010425   Shukla D;Trivedi M (Mathematics and Statistics Dep, Dr. H.S. Gour University, Sagar-470 003) : Estimator under post-stratified cluster sampling. Appl Sci Period 2005, 7(2), 130-4.

Suppose a population contains clusters of unequal size and stratified into several strata. The post-stratification is useful when frame of each stratum is unknown in the setup of a stratified population. Presents an estimation strategy for population mean in the set of post-stratification assuming that a sample of unequal cluster is drawn randomly from the population. The sample of clusters is post stratified and a weighting system is proposed. The expression of optimum strategy is derived and results are numerically supported.

010424   Shorey T N (School of Math, Tata Institute of Fundamental Res, Homi Bhabha Road, Mumbai-400 005, Email: shorey@math.tifr.res.in) : Diophantine approximations, diophantine equations, transcendence and applications. Indian J pure appl Math 2006, 37(1), 9-39.

216 ref

010423   Sanyal M K;Panda R M (Business Administration Dep, University of Kalyani, Kalyani, Nadia, West Bengal, Email: manas_sanyal@rediffmail.com) : Robustness study of static inventory model with complete insepection. Opsearch 2006, 43(1), 63-70.

Static inventory model with time-independent cost elements has been considered. The lead-time is assumed to be zero. The order amount is instantaneously received and is subject to complete inspection. On the basis of such inspection items failing to meet specification requirements are discarded and other elements are stocked to meet future demand. Demand for the entire period is known. The best order size comes out to be the solution of an equation, which involves a probability distribution of proportion of good items. Assuming beta distribution for the proportion an investigation is made how the best order size changes with the change in any or both of the two parameters involved in beta distribution.

4 ref

010422   Saadati R;Yousefi S (NO, Islamic Azad University, Aiatollah Amoli Branch, Amol 678, Iran, Email: rsaadati@eml.cc ) : Common fixed point theorem in fuzzy metric spaces. Int J appl Math Statist 2006, 4(J06), 84-7.

4 ref

010421   Razzaq A;Ismail M V;Khan S U (Department of Statistics & Operations Research, Aligarh Muslim University, Aligarh-202 002) : Fuzzy programming approach for the multivariate allocation problem. Int J Mgmt Syst 2006, 22(1), 13-22.

Multivariate allocation problem with upper limits on the available costs for various characters has been considerd. The problem is formulated as a multiobjective programming problem with several convex objective functions and linear constraints. The convex functions are linearized by using the cutting plane technique and the resulting multiobjective LPP is solved by Fuzzy programming approach. Post optimal adjustments for the solution has been also discussed.

4 tables, 3 ref

010420   Ramji Lal;Shukla R P (Mathematics Dep, Univ of Allahabad, Allahabad-211 002, Email: ramjilal@mri.ernet.in) : Characterization of tarski monsters. Indian J pure appl Math 2005, 36(12), 673-8.

Tarski monsters have been characterized in terms of transversals. It is also proved that an infinite group all of whose proper right transversals are isomorphic as right quasigroups is isomorphic to the p-component of Q / Z for some prime p.

9 ref

010419   Rama Krishna K;Sobha V V;Hema Latha K (Mechanical Engineering Dep, Narasaraopet Engineering College, Narasaraopet-522 601) : Subcooled film boiling in porous medium about at heated vertical plate with variable wall temperature. Appl Sci Period 2005, 7(2), 102-15.

Examines the study natural convective film boiling in porous medium about a heated vertical plate whose wall temperature varies as a power funciton of height of the plate. It is assumed that porous medium is filled with sub-cooled liquid. Analytical expressions are obtained for the thickness of layer, velocity and temperature distribution in both the vapour and liquid regions. Correlations are obtained for determining the Rayleigh number and Nusselt number. It is found that with increase in power coefficient the Nusselt number increases. Further the effect of subcolling on Nusselt number is found more dominant at lower power coefficients.

7 illus, 8 ref

010418   Qiu Y;Changwen L;Na T (Department of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P.R. China, Email: property1111@yahoo.com.cn) : The influence of weakly c-normality of subgroups on the structure of π-closed-Sylow-tower groups. J appl Algebra Discrete Structs 2006, 4(2), 117-22.

Group is called a π-closed-Sylow-tower group if there exists a normal Hall π-subgroup, which is a Sylow-tower group. The influence of weakly c-normality of subgroups on the structure of π-closed-Sylow-tower groups is investigated.

8 ref

010417   Pilehrood K H;Pilehrood T H (Math Dep, Shahrekord Univ, Iran, Email: hessamik@ipm.ir) : On sums of two rational cubes. Indian J pure appl Math 2005, 36(12), 707-17.

Let p, q be prime numbers, [p = 2 (mod 3), q = 1 (mod 3), 4q-p² <35> 3 (mod 9). Suppose, furthermore, that p is not a cubic residue modulo q. Then the equation x³+y³ = pqz³ has no solutions in monzero integers x, y, z.

10 ref

010416   Pestov V G;Uspenskij V V (Mathematics and Statistics Dep, University of Ottawa, 585 King Edward Ave., Ottawa, Ontario, Canada K1, , Email: vpest283@uottawa.ca) : Representations of residually finite groups by isometries of the urysohn space. J Ramanujan Mathl Soc 2006, 21(2), 189-203.

As a consequence of Kirchberg's work, Connes' Embedding Conjecture is equivalent to the property that every homomorphism of the group F_∞ x F_∞ into the unitary group U (l²) with the strong topology is pointwise approximated by homomorphisms with a precompact range. In this form, the property (which we call kirchberg's property) makes sense for an arbitrary topological group Iso(U) of the universal Urysohn metric space U as a consequence of a stronger result: every representation of a residually finite group by isometries of U can be pointwise approximated by representations with a finite range. This brings up the natural question of which other concrete infinite-dimensional groups satisfy the kirchberg property.

30 ref

010415   Om Prakash;Tuli R K (Department of Mathematics, Gurunanak Dev University, Amritsar-143 005, Email: omprakash777@yahoo.co.in) : Maximum fuzziness in different measures of entropy. Int J Mgmt Syst 2006, 22(1), 35-44.

With a given fuzzy set having n support points and under the condition that the total fuzziness in a set is constant, maximum values of different fuzzy entropies have been studied. A new measure of fuzzy entropy which corresponds to Ferreri's probabilistic entropy has been developed and its maximum fuzziness is obtained.

15 ref

010414   Nwabueze K K (Department of Mathematics, University of Brunei Darussalam, BE 1410, Gadong, Brunei, Email: nwabueze@fos.ubd.edu.bn) : The twisted limits of profinite groups. J appl Algebra Discrete Structs 2006, 4(2), 93-8.

Notion of "twisted limits" of finite groups is a group theoretic analogue of the notion of "global sections" of rings. In the paper, the construction of the "twisted limits" of pro-C-groups over partial ordered sets is proposed.

3 ref

010413   Narang B S;Sushil Kumar;Kumar R;Narayan A (Electrical Engineering Dep, Bhilai Institute of Technology, Bhilai House, Durg-491 001, Email: nrgbs@sancharnet.in) : Stabilization of period doubling bifurcations and implications for control of chaos. Appl Sci Period 2005, 7(2), 69-81.

Stabilization of period doubling bifurcations for discrete-time nonlinear system is investigated. Both static and dynamic feedback controllers are studied. In the course of analysis, expressions are derived for bifurcation stability co-efficients of general n-dimensional systems undergoing period doubling bifurcations. A connection is determined between control of the amplitude of a period doubled orbit and the elimination of a period doubling cascade to chaos. For illustration, the results are applied to the Henon system.

1 illus, 8 ref

010412   Mishra B K;Panda T C (Mathematics Group, Birla Institute of Technology Science, Pilani-333 031, Email: bimal@bits_pilani.ac.in) : Mathematical model of blood flow under axi-symmetric peristalsis. Appl Sci Period 2005, 7(2), 122-9.

Investigates the effect of peristalsis on blood through a circular cylindrical channel. The velocity profiles have been numerically computed for various values of amplitude ratio for physiological insight of the present analysis.

3 illus, 3 tables, 9 ref

010411   Machado L;Leite F S (Mathematics Dep, University of Tras-os-Montes e Alto Douro, 5000-911 Vila Real, Portugal, Email: lmiguel@utad.pt) : Fitting smooth paths on Riemannian manifolds. Int J appl Math Statist 2006, 4(J06), 25-33.

The author formulate a least squares problem on a Riemannian manifold M, in order to generate smoothing spline curves fitting a given data set of points in M, q₀, q₁,....q_N, at given instants of time to <60>t₁ <60>...<60>t_N. Using tools from Riemannian geometry, derived the Euler-Lagrange equations associated to this variational problem and prove that its solutions are Riemannian cubic polynomials defined at each interval [t_i, t_i+1[,i=0,...,N-1, and satisfying some smoothing constraints at the knot points t₁. The geodesic that best fits the data, arises as a limiting process of the above. When M is replaced by the Euclidean space R", the proposed problem has a unique solution which is a natural cubic spline given explicitly in terms of the data. It was proved that, in this case, the straight line obtained from the limiting process is precisely the linear regression line associated to the data. Using tools from optimization on Riemannian manifolds, author also present a direct procedure to generate geodesics fitting a given data set of time labeled points for the particular cases when M is the Lie group SO(n) and the unit n-sphere S".

3 illus, 27 ref

010410   Lalin M N (NO, Institute for Advanced Study, School of Mathematics, 1 Einstein Drive, Princeton, NJ 98540, USA) : On certain combination of colored multizeta values. J Ramanujan Mathl Soc 2006, 21(1), 115-27.

The sum ∑^∞_k=1 ∑^k-1_j=0 (-1^j+k+1/(2j+1)^mk has been reduced in terms of special values of the Dirichlet L-series in the character of conductor 4. This sum is a combination of colored zeta values.

23 ref

010409   Kurokawa N;Ochiai H;Wakayama M (Mathematics Dep, Tokyo Institute of Technology, Oh-okayama Meguro, Tokyo, 152-0033, Japan, Email: kurokawa@math.titech.ac.jp) : Milnor's multiple gamma functions. J Ramanujan Mathl Soc 2006, 21(2), 153-67.

Basic properties of Milnor's multiple gamma functions have been studied. Few multiple sine functions from these Milnor's functions have been introduced and show the difficult special values of the Dirichlet L functions can be expressed by these functions.

11 ref

010408   Kowalski E (NO, Universite Bordeaux I - A2X, 351, cours de la Liberation, 33405 Talence Cedex, France, Email: emmanuel.kowalski@math.u-bordeauxl.fr) : Analytic problems for elliptic curves. J Ramanujan Mathl Soc 2006, 21(1), 19-114.

Some problems of analytic number theory for elliptic curves which can be considered as analogues of classical questions around the distribution of primes in arithmetic progressions to large moduli, and to the question of twin primes have been considered. This leads to some local results on the distribution of the group structures of elliptic curves defined over a prime finite field, exhibiting an interesting dichotomy for the occurence of the possible groups.

55 ref

010407   Kientega G (UFR-SEA, Universite de Ouagadougou 03 B.P. 7021 Ouagadougou 03, Burkina Faso, Email: kientega@univ-ouaga.bf) : Homogeneous relations and Bergman's property. J appl Algebra Discrete Structs 2006, 4(2), 73-83.

Notion of homogeneous relation introduced by Roland Fraisse has been generalized and give a partial answer to a question he raised. New insights to the problem by using the language of universal algebra has also been given.

8 ref

010406   Janakiram B;Soner N D;Chaluvaraju B (Department of Planning (P.F.R.D.), M.S. Building, , Bangalore-560 001) : The k-Nonsplit domination number of a graph. Int J Mgmt Syst 2006, 22(1), 53-8.

Let G = (V, E) be a connected graph. The k-nonsplit domination number γkn(G) of G is a least positive integer k such that any set with k vertices is a nonsplit dominating set of G. In the paper, some of the properties of this new parameter has been developed.

5 ref

010405   Elkin A;Zarhin Y G (NO, Institute of Mathematics, Hebrew University of Jerusalem, Givar Ram, Jerusalem, 91904, Israel, Email: arsen@math.huji.ac.il) : Endomorphism algebras of hyperelliptic jacobians and finite projective lines. J Ramanujan Mathl Soc 2006, 21(2), 169-87.

39 ref

010404   El-Ghoul M;El-Ahmady A E;Homoda T (Mathematics Dep, Faculty of Science, Tanta University, Tanta, Egypt, Email: Dr_Taha_Homoda@yahoo.com) : Retraction of simplicial complexes. Int J appl Math Statist 2006, 4(J06), 54-67.

Introduces the retraction of simplicial complelxes in its different types. The incidence matrices representing these retractions will be obtained. Theorems governing these studies will be achieved.

12 illus, 12 ref

010403   Dzenite I A;Torres D F M (Engineering Mathematics Dep, Riga Technical University, Kalku 1, Riga LV-1658, Latvia, Email: ilona.dzenite@yahoo.com) : Remark on Noether's theorem of optimal control. Int J appl Math Statist 2006, 4(J06), 88-93.

In 1918 Emmy Noether proved a central result of Mathematical Physics connecting the invariance of problems of the Calculus of Variations with the existence of conservation laws (conserved quantities along the extremals of the problem). Recently, many extensions of Noether's theorem have been provided in the literature for more general problems of Optimal Control - see (Gogodze, 1988; Torres, 2004). These results are obtained considering a group of transformations that depend on a small real parameter. Since the small parameter does not appear in the obtained conservation laws, Author propose a different proof of the the Noether-like theorems found in (Gogodze, 1988; Torres, 2004) by using transformations of time, state and control variations which do not depend also on the small real parameter.

7 ref

010402   Dixit V;Shah N H (Department of Mathematics, Gujarat University, Ahmedabad-380 009) : An order level inventory model with decreasing demand and time dependent deterioration. Int J Mgmt Syst 2006, 22(1), 71-8.

Order level inventory model for deteriorating items has been developed. The demand is taken as decreasing function of time and production rate to be function of demand function. The deterioration of unit in an inventory system is taken to be time dependent.

1 illus, 1 table, 6 ref

010401   Das S;Borthakur M (Statistics Dep, Dibrugarh University, Dibrugarh-786 004, Email: shila_d@mailcity.com) : Mixed constrained (Identical) vehicle routing problem for time minimisation. Opsearch 2006, 43(1), 31-48.

Considers a version of the Vehicle routing Problem (VR) for time minimisation with mixed constraints (Precedence and Fixed Position). With `precedence' constraints, the cities are visited in such a way that a particular city is preceded by another city (the precedence relation need not be immediate) and with `Fixed Position' constraints, the positions of some cities are fixed at certain steps to be visited by a particular vehicle. All the vehicles are identical and have the same capacity. The constraints are assumed to be consistent so the feasible solutions exist. Except for assuring consistency, the two sets of constraints are independent of one another. The Lexicographic Search Approach has been employed here to solve a general VRP problem. A useful and effective lower bound is utilised for quick convergence to the optimum solution.

4 tables, 14 ref

010400   Dalawat C S (Harish-Chandra Research Institute, , Chhatnag Road, Jhunsi, Allahabad-211 019) : Some aspects of the functor K₂ of fields. J Ramanujan Mathl Soc 2006, 21(2), 129-51.

Connections between the group K₂ of a filed and universal central extensions, quadratic forms, central simple algebras, differential forms, abelian extensions, abelian coverings, explicit reciprocity laws, special values of zeta functions, and special values of L-functions have been reviewed. No proofs, minimal bibliography.

32 ref

010399   Choi S H;Nam K B (Department of Mathematics, Jeonju University, Chon-ju 560-759, Korea, Email: chois@jj.ac.kr) : Derivations of a restricted non-associative algebras with exponential functions I. J appl Algebra Discrete Structs 2006, 4(2), 65-71.

Non-associative algebra W(n, m, m + s) is simple [1], [2], [3]. Found all the derivations of the non-associative algebra W (2, 0, 0)₁. There are two non-isomorphic non-associative algebras as non-associative algebras, but their symmetric Lie algebras are isomorphic as Lie algebras using the commutators of the non-associative algebras.

14 ref

010398   Chitrakala Rani T;Ramaraj T (Mathematics Dep, K.N.G. Arts College, Thanjavur, Tamil Nadu) : Time to breakdown point-shock model approach. Appl Sci Period 2005, 7(2), 116-21.

Estimates the expected time to reach the breakdown point of an organization due to successive occurrence iof industrial accidents in (o,t) by using the applications of cumulative damage process.

2 illus, 2 tables, 6 ref

010397   Chaudhary R C;Gupta U;Jha A K (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Radiation effect on MHD three dimensional flow between two horizontal parallel porous plates. Asian J expl Sci 2007, 21(1), 93-103.

Effect of radiation on three dimensional flow of the electrically conducting viscous incompressible fluid between two horizontal parallel porous flat plates moving in the same and in the opposite direction has been analyzed. When the injection of the fluid at the lower plate and its corresponding removal by constant suction through the upper plate is transverse sinusoidal one, the flow becomes three-dimensional. A magnetic field of uniform strength is applied normal to the plane of the plates. To obtain the expression for the velocity and temperature fields, the method of solution for a small perturbation approximation is used. The effect of injection/suction velocity on the flow field, skin friction and the effect of radiation on heat transfer is reported and discussed with the help of graphs.

010396   Castano Iglesias F (Departamento de Estadistica y Mathematica Aplicada, Universidad de Almeria, Spain, Email: fci@ual.es) : A topological version of Kato-Muller theorem for modules. J appl Algebra Discrete Structs 2006, 4(2), 109-15.

Any topological Morita context between complete right linearly topological rings (R,σ) and (S, τ), induces a topological equivalence between quotient categories of CLT-(R,σ) and CLT-(S,τ) has been proved.

6 ref

010395   Cai Z;Li J (Math Dep, Guangxi Teachers College, Nanning 530 001, People's Republic of China, Email: zycaigxu2002@126.com) : On the images of paracompact locally lindel of spaces. Indian J pure appl Math 2005, 36(12), 679-84.

At first, shows that for a K-space X, the following conditions and are equivalent. X is the closed image of a paracompact locally Lindelof space. X has a σ-hereditarily closure-preserving L-system whose every element is closed. X has a σ-hereditarily closure-preserving k-cover consisting of closed Lindelof subsets. Secondly, the compact-covering L-images of paracompact locally Lindelof spaces are characterized.

7 ref

010394   Auroux D (Mip Lab, UniversitE Paul Sabatier Toulouse 3, 31062 Toulouse Cedex 9, France, , Email: auroux@mip.ups-tlse.fr) : Several data assimilation methods for geophysical problems. Indian J pure appl Math 2006, 37(1), 41-58.

Presents an overview of various data assimilation methods, in order to identify the initial condition of a geophysical system and reconstruct its evolution in time and space. The well known four dimensional variational adjoint method, the 4D-VAR algorithm, and then the four dimensional variational dual method, the 4D-PSAS algorithm, extended to nonlinear models. Presents an improved sequential data assimilation algorithm, the SEEK filter. Finally introduces a new simple algorithm, the Back and Forth Nudging. Some theoretical and numerical results about the BFN algorithm are finally given.

3 illus, 50 ref

010393   Arora S R;Gaur A (Mathematics Dep, Hans Raj College, University of Delhi, Delhi-110 007) : On the non-linear multilevel programming problems. Opsearch 2006, 43(1), 49-62.

A multilevel programming problem viz. three level programming problem (TPP) is considered. It involves three optimization problems where the constraint region of the first level problem is implicitly determined by two other optimization problems. The objective function of the first level is indefinite quadratic, the second one is linear and the third one is linear fractional: The feasible region is a convex polyhedron. At first it is shown that minimiziang the indefinite quadratic programming problem is equivalent to minimizing a quasiconcave function over a feasible region comprised of the faces of the convex polyhedron. Also, the second objective function being linear and the third being linear fractional, the optimal solution occurs at an extreme point. It is illustrated with the help of an example.

4 tables, 11 ref

010392   Arora S;Arora S R (Mathematics Dep, Deen Dayal Upadhyaya College, Uniersity of Delhi, Shivaji Marg, Karam Pura, Delhi-110 001, Email: arorasudha@rediffmail.com) : Branch and bound algorithm for the warehouse location problem with the objective function as linear fractional. Opsearch 2006, 43(1), 18-30.

Branch and bound algorithm for a special class of warehouse location problems when the objective function is fractional, is developed. The branching decision rules help us to decide which warehouse has tobe opened or closed from any node of branching tree. Proposes the revised version of the algorithm suggested by Basheer M. Khumawala (1972). It is aillustrated with the help of a numberical example

7 ref

010391   Arora A;Dewangan M L (Faculty, Mechanical Engineering, Bhilai Institute of Technology, Durg-491 001) : Relevance of bio oil for India with respect to substitution of fossil fuel oil. Appl Sci Period 2005, 7(2), 92-101.

Biomass dervied fuels have the potential to substitute fossil fuels. Relevance of bio oil, derived from fast pyrolysis of biomass, with respect to substitution of fossil fuel oil has been discussed. Technology development of produciton of bio oil has been reviewed and the technical feasibility of substituting fossil fuel oil by bio oil has been analysed. The availability of biomass and the economics of production of bio oil have also been evaluated. The technical and economic feasibility of production of bio oil and substitution of fossil fuel oil appears promising. However, the technology is still in initial stages of development and commercial exploitation is yet to begin.

2 illus, 6 tables, 19 ref

010390   Agarwal M;Aggarwal S (Operational Reasearch Dep, University of Delhi-Delhi-110 007, , Email: agarwal_manjulata@yahoo.com) : Heuristic algorithms for constrained redundancy optimization in complex systems based on new measures of importance. Opsearch 2006, 43(1), 88-102.

New measures of importance in respect of minimal path sets and minimal cut sets, respectively, are defined and used to develop efficient heuristic algorithms for solving the problem of constrained redundancy optimization in complex systems. These measures take into account design reliability analysis of a system. With some examples, the effect of the proposed algorithms over other heuristic algorithms existing in literature is discussed. Computational results show that out algorithms can be used as attractive alternatives to other heuristic algorithms keeping in view, both, the solution quality and computational effort.

7 tables, 5 ref

009340   Wen W;Zuhe S (NO, XuZhou Institute of Technology, XuZhou, 221008, P.R. China, Email: ww@xzit.edu.cn) : On the periodic boundary value problem of a generalized lienard equation. J Analysis Applic 2005, 3(3), 191-203.

Global inverse function theorems are used to prove the existence and uniqueness for periodic solution of generalized Lienard equation x" + f(x,x')x' + g(t, x, x') = e(t). The results generalize and improve some known results.

12 ref

009339   Srivatsan Laxman;Sastry P S (Department of Electrical Engineering, Indian Institute of Science, Bangalore-560 012, Email: {srivats,sastry}@ee.iisc.ernet.in) : A survey of temporal data mining. Sadhana 2006, 31(148), 173-98.

Data mining is concerned with analysing large volumes of (often unstructured) data to automatically discover interesting regularities or relationships which in turn lead to better understanding of the underlying processes. The field of temporal data mining is concerned with such analysis in the case of ordered data streams with temporal interdependencies. Over the last decade many interesting techniques of temporal data mining were proposed and shown to be useful in many applications. Since temporal data mining brings together techniques from different fields such as statistics, machine learning and databases, the literature is scattered among many different sources. Present an overview of techniques of temporal data mining. Mainly concentrate on algorithms for pattern discovery in sequential data streams. Also describe some recent results regarding statistical analysis of pattern discovery methods.

102 ref

009338   Molina Jal;Trujillo M (E.T.S. Ingenieros Agronomos, Camino de Vera, , 46072 Valencia, Spain, Email: jalopez@mat.upv.es) : On the regularity of solutions of the homogeneour mixed neumann problem for the hyperbolic heat equation in anisotropic bodies. J Analysis Applic 2005, 3(3), 175-89.

Mixed homogeneous Neumann boundary value problems are considered for the equation A(u) = g with regular data for a wide class of differential operators A including as more representative the operator of the hyperbolic heat equation in bounded bodies which are neither homogeneous nor isotropic. The main result states that when g lies in certain subspace of the Sobolev space H^2r-1.22r (Ωx]0,T[), r ∈]1/2, ∞[, then there is a unique solution in H^2r+1,2r+1 (Ωx]0,T[).

10 ref

009337   Miura Y;Takahasi S E;Miura T;Tsukada M (Department of Mathematics, Faculty of Humanities and Social Sciences, Iwate University, Morioka 020-8550 Japan, Email: ymiura@iwate-u.ac.jp) : Convergency of a recursive sequence x_n+1 = βx_n-1/1+α(x_n-1 + x_n) and its application to a model for competing species. J Analysis Applic 2005, 3(3), 205-22.

Convergency of the recursive sequence xn+1 =f(x_n-1, xn)(n = 0, 1, 2, ...) is discussed and the sequence defined by x_n+1 = βx_n-1/1+α(x_n-1+x_n) is applied to a time-discrete model of competing species.

5 ref

009336   Le R J;Zhou S P (Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, P.R. China) : Generalization of an important trigonometric inequality. J Analysis Applic 2005, 3(3), 163-8.

An essential generalization has been given to an inequality originally established by Telyakovskii by more general positive sequence {Cn}^∞_n=1 to replace 1/k.

9 ref

009335   Karandikar R L (7, SJS Sansanwal Marg, Indian Statistical Institute, New Delhi-110 016, Email: rlk@isid.ac.in) : On the Markov chain monte carlo (MCMC) method. Sadhana 2006, 31(148), 1-104.

Markov Chain Monte Carlo (MCMC) is a popular method used to generate samples from arbitrary distributions, which may be specified indirectly. Gives an introduction to this method along with some examples.

3 table, 7 ref

009334   Jalnapurkar S M (Department of Mathematics, Indian Institute of Science, Bangalore-560 012, Email: smj@math.iisc.ernet.in) : Complexity control in statistical learning. Sadhana 2006, 31(148), 155-71.

Problem of determining a model for a given system on the basis of experimental data has been considered. The amount of data available is limited and, further, may be corrupted by noise. In this situation, it is important to control the complexity of the class of models from which authors are to choose the model. Simplified overview of the principal features of learning theory has been given. The method of regularization is used to control complexity in learning has been described. Discusses two examples of regularization, one in which the function space used is finite dimensional, and another in which it is a reproducing kernel Hilbert space. Authors exposition follows the formulation of cucker and Smale. Gives a new method of bounding the sample error in the regularization scenario, which avoids some difficulties in the derivation given by Cucker and Smale.

12 ref

009333   Ebadian A;Medghalchi A R (Department of Mathematics, Faculty of Science and Computer Engineering, Urmia University, Iran, Email: a.ebadian@mail.urmia.ac.ir) : Carrier space of a real group algebra. J Analysis Applic 2005, 3(3), 169-74.

Let G be a locally compact abelian group with a Haar measure λ and T be a topological group involution on G. The real group algebra L¹(G,T) and the real measure algebra M(G,T) were introduced earlier. Let G be the character group of G. A topological involution on G has been defined and the carrier space of L¹(G, T) has been determined. Also, the Bochner's theorem has been extended to the real group algebras.

5 ref

009332   Darus M;Saibah (School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, Bangi 43600 Selangor D.E. Malaysia, Email: maslina@pkrisc.cc.ukm.my) : Unified presentation of prestarlike univalent functions. J Analysis Applic 2005, 3(3), 151-61.

Various properties and characteristic of the following new general class ε_T[α,λ,K,L],0 ≤ α <60> 1; λ ≥0; -1 ≤ K <60> L ≤ 1; K + L ≥ 0, 0 <60> L ≤ 1, which unifies (known or new) of prestarlike univalent functions has been introduced and investigated. The results involve distortion inequalities and modified Hadamard products (or convolution) of functions belonging to the class ε_T[α,λ,K,L]. The radii of starlikeness and the radii of convexity are also considered.

4 ref

009331   Bhatt A G (NO, Indian Statistical Institute, 7, S J S Sansanwal Marg, New Delhi-110 016, Email: abhay@isid.ac.in) : Linear filtering with ornstein-ulhenbeck process as noise. Sadhana 2006, 31(148), 141-53.

Linear filtering model (with feedback) is considered when the observation noise is an Ornstein-Ulhenbeck (OU) process with parameter β has been introduced. The coefficients appearing in the model are all assumed to be bounded. In addition, the coefficients appearing in the observation equation are also assumed to be differentiable. Consider the general case when the OU noise is also correlated with the signal. Under these conditions, the filtering equations for the optimal filter has been derived.

19 ref

008246   Yuan X H;Yang W C;Li X S (Department of Mathematics and Physics, Henan University of Science and Technology, Luoyang 471003, P R China) : Fuzzy topology based on the consensus space. Int Rev Fuzzy Math 2006, 1(1), 65-71.

By the use of the theory of a consensus space presented by Hisakichi Suzuki, concept of C-fuzzy topology is acquired. It is proved that a Ying's fuzzifying topology is a C-fuzzy topology and each C-fuzzy topology is homeomorphic a special of fuzzy topology. These discussions have built up a new theoretical approach for the fuzzifying topology.

9 ref

008245   Yan X;Fu X;Tang Y (College of Mathematics & Computation Science, Hunan University of Science & Technology, Xiangtan-411 201, Email: yq19801124@163.com) : Oscillatory behavior of solutions of certain second order nonlinear difference equations. J Computnl Math optimiz 2006, 2(1), 25-34.

Second order nonlinear difference equation has been considered Δ[a_n-1(Δy_n-1)^{<100>< F255>}]+ q_nf(y_n)= r_n (n=1,2,...), (1) where 0 <60> δ = p/q with p, q odd integers, Δy_n = y_n+1 _ y_n is the forward difference operator, f ε C(R,R), f is nondecreasing, uf(u) <62> 0 as u ≠ 0, {a_n} is an eventually positive real sequence, {q_n}, {r_n} are real sequences. Some new sufficient conditions for the oscillation of all solutions of (1) are obtained.

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008244   Xiaoji L (Department of Mathematics, College of Computer and Information Science, Guangxi University for N, Nanning-530 006, P.R. China, Email: xiaojiliu72@yahoo.com.cn) : The weighted-star partial ordering of matrices. J Computnl Math optimiz 2006, 2(1), 57-64.

Weighted-star partial ordering is defined and the characterization of it is obtained by using the weighted generalized inverse, some known results for star partial ordering are generalized to the case of weighted-star partial ordering.

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008243   Valero O (Departamento de Ciencias Matematicas e Informatica, Edificio Anselm Tu, Universidad de las Islas Baleares, 07122 Palma, Spain, Email: o.valero@uib.es) : Quotient normed cones. Proc Math Sci 2006, 116(2), 175-91.

Given a normed cone (X, p) and a subcone Y, construct and study the quotient normed cone (X/Y, p) generated by Y. In particular characterize the bicompleteness of (X/Y, p) in terms of the bicompleteness of (X, p), and prove that the dual quotient cone ((X/Y)*, p<157>_pu) can be identified as a distinguished subcone of the dual cone (X*, p<157>_pu)). Furthermore, some parts of the theory has been presented in the general setting of the space C L (X, Y) of all continuous linear mappings from a normed cone (X, p) to a normed cone (Y, q), extending several well-known results related to open continuous linear mappings between normed linear spaces.

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