019904   Malik S C;Pawar D (Statistics Dep, M.D. Univ, Rohtak-124 001, Email: sc_malik@rediffmail.com) : Reliability and economic measures of a system with inspection for on-line repair and no repair activity in abnormal weather. Bull pure appl Sci-Sect E 2010, 29(2), 355-68.

The focus of this paper is to analyze some reliability and economic measures of a single-unit system operating under two weather conditions - normal and abnormal. For this purpose two reliability models are developed in which unit fails completely via partial failure. In model I, server appears and disappears randomly from the system. And, in model II he comes immediately whenever needed. Server inspects the unit at its partial failure to see the possibility of on-line repair. If on-line repair is not possible, it is repaired in down-state. However, repair of the unit at its complete failure is done without inspection. Repair activities are stopped in abnormal weather while system remains operative. It is assumed that the server remains with the system in abnormal weather. The failure time and time to change of weather conditions are distributed exponentially whereas the distributions of inspection and repair times are taken as arbitrary. The regenerative point technique is adopted to carry out the analysis. Graphs for a particular case are drawn to compare and depict the behaviour of MTSF and profit of the models.

6 illus, 5 ref

019903   Malik S C;J Anand (Statistics Dep, M.D. Univ, Rohtak-124 001, Email: sc_malik@rediffmail.com) : Reliability and economic analysis of a computer system with independent hardware and software failures. Bull pure appl Sci-Sect E 2010, 29(1), 141-53.

The object of this study is to establish and analyse a reliability model for a computer system with considerations of independent hardware and software failures. There are two identical units in the system-one is operative and other is kept as spare in cold standby. A single server is available to the system who inspects the unit only at its hardware failure to examine the feasibility of repair. If repair of the defective component is not feasible, it is replaced immediately by new one. However, only replacement of the software is made by new one whenever it fails. The failure time of the unit is exponentially distributed while the distributions of inspection, repair and replacement of the software are taken as arbitrary with different probability density functions. The expressions for some reliability and economic measures of the computer system are derived using semi-Markov process and regenerative point technique. The numerical results for a particular case are also obtained to depict the behaviour of MTSF, availability and profit of the system.

1 illus, 1 table, 4 ref

019902   Malik P (Mathematics Dep, Ramkrishna Mission Vidyamandira, Belur Nath Hawrah-711 202, Email: pmjupm@yahoo.co.in ) : I and I-continuity on normed linear spaces and I-bounded sequences. Bull Calcutta Mathl Soc 2010, 102(3), 241-52.

In this paper we first, extend the idea of I-contiliuity and I*-continuity of functions to a normed linear space and derive some basic properties of these concepts. Next, we consider the idea of I-boiindedness and study some of its consequences regarding I and I*-convergence.

12 ref

019901   Mahto G (Mathematics Dep, G.D. College, Begusarai, Bihar) : Effect of perturbations and oblateness of more massive primary on the location of triangular points in the restricted three body problem. Bull pure appl Sci-Sect E 2010, 29(2), 193-8.

The effect of perturbations in the coriolis and the centrifugal forces together with the obiateness of more massive primary on the location of triangular points in the restricted three body problem has been studied. It is found that the points L, and L, form triangles with the primaries. The positions of these points are not effected by the change in the coriolis force. They are affected by the change in the centrifugal force and obiateness of the more massive primary.

7 ref

019900   Li Z Q;Peng J W (Department of Mathematics Nachang, University Nanchang 330 047, P.R.China, Email: zhenqili@263.net ) : Rigidity of 3-dimensional minimal cr-submanifolds with constant curvature in CP<. Far East J mathl Sci 2009, 34(3), 303-15.

If M is a minimal CR-submanifold of dimension 3 in the complex projective space CPⁿ and the induced metric of Mhas constant sectional curvature c, then we obtain that c = 1/(m² - 1) for an integer m ≥ 2, and Mis rigid.

9 ref

019899   Kousalya Devi S;Gayathri B (PG and Research Mathematics Dep, Periyar EVR College, Trichy-23, Email: rvishnu21@gmail.com) : K-even edge-graceful labeling of the graph P_n @ K_1,m. Bull pure appl Sci-Sect E 2010, 29(2), 387-407.

In 1985, Lo[6] introduced the notion of edge-graceful graphs. In [2], Gayathri et a/., introduced the even edge-graceful graphs. In [8], Sin-Min Lee, introduced the k-edge-graceful graphs. In [3], we introduced k-even edge-graceful graphs. In this paper, we investigate the k-even edge-gracefulness of the graph P_n @ Ki_m.

29 illus, 8 ref

019898   Koshy T (Mathematics Dep, Framingham State College, 100 State Streets, P.O. Box 9101, Framingham, Massachusetts 01701-9101, Email: tkoshy@framingham.edu) : Cassini-like formula for an extended Fibonacci family. Bull Calcutta Mathl Soc 2010, 102(2), 205-12.

This article presents an extended Pell family of polynomial functions gn (x) which includes the well known Fibonacci, Lucas, Pell, and Pell-Lucas polynomials f_n(x), f_n(x), p_n(x), and q_n(x), respectively. Using matrices and determinants, it extends the generalized Cassini's formula F_m+rF_n-r - F_mF_n = (-1)^n-r-1 F_rF^m-n+r to the generalized family {g_n(x)}; g_m+r(x)g_n-r(x) - g_m(x)g_n(x) = (-1)^n-r(a² - b² + 2abx)p_r(x)P_m-n+r(x).

5 ref

019897   Koshy T (Mathematics Dep, Framingham State College, 100 State Street P.O. Box 9101 Framingham Massachusetts 01701-9101, U.S.A, Email: tkoshy@Framingham) : Generalized nested pell radical sums. Bull Calcutta Mathl Soc 2010, 102(1), 37-42.

This article presents an extended Pell family of polynomial functions g_n(x) which includes the well known Fibonacci, Lucas, Pell, and Pell-Lucas polynomials f_n(x),l_n(x), p_n(x), and q_n(x), respectively. It investigates the convergence of the sequence {S_n(x)} of nested radical sums.

3 ref

019896   Kim I (Mathematics Education Dep, Wonkwang University Iksan, Jeonburk, 540 749, Korea, Email: iki@wonkwang.ac.kr) : Canonical involution on the certain space of modular forms of weight 2. Far East J mathl Sci 2009, 34(3), 405-11.

The canonical involution commutes with the action of Hecke operators T(n). Here authors studied the action of the involution on T₀(N).

11 ref

019895   Khalaf A M;Peng H (Mathematics Dep, Science Faculty, Universiti Putra Malaysia 434 00 Serdang, Selangor, Malaysia, Email: khalaf@math.upm.edu.my) : Note chromaticity of k-bridge graphs. Far East J mathl Sci 2009, 34(3), 353-9.

Let P(G, λ) denote the chromatic polynomial of a graph G. Two graphs G and H. are chromatically equivalent, written G<126> H, if P(G, λ) = P(H, λA). A graph G is chromatically unique, written χ-unique, if for any graph H, G <126>H implies that G is isomorphic with H. In this paper, we prove the chromatic uniqueness of a new family of A-bridge graphs.

12 ref

019894   Kaushal R S (Physics Dep, Ramjas College (University Enclave), Delhi Univ, Delhi-110 007, Email: rkaushal@physics.du.ac.in) : Classical and quantum machanics of complex Hamiltonain systems: an extended complex phase space approach. Pramana J Phys 2009, 73(2), 287-97.

Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation x = x₁ + ip₂, P = P₁ + ix₂, are revisited. It is argued that Carl Bender inducted PT symmetry in the studies of complex power potentials as a particular case of the present general framework in which two additional degrees of freedom are produced by extending each coordinate and momentum into complex planes. With a view to account for the subjective component of physical reality inherent in the collected data, e.g., using a Chevreul (hand-held) pendulum, a generalization of the Hamilton's principle of least action is suggested.

28 ref

019893   Kaladevi V (Mathematics Dep, Seethalakshmi Ramaswami College(Autonomous), Tiruchirappalli-02, Email: kaladevi1956@gmail.com) : On harmonious colouring of super subdivision of paths and stars. Bull pure appl Sci-Sect E 2010, 29(2), 337-42.

In this paper the harmonious chromatic number of super subdivision of paths and stars is found.

6 illus, 8 ref

019892   Kala Devi V (Mathematics Dep, Seethalakshmi Ramaswami College, Trichy-620 002, Email: kaladevi1956@gmail.com) : Graceful labelings of super-subdivision of f-tree and P<. Bull pure appl Sci-Sect E 2010, 29(2), 283-90.

In this paper, any graph different from paths whose arbitrary super subdivision graceful is discussed. The given open problem is answered for two graphs, one is arbitrary super-subdivision of F-tree and another is finite super-subdivision of P⁺_n -tree.

7 illus, 6 ref

019891   Kadyan M S;Malik S C;Jitender Kumar (Statistics & O.R. Dep, Kurushetra Univ, Kurukshetra, Email: imukendersk@yahoo.com) : Stochastic analysis of a redundant system subject to degradation and priority for operation to new unit. Bull pure appl Sci-Sect E 2010, 29(1), 1-12.

A cold standby system of identical units has been analyzed stochastically considering the concepts of degradation and priority. The unit becomes degraded after repair. The server inspects the degraded unit at its failure to see the feasibility of repair. If the repair of the degraded unit is not feasible, it is replaced by the new unit. The priority for operation to the new unit is given over the degraded unit. The system is considered in up-state if any of new/degraded unit is operative. The failure time of the units are exponentially distributed while the distribution of inspection and repair times are taken as arbitrary. The regenerative point technique is adopted to drive the expressions for some reliability and economic measures. A particular case is considered to depict the behavior of some reliability characteristics graphically.

1 illus, 6 ref

019890   Jasmine Rita M;Uma Devi S (Engineering Mathematics Dep, A.U. College of Engineering, Andhra Univ, Visakhapatnam-530 003, Email: jritam@hotmail.com) : Domain pairs of the single ferroic crystal Gd₂ (MoO₄)₃(GMO). Bull pure appl Sci-Sect E 2010, 29(1), 49-57.

Gadolinium Molybdate is an electrical transport in rare earth molybdates. The single ferroic crystal Gadolinium Molybdate Gda (MoO4)s(GMO) which is exhibiting different higher order physical properties at various phase transition temperatures. In this paper we have taken this crystal and found it's higher order physical properties like electric, elastic, magnetic and magneto electric polarizability domain pairs at different phase transition temperatures with the help of group theoretical methods of studying the effect of symmetry on physical properties.

9 tables, 11 ref

019889   Ibtombi Singh N;Sumati Devi A (Mathematics Dep, Manipur Univ, Imphal-795 003) : Particle creation in Brans-Dicke theory in relativistic cosmology. Bull pure appl Sci-Sect E 2010, 29(2), 199-205.

By considering the Robertson-Walker line element exact cosmological solution have been obtained with the assumption that the radius of the universe varies directly as the nth power of cosmic time t and the generated particles are considered as the matter sources in Jordan-Brans-Dicke Theory. Both density and pressure vary inversely as the age of the universe where Brans-Dicke scalar φ varies directly as the age of the universe. The exact solutions corresponding to the 3 values of k (0, 1, -1) are investigated. The gravitation variable G varies inversely as the age of the universe.

11 ref

019888   Hazarika G C;Borgohain B (Mathematics Dep, Dibrugarh Univ, Dibrugarh-786 004, Email: gchazarika@gmail.com) : Effect of variable viscosity and thermal conductivity of stagnation point flow and heat transfer of micropolar fluid in a porous medium. Bull Calcutta Mathl Soc 2010, 102(1), 47-58.

The effect of variable viscosity and thermal conductivity of the steady laminar flow in a. porous medium of a,n incompressible non-Newtonian micropolar fluid impinging on a permeable plate with heat transfer is investigated. The micropolar model due to Eringen is used to describe the working fluid. The partial differential equations governing the motion, angular momentum and energy are reduced to ordinary differential equations using similarity transformations and then solved numerically using Runga-Kutta shooting technique. The effect of the porosity of the medium and the characteristics of the fluid on both the flow and heat transfer is obtained. The results are presented graphically for velocity distribution, temperature distribution and micropolar distributions for various values of non-dimensional parameters, it is found that the effects of a parameter representing variable property of viscosity and thermal conductivity are significant.

10 illus, 17 ref

019887   Guseinov G S (Mathematics Dep, Atilim Univ, 06836 Incek, Ankara, Turkey, Email: guseinov@atilim.edu.tr) : On the concept of spectral singularities. Pramana J Phys 2009, 73(3), 587-603.

Discussed the concept of spectral singularities for non-Hermitian Hamiltonians. We exihibit spectral singularities of some well-known concrete Hamiltonians with complex-valued coefficients.

21 ref

019886   Gopalan M A;Shanmuganandham P (Mathematics Dep, National College, Trichy-620 001, Email: gopalanma@yahoo.com) : On the equation x<. Bull pure appl Sci-Sect E 2010, 29(2), 231-5.

Obtained non-trivial integral solutions for the ternary cubic equation x² + xy-y² = n² + 4n - 1) z³. A few interesting relations among the solutions are presented.

9 ref

019885   Gopalan M A;Sangeetha G (Mathematics Dep, Saranathan College of Engineering, Panjappur, Trichy-12, Email: gopalanma@yahoo.com) : Integral solutions of ternary quintic diophantine equation x<. Bull pure appl Sci-Sect E 2010, 29(1), 23-8.

The Diophantine equation of degree five with three unknowns represented by x² +y² =(k²+)z² is investigated for its non-zero distinct integral solutions. A few interesting relations between the values of x, y, z and special numbers are presented.

16 ref

019884   Gopalan M A;Pandichelvi V (Mathematics Dep, National College, Trichy, Tamil Nadu, Email: gopalanma@yahoo.com) : Integral solutions of ternary quartic equation x<. Bull pure appl Sci-Sect E 2010, 29(1), 135-40.

The ternary quartic Diophantine equation x² - y² + x + y = 2z⁴ is studied for its non-trivial integral solutions. A few relations among the solutions are presented.

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019883   Gopalan M A;Kaliga Rani J (Mathematics Dep, Saranathan College of Engineering, Trichy, Email: gopalanma@yahoo.com) : Integral solutions of x<. Bull pure appl Sci-Sect E 2010, 29(1), 169-73.

Integral solutions of the cubic diophantine equation with four unknowns are obtained by employing linear transformation.

5 ref

019882   Gopalan M A;Kalga Rani J (Mathematics Dep, Saranathan College of Engineering, Trichy, Email: gopalanma@yahoo.com) : Integral solutions of x<. Bull pure appl Sci-Sect E 2010, 29(1), 95-9.

The ternary cubic diophantine equation x³ + y³ + 8k(x + y) = (2k + 1)z³ is analysed for its non- zero distinct integral solutions. A few relations among the solutions are presented.

10 ref

019881   Gopalan M A;Gnanam A (Mathematics Dep, Saranathan College of Engineering, Trichy-620 012, Email: gopalanma@yahoo.com) : Kynea numbers. Bull pure appl Sci-Sect E 2010, 29(1), 73-6.

Kynea numbers together with its twins Carol numbers have been analysed. Some identities relating Kynea numbers and Jacobsthal numbers are presented.

9 ref

019880   Ghosh S (NO, Madanpur K.A. Vidyalaya (H.S), Vill + P.O. Madanpur, Dist. Nadia-741 245, Email: ghosh.sujit6@gmail.com) : On a class of (k, μ)-contact manifolds. Bull Calcutta Mathl Soc 2010, 102(3), 219-26.

Presents a study of projective curvature tensor satisfying certain curvature conditions on a (2n + l)-dimensional (k, μ)-contact metric manifold.

15 ref

019879   Ghonge B E;Ghadle K P (Mathematics Dep, Dr. Babasaheb Ambedkar Marathwada Univ, Auragabad-431 004, Email: badrighonge@gmail.com) : Inverse transient thermoelastic problem of solid sphere. Bull pure appl Sci-Sect E 2010, 29(1), 13-21.

Deal with an inverse transient thermoelastic problem in which we need to determine the unknown temperature, radial displacement and stress function on outer curve surface of a solid sphere when temperature is known at interior under consideration and initially is kept at zero. The governing heat conduction equation has been solved by using Laplace transform technique. The results are obtained in a series form of trigonometric functions. The results for temperature, radial displacement and stresses have been computed numerically and illustrated graphically.

4 illus, 9 ref

019878   Ghiasvand P;Farzalipour F (Mathematics Dep, Payame Noor Univ (PNU) P.O. Box 1161, Manjil, Iran, Email: p_ghiasvand@pnu.ac.ir) : Some properties of graded multiplication modules. Far East J mathl Sci 2009, 34(3), 341-52.

Let G be a group with identity e, R be a G-graded commutative ring, and M be a graded R-module. This paper is devoted to study some properties of graded multiplication modules. First, we characterize graded multiplication modules by using the graded localization of graded S-module M. Next, we give a condition which allows us to determine whether graded submodules of a graded module have graded prime radical.

12 ref

019877   Fakir Chand;Mishra S C;Singh R M (Physics Dep, Kurukshetra Univ, Kurukshetra-139 119, Email: fchand72kuk@gmail.com ) : Solution of an analogous Schrodinger equation for PT-symmetric sextic potential in two dimensions. Pramana J Phys 2009, 73(2), 349-61.

Investigates the quasi-exact solutions of an analogous Schrodinger wave equation for two-dimensional non-Hermitian complex Hamiltonian systems within the framework of an extended complex phase space characterized by x = x₁ + ip₃,y = x₂ + ip₄,p_x - P₁ + ix₃,p_y = P₂ + 1x₄,. Explicit expressions for the energy eigenvalues and eigenfunctions for ground and first excited states of a two-dimensional PT-symmetric sextic potential and some of its variants are obtained. The eigenvalue spectra are found to be real within some parametric domains.

22 ref

019876   Dorey P;Dunning C;Tateo R (Mathematical Sciences Dep, Durham Univ, Durham DH1 3LE, UK, Email: p.e.deorey@durham.ac.uk) : From PT-symmetric quantum mechanics to conformal field theory. Pramana J Phys 2009, 73(2), 217-39.

One of the simplest examples of a PT-symmetric quantum system is the scaling Yang-Lee model, a quantum field theory with cubic interaction and purely imaginary coupling. We give a historical review of some facts about this model in d ≤ dimensions, from its original definition in connection with phase transitions in the Ising model and its relevance to polymer physics, to the role it has played in studies of integrable quantum field theory and 'PT-symmetric quantum mechanics. We also discuss some more general results on PT-symmetric quantum mechanics and the ODE/IM correspondence, and mention applications to magnetic systems and cold atom physics.

10 illuss, 71 ref

019875   Dixit K K;Porwal S (Mathematics Dep, Janta College, Bakewar, Etawah-206 124) : Application of fractional calculus to harmonic univalent functions. Bull Calcutta Mathl Soc 2010, 102(4), 343-52.

In this paper authors introduce a new subclass S*_H,λ(α) of S_H by using fractional calculus. We give univalence criteria and sufficient coefficient conditions for normalized harmonic functions belonging to the class S*_H,λ(α, where (0 ≤ α <60> 1), (0 ≤ A <60> 1). These coefficient conditions are also shown to be necessary for subclass TS*_H,λ(α) of S*_H,λ(α) in which h has negative and g has positive coefficients. This leads to extreme points, distortion bounds and radius of convexity. We also discuss a class preserving integral operator and show that the class studied in this paper is closed under convolution and convex combinations.

11 ref

019874   Dixit K K;Porwal S (Mathematics Dep, Janta College, Bakewar, Etawah-206 124) : Harmonic univalent functions with fixed point and negative coefficients. Bull Calcutta Mathl Soc 2010, 102(1), 9-16.

Let T*_H⁰ (Z₀) and TK⁰_H (z_o) donate the class of functions f = h + g, where h(z) = a₁z - Σ^∞_n=2 a_nZⁿ, g(z) = -Σ^∞_n=2 b_nzⁿ, a₁ <62> 0, a_n ≥ 0 and b_n ≥ 0, that map the unit disc U = {z : z |z| <60> 1} onto starlike and convex domains respectively satisfying f(z₀) = z₀, -1 <60> z₀ <60> 1 z₀ ≠ 0. In this paper, sharp coefficient estimates, distortion properties for function in T*⁰_H(z₀) and Tk⁰_H(z_o) have been obtained. This leads to extreme points.

6 ref

019873   Demir O;Akdogan Z (Gaziosmanpasa Univ, Koyulhisar vocational High School, 58660 Koyulhisar, Sivas,Turkey, Email: mosmandemir@hotmail.com) : Green function of one discontinuous Sturm-Liouville problem. Bull pure appl Sci-Sect E 2010, 29(2), 435-52.

In this study, we consider one discontinuous Sturm-liouville problem with two supplementary transmission at the one inner point of discontinuity and seek some spectral properties of this problem when the potential of the differantial equation may have discontinuity at the one iner point and the eigenparameter appears in the differential equation. We give an operator-theoretic interpretation and obtain asymptotic formulas for eigenvalues and corresponding eigenfunctions. Finally, we construct Green's function and obtain the asymptotic representation of Green's function.

13 ref

019872   Datta S K;Mandal S (Mathematics Dep, North Bengal Univ, Raja Rammohunpur, Darjeeling-734 009, Email: sanjib_kr_datta@yahoo.co.in) : On the L*-(p,q)th order of entire and meromorphic functions based on relative sharing. Bull Calcutta Mathl Soc 2010, 102(2), 139-46.

In this paper auther study on the equality of L*-(p,q)th order (L*-(p,q)th lower order) of entire and meromorphic functions based on relative sharing of values of them where L = L(T) is a slowly changing function and p, q are positive integers with p <62> q.

7 ref

019871   Datta S K;Biswas T (Mathematics Dep, North Bengal Univ, P.O. North Bengal Univ, Raja Rammohunpur Dist: Darjeeling-734 013, Email: sanjib_kr_datta@yahoo.co.in) : Relative order of composite entire functions and some related growth properties. Bull Calcutta Mathl Soc 2010, 102(3), 259-66.

In this paper we study the comparative growth properties of entire function on the basis of relative order (relative lower order) and relative hyper order (relative hyper lower order) with respect to another entire function.

4 ref

019870   Das N (P.G. Mathematics Dep, Sambalpur Univ, Jyotivihar, Burla-768 019) : Fredholm toeplitz operators on the bergman space over bounded symmetric domains. Bull Calcutta Mathl Soc 2010, 102(1), 89-98.

In this paper it is shown that a Toeplitz operator on the Bergman space over bounded symmetric domain with bounded harmonic symbol is invertible if and only if the Toeplitz operator is Fredholm and of index zero.

8 ref

019869   Darus M;Ibrahim R W (Mathematical Sciences School, Faculty Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor Darul Ehsan, Malaysia, Email: maslina@ukm.my) : On subclasses of uniformily bazilevic type functions involving generalised differential and integral operators. Far East J mathl Sci 2009, 33(3), 401-11.

Introduces generalised differential and integral operators on the class A of analytic functions in the unit disk U := {z ∈ C : | z | <60> 1} of the form f(z) = z + Σ^∞_n=2 a_nzⁿ, (z ∈ U), involving kth Hadamard product. ??

18 ref

019868   Darus M;Ibrahim R W (Mathematical Sciences School, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan, Malaysia, Email: maslina@ukm.my) : On inclusion properties of generalized integral operator involving noor integral. Far East J mathl Sci 2009, 33(3), 309-21.

New classes containing generalization of integral operator are introduced. Inclusion properties of these classes are studied.

11 ref

019867   Darus M;Ibrahim R W (Mathematical Sciences School, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600, Selangor Darul Ehsan, Malaysia, Email: maslina@ukm.my) : On subclasses for generalized operators of complex order. Far East J mathl Sci 2009, 33(3), 299-308.

Defines generalized differential and integral operators on the class A. of analytic functions f(z) = z + ^∞∑_n =2ⁿn^{zn in the unit disk U := {z e C : | z | <62> 1} involving A:-th Hadamard product (convolution) as follows: n=2. These operators are the generalized form of some well-known operators, for example, Salagean operator and Al-Oboudi operator. New classes containing these operators of complex order are investigated.}

5 ref

019866   Chavhan S B;Borkar V C;Gudadhe A S (Mathematics & Statistics Dep, Yeshwant Mahavidyalaya, Nanded-431 605) : Some aspect of canonical cosine transform of generalized function. Bull pure appl Sci-Sect E 2010, 29(1), 101-10.

Studies different testing function spaces of canonical cosine transform. Analyticity theorem is also proved. Some operational transform formulae have been obtained and applications of canonical cosine transforms are discussed.

8 ref

019865   Chandulal A;Sambaiah K (Mathematics Dep, Kalkatiya Univ, Warangal-506 009) : Dilatation and distortional waves in micro-isotropic, micro-elastic medium. Bull pure appl Sci-Sect E 2010, 29(2), 309-17.

In this paper, the propagation of dilatation and distortional waves in micro-isotropic, microelastic medium has been discussed. Frequency equations have been deduced in both the cases. It is found that additional waves are propagating in the medium. The classical results are obtained as a particular cases of these.

4 ref

019864   Chandrasekhara Rao K;Padma P (Mathematics Dep, Srinivasa Ramanujan Research Centre, Sastra Univ, Kumbakonam-612 001, Email: chandrasekhararaok@rediffmail.com) : On low bitopological separation properties. Bull pure appl Sci-Sect E 2010, 29(2), 237-42.

This paper is devoted to low separation axioms such as pairwise T₀, T₁, T_1/2 T_3/4, T_11/3n/3 T_12/3 - spaces. This paper is partly a survey of known results Further results are supplemented.

8 ref

019863   Chakrabarty D (Statistics Dep, Handique Girl's College, Guwahati-781 001, Email: dhritikesh.c@rediffmail.com) : Chakrabarty's definition of probability: additive and multiplicative laws. Bull pure appl Sci-Sect E 2010, 29(2), 265-74.

In 2004, Chakrabarty has constructed a theoretical definition of probability, in terms of its measurement, with a view to search for some method of determining the value of the probability of an event to a random experiment. The proofs, of the two well-known laws of probability namely the additive law and the multiplicative law, by this definition have been presented in this paper.

18 ref

019862   Caliceti E;Graffi S (Departimento di Matematica, Universita di Bologna and INFN, Bologna, Italy, Email: caliceti@dm.unibo.it) : Relity and non-reality of the spectrum of PT -symmetric operators: opretor-theoretic criteria. Pramana J Phys 2009, 73(2), 241-9.

Generalized some recently established criteria for the reality and non-reality of the spectrum of some classes of PT-symmetric Schrodinger operators. The criteria include cases of discrete spectra and continuous ones.

19 ref

019861   Braz E Silva P;Schutz L;Zingano P R (Departamento de Matematica, Universidade Federal de Pernambuco Recife, PE 50740, Brazil, Email: pablo@dmat.ufpe.br) : On solution boundedness for parabolic equtions. Far East J mathl Sci 2009, 33(3), 379-85.

Gives a short proof that solutions u(., t) of 2nd-order quasilinear parabolic equations in general heterogeneous non-isotropic media, with initial states u(., 0) = u₀ ∈ L^P(Rⁿ) for some 1 ≤ p <60> ∞, satisfy, under fairly general assumptions, a supnorm estimate ||u(., t)||_L^∞(Rⁿ) ≤ K(T)||u₀||_L^P(R^N), T<62> 0 for some continuous K independent of u₀. Other results of interest are also discussed.

6 ref

019860   Borges M F;Benzatti L F I (NO, UNESP-Sao Paulo State Univ, S.J. Rio Preto Campus, 15054-000, Sao Jose do Rio Preto Brazil, Email: borges@ibilce.unesp.br) : Quasiconformal mappings in octonionic algebra: a graphical and analytical comparison. Far East J mathl Sci 2009, 33(3), 355-61.

In this article, author present quasiconformal mappings related to octonionic algebra. Based on the metric definition of quasiconformal mappings and using transformations of the type /(z) = zⁿ, compared the graphical and analytic results.

6 ref

019859   Bondar K L;Borkar V C;Patil S T (P.G. mathematics Dep, N.E.S. Science College, Nanded-431 605, Email: klbondar_75@rediffmail.com) : Some existence and uniqueness results for difference boundry value problems. Bull pure appl Sci-Sect E 2010, 29(2), 291-6.

Discusses some existence and uniqueness theorems related to second order difference equations.

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019858   Biasi C;Libardi A M;Rossini I C (Departamento de Matematica ICMC-USP- Campus de Sao Carlos Caixa Posta, Sao Carlos, SP, Brazil, Email: biasi@icmc.usp.br) : Remarks on the normal bordism forgetful homomorphim. Far East J mathl Sci 2009, 34(3), (NULL).

Assume that X is an oriented smooth (n + k) -manifold. Then the kernel of the forgetful map F considered in this work consists of immersions f : Mⁿ → X nullbordant as a continuous map. Using an exact sequence of normal bordism groups previously given, presents a homological characterization of the kernel of the forgetful map F. Also, proves that Ω_i(X, ε^s - η^s) and H_i(X, Z) are C_2,3-isomorphic for i ≤ 3 and C₂-isomorphic for i ≤ 2, where C_2,3 (resp. C₂) is the class of abelian groups whose elements have order 2^p. 3^q (resp. 2^p), and η^s is an orientable stable vector bundle over X.

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019857   Bhadra N K (Lakshmipur Swamiji Seva Sangh High School, Lakshmipur Gobardanga, 24-Parganas(N), West Bengal) : Complex model of the universe. Bull Calcutta Mathl Soc 2010, 102(4), 381-96.

Study unified theory with gauge group SU(11). The subgroup SU(6) has been interpreted as a new type of energy source other than SU(5). Considers a (4 + D)-dimensional Friedmann-Robertson-Walker type Universe having complex scale factor R + iR_I, where R is the scale factor corresponding to the usual 4-dimensional Universe while R_I is that of D-dimensional space. It is then compared with (4+D)-dimensional Kaluza-Klein Cosmology having two scale factors R and a(= iRj). It is shown that the rate of compactification of higher dimension depends on extra dimension 'D'. The Wheeler-DeWitt equation and general solution is obtained. It is founded that for D = 6 (i.e. in 10 dimension), the Wheeler-DeWitt equation is symmetric under the exchange R_I ↔ R.

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019856   Basheer Ahamed M;Bagyam I (Mathematics Dep, Karunya Univ, Coimbatore-641 114) : Double-critical k-chromatic graphs. Bull pure appl Sci-Sect E 2010, 29(2), 409-11.

A long-standing conjecture due to Erdos [2] states that the complete graphs are the only double-critical graphs, which is referred as the double-critical graph conjecture. In this paper, we prove the double-critical graph conjecture fork <62> 5.

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019855   Bagghi B;Quesne C;Roychoudhury R (Applied Mathematics Dep, Calcutta Univ, 92 Acharya Prafulla Chandra Road, Kolkata-700 009, Email: bbagchhil123@rediffmail.com) : Isospectrality of conventional and new extended potentials, second-order supersymmetry and role of PT symmetry. Pramana J Phys 2009, 73(2), 337-47.

Develops a systematic approach to construct novel completely solvable rational potentials. Second-order supersymmetric quantum mechanics dictates the latter to be isospectral to some well-studied quantum systems. PT symmetry may facilitate reconciling our approach to the requirement that the rationally extended potentials be singularity free. Some examples are shown.

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