000102   Sarsak M;Rajesh N (Mathematics Dep, Faculty of Science, Hashemite Univ, P.O. Box 150459, Zarqa 13115, Jordan, Email: sarsak@hu.edu.jo) : Weak separation axioms via g-open sets. Far East J mathl Sci 2008, 30(3), 457-71.

g -open sets are used to define some weak separation axioms and to study some of their basic properties. The implications of these axioms among themselves and with the known axioms T_i, (i = 0, 1/2. 1, 2) are investigated.

14 ref

000101   Samanta S C;Maishal R K (NO, Midnapore College, Midnapore-721 101) : Magneto-thermo-visco-elastic interaction in a homogeneous rotating anisotropic solid cylinder. Bull Calcutta Mathl Soc 2009, 101(2), 157-74.

One-dimensional viscoelastic analysis is based on generalized thermoelasticity theory. The expressions of field quantities for a rotating anisotropic solid cylinder in presence of primary magnetic field are obtained. The visco-elastic material behaviour is described by Voigt model. Laplace transform technique is applied to obtain the short time approximate solutions for the displacement, temperature, stresses and peturbed magnetic field. Numerical results are displayed graphically for different cases.

5 illus, 2 tables, 12 ref

000100   Ramli A L A;Ismail A Z M;Karim M F A (NO, School of Mathematical Sciences, USM 11800, Penang, Malaysia, Email: lutfiamri@live.com) : Qualitative aspects of a model fo hantavirus infection. Far East J mathl Sci 2008, 29(3), 653-60.

Hantaviruses are a group of viruses which have been identified as being responsible for the outbreak of diseases such as the Hantavirus Pulmonary Syndrome. In an effort to understand the dynamics of hantavirus infection, a basic model consists of a system of two nonlinear ordinary differential equations has been developed by Abramson and Kenkre [1]. This paper pursues a qualitative analysis approach system of the differential equation.

1 illus, 7 ref

000099   Ramasamujh T I (Mathematics Dep, Florida International Univ, Miami, Florida 33199, U.S.A., Email: ramsamuj@fiu.edu ) : Nullary relations, function and matrices and truth in empty domains. Far East J mathl Sci 2008, 30(1), 193-203.

Nullary relations, functions and matrices are introduced in a natural way and some applications are given to indicate the usefulness of these concepts. The key point is that nullary concepts should be incorporated into existing theories; they should not be treated as special cases using ad hoc conventions. Also if a nullary concept does more harm than good, as in the case of truth in empty domains, it should be avoided.

8 ref

000098   Prasad B N;Pandey T N;Srivastava E (NO, , C-10 Surajkund Colony Gorakhpur) : Wagner connection of a Finsler space with mTH-root metric. Bull Calcutta Mathl Soc 2009, 101(2), 187-96.

The purpose of this paper is to obtain the Wagner connection of Finsler space with mth-root metric.

16 ref

000097   Pintarelli M B;Vericat F (Grupo de Aplicaciones Mathematicas y Estadisticas de la Facultad de In, Universidad Nacional de La Plata, La Plata, Argentina, Email: vericat@iflysib.unlp.edu.ar) : Stability theorem and inversion algorithm for a generalized moment problem. Far East J mathl Sci 2008, 30(2), 253-74.

Considers the problem of recovering a function f(x) given the generalized moments μk = ∫_a^bgk(x)f(x)dx, where {gk(x)}_k∈ICN is a set of linearly independent, continuous functions over a Hilbert space. A stability theorem and an inversion algorithm are presented. Considers the application of the algorithm to estimate density functions and also the relation of the generalized inverse moment problem with Fredholm integral equation of the first kind.

7 illus, 3 tables, 18 ref

000096   Pathak R S;Singh S K (Mathematics Dep, Banaras Hindu Univ, Varanasi-221 005, Email: ramshankarpathak@yahoo.co.in ) : Infraexponential decay of wavelets. Proc Natn Acad Sci India-Sect A 2008, 78(Pt 2), 155-62.

Using the theory of ultradifferentiable functions it is shown that there exist band-limited wavelets of infraexponential decay.

9 ref

000095   Park J (Mathematics Dep, Hanseo Univ, Chungnam 356-820, Korea, Email: jkpark@hanseo.ac.kr) : New proof on the generalized hierarchy of relative convexity of higher orders. Far East J mathl Sci 2008, 30(3), 523-35.

Using Vandermonde matrices obtain new proofs for the classes of n-convex, n-starshaped, n-superadditive and J-convex functions relative to a fixed point of higher order and some inclusion relations among them.

9 ref

000094   Pansera B A (NO, Dipartimento diu Matematics Universita di Messina, Contrada Papardo, Salita Sperone, 31 98166 Sant'Agata - Messina, Italy, Email: bpansera@dipmat.unime.it) : Relative properties and function spaces. Far East J mathl Sci 2008, 30(2), 359-72.

Investigates duality between (covering) properties in topological spaces and the closure-type properties of mappings, Gives a version of the Pytkeev property for continuous mappings.

22 ref

000093   Pandey P N;Chaturvedi B B (Mathematics Dep, Allahabad Univ, Allahabad-211 002, Email: pnpiaps@rediffmail.com) : Recurrences with respect to a semi-symmetric metric connection on an almost Hermite manifold. Proc Natn Acad Sci India-Sect A 2008, 78(Pt 2), 137-44.

In the present paper recurrent almost Hermite manifolds with respect to a Riemannian connection and a semi-symmetric metric connection have been introduced and the necessary and sufficient condition for a recurrent almost Hermite manifold with respect to Riemannian connection to be recurrent almost Hermite manifold with respect to semi-symmetric metric connection has been obtained. The relation between the recurrences of Ricci tensor, H-projective tensor and projective tensor with respect to these connections have also been discussed.

10 ref

000092   Nigam S K (Mathematics and Astronomy Dep, Lucknow Univ, Lucknow-226 007) : On infinite integrals involving product of Laguerre functions, multivariable H-function and integral function of two complex variables. Bull Calcutta Mathl Soc 2009, 101(1), 37-48.

Two main theorems have been given. The first theorem involves the product of two Laguerre functions of degree α and γ respectively, the multivariable H-function and the integral function of two complex variables, whereas the second theorem involves the product of Laguerre function of degree α, the multivariable H-function, the general class of polynomials S_V^U(x) and the integral function of two complex variables.

10 ref

000091   Narsimha Reddy K;Sreenivas A (Mathematics Dep, Osmania Univ, Hyderabad, Email: sreenivas.ananthy@rediff.com) : On integral inequalities in n-independent variables. Bull Calcutta Mathl Soc 2009, 101(1), 63-70.

Studied the linear and nonlinear integral inequalities in n-independeiit variables and discuss some of their extensions and application.

11 ref

000090   Narita K (Information System Creation Dep, Faculty of Engineering, Kanagawa Univ, Rokkakubashi 3-27-1, Kanagawa-ku, Yokohama 221-8686, Email: narita@math.ie.kanagawa-u.ac.jp) : Stochastic analysis of fractional Brownian motion and application to black-scholes market. Far East J mathl Sci 2008, 30(1), 65-135.

Stochastic analysis is given for a Black-Scholes (BS) market driven by fractional Brownian motion (fBm) B_H with Hurst parameter H in (1/2, 1). The stochastic integrals with respect to B_H are in the Wick-Ito sense, not pathwise which is known to lead to arbitrage opportunity. A fBm B_H has the statistical self-similarity and dependence on the long memory of the past. Since for H ≠ 1/2 fBm is neither a Markov process, nor a semimartingale, usual stochastic calculus cannot be applied to the field of network traffic analysis and mathematical finance. Hence researches in problems are made by the Wick-Ito calculus. In this model, the underlying asset contains time-dependent deterministic volatility function with a small parameter 0 < ε <<K 1, whereas a classical model in Hu and ®ksendal [11] and Necula [16] assumes constant values for the volatility. Then, our first purpose is to obtain a fractional BS formula for the price of European call option for every time, a fractional BS partial differential equation and a risk-neutral valuation theorem. Moreover, e-dependent fractional BS model is considered, where there is a closed-form solution known as the BS formula. Our second purpose is to obtain an asymptotic order for E-dependent price of a call as ε → 0. For proof, quasi-conditional expectations on suitable functions of quasi-martingale process are explicitly calculated by using fractional Girsanov transform, Malliavin derivative and fractional Ito formula.

17 ref

000089   Mothebe M (Mathematics Dep, Botswana, Botswana, , Email: mothebem@mopipi.ub.bw) : Dimensions of subspaces of the polynomial algebra F₂[x₁,..., x_n] generated by spikes II. Far East J mathl Sci 2008, 30(1), 185-92.

Let n ≥ 1 and d ≥ 0 be integers. Let P(n) = F₂[X₁, ..., x_n] be the polynomial algebra in n-variables xi over the field F₂ of two elements. In [1] we give a formula for computing B(n, d), the number of degree d monomials of the form x₁^2λ1-1 x₂^2λn-1 (called spikes) in P(n). The formula is recursive and is dependent on values B(n, 2^n-1 - n) for all n ≥ 2. In this note we give an effective algorithm for computing B(n, 2^{n-1 -n).}

5 ref

000088   Mondal C R (Mathematics Dep, North-Eastern Hill Univ, Shillong-793 022) : Shallow-water waves in a rotating ocean. Bull Calcutta Mathl Soc 2009, 101(1), 1-10.

Initial-value problem of shallow-water waves due to oscillatory surface stress distribution on a homogeneous rotating ocean is solved by the method of integral transforms. For wave integral, uniform asymptotic analysis is given for the unsteady state, the result, unlike previous findings, is non-singular when the circular frequency of oscillation equals the Coriolis parameter.

6 ref

000087   Mondal A K (Dum Dum Subhasnagar High School (H.S.) 43, , Sarat Bose Road, Kolkata-700 065, Email: kalam_ju@yahoo.co.in) : M-projective curvature tensor on a Sasakian manifold. Bull Calcutta Mathl Soc 2009, 101(2), 143-8.

Deals with M-projective curvature tensor on a Sasakian manifold. It proved that a Sasakian manifold is M-projectively recurrent if and only if the manifold is M-projectively flat.

6 ref

000086   Misra O P;Sinha P;Rathore S K S (School of Mathematics and Allied Sciences, Jiwaji Univ, Gwalior-474 011) : Effect of polluted soil on the growth dynamics of plant-herbivore system: a mathematical model. Proc Natn Acad Sci India-Sect A 2008, 78(Pt 2), 145-54.

A mathematical model is proposed to study the effect of soil pollution on the growth dynamics of plant-herbivore system. In the model the plant biomass is divided into two compartments consisting of leaves and roots. In the modeling process, it has been assumed that the pollution in the soil causes damage to the root compartment, thereby destroying the substrates in the soil that causes damage to the root compartment thereby destroying the substrates in this compartment. Also it is assumed in the model that the pollutant is being transferred from root compartment to the leaf compartment which in turn adversely affects the substrates in this compartment also. Since the growth of plant biomass in both the compartments depend on the substrate concentration, the weight of the leaf and root compartments of plant biomass will decrease on account of the polluted soil. In the model a separate equation has been considered to study the dynamics of herbivore population. The stability analysis of the two equilibrium points of the model has been conducted. From the stability of the positive equilibrium point it has been concluded that both the plant biomass and the herbivore population would co-exist but the equilibrium densities of these two population will be reduced due to the presence of pollutant in the soil.

13 ref

000085   May R;Landy J (Mathematics and Computer Science Dep, Morehead State Univ, 150 Univ Blvd., UPO 701, Morehead, KY 40351, U.S.A., Email: r.may@moreheadstate.edu) : Some problems with generating function solutions. Far East J mathl Sci 2008, 30(2), 227-32.

Presents three new combinatorial problems with solutions involving generating functions and asymptotic approximations.

3 ref

000084   Mansour M (Mathematics Dep, Faculty of Science, Mansoura Univ, Mansoura, 35516, Egypt, Email: mansour@mans.edu.eg) : Determining Γ_q(x) by functional equations. Far East J mathl Sci 2008, 29(3), 693-9.

Technique of Artin [1] to determine the g-gamma function by a combination of some functional equations has been used. In case of q → 1, we get the functional equations which determine the case of q → 1, we get the function ordinary gamma function.

5 ref

000083   Mansour M (Mathematics Dep, Faculty of Science, Mansoura Univ, Mansoura, 35516, Egypt, Email: mansour@mans.edu.eg) : Bounds of q-euler reflection formula. Far East J mathl Sci 2008, 29(3), 685-92.

Deduce upper and lower bounds for the function ϕ_q(x) = q^{x(1-x)Γ q22(X) Γ q2 for 0 < q < 1 and study some of its properties. Also, we use the concept of convexity to prove the ordinary Euler reflection formula.}

10 ref

000082   Majumdar S;Akhter N (Mathematics Dep, Rajshahi Univ, Rajshahi 6205, Bangladesh) : Determination of the homology and the cohomology of a class of infinite groups associated with groups of fibonacci type. Bull Calcutta Mathl Soc 2009, 101(1), 11-24.

Constructed free resolutions of Z for a class G(a, b, c, k, l) of infinite groups which were studied by (Campbell and Thomas) in connection with investigation of infiniteness of a number of groups of Fibonacci type. Computed the homology and the cohomology. The importance and significance of the resolutions lie in the fact that these have been built up directly from the presentation just by solving systems of linear equations over the integral group rings and are immediately applicable, without further simplification, for direct computation of the homology and the cohomology. A series of forthcoming papers will describe the technique and use it to different classes of groups.

23 ref

000081   Lee I Y (Mathematics Dep, Kyungsung Univ, Busan, 608-736, Korea, Email: iylee@ks.ac.kr) : On berwald space with an approximate infinite series (α, <128><98>)-metric. Far East J mathl Sci 2008, 29(3), 701-10.

Authour treat an approximate infinite series (α, β)- metric L = βΣ^r_k=0 (α/β)^k. also find the condition that a Finsler space Fⁿ metric L = β Σ (α/β)^k. Also find the conditior with the metric above be a Berwald space.

11 ref

000080   Lee D W (Mathematics Dep, Institute of Pure and Applied Mathematics Chonbuk National Univ, Jeonju, Jeonbuk, 561-756, Republic of Korea, Email: dwlee@math.chonbuk.ac.kr) : On the same homotopy types, self-maps and rational morphisms. Far East J mathl Sci 2008, 30(2), 205-9.

Shows that there exist some spaces whose homology and homotopy groups are isomorphic, but they do not have the same homotopy type. Also deals with the self-maps and rational morphisms in the suspension structure.

5 ref

000079   Leandre R (Institut de Mathematiques, Universite' de Bourgogne, 2100, Dijon, France) : Malliavin calculus of bismut type in semi-group theory. Far East J mathl Sci 2008, 30(1), 1-26.

Authour translate into semi-group theory various results which were obtained by using stochastic analysis. Use the classical relation between the theory of stochastic processes and the theory of Markovian semi-groups.

62 ref

000078   Laila M M (Mathematics Dep, Faculty of Science, Menoufia Univ, Shebin El-Kom, Egypt) : Integral representation of positive definite functions on infinite dimensional spaces. Far East J mathl Sci 2008, 29(3), 629-41.

Authour extended the Bochner's theorem in to a mapping taking values in a Banach space X. Results obtained generalize the extension of Bochner's theorem.

7 ref

000077   Kim S M;Cheong M (General Education-Mathematics Div, Kwangwoon Univ, Seoul, Korea, Email: smkim@kw.ac.kr) : Linear discrepancy of the product of three chains of size 2n. Far East J mathl Sci 2008, 30(2), 285-98.

The linear discrepancy of a partially ordered set P = (X, ≤) is defined by ld(P) = min_f∈F maxα||b∈P|f(a)-f(b)|, where F is the set of isotones f : P → Z on P. The linear discrepancy of the product of arbitrary three chains has not been found yet. Shows ld(2n x 2n x 2n) = 6n³ - 2n² - 1.

4 illus, 4 ref

000076   Khongtham Y;Plubtieng S (Mathematics Dep, Faculty of Science, Naresuan Univ, Phitsanulok 65000, Thailand, Email: somyotp@nu.ac.th) : General iterative for equilibrium problems of a countable family of nonexpansive mappings in Hilbert spaces. Far East J mathl Sci 2008, 30(3), 583-604.

Introduces two iterative schemes by the general iterative method for finding a common fixed point of a countable family of nonexpansive mappings in Hilbert spaces. Then, we prove a strong convergence theorem to solve a unique solution of the variational inequality which is the optimization problem. Results extends and improves the corresponding results of Plubtieng and Punpaeng [11] and many others.

17 ref

000075   Khan M A;Mandal A K (Mathematics Dep, Palaschabri N. High School, (H.S.), Korasia, Paschim Medinipur, West Bengal) : Generalized chaos synchronization of coupled rossler systems. Bull Calcutta Mathl Soc 2009, 101(2), 197-204.

Generalized approach for constructing chaotically synchronized Rossler systems via linear transformations is proposed. Proposed method is much simpler than the method proposed by Pecora and Carroll (1990). This method is very useful for synchronization of hyper-chaotic system because Lyapunov exponents need not required to calculate. In this method, we can predict the response systems behaviour in advance, knowing the driving systems behaviour.

3 illus, 7 ref

000074   Kawakami T (Mathematics Dep, Faculty of Education, Wakayama Univ, Sakaedani Wakayama 640-8510, Japan, Email: kawa@center.wakayama-u.ac.jp) : Definable C∞ fiber bundles and definable C∞ G vector bundles. Far East J mathl Sci 2008, 30(1), 27-44.

Let G be a finite abelian group and K be a compact subgroup of an orthogonal group. Authours prove that every topological fiber bundle over a definable C^∞ mamfold whose structure group is K admits a unique strongly definable C^∞ fiber bundle structure up to definable C^∞ fiber bundle isomorphism. Moreover, prove that every G vector bundle over a definable C^∞G manifold admits a unique strongly definable C^∞G vector bundle structure up to definable C^∞G vector bundle isomorphism.

3 illus, 2 tables

000073   Kawai S (Mathematics Dep, Faculty of Culture and Education, Saga Univ, Saga 840, Japan, Email: kawais@cc.saga-u.ac.jp ) : Essential spectrums of the dirac operators on non-compact positively curved manifolds. Far East J mathl Sci 2008, 30(2), 309-24.

The essential spectrums σ_ess of the Dirac operators on Riemannian manifolds are investigated. It is proved that σ_ess = R if the curvatures satisfy some positivity conditions and decay at infinity.

18 ref

000072   Kalas J (Mathematics and Statistics Dep, Masaryk Univ, Janackovo nam. 2a, 602 00 Brno, Czech Republic, Email: kalas@math.muni.cz) : Asymptotic properties of a two-dimensional differential system with a bounded nonconstant delay under the conditions of instability. Far East J mathl Sci 2008, 29(3), 513-32.

Asymptotic behaviour for the solutions of a real two-dimensional system x' = A(t)x(t) + B(t)x(θ(t)) + h(t, x(t) x(θ(t)))) with a nonconstant delay t - θ(t) ≥ 0 is studied under the assumption of instability. A, B and h are supposed to be matrix functions and a vector function, respectively. The conditions for the instable properties of solutions together with the conditions for the existence of bounded solutions or solutions tending to the origin as t → ∞ are given. The method of investigation is based on the transformation of the considered real system to one equation with complex-valued coefficients. Asymptotic properties of this equation are studied by means of a suitable Lyapunov-Krasovskii functional and by virtue of the Wazewski topological principle. The results generalize those of [7], where the asymptotic properties for two-dimensional systems with a constant delay were studied.

15 ref

000071   Itoh M (NO, Oyama National College of Technology, Oyama, Tochigi 323-0806, Japan, Email: mitoh@oyama-ct.ac.jp) : Orbits of paranormal operators. Far East J mathl Sci 2008, 30(2), 275-83.

Shows the following facts. If T is paranormal operator, then T is never supercyclic, is power regular, has a non-trivial hyperinvariant subspace and is not weakly hypercyclic, which generalizes a result due to Bourdon [2] and Sanders [4].

4 ref

000070   Hussain Khan M;Subramanian K G (Mathematics Dep, Islamiah College, Vaniyambadi-635 751, Email: khanhussaff@yahoo.co.in) : Class of p-valent function defined using Dziok-srivastava operator. Bull Calcutta Mathl Soc 2009, 101(1), 49-54.

4 ref

000069   Hou T Y;Huang X L;Meng F W (Mathematics Dep, Zaozhuang Vocational College, Tengzhou 277500, Shandong, P.R. China, Email: huangxiulisx@163.com) : Oscillation for solutions of partial differential equations with delays. Far East J mathl Sci 2008, 30(1), 137-46.

Some new oscillation criteria for partial differential equations with delays are established. The results extend and improve some known oscillation criteria of differential equations.

11 ref

000068   Hossen H M;Al-Hamed M A (Mathematics Dep, Science Sections Girls College of Education, Jazan, Saudi Arabia, Email: halahossen@yahoo.com) : On a subclas of multivalent functions defined by a new differential operator. Far East J mathl Sci 2008, 29(3), 719-28.

6 ref

000067   Hedayati H;Ameri R (Basic Science Dep, Babol Univ of Technology, Babol, Iran, Email: h.hedayati@nit.ac.ir) : Regular and fundamental relations on k-hyperideals of semi-hyperrings. Bull Calcutta Mathl Soc 2009, 101(2), 105-14.

Deals with regular and fundamental relations on a semi-hyperring R to construct k-ideals from given k-hyperideals of R. In particular, by considering a special form of a regular relation a kind of isomorphism theorem is proved and the commutativity of some diagrams of semihyperrings and k-hyperideals are investigated. Finally, a functor from the category of semihyperrings SHR to the category of semirings SR is defined.

20 ref

000066   Hatomoto J (Mathematics Dep, Tokyo Institute of Technology Ohokayama, Meguro, Tokyo, 152-8551, Japan, Email: hatomoto-jin@tmu.ac.jp) : Central limit theorem for invertible maps with weak hyperbolic product structure. Far East J mathl Sci 2008, 29(3), 729-52.

Study an invertible map f which admits a weak hyperbolic product structure region, which is the intersection of two transversal families of weak stable and weak unstable disks, with countably many branches and variable return times. In [6], we have obtained that f has an invariant probability measure v whose conditional measures on the. weak unstable disks are absolutely continuous with respect to the Lebesgue measures on these disks such that the correlation function of (f, v) for Holder continuous functions satisfies some formula which includes exponential, polynomial and stretched exponential decay of correlations. In this paper we establish that (f, v) satisfies the Central Limit Theorem (CLT) in the class of Holder continuous functions under some asymptotic conditions related to the asymptotic mass of the return times on the weak unstable disks. For applications, we obtain the CLT of some partially hyperbolic diffeomorphisms with intermittency on one dimensional center unstable direction.

15 ref

000065   Hatomoto J (Mathematics Dep, Tokyo Institute of technology, Ohokayama Meguro, Tokyo, 152-8551, Japan, Email: hatomoto.j.aa@m.titech.ac.jp) : Fast mixing of weak hyperbolic product structure. Far East J mathl Sci 2008, 30(3), 537-46.

Study an invertible map/which admits a weak hyperbolic product structure region, which is the intersection of two transeversal families of weak stable and weak unstable disks, with countably many branches and variable return times. Established that f has an invariant probability measure v whose conditional measures on the weak unstable disks are absolutely continuous with respect to the Lebesgue measures on these disks such that the correlation function Cor_n (φ, Ψ, v) of (f, v) for Holder continuous functions φ and Ψ with Holder exponent η satisfies the following formula: Cor_{n (φ, Ψ, v) = max {O(v(n/r)^-1-}, O(λ(pn n)ⁿ), O(τ(pn n)ⁿ)}, (0.1), where v(t) is a positive increasing function with t ≥ 0 in a way related to asymptotic mass of the return times on the weak unstable disks, and λ(l) (resp. τ(l)) is the supremum of the diameters of the l-th forward (resp. backward) iterate of the weak stable (resp. unstable) disks. Under some asymptotic condition on the weak unstable disks, the above formula holds with replacing τ(n) by exponential decay rates with n.}

11 ref

000064   Han S E;Lee S (NO, College of Environmental Sciences and Engineering, Honam Univ, Gwangju, 506-714, Email: sehan2020@yahoo.co.kr) : Weak k-deformation retract and its applications. Far East J mathl Sci 2008, 30(1), 157-74.

Introduce the notion of weak k-deformation retract and study its properties. Furthermore, we survey several kinds of k-deformation retracts and compare them. Besides, we discuss an importance of the choice of a base point for calculating the digital k-fundamental group. To be specific, unlike the choice of a base point of the fundamental group of path connected space in algebraic topology, in digital topology we show that for even k-connected digital image, such as a closed k-curve which is not a simple closed k-curve, we should choose a base point not strongly k-retractible for calculating its k-fundamental group.

28 ref

000063   Gomez-Calderon J;Perriello A (Mathematics Dep, The Pennsylvania State Univ, New Kensington Campus, New Kensington, Pennsylvania 15068, U.S.A., Email: jxg11@psu.edu) : Cyclotomic polynomials of the second kind. Far East J mathl Sci 2008, 30(2), 211-19.

Let ςd be a primative dth root of unity. Let R_d(x) denote the polynomial. Shows a list of similarities between R_d(x) and the cyclotomic polynomial C_d(x). Provides a recursive method to determine R_n(x), calculate the discriminant of S = ANQ (ς_d + ς_d^-1), and state an expected integral basis for S.

4 ref

000062   Gomes L A P;Silva E B (Departamento de Matematica, Universidade Estadual de Maringa Av. Colombo 5790, Maringa - PR, 87020-900, Brazil, Email: lapgomes@uem.br) : On the product hardy space H<. Far East J mathl Sci 2008, 29(3), 661-75.

New proof for the immersion of the product Hardy space H_at¹ defined by using Chang-Fefferman atoms, in the product Hardy space H_s¹ defined by double area integral operator has been presented. The proof uses a version of J. L. Journe's lemma.

16 ref

000061   Fujioka A (Graduate School of Economics, Hitotsubashi Univ, 2-1, Naka, Kunitachi, Tokyo 186-8601, Japan, Email: fujioka@math.hit-u.ac.jp) : Bonnet surfaces with non-flat normal bundle in the hyperbolic four-space. Far East J mathl Sci 2008, 30(2), 381-7.

Studies surfaces in the hyperbolic four-space admitting isometric deformations preserving the length of the mean curvature vector and especially focus on the case that surfaces are non-minimal and have non-flat normal bundle.

7 ref

000060   Dixit K K;Pathak A L (NO, Janta College Bakewar, Etawah-206 124) : New subclass of analytic functions defined by Salagean operator. Bull Calcutta Mathl Soc 2009, 101(2), 123-36.

Author introduced the subclass T_j(n,α) of analytic functions with negative coefficients defined by Salagean operator Dⁿ. Obtained numerous sharp results including coefficient estimates, distortion theorems, closure theorems and modified Hadamard product of several functions belonging to the class T_j(n, α). Also obtained radii of close to convexity, starlikeness and convexity for functions belonging to the class T_j (n, α) and other interesting properties.

10 ref

000059   De A;Chaudhuri M (Ashram Chaumohani, P.O. Agartala College, Tripura-799 004) : Free torsional vibration of a non-homogeneous semi-infinite solid circular cylinder. Bull Calcutta Mathl Soc 2009, 101(2), 115-22.

Free torsional vibration of a non-homogeneous semi-infinite solid circular cylinder with stress free and rigid boundary is solved. The non-homogeneity of rigidity μ and density ρ is chosen in the form μ = μ₀e^n,z, ρ = ρ₀^n,z. the displacement and stress components for different values of n are numerically evaluated.

3 illus, 10 ref

000058   Chinram R (Mathematics Dep, Faculty of Science, Prince of Songkla Univ, Hat Yai, Songkhla 90112, Thailand, Email: ronnason.c@psu.ac.th) : Regularity and green's relations of generalized one-to-one partial tranformation semigroups. Far East J mathl Sci 2008, 30(3), 513-21.

Let X be any set and I(X) be the one-to-one partial transformation semigroup on X. It is well known that I(X) is regular. Generalizes this, let X and Y be any sets and I(X, Y) be the set of all one-to-one partial transformations from X to Y. For θ ∈ I(Y, X), let (I(X, Y), θ) be a semigroup (I(X, Y), *), where α * β = αθβ for all α, β ∈ I(X, Y). In this paper, we characterize the semigroup (I(X, Y), θ) to be regular. Characterizes regular elements of the semigroup (I(X, Y), θ). Characterize L-classes, R-classes, H-classes and D-classes of the semigroup (I(X, Y), θ).

11 ref

000057   Chinram R (Mahematics Dep, Faculty of Science, Prince of Songkla Univ, Hat Yai, Songkhla 90112, Thailand, Email: ronnason.c@psu.ac.th) : Note on (m, n)-quasi-ideals in rings. Far East J mathl Sci 2008, 30(2), 299-308.

The notion of quasi-ideals for rings was introduced by O. Steinfeld in the year 1953 and it has been widely studied. Studies (m, n) -quasi-ideals of rings. We Quasi-ideal of a ring R is a (1, 1) -quasi-ideal of R. Generalizes some facts for left ideals, right ideals and quasi-ideals of rings.

11 ref

000056   Chiba K (Mathematics Dep, Faculty of Science, Shizuoka Univ, Ohya, Shizuoka, 422-8529, Japan, Email: smktiba@sci.shizuoka.ac.jp) : Covering properties in σ-products, II. Far East J mathl Sci 2008, 30(3), 401-22.

Investigates strong δθ-refinability, property B(LF, τ), property B(D, ω), [φ₁, ∞)' -refinability and weak [ω₁, ∞])' -refinability in σ-products. Main results are: Let S be spaces and let a be a σ-product space of S and K be the cardinal number of S. (1) If every finite subproduct of a is strongly δθ-refinable, then so is σ. (2) If every finite subproduct of a has property B(LF, τ), then so has σ under the assumption of σ is K-paracompact. (3) If every finite subproduct of σ has property B(D, ω), then so has σ under the assumption of a is subnormal and K-paracompact. (4) Suppose | S | = ω_m, for some m ∈ ω and σ is normal. If every finite subproduct of σ has [ω₁, ∞)^r -refinability, then so has c. (5) Suppose | S | = ω_m for some m ∈ ω. If every finite subproduct of σ has weak [ω₁, ∞)^r -refinability, then so has σ

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000055   Chang Y H;Hong C H (Mathematics Dep, National Taiwan Normal Univ, 88 Sec. 4, Ting Choun Road, Taipei, Taiwan, R.O.C., Email: changyh@math.ntnu.edu.tw) : Relative bounded perturbation of abstract cauchy problem. Far East J mathl Sci 2008, 29(3), 555-75.

Describe the perturbed abstract Cauchy equation du(t)/dt = (A + B)u(t) with initial condition u(0) = x, where A is a generator of a C-semigroup on a Banach space X and B is a relatively bounded linear operator on X. Author show that if the perturbation operator B is an A-bounded linear operator which commutates with C and its A-bound is sufficiently small, then (A + B) generates a C-semigroup {V(0)}t≥0 on X, and hence the perturbed abstract Cauchy problem has a unique mild solution as long as the initial data x is in the subspace [Im(C)]. It is remarkable that we can directly apply these results to some differential equations.

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000054   Catda-Ghimire S;Roslan H;Peng Y H (NO, School of Mathematical Sciences Univ, Sains Malaysia, 11800 Penang, Malaysia, Email: aspa777@gmail.com) : On chromatic equivalence of a family of K₄-homeomorphs. Far East J mathl Sci 2008, 30(2), 389-400.

Discusses a chromatically equivalent pair of one family of K₄ - homeomorphs, K₄(1, 2, 7, d, e, f) and K₄(1, 2, 7, d', e', f'),. and thus providing a result that can be extended in the study of chromatic equivalence classes of K₄(1, 2, 7, d,e, f) and chromatic uniqueness of K₄ -homeomorphs with girth 10.

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000053   Catada-Ghimire S;Roslan H;Peng Y H (School of Mathematical Sciences, Universiti Sains Malaysia, 11800 Penang, Malaysia, Email: aspa777@gmail.com) : On chromatic equivalence of a pair of K₄-homeomorphs II. Far East J mathl Sci 2008, 30(3), 499-512.

Discusses a chromatically equivalent pair of graphs in one family of K₄ -homeomorphs, K₄(1, 2, 9, d, e, f) and K₄(1, 2, 9, d', e', f'), and thus providing a result that can be extended in the study of chromatic equivalence classes of K₄(1, 2, 9, d, e, f) and chromatic uniqueness of K₄ -homeomorphs with girth 12.

2 illus, 15 ref