022292   Scardua B (Instituto De Maematica, Universidade Federal Do Rio De Janeiro, Caixa Postal 68530 21945-970 Rio De Janeiro - RJ Brazil, Email: scardua@impa.br) : On the classification of C<. Indian J Math 2008, 50(1), 125-48.

Classification of Stein manifolds equipped with codimension one (holomorphic) actions of Cⁿ. Case of algebraic foliations on Cⁿ⁺¹ and prove a linearization result. The other main result of this paper states that a Stein manifold M of dimension n + 1 and equipped with a holomorphic action of the complex additive group C" such that the corresponding foliation has a suitable dicritical singularity is biholomorphic to Cⁿ⁺¹. Indeed, there is a partial linearization for the action on M.

24 ref

022291   Santhanam G (Mathematics and Statistics, Indian Institute of Technology, Kanpur-208 016, Email: santhana@iitk.ac.in ) : Sharp upper bound for the first eigenvalue of the Laplacian of compact hypersurfaces in rank-1 symmetric spaces. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 307-15.

Let M be a closed hypersurface in a simply connected rank-1 symmetric space M. In this paper, we give an upper bound for the first eigenvalue of the Laplacian of M in terms of the Ricci curvature of M and the square of the length of the second fundamental form of the geodesic spheres with center at the center-of-mass of M.

10 ref

022290   Saker S H;Wong P J Y (Mathematics Dep, Faculty of Science, Mansoura Univ, Mansoura 35516, Egypt, Email: shsaker@mans.edu.eg) : Oscillation and asymptotic behavior of Perturbed nonlinear difference equations. Indian J pure appl Math 2008, 39(2), 105-22.

By employing the generalized Riccati technique, establishes some new oscillation criteria for the second-order perturbed nonlinear difference equation Δ(a_n-1) (Δx_n_1)^β + F(n,x_n) = G(n,x_n,Δx_n), n ≥ n₀. where β <62> 0 is quotient of odd positive integers. These results improve some well-known results in the literature. Some comparison between theorems and those previously known results are indicated. Some examples are included to illustrate the relevance of the main results.

20 ref

022289   Rosalsky A;Volodin A (Statistics Dep, Univ of Florida Gainesville, FL 32611, USA, Email: rosalsky@stat.ufl.edu) : On the weak law with random indices for arrays of banach space valued random elements. Sankhya 2007, 69(2), 330-43.

For a sequence of constants {an, n ≥ 1}, an array of rowwise independent and stochastically dominated random elements {Vnj, j ≥ 1, n ≥ 1} in a real separable Rademacher type p Banach space for some p ∈ [1, 2], and a sequence of positive integer-valued random variables {Tn, n ≥ 1}, a general weak law of large numbers of the form ΣTnj=1 aj(Vnj-cnj)/b → 0 is established, where {cnj, j ≥ 1, n ≥ 1} is an array of truncated expectations, and αn → ∞, bnnj, j ≥ 1, n ≥ 1}. The current work is a new version of a result of Adler, Rosalsky, and Volodin.

14 ref

022288   Rashid M H M;Noorani M S M;Saari A S (School Mathematics Science, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, 436 UKM Bangi, Selangor, Malaysia, Email: malik_okasha@yahoo.com) : Some results on the (p, k)-quasihyponormal operators. Far East J mathl Sci 2007, 27(2), 431-42.

It has been shown that every (p, k) -quasihyponormal operator whose Weyl's spectrum equals to the one-point set {O} is always compact and normal. Authors also obtain some related properties of (p, k)-quasihyponormal operators.

21 ref

022287   Radhakrishna Rao C;Bhaskara Rao M;Zhang H (Statistics Dep, Pennsylvania State Univ, Univ Park, USA, Email: crrl@psu.edu) : One bulb? Two bulbs? How many bulbs light up? - A discrete probability problem involving dermal patches. Sankhya 2007, 69(2), 137-61.

A dermal patch is designed to activate some targeted receptors. On Day 1, the patch releases one dose of medicine, which latches onto a receptor and makes it active. On Day 2, the patch releases two doses of medicine, which latch onto two receptors, one dose per receptor. If the receptor is already active, the new dose makes it inactive. If the receptor is inactive, the new dose makes it active. On Day 3, the patch releases three doses of medicine, which latch onto three receptors, one dose per receptor. This continues for ten days with the patch releasing a total of 55 doses progressively. In this paper, author obtained the distribution of the number of receptors active at the end of Day 10.

3 ref

022286   Qin X;Shang M;Su Y (Mathematics Dep, Gyeongsang National Univ, Chinju-660 701, Korea, Email: qxlxajh@163.com) : (A,η)-resolvent operator technique for generalized relaxed cocoercive variational inclusions. Indian J Math 2008, 50(1), 87-97.

Based on (A, η)-monotonicity, a new class of nonlinear variational inclusion problems is presented. Since (A, η) monotonicity generalizes yl-monotonicity and H-monotonicity and in turn, generalizes maximal monotonicity, results thus obtained are general in nature and encompass a broad range of previous results.

16 ref

022285   Plubtieng S;Wangkeeree R (Mathematics Dep, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand, Email: somyotp@nu.ac.th) : Strong convergence theorems of viscosity averaging sequences for asymptotically nonexpansive nonself-mappings. Far East J mathl Sci 2007, 27(2), 483-96.

14 ref

022284   Ozgur C (Mathematics Dep, Balikesir Univ, 10145, Cagis, Balikesir, Turkey, Email: cozgur@balikesir.edu.tr) : On generalized recurrent contact metric manifolds. Indian J Math 2008, 50(1), 11-19.

In this study, we consider generalized recurrent, generalized Ricci-recurrcnt and generalized concircular recurrent contact metric manifolds, ξ belonging to k-nullity distribution. We show that there exist no generalized recurrent and generalized Ricci-recurrcnt contact metric manifolds, ξ belonging to k-nullity distribution, unless kα + α) is everywhere zero. Furthermore, we find the characterizations of scalar curvatures of generalized recurrent and concircular recurrent manifolds of such type.

9 ref

022283   Natarajan P N;Sakthivel S (NO, , Old No. 2/3, New No. 3/3 Second manin Roa, R.A. Puram, Chennai-600 028, Email: pinnangudinatarajan@gmail.com) : Multiplication of double series and convolution of double infinite matrices in non-archimedean fields. Indian J Math 2008, 50(1), 115-23.

K denotes a complete, non-trivially valued, non-archiniedean field. Entries of sequences, series and infinite matrices are in K. Theorem 1 of [2] for double series, introduce the concept of convolution for double infinite matrices and to prove some basic results related to that concept in non-arehimedean fields.

5 ref

022282   Nakao M (Graduate School of Mathematics, Kyushu University, Ropponmatsu, Fukuoka 810-8560, Japan, Email: mnakao@math.kyushu-u.ac.jp) : Local attractors for nonlinear wave equations with some dissipative terms. Far East J mathl Sci 2007, 27(2), 497-515.

Shows the existence, size and some absorbing properties of 'local' attractors of nonlinear wave equations with nonlinear dissipations like p(x, U_t) = a(x) <157>_t U_t<157>^r U_t.

16 ref

022281   Musafirov E V (NO, Polesskii State University, Dneprovskoi Flotilii str. 23 Pinsk Brresk Region 225 710, Belarus, Email: musafirov@bk.ru) : Reflecting function and periodic solutions of differential systems with small parameter. Indian J Math 2008, 50(1), 63-76.

The aim of this paper is to combine the method of reflective function and the perturbation method. The set of a linear differential systems, the reflecting matrix for which is represented by a product of three exponential matrixes is allocated. It has allowed to obtain the sufficient conditions of existence of a family of periodic solutions close to a given solution of multidimensional nonlinear differential systems. Obtained results are illustrated by examples.

17 ref

022280   Mulase M;Safnuk B (Mathematics Dep, California Univ, Davis CA 95616-8633, Email: mulase@math.ucdavis.edu) : Mirzakhani's recursion relations, virasoro constraints and the kdv hierarchy. Indian J Math 2008, 50(1), 180-218.

Differential version of Miraakhani's recur-sion relation for the Weil-Pctersson volumes of the moduli spaces of bordered Riemann surfaces. We discover that the differential relation, which is equivalent to the original integral formula of Mirzakhani, is a Virasoro constraint condition on a generating function for these vol- . umes. We also show that the generating function for Å and k1 intersections on M_g,n is a 1-parameter solution to the KdV hierarchy. It recovers the Witten-Kontsevich generating function when the parameter is set to be 0.

27 ref

022279   Mukherejee R N (Mathematics Dep, Univ of Burdwan, Burdwan-713 104) : Existence theorems and necessary conditions for general formulation of linear bounded phase co-ordinate control problems. Far East J mathl Sci 2007, 27(2), 381-94.

Generalized bounded phase co-ordinate control problem (involving certain unbounded operators) is considered by functional analytic approach. Existence and uniqueness of the solution is given in terms of certain closed linear operators. The optimal solutions are characterised in terms of adjoint operators. These results are applicable to linear minimum effort problems, constrained variational problems, optimal control of distributive systems and certain illposed variational problems.

10 ref

022278   Mostafa Taheri S (Faculty of Mathematics, Gorgan University of Agricultural Science and Natural Resources, Gorgan, Iran, Email: sm_taheri2000@yahoo.com) : Product of varieties and perfect groups. Far East J mathl Sci 2007, 27(2), 467-72.

Let <57> be a variety of groups defined by the set of laws V. A group G is called V-perfect if G = V(G), where V(G) is the verbal subgroup of G. Let v and <57> be two varieties of group, and ω = v^* <57> be the product of v and <57>. If G is U- and V-perfect group, then so is W-perfect. A group G is said to be a subgroup irreducible with respect to V-isologism if whenever G HV^* (G), then H + G. Show that if G₁ is V-isologism to G₂ and if G₁ is a subgroup irreducible with respect to V-isologism, then so is G₂.

4 ref

022277   Mizuno H;Sato I (NO, Iond Univ, Tokyo, Japan, Email: isato@oyama-ct.ac.jp) : Weighted Bartholdi zeta functions of digraphs. Far East J mathl Sci 2007, 27(2), 323-44.

Introduced a weighted Bartholdi zeta function of a digraph D, and give a determinant expression of it. Furthermore, defined a weighted L-function of D, and gave a determinant expression of it. As a corollary, obtained a decomposition formula for the weighted Bartholdi zeta function of a group covering of D by L-functions of D.

15 ref

022276   Mizuno H;Sato I (Oyama National Coll of Technol, , Oyama, Tochigi 323-0806, Japan, Email: isato@oyama-ct.ac.jp) : Weighted Bartholdi zeta functions of some graphs. Far East J mathl Sci 2007, 27(2), 301-21.

Composition formula is given for the weighted Bartholdi zeta function of a graph G which is partitioned into some irregular coverings. As a corollary, authors obtain a decomposition formula for the weighted Bartholdi zeta function of G which is partitioned into some regular coverings.

16 ref

022275   Malik S (Hindu College, Imperial Avenue, Delhi-110 017, Email: saroj.malik@gmail.com) : Matrix partial orders and reversal law. Indian J pure appl Math 2007, 38(6), 569-77.

Let A, B be any m x n matrices such that A is below B under any of the three matrix order relations, namely space pre-order and therefore minus, star and also when matrices are square under the sharp order. Gives conditions on matrices that ensure the validity of the reverse order law for various g- inverses.

8 ref

022274   Lin C Y;Wang Q W;Qin F (School of Statics and Sciences, Shandong Finance Univ, 40 Shungeng Road, Jinan 250014, People's Republic of China, Email: wqw858@yahoo.com.cn) : System of matrix equation over regular rings. Indian J pure appl Math 2007, 38(6), 517-32.

Establishes necessary and sufficient conditions for the existence of the general solution to the system of five linear matrix equations X₁B₁ = C₁,X₁B₂ = C₂,X₂B₃ = C₃,X₂B₄ = C₄,X₂B₄ = C₄,A₅X₁B₅ + A6X2B6 = C₅ over an arbitrary regular ring with identity R. An expression of the general solution to the system is also derived when the solvable conditions are satisfied. As an application, necessary and sufficient conditions for the existence and a representation of the centrosymmetric solution to the system of matrix equations XB_a = C_a,XB_b= C_b,A_cXB_c - C_c over R with char R ≠ 2 are presented. Thus, the open problem, which was proposed in the end of the paper published in Indian J. Pure Appl. Math. 36 (12) (2005): 655-672, is solved.

21 ref

022273   Li X (School of Mathematics and Physics, Nandhua Univ, Hengyang, Hunan 421001, P.R. China, Email: xianyili6590@163.com) : Rule of trajectory structure and global asymptotic stability for a nonlinear difference equation. Indian J pure appl Math 2007, 38(6), 579-87.

Fourth-order rational difference equation x_n+1 = x_nx^b_n-2+x^b_n-3+a/x^b_n-2+x_{n< D>x^bn-3+a, n=0,1,2, ..., where a, b ∈ (0, ∞) and the initial values x-3, x-2, x-1, x0 ∈ (0, ∞, is considered. It is found that the perturbation of the initial values may lead to the variation of the trajectory structure rule for the solutions of the above equation. That is, with the change of the initial values, the successive lengths of positive and negative semicycles for nontrivial solutions of this equation is found to periodically occur with prime period 15, i.e., ... 4⁺, 1^-, 1⁺, 1^-, 2⁺, 2^-, 1⁺, 3^-, 4⁺, 1^-, 1⁺, 1^-, 2⁺, 2^-, 1⁺, 3^-, 4⁺, 1^-, 1⁺, l^-, 2⁺, 2^-, 1⁺, 3^-, .... By the use of the rule, the positive equilibrium point of the equation is verified to be globally asymptotically stable.}

12 ref

022272   Li S;Stevic S (Mathematics Dep, Shantou Univ, 515 063, Shantou, Guang Dongh, China) : Riemann-stieltjes operators between mixed norm spaces. Indian J Math 2008, 50(1), 177-88.

Let g : B → C¹ be a holomorphic map on the unit ball B. This note studies the boundedness and compactness of the Riemann-Sticltjes type integral operators z 6 B, between different mixed norm spaces of holomorphic functions H_pi, _q1. _y1(B) and H_p2,_q2, _y2(B).

19 ref

022271   Lashkarizadem Bami M;Pourghol Amhossein M; Samea H (Mathematics Dep, Isfahan Univ, Isfahan, Iran, Email: lashkari@sci.ui.ac.ir) : Left cancellative and left shiftable hypergroups. Indian J pure appl Math 2008, 39(1), 87-97.

Many of interesting results on a locally compact group G heavily depend on. the fact that ε_x|m| = |ε_x.m| for every x ∈ G and m ∈ C_b,(G)*. By introducing the two notions of left cancellative and left shiftable hypergroups and investigating their properties, authors have been able (among other results) to prove that if K is a locally compact hypergroup for which x * y is a finite set for every x, y ∈ K, then ε_x.|m| = |ε_x.m| for every x ∈ K and m ∈ C_b(K) if and only if K is a group.

7 ref

022270   Kumar S (NO, Coal Mines Provident Fund Office, Dhanbad 2 Region Dhanbad-826 001, Email: shivam.isi@gmail.com) : Theorema Aurema-2. Resonance 2007, 12(10), 18-29.

Introduced the notion of quadratic reciprocity and dwelt briefly on its history, which goes back all the way to the work of Fermat. Author discussed the Law of Quadratic Reciprocity ('QRL'), which Gauss named Theorema Aureum. Following this, gave a not too well known proof of the QRL, due to G Rousseau. Provides two more proofs of the QRL, drawing respectively from ideas in linear algebra and field extensions; they too are not very well known.

8 ref

022269   Kulkarni S H;Ramesh G (Matematics Dep, IIT Madras, Chennai, India-600 036, Email: shk@iitm.ac.in) : Projection methods for inversion of unbounded operators. Indian J pure appl Math 2008, 39(2), 185-202.

Let T be a closed linear operator defined on a dense subspace D(T) of a separable complex Hilbert space H and suppose that T has a bounded inverse. Characterizes the convergence of projection methods for solving the operator equation Tx = y. Discusses the stability of convergence of projection methods under bounded perturbations. Also discusses convergence of modified projection methods. Examples to illustrate results are also given.

12 ref

022268   Krsteska B;Ekici E (Faculty of Mathematics and Natural Sciences University, St. Cyril and Methodius, Skopje Macedonia, Email: madob2006@yahoo.com) : Fuzzy contra strong precontinuity. Indian J Math 2008, 50(1), 149-61.

Concept of fuzzy contra strongly precontinuous mapping arc introduced and studied. Properties and relationship of fuzzy contra strongly precontinuous mapping are established. Also, some applications to fuzzy compact spaces are given.

14 ref

022267   Krishna M (Institute for Mathematical Sciences, Taramani, Chennai-600 113, Email: krishna@imsc.res.in) : Continuity of intergrated density of states - independent randomness. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 401-10.

Continuity properties of the integrated density of states for random models based on that of the single site distribution. Our results are valid for models with independent randomness with arbitrary free parts. In particular in the case of the Anderson type models (with stationary, growing, decaying randomness) on the v dimensional lattice, with or without periodic and almost periodic backgrounds, we show that if the single site distribution is uniformly α-H61der continuous, 0 <60> a <147> 1, then the density of states is also uniformly a-Holder continuous.

14 ref

022266   Koukouvinos C;Mantas P;Mylona K (Mathematics Dep, National Technical Univ of Athens Zografou 15773, Athens, Greece, Email: ckoukouv@math.ntua.gr) : General construction of E(fnod)-optimal mixed-level supersaturated designs. Sankhya 2007, 69(2), 358-72.

A general method for constructing E(f_NOD)-optimal mixed-level supersaturated designs possessing the equal occurrence property is introduced. The method, which gives promising results, is based on new techniques for the construction of supplementary difference sets.

4 tables, 17 ref

022265   Jana J;Sarkar R P (Theoretical Statistics and Mathematics Div, Indian Statistical Institute, 203 B.T. Road, Kolkata-700 108, Email: joydip_r@isical.ac.in) : On the schwartz space isomorphism theorem for rank one symmetric space. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 333-48.

Simpler proof of the L^p-Schwartz space isomorphism (0 <60> p ≤ 2) under the Fourier transform for the class of functions of left δ-type on a Riemannian symmetric space of rank one. Treatment rests on Anker's [2] proof of the corresponding result in the case of left K-invariant functions on X. Proof which relies only on the Paley-Wiener theorem is given.

12 ref

022264   Jain M;Sharma G C;Sharma S K (Mathematics Dep, Institute of Basic Sciences, Khandari, Agra-282 002, Email: Madujain@sancharnet.in) : Mathmetical modelling for growth and development of capillary sprouts with neuro-fuzzy approach. Int J Inf Comput Sci 2007, 10(2), 73-88.

Model for tumor related capillary sprouts growth is considered. It has been assumed that a Capillary sprout growth is in direction of the line connecting the tumor to the nearest site of endothelial cells (E. C.) i. e. it is unidirectional. For the chemotactant concentration, the forward and backward chemical reactions have been taken into consideration. We present analytical as well as neuro-fuzzy analysis of the model to describe the growth of the capillary sprouts during tumor angiogenesis. The results obtained by analytical method are compared with neuro-fuzzy approach. The numerical results are facilitated to explore the effect of system parameters.

8 illus, 36 ref

022263   Jain M;Mishra A (Mathematics Dep, Institute of Basic Science, Khandari, Agra-282 002) : System reliability of redundant components and optimization for series system. Int J Inf Comput Sci 2007, 10(2), 47-56.

Analysis of reliability optimization is of concern for the design engineers. A system of electronics equipments may be considered as a series of different stages. For smooth running of a system, the number of redundant components-to be included at each stage at the design stage. In most of the cases, many resource constraints should also be satisfied. This makes the problem quite complex for such a system. In-the present investigation, the reliability indices for redundant machining system have been taken in to consideration. As failure is dependent on time, for life time of components, Weibull distribution has been chosen. An algorithm for optimal redundancy problem is developed. Illustration is provided to validate the algorithm for non-linear programming problem.

30 ref

022262   Jacroux M (Statistics Dep, Washington State Univ, Pullman, WA 99164. USA, Email: jacroux@wsu.edu) : Maximal rank - minimum aberration regular two-level split-plot fractional factorial designs. Sankhya 2007, 69(2), 344-57.

Regular two-level fractional factorial designs are often used in industrial experiments as screening experiments. When some factors have levels which are hard or expensive to change, restrictions are often placed on the order in which runs can be performed, resulting in a split-plot factorial design. In these cases, the hard or expensive to change factors are applied to whole plots, whereas the easier or less expensive to change factors are applied to the subplots within the split plot designs. For such experimental situations the minimum aberration criterion has been used by a number of authors to find optimal regular fractional factorial split plot designs. In this paper, author suggested an alternative criterion called the maximal rank-minimum aberration criterion for selecting optimal fractional factorial split plot designs and study how this alternative criterion performs in terms of the optimal designs it selects, and how it compares to the minimum aberration criterion.

1 tables, 11 ref

022261   Ikram M;Singh K (Mathematics Dep, NIT, Srinagar (Kashmir)) : Heuristic method to minimize the range of lateness in a special class of n-jobs, 2-machines sequencing problem with due-dates, transportation times and equivalent job for block of jobs. Pure appl Math Sci 2008, 67(1-2), 155-62.

Heuristic method has been developed to minimize the range of lateness in a sequencing/scheduling problem of n-job, 2-machine with due-date and equivalent job for block of jobs. Transportation times of jobs from first machine to second machine have also been included in the problem. The heuristic method is based on three theorems.Investigates some conditions to be imposed on processing times and transportation times. The criterion to find optimal sequence is the minimization of range of lateness. In the paper a rule to find equivalent job and its processing times for jobs in block has been determined. The work has been supported by a numerical example.

7 ref

022260   Iampan A (Mathematics Dep, School of Science and Technology, Naresuan University Phayao, Phayao 56000, Thailand, Email: aiyaredi@nu.ac.th) : On minimal and maximal ordered bi-ideals in ordered semigroups. Far East J mathl Sci 2007, 27(2), 473-82.

Minimal and maximal ordered bi-ideals in ordered semigroups in an analogous way to that of the charactions of minimal and maximal ordered left ideals in ordered semigroups considered by Cao and Xu [1] are characterized.

3 ref

022259   Huillet T (Avenue Adolphe Chauvin, 95302 Cergy-Pontoise, France, Email: huillet@u-cergy.fr) : Statistics of Bose samples from dirichlet proportions. Sankhya 2007, 69(2), 190-220.

To fix the background and notations, we shall first briefly revisit some aspects of the following Ewens-like randomized occupancy problem: assume that distinguishable particles are to be placed at random into the cells of the unit interval which was previously broken into random pieces according to the (Poisson-)Dirichlet partitioning model. Particles being distinguishable, the statistical structure of the problem can be understood within the Maxwell-Boltzmann setup. In this note, we shall address the following sampling problem of a different nature: assume now that indistinguishable particles are to be placed at random within the cells with (Poisson-) Dirichlet distributed sizes. Then the statistical formalism to be used is the one of Bose-Einstein. We show that in the grand canonical ensemble, the Bose sampling procedure from (Poisson-) Dirichlet proportions is, to a large extent, amenable to exact analytic calculations. This concerns, for example, the full Bose occupancy distributions, the distribution of the number of distinct occupied fragments, the number of cells with a prescribed amount of particles. Using a grand canonical approach, a phase transition phenomenon is shown to take place provided the disorder parameter of the (Poisson-) Dirichlet partition is large enough; we describe this phase transition in some details.

17 ref

022258   Hui Chun P (Mathematics and Physics Dep, North China Electric Power Univ, Beijing, 102206, P.R. China, Email: penghuichun@sina.com.cn) : Note on totally real riemannian foliations with parallel mean curvature in a quaternio projective space. Far East J mathl Sci 2007, 27(2), 265-76.

Totally real Riemannian foliations with parallel mean curvature on a quaternion projective space are discussed and obtained a pinching theorem about it.

9 ref

022257   Hao J;Ding J;Li S (School of Mathematical Science, Shanxi Univ, Taiyuan, Shanxi 030006, People's Republic of China) : Blow-up solutions for some reaction difffusion equations. Indian J pure appl Math 2007, 38(6), 553-67.

Investigates the blow-up solutions of the quasilinear reaction diffusion equation u_t = ∇(a(u)b(t)∇u) + f(x, t, u) with nonlinear boundary condition δu/δn + σ(u) = 0 and the semilinear reaction diffusion equation u_t - ∇(g(x)∇u) + h(x, t, u, q) with the Neumann boundary condition δu/δn = 0 where q - |Δu|². By constructing auxiliary functions and using maximum principles, the sufficient conditions for blow-up solution are obtained. It is shown that under some assumptions on a, b, f, g, h, cr, and the initial datas, the solutions blow up in certain finite time. Furthermore we yield the bound of the blow-up time and the blow up rate.

12 ref

022256   Gupta R;Chaudhary P;Kailash K (Statistics Dep, C.C.S. Univ, Meerut-250 005) : Cost benefit analysis of a single unit system model with helping unit. Pure appl Math Sci 2008, 67(1-2), 53-62.

Deals with the cost benefit analysis of a single unit system model with one additional unit called helping unit which plays the role to save the system from the external effects if any. All failure time distributions are taken as exponential whereas the distributions of repair times are arbitrary. The system model has been analysed by using supplementary variable technique. The graphical behaviour of MTSF and profit function have been studied in a particular case.

3 illus, 9 ref

022255   Gupta P;Mamta R;Trivedi M C (NO, I.I.T., Kanpur) : New Beautiful fractals. Pure appl Math Sci 2008, 67(1-2), 125-8.

Concept of multiple reduction copy machines has been used for creating fractals since long. The purpose of this paper is to generate the beautiful fractals by the method of averaging and unequal sizing using MRCM.

4 illus, 10 ref

022254   Gupta M;Pradhan S (Mathematics Dep, Indian Institute of Technology, Kanpur-208 016, Email: manjul@iitk.ac.in) : On orlicz spaces entire functions. Indian J pure appl Math 2008, 39(2), 123-35.

Defines Banach spaces E^M(γ) of entire functions defined with the help of an Orlicz function M and a particular type of an entire function r, and studies their structural properties. For finding the topological duals of these spaces, introduces the sequential analogue λ_γ,M of these spaces, show that they are AK-BK spaces and investigates their Kothe duals.

12 ref

022253   Gopalan M A;Vidyalakshmi S (Mathematics Dep,, National College, Trichy.) : Interesting diophantine problem. Pure appl Math Sci 2008, 67(1-2), 129-33.

Non-zero integer pairs (x,y) satisfying the binary cubic equation (x + y)³ + (x + y)² = 2 (x³ +y³). The recurrence relations for x and y are obtained. A few interesting properties are also given.

5 illus, 10 ref

022252   Gopalan M A;Anbu Selvi R (Mathamatics Dep, National College, Trichy, Tamilnadu) : Integral solutions of ternary cubic diophantine equation x<. Pure appl Math Sci 2008, 67(1-2), 107-11.

Ternary cubic diophantine equation x² + y² + 4N = zxy,N∈ Z - {0} is analyzed for non-zero integral solutions when N = 2k + l,N=4δ and N = n² + 4n. A few interesting properties among the solutions are presented.

2 tables, 5 ref

022251   Gargoum A S (Statistics Dep College of Business & Economics UAE Univ P.O. Box 17555, , United Arab Emirates, Email: alig@uaeu.ac.ae) : Some Structural Approximations for Efficient Probability Propagation in Evolving High Dimensional Gaussian Processes. Sankhya 2007, 69(2), 265-88.

One of the main issues that have emerged from learning Bayesian networks from data is the need for computational efficiency. In recent years, it has been shown that exact probabilistic propagation algorithms can be used for a quick and efficient absorption of information on dynamic junction trees of cliques. These algorithms were applied on Gaussian networks, where the underlying relationships between variables evolve dynamically. However, these algorithms work when each observation is taken under only a single clique of the original junction tree. In this paper, I outline how approximate techniques can be used to address the issue of how to adapt the system when an observation is taken under several cliques and consequently improve the system speed. These approximations are used in conjunction with Kullback-Leibler divergence or Hellinger distance between the true density and its approximation to indicate the approximation accuracy.

1 illus, 1 table, 12 ref

022250   Fei J X;Zheng C L;Wu H Y (NO, College Mathematics and Physics, Lishui University, Lishui, Zhejiang 323000, P.R.China, Email: zjixfei@yahoo.com.cn) : Complex wave excitations in the (2+1)-dimensional asymmetric nizhnik-novikov-veselov system. Far East J mathl Sci 2007, 27(2), 453-65.

Starting from an improved projective method and a linear variable separation approach, new families of variable separation solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for the (2 + 1) -dimensional asymmetric Nizhnik-Novikov-Veselov (ANNV) system are derived. Usually, in terms of solitary wave solutions and/or rational function solutions, one can find abundant important localized excitations. However, based on the derived periodic wave solution authors reveal some complex wave excitations in the (2 + 1) -dimensional ANNV system, which describe solitons moving on a periodic wave background. Some interesting evolutional properties for these solitary waves propagating on the periodic wave background are also briefly discussed.

2 illus, 19 ref

022249   Fahmy E S;Abdusalam H A;Lahlouh M (Mathematics Dep, Women Students Medical Studies & Science Sections, King Saud Universit, P.O. Box 22452, Riyadh 11495, Saudi Arabia, Email: esfahmy@operamail.com) : Exact travelling wave solutiosn for Cattaneo's reaction diffusion for prisoner's dilemma game. Far East J mathl Sci 2007, 27(2), 395-400.

Factorization method is used to find explicit exact particular travelling wave solutions for Cattaneo's reaction diffusion for Prisoner's dilemma (PD) game. Using the particular solutions for these equations two-parameter solutions for the equation are found.

8 ref

022248   El-Tawil M A;El-Hazmy M A (Engineering Mathematics Dep, Faculty of Engineering, Cairo University, Giza, Egypt, Email: magdyeltawil@yahoo.com) : Perturbative nonlinear schrodinger equations under variable group velocity dissipation. Far East J mathl Sci 2007, 27(2), 415-30.

Nonlinear Schrodinger equation is solved approximately under variable group velocity dissipation in a limited time interval. Complex initial conditions and zero Neumann conditions are considered. The perturbation method together with the eigenfunction expansion and variation of parameters method are used to introduce an approximate solution for the perturbative nonlinear case for which a power series solution is proved to exist. Using Mathematica, the solution algorithm is tested through computing the only possible first order approximation for some variations of the variable group velocity. The method of solution is illustrated through case studies and figures.

7 illus, 18 ref

022247   El Kholy E M;Lashin E S R (Mathematics Dep, Faculty of Science, Tanta Univ, Tanta, Egypt) : Equi-gaussian curvature folding. Proc Indian Acad Sci-Mathl Sci 2007, 117(3), 293-300.

New type of folding called equi-Gaussian curvature folding of connected Riemannian 2-manifolds. We prove that the composition and the cartesian product of such foldings is again an equi-Gaussian curvature folding. In case of equi-Gaussian curvature foldings, f: M → P_n, of an orientable surface M onto a polygon P_n prove that f ∈ F_EG (S²) ⇔ = 3, f ∈ F_EG(T²) ⇒ n = 4 and f ∈ F_EG(#T²) ⇒ n = 5.6 and generalize (iii) for #nT².

10 illus, 2 ref

022246   Das B;Pati K C (Physics Dep, B.A. Govt. College, Berhampur, Orissa, India) : Langlands decomposition of affine Kac-moody algebras. Indian J pure appl Math 2007, 38(6), 533-52.

Langlands decompositions of affine Kac-Moody algebras have been obtained by the method of direct determination as introduced by Cornwell for Lie algebras. This method is particularly helpful in the case of lower rank algebras. The involutive automorphisms required for such a study are obtained from the Satake diagrams of the corresponding algebras. This has been well illustrated by taking A₃ ⁽¹⁾(untwisted) and A₄⁽²⁾' (twisted) as representative examples.

1 table, 16 ref

022245   Darus M;Al-Shaqsi K (School of Mathematics Science, Faculty of Science and Technology, Univ Kebangsaan Malaysia, Bangi 43600 Selangor D. Ehsan, Malaysia, Email: maslina@pkrisc.cc.ukm.my ) : On subclass of harmonic mappings with positive real part. Far East J mathl Sci 2007, 27(2), 345-54.

Complex-valued harmonic functions that are univalent and sense preserving in the unit disk U can be written in the form f = h + g^-, where h and g are analytic in U. A class H P(α, γ), of all functions f = h + g^- for which Re{αz(h'(z) + g'(z)) + h(z) + g(z)} > 1- <157> y <157>, <9701> ≥ 0, γ ε C and f(0) = 1 is introduced. Sufficient coefficient conditions for normalized harmonic functions to be in HP(α, y) are given. These conditions are also shown to be necessary when the coefficients are negative. Distortion theorems, extreme points, closure theorems, neighborhood belonging to the class HP(α, y) are obtained. Further, result on integral operator is also given.

4 ref

022244   Danchev P V (NO, , 13, General Kutuzov Street bl. 7, fl. 2, ap. 4 4003, Plovdiv, Bulgaria) : EFI p<. Indian J Math 2008, 50(1), 1-9.

Extend an example due to Cutler-Missel (Comm. Alg., 1984) of a separable efi p^w+2 projectivc abelian p-group which is not C-decomposable and thick by showing that there exists even an inseparable efi p^ω+3-projective p-torsion ∑-group which is neither C-decomposable nor thick. This supplies two recent results of ours in (Comm. Alg., 2008).

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022243   Cureg E;Mukherjea A (Mathematics & Statistics Dep, Univ of South Florida, 4202 E. Fowler Avenue, PHY114 Tampa, Email: Cureg.Edgardo@spcollege.edu) : Convergence of convolution powers of a probability measure on d x d stochastic matrices and a cyclicity condition. Sankhya 2007, 69(2), 289-303.

This is concerned with a very interesting cyclicity condition introduced by Chakraborty and Rao (1998). The results show that if μ is a probability measure on 3 x 3 stochastic matrices, and the minimal rank r of the matrices in the closed semigroup S generated by S_μ, the support of μ, is 2, then the sequence (μⁿ) of convolution powers of μ does not converge weakly if and only if S_μ is cyclic. Here we extend this result to any d <62> 3. Moreover, authors show that when the minimal rank r above is not 2, this result does not always hold.

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