itself using group actions and allow to determine additional equivalences.

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002031   Gopalan M A;Vidhyalakshmi S;Devibala S (Mathematics Dep, National College, Trichy) : On the diophantine equation 3x<. Acta Cienc Indica-Math 2007, 33(2), 645-6.

The binary quadratic equation 3x² + xy = 14 has limited number of integral solutions.

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002030   Gopalan M A;Somanath M;Vanitha N (Mathematics Dep, National College, Trichy) : On R₂ numbers. Acta Cienc Indica-Math 2007, 33(2), 617-19.

An elegant formulation to construct triple coincidence among R₂ numbers is presented together with generation of quadruple coincidence.

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002029   Gopalan M A;Somanath M;Vanitha N (Mathematics Dep, National College, Trichy (T.N.) India) : Fourth order Ramanujan numbers (or) R₄ numbers. Acta Cienc Indica-Math 2007, 33(2), 615-16.

Gaussian integral solutions of R₄ numbers are presented. A few interesting relations among the solutions are given.

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002028   Gopalan M A;Somanath M;Vanitha N (Mathematics Dep, National College, Trichy (T.N.)) : M-gonal number - 1 = a perfect square. Acta Cienc Indica-Math 2007, 33(2), 479-80.

We search for the ranks of Triangular, Pentagonal, Hexagonal, Heptagonal, Octagonal, and Dodecagonal numbers such that each of these m-gonal number - 1 = a perfect square.

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002027   Gopalan M A;Gokila K;Vidhyalakahmi S (Mathematics Dep, National College, Trichy (T.N.)) : On the diophantine equation x<. Acta Cienc Indica-Math 2007, 33(2), 567-70.

Two different .sequences of integral points on the hyperbola x²+ 4xy + y²-2x + 2y-6 = 0 are obtained. A few interesting observations on the solutions are presented.

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002026   Gautam A;Rajan S;Singh B K (Mathematics Dep, Hindu College, Moradabad (U.P.)) : Backbones in optimization and approximation. Acta Cienc Indica-Math 2007, 33(2), 227-32.

An attempt has been made to study the impact of backbones in optimization and approximation problems. For some optimization problems like blocks world planning and travelling salesperson problems, Author trys to correlate negatively and weakly, problems hardness with backbone size; while the cost of finding optimal and approximate solutions is positively correlated with backbone size.

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002025   Gautam A;Rajan S (Mathematics Dep, Hindu College, Moradabad) : State estimation as a convex optimization problem. Acta Cienc Indica-Math 2007, 33(2), 233-7.

An attempt has been made to study the State Estimation as a convex optimization problem. Here, author illustrated the principle on a hidden Markov model, where the state vector contains probabilities that are positive and sum to one.

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002024   Fernandez Valles A (Mathematics Dep, Cadiz Univ, Avda. de la Universidad, s/n 11402-Jerez de la Frontera, Spain, Email: aurora.fernandez@uca.es) : Joint local quasinilpotence and common invariant subspaces. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 317-23.

Obtain some positive results about the existence of a common nontrivial invariant subspace for N-tuples of not necessarily commuting operators on Banach spares with a Schauder basis. The concept of joint quasinilpotence plays a basic role. The results complement recent work by Kosiek [6] and Ptak [8].

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002023   Farnam B (Mathematics Dep, Pune Univ, (M.S.)) : Transient free convection flow on an isothermal plate. Acta Cienc Indica-Math 2007, 33(2), 439-43.

Free convection flow of a viscous incompressible fluid past a semi-infinite isothermal vertical plate with temperature dependent heat source is studied. Implicit finite difference scheme which is unconditionally stable has been used to solve governing partial differential equations of the flow. Transient temperature and velocity profiles are plotted to show the effect of heat source. Average skin-friction and average Nusselt number against time are plotted.

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002022   Dhana Balan A P (Mathematics Dep, N.I. College, of Engineering, Thuckalay-629 175) : On Q-spaces and Q-sets. Acta Cienc Indica-Math 2007, 33(2), 225-6.

Discusses several concepts of Q-Spaces and Q-Sets with that of semi-sub maximal and regular sub maximal space.

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002021   Cho M;Chang J (Mathematics Education Dep, Korea National University of Education Chongwon 363-791, Korea, , Email: mscho@knue.ac.kr) : On the estimation of the total Betti numbers of Alexandrov spaces. Far East J mathl Sci 2006, 22(1), 115-28.

Establishes a refined upper bound for the sum of betti numbers of Alexandrov spaces. In order to obtain an improved upper bound we formulates a sphere packing theorem in Alexandrov space and revise almost all the estimates and constants used in earlier results.

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002020   Chellappa B;Natarajan R (Mathematics Dep, Alagappa Govt. Arts College, Karaikudi-630 003) : Dually standard convex sublattice. Acta Cienc Indica-Math 2007, 33(2), 527-38.

The concept of standard ideals and dually standard ideals in lattice were introduced and studied by G. Gratzer and E.T. Schmidt. A generalization of standard ideals for convex sublattice is called standard convex sublattice has been introduced and studied by E. Fried and E.F. Schmidt. Further a generalization of dually standard ideals for convex sublattice called dually standard convex sublattice is introduced and developed in this paper. Many important properties of dually standard convex sublattice are proved. Its connection with congruence class of lattices are also established.

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002019   Chae G B;Cheong M;Kim S M (Mathematics Dep, Yonsei Univ, Wonsei Univ, Email: rivendell@yonsei.ac.kr) : Irreducible posets of linear discrepancy 1 and 2. Far East J mathl Sci 2006, 22(2), 217-26.

The linear discrepancy of a spartially ordered set P = (X, ∝) is defined by ld(P) = min_fεF max_{a<157><157>bεP<157 > f(a) - f(b)<157>, where F is the set of isotones f : P → Z. A poset P is ireducible if ld(P{x}) <60> ld(P) for any x ε P. Irreducible posets of linear discrepancy 1 and 2, respectively were found. As an application, author characterised posets of linear discrepancy 1 in terms of irreducibility.}

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002018   Cerin Z;Vlah S (NO, , Kopernikova 7, 10020 Zagreb Hrvatska, Europa, Email: cerin@math.hr) : Generalization of an IMO inequality. Far East J mathl Sci 2006, 22(2), 205-12.

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002017   Boukaroura A (Mathematics Dep, Univ of Ferhat Abbas, Satif 19000, Algeria, Email: ali_boukaroura@yahoo.fr) : Combinatiorial condition in certain class of groups. Far East J mathl Sci 2006, 22(2), 185-91.

Let X be a class of groups, Group G has the property (X, ∞) if every infinite set of elements of G contains two distinct elements x and γ such that (x, γ) ε X. Supose A, ε, F, N and Ω are respectively the classes of abelian groups, Engel groups, finite groups, nilpotent groups and groups Finite depth and let X be any class of groups whose members satisfy minimal condition on subgroups. In this paper we prove that if G is a finitely generated soluble group, then G has the property (XA, ∞) if and only if it is in XA, and G has the property (Xε, ∞) if and only if it is in XN. Also proves that if G is a finitely generated residually finite group of finite rank in (Ω, ∞), then G is in FN.

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002016   Bouchair A;Kelaiaia S (Mathematics Dep, Univ of Jijel, P.O. Box 98, Jijel, Algeria) : α-favorability of C(X) with a set open topology II. Far East J mathl Sci 2006, 22(2), 175-84.

Consideres [C(X) the set of all continuous real valued functions on a topological space X, when it is equipped with a set open topology defined with the help of a particular non-empty family γ of compact subsets of X. Necessary condition was given for C(X) to be weakly-α-favorable and extend a result obtained of McCoy and Ntantu in the framework of the compact-open topology [Topology Appl. 2 (1986), 191-206], Obtaining this result is essentially due to a hypothesis of admissibility of the family Y. introduced in [Topology Proc, 10 (1985), 329-345].

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002015   Bongioanni B;Torrea J L (Departamento de Matematica, Facultad de Ingenieria Qimica, Universidad Nacional del Litoral, and Instituto de Matematica Aplicada, Santa Fe (3000, Argentina, Email: bbongio@math.unl.edu.ar) : Sobolev spaces associated to the harmonic oscillator. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 337-60.

Authors define the Hermite-Sobolev spaces naturally associated to the harmonic oscillator H = - Δ + x². Structural properties, relations with the classical Sobolev spaces, boundedness of operators and almost everywhere convergence of solutions of the Schrodinger equation are also considered.

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002014   Bijendra Singh;Jain A;Sharma M (School of Studies in Mathematics, Vikram Univ, Ujjain-456 010) : S-fuzzy contraction mapping theorem for s-fuzzy metric space. Acta Cienc Indica-Math 2007, 33(2), 202-8.

The concept of S-Fuzzy contraction mapping on S-Fuzzy metric space is introduced and it is proved that every S-Fuzzy contraction mapping on a complete S-Fuzzy metric space has a unique fixed point.

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002013   Biase G D;Manca R (Dipartimento di Sci, Univ di Chieti, Viale Pindaro 42, 65127 Pescara, Italy, Email: dibiase@sci.unich.it) : Atoms, binary trees and dichotomic non-markovian processes. Far East J mathl Sci 2006, 22(1), 1-16.

After stating the bijection between the space of all possible sets of atoms obtainable from a binary trial sequence or length n and the space of all possible n-level binary trees, author considered the probability distributions on n-level binary trees and then author described the binary trial processes by -means of the weighted n-level binary trees. In this way, simple tools were constructed for analysing dichotomic non-markovian process.

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002012   Bhattacharyya T;Eschmeier J;Sarkar J (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: tirtha@math.iisc.ernet.in) : On CNC commuting contractive tuples. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 299-316.

Characteristic function has been an important tool for studying completely non-unitary contractions on Hilbert spaces. In this note, we consider completely non-coisometric contractive tuples of commuting operators on a Hilbert space <72>. We show that the characteristic function, which is now an operator-valued analytic function on the open Euclidean unit ball in Cⁿ, is a complete unitary invariant for such a tuple. Authors prove that the characteristic function satisfies a natural transformation law under biholomorphic mappings of the unit ball and also characterize all operator-valued analytic functions which arise as characteristic functions of pure commuting contractive tuples.

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002011   Baskar Babujee J;Joshi A (Mathematics Dep, DMI College of Engineering, Chennai-602 103) : Wiener number for some graphs with cycles. Acta Cienc Indica-Math 2007, 33(2), 409-12.

The Wiener number W is the oldest topological indices. Numerous of its applications various methods-numerical approaches and analytical formulas have been proposed to compute W. The Wiener number is defined as the total sum of distances between every pair of vertices. Author determined Wiener number for some graphs with cycles such as 4-regular graphs (Quartic graphs),P₂(Umk₁+ N₂ and Umbrella graph which has cycles.

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002010   Baskar Babujee J;Jagadesh R (Mathematics Dep, DMI College of Engineering, Chennai-602 103) : Graph operators and its applications to context free languages. Acta Cienc Indica-Math 2007, 33(2), 433-7.

A binary operation is performed between two graphs to construct compound graph that are of interest to computer scientists in the design of efficient large-scale computer network. Binary operations like direct sum, superposition, Cartesian product, tensor product and general product are used to frame several new graphs. Introduced two new operations e and o on the fundamental class of graphs like trees and cycles, which preserves their structure of the class and forms a monoid. Further, was shown an application of a new operator on trees was shown which playes a role of substitution in context-free languages with the help of derivation tree.

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002009   Banica C;Putinar M (Mathematics Dep, California Univ, Santa Barbara, CA 93106, USA, Email: mputinar@math.ucsb.edu) : On the classification of complex vector bundles of stable rank. Proc Indian Acad Sci-Mathl Sci 2006, 116(3), 271-91.

One describes, using a detailed analysis of Atiyah-Hirzebruch spectral sequence, the tuples of cohomology classes on a compact, complex manifold, corresponding to the Chern classes of a complex vector bundle of stable rank. This classification becomes more effective on generalized flag manifolds, where the Lie algebra formalism and concrete integrability conditions describe in constructive terms the Chern classes of a vector bundle.

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