004234   Adiga C;Kim T;Mahadeva Naika M S;Madhusudhan H S (Dep of Studies in Math, Univ of Mysore, Manasagangotri, Mysore 570 006) : On ramanujan's cubic continued fraction and explicit evaluations of theta-functions. Indian J pure appl Math 2004, 35(9), 1047-62.

Two integral representations for the Ramanujan's cubic continued fraction V (q) have been given and a modular equation relating V (q) and V(q³) has been required. Some modular equations and a transformation formula for Ramanujan's theta-function ψ(-q) have been established. As an application of these several new explicit evaluations of theta-functions and Ramanujan's cubic continued fraction have been computed.

21 ref

003081   Vonocha O P (Math Dep, S G N Khalsa Voll, Sriganganagar-335 001) : Application of fuzzy sets in diagnosis and treatment of patients with entropy. Int J Mgmt Syst 2003, 19(2), 157-64.

Vinocha (1998) proved that Shannon's entropy is better then Renyi' entropy. In the present paper author has tried to utilize application of fuzzy sets in diagnosis and treatment of patients with entropy.

1 illus, 4 tables, 4 ref

003080   Srinivasan L;Kalyanaraman R K;Sekar R (Meth Dep, Tagore Arts Coll, Pondicherry, Email: srini1945@sify.com) : Computational analysis of bulk service queues with vacation using analytical approach and steady state results. Int J Mgmt Syst 2003, 19(2), 117-28.

A M/G^B/1 queue with infinite waiting space is considered. The server is free to take vacation and the customer has a feedback facility. For such a system the LST, pgf and some performance measure are derived. The steady state equations for such a system with the distribution of service length and vacation length as exponential, are formulated. These equations are solved using linear operators. Then using recursive algorithm, the individual probabilities of the number in queue when the system is busy and on vacation are calculated. The results obtained are found to agree will with the results calculated from the probability generating founction, using root-finding method.

2 tables, 9 ref

003079   Singh G p;Deshpande R V;Singh T (Math Dep, Visvesvaraya Natnl Inst of Technol, Nagpur-440 011) : Higher-dimensional cosmological model with variable gravitational constant and bulk viscosity in layra geometry. Pramana J Phys 2004, 63(5), 937-45.

Studies five-dimensional homogeneous cosmological models was variable G and bulk viscosity in Lyra geometry. Exact solution for the field equations have been obtained and physical properties of the models are discussed. It has been observed that the results of new models are well within the observational limit.

32 ref

003078   Satpathy B;Hota S K (P.G. Business Administration Dep, Sambalpur University, Burla, Sambalpur-768 019) : DEA modeling for optimal resource use in rice production. Opsearch 2004, 41(3), 148-54.

The techniqude of Data Envelopment Analysis is used to evaluate the technical efficency of individual farms cultivating rice for three different villages with different agrarian conditions. The result shows that there is ample scope for improvements in input utilization in all the villages. The importance of productivity management in rice cultivation in terms of improving the technical efficiency of the farmers through proper management and judicious utilization of the resource has been established.

23 ref

003077   Pandey D;Kalra B S (Math Dep, Ch.Charan Singh Univ, Meerut-4) : System with deteriorated performance and degraded failures under circumstantial and common cause failures. Int J Mgmt Syst 2003, 19(2), 181-92.

Deals with reliability analysis of a Two-unit system with deteriorated performance and degraded failures under circumstantial and common cause failures. Supplementary variable technique has been used to derive expressions of interest. Effect of different failures have been critically examined on the basis of numerical computations.

2 tables, 4 ref

003076   Nam K B;Choi S H (Mathematics Dep, University of Wisconsin-Whitewate, Whitewater, WI 53190, USA, Email: Namk@uww.edu) : Automorphism group of non-associative algebra WN_2,0,0,1. J Computnl Math optimiz 2005, 1(1), 35-44.

Non-associative algebra automorphism group Aut_non (WN_2,0,0,1) of the non-associative algebra WN_2,0,0,1 has been found. It has been shown that the non-associative algebra is not isomorphic to the non-associative algebra WN_2,0,0,1 as non-associative algebras. It has been shown that there are two non-isomorphic Lie-admissible algebras as non-associative algebras such that their corresponding Lie algebras using their commutators are isomorphic as Lie algebras.

9 ref

003075   Miwa M;Oyama T (NO, Railway Technical Research Institute, Japan) : All-integer type linear programming model analysis for the optimal railway track maintenance scheduling. Opsearch 2004, 41(3), 155-64.

Railway track irregularities have to be kept at a satisfactory level by taking appropriate maintenance activities on the ballasted track. Obtaining an optimal maintenance schedule for the railway track irregularities using all-integer type linear programming model aimed. In order to determine an effective maintenance strategy. A mathematical programming model to make an optimal schedule for the multiple tie tamper (MTT) operation aiming at the largest improvements for the level of surface irregularities reflecting high riding quality and safety for the railway vehicles. The optimization modeling approach is applied to the actual Japanese railway network system, and it is confirmed that the model is effective and useful for the practical use.

3 illus, 1 table, 10 ref

003074   Mishra S S;Mishra V (Mathematics and Statistics Dep, Dr. M.M.L. Avadh University, Faizabad-224 001) : The cost analysis of machine interference model with balking, reneging and spares. Opsearch 2004, 41(3), 188-99.

An attempt has been made to discuss the cost analysis of the machine interference model M/M/C/K/N. A cost function is constructed in order to determine the optimum cost of the system. In this analysis, a fast converging N - R method has been used to solve the non-linear function involving service rate and hyper geometric functions including other parameters. A computer program of above method has enabled us to crack down the root value of this exhaustive non-linear function to yield an optimal solution. In this way, an efficient evaluation of performance measure in the form of cost analysis has been possible to be carried out and consequently an important dimension of this investigation has been attempted successfully.

5 illus, 3 tables, 11 ref

003073   Matsuura T;Saitoh S (Mechanical Engineering Dep, Faculty of Engineering, Gunma University, Kiryu 376-8515 Japan, Email: matsura@me.gunma-u.ac.jp) : Numerical inversion formulas in the wave equation. J Computnl Math optimiz 2005, 1(1), 1-19.

Practical inversion formulas in the one dimensional wave equation have been given and their numerical experiments have been shown by using computers.

8 illus, 6 ref

003072   Kumar K V (Chem Engng Dep, Sri Ram Engng Coll, Perumalpathi, thiruvallur-602 024) : Studies on adsorption of basic dyes onto agro-based wastes: part 2-equillibrium and diffusion studies. Indian J envir Prot 2003, 23(4), 392-5.

Equillibrium studies for adsorption of malachite green onto carbonized coconut shell was studied using Langmuir and Freundlich isotherm equations. Diffusion studies shows that adsorption is controlled by intraparticle diffusion process for all the 3 adsorbents (coconut shell, groundnut shell and rick husk.

6 illus, 4 tables, 3 ref

003071   Jain M;Sharma G C;Sharma S K;Kushwaha S C (Mathematics Dep, I.B.S. Khandari, Agra) : Computational study on malarial parasites. Int J Inf Comput Sci 2004, 7(1), 14-24.

Focus has been placed on the dynamics of malaria transmission by considering the aspects of non-random host choice, which may affect quantitative and qualitative aspects of the interaction of human hosts and mosquito vectors. The study incorporates biting preference by mosquitoes with respect to infection in their host, which is evident from a few laboratory experiments. In determining levels of malarial infection, it is showed that mosquitoes are preferentially attracted to infected host even when biting doses not occur. The increasing-preference and switching models have been developed to understand the equilibrium and stability.

9 illus, 20 ref

003070   Huang H (Mathematics Dep, Zhongshan University, Guangzhou 510275 P.R. China,, Email: huanghui@ynu.edu.cn) : Set-valued versions of Ky fan's inequality with application to vector optimization. J Computnl Math optimiz 2005, 1(1), 21-34.

A vector set-valued version of Ky Fan's minimax inequality has been given. A differential inclusion problem for set-valued map which concerns the contingent derivative formulated. Sufficient conditions for the existence of weakly efficient solutions for vector optimization problems are obtained by means of the cone pseudo-convex differential inclusion problem.

9 ref

003069   Duraivelu K (Industrial Engineering Dep, Anna University, Chennai) : Quality metrics for information systems. Opsearch 2004, 41(3), 200-7.

An attempt has been made to identify the practical quality metrics for Information systems. It explores how the quality metrics are evaluated to analyse the performance of Information Systems. The experimental analysis is validated by means of user satisfaction survey. First, the key quality characteristics are determined from the ISO model of the system and / or from the results of a user survey. These metrics are then computed and the values are compared with the results from a user satisfaction survey. Correlation analysis for the rankings from the experiment of quality metrics and the user satisfaction survey is carried out. Based on the values of the quality metrics, the quality characteristics are ranked. Several hypotheses are tested to check the correlation between the ranking of specific quality metrics and ranking of specific quality characteristics and ranking of overall user satisfaction. The functional requirements of the systems to achieve the quality characteristics are then identified and their strengths of association with the key quality characteristics are determined using quality houses of Quality Function Deployment. Using QFD, the seystem is redesigned to achieve higher performance in terms of higher values of the quality metrics.

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003068   Deep K;Pant M (Math Dep, Indian Inst of Technol, Roorkee, Uttranchal, Email: kusumfma@isc.rurkiu.ernet.in) : Solution of fractional programming problems using genetic random search technique. Int J Mgmt Syst 2003, 19(2), 101-16.

An algorithm F-GRST, has been proposed for solving Fractional Programming Problems. It is modified version of Genetic Random Search Technique (GRST) algorithm developed earlier by Deep and Pant. F-GRST has been coded in C++ and has been tested on 15 linear and nonlinear Fractional Programming test problems appearing in literature. The results indicate the advantage of the F-GRST over the conventional methods.

2 illus, 3 tables, 13 ref

003067   Darus M (School of Mathematical Sciences faculty of Science and Technology, Universiti Kebangsaan Malaysia Bangi 43600 Selangor D.E. Malaysis, , Email: maslina@pkrisc.cc.ukm.my) : Fekete-Szego problem for α-close-to-convex functions. J Computnl Math optimiz 2005, 1(1), 45-53.

23 ref

003066   Crnkovic D;Rukavina S (Mathematics Dep, Faculty of Philosophy, , Omladinska 14 51000 Rijeka Croatia) : On some symmetric (45, 12, 3) and (40, 13, 4) Designs. J Computnl Math optimiz 2005, 1(1), 55-63.

It has been shown that a symmetric (45, 12, 3) design and two symmetric (40, 13, 4) designs can be constructed from the group P Sp(4,4), defining an incidence relation on the conjugacy classes of maximal subgroups. These designs possess symmetric incidence matrices with constant diagonal, which are adjacency matrices of strongly regular graphs. Symplectic group PSp(4,3) acts transitiely on the constructed designs and strongly regular graphs.

12 ref

003065   Chatterjee S;Misra R B;Alam S S (Maths Dep, Sikkim Manipal Institute of Technology, Majitar-737 132) : Symbolic reliability evaluation of a software with network structure. Opsearch 2004, 41(3), 165-77.

A graph theoretic approach is proposed for enumeration of paths and symbolic reliability expression of a large software from the program graph having a series, parallel or complex network structure. A brief account of the factors which influence the overall reliability of a software is presented. One space application program has been used for illustration purpose.

2 illus, 12 ref

003064   Chakraborty S;Chanda P K (Central Drugs Lab, , 3 Kyd Street, Kolkata-700 016) : Some physical solutions of Yang's equations for SU(2) gauge fields, charap's equations for pion dynamics and their combination. Pramana J Phys 2004, 63(5), 1039-45.

Some previously obtained physical solution of Yang's equations for SU(2) gauge fields, charap's equations for pion dynamics and their combination as proposed by Chakraborty and Chanda have been presented. They represent different physical characteristics, e.g. spreading wave packets, solitary wave with oscillatory profile, localised wave with solitary profile which becomes plane wave preiodically, and wave packets which are oscillatory in nature.

5 illus, 6 ref

003063   Ahmad I (Math Dep, Aligarh Muslim Univ, aligarh-202 002) : Optimality conditions and duality in fractional minimax programming involving generalized ρ-invexity. Int J Mgmt Syst 2003, 19(2), 165-79.

Sufficient conditions are discussed for fractional minimax programming problem under generalized ρ-invex functions. These conditions are utilized to formulate the dual models and duality theorems are derived.

15 ref

002035   Zeltser M (Tartu Univ, , Vanemuise 46, r.250 Tartu, 51014, Estonia, Email: mzeltser@math.ut.ee) : Weak sequential completeness of beta-duals of double sequence spaces II*. J Analysis 2003, 11, 1-22.

Two types of oscillating properties have been defined for a double sequence space E guaranteeing the weak sequential completeness of its beta-duals defined by the Pringsheim, the bounded Pringsheim and the Hardy regular notions of convergence. Another pair of oscillating properties guaranteeing the weak sequential completeness of the beta-duals of E defined by three weaker notions of convergence have been introduced and studied.

13 ref

002034   Fisher B;Telci M (Math Dep, , Leicester Univ, LE1 7RH, England, Email: fbr@le.ac.uk) : Some neutrix convolutions of functions and distributions. J Analysis 2003, 11, 23-32.

The neutrix convolution of two locally summable functions of distributions f and g is defined to be the limit of the sequence {f_n*g), where f_n(x) = fxτ_nx is a certain function with compact support and the sequence {τ_n} converges to the identity function on the real line. the neutrix convolution of the functions ^r₊ lnx₊ and eλ^x is evaluated for r = 0,1,2,... and all λ≠0. Further neutrix convolutions are then deduced

5 ref

002033   Yadav R P;Nayak N K;Yadav A K (Dep of Math, Parwati Sci Coll, Madhepura) : Critical study of probabilistic structure of quantum mechanics. Appl Sci Period 2004, 6(3), 179-83.

5 ref

002032   Valarmathi J;Seetha H (ECE Department, Vellore Institute of Technology, Vellore-632 014) : Adaptive reduction of motion artifact in ECG using LMS algorithm. Appl Sci Period 2004, 6(3), 135-9.

One of the main problems when picking signals so weak as the electracardiogram is noise. There are several kinds of noise that can affect the ECG but one of the strongest is the 50 Hz power-line interference in the measurement signal because of magnetic induction, displacement currents in leads or in the body of the patient, and equipment interconnections and imperfections. This system is based on how to build adaptive digital filter using Least Mean Square algorithm to perform noise cancellation and signal extraction. These adaptive techniques are advantages because they do no require a prior knowledge of the signal or noise characteristics as needed for other filters.

6 illus, 5 ref

002031   Srinivasan V S (C-41/3, Phase-2, DRDO Township, CV Raman Nagar, Bangalore-560 093, , ) : Estimation of probability density function of a random variable for small samples. Def Sci J 2004, 54(1), 17-9.

A theoretical method of estimating the most general form of probability density functions of random variables has been described. The estimated probability density function depends on the mean value of exponential distribution of the initial random variable. By the most general form of the probability density function, it is meant that the survivour function are of exp (λt²) or exp (-γt³) or combinations of these functions for different values of <-F128><108> and γ.

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002030   Singh T N;Gupta A R;Sain R (Earth Sci Dep, IIT-Bombay, Mumbai-76) : Intelligent analysis of compressive behavior of ice. Indian Min Engng J 2003, 42(11-12), 37-42.

The applicability of neurofuzzy systems in predicting the compressive behavior of ice under various geomechanical conditions has been demonstrated. In order to supplement the prediction efficiency of fuzzy inference systems, adaptive networks have been used. The data from rock tests at different temperatures reported in literature were used as inputs for training the network and the strain rate was predicted. This approach gives a more realistic realization of the problem. This method scores over the use of multi-layer perceptrons because of the fact the knowledge gained in training by the latter is spread throughout the network connections by optimizing the weight distribution in a way which is hard to be interpreted. Subrractive clustering has been used to preprocess the available data, which in a way increases the efficiency of the system. The method rules out unneeded correlations existing in the data. Results from the analysis demonstrate that the neurofuzzy method is efficient in the prediction of strain rate of ice by the effective mapping of complex relationships affecting compressive behavior of ice.

5 illus, 2 tables, 21 ref

002029   Singh S P;Sahu D P;Sao G S (Dep of Math, G G D Univ, U T D Bilaspur 495 001) : Common fixed point theorem for the mapping in Saks space. Appl Sci Period 2004, 6(3), 140-4.

Some fixed point theorem using weakly uniformly contraction pair of mappings in Saks spaces have been established. The result generalizes the result of Cho & Singh.

10 ref

002028   Sharma A;Sharma M K (Dep of Math, Univ of Rajasthan, Jaipur 302 004) : Unsteady free convection flow between horizontal parallel porous plates in the presence of heat source. Appl Sci Period 2004, 6(3), 145-54.

Unsteady free convection flow of an incompressible viscous fluid between horizontal parallel porous plates in the presence of constant heat source is investigated. The upper plate is oscillating in its own plane periodically with time. The governing equations of motion and energy are solved by using the perturbation technique. The expressions of velocity and temperature distributions are derived, discussed numerically and presented through graphs.

6 illus, 7 ref

002027   Patil D S;Gautam D K (Electronics Dep, North Maharashtra Univ, Jalgaon-425 001) : Computer aided simulation tools for the analysis of semiconductor lasers. IETE Tech Rev 2003, 20(6), 533-40.

The computer aided simulation tools have been developed for the analysis and optimisation of various physical parameters of the semiconductor lasers. For computer analysis, Poisson's equation and current continuity equations have been numerically solved iteratively to obtain electrostatic potential and quasi-Fermi potentials at various positions in the device structure respectively. The wave equation has been solved to obtain the optical field for the transverse electric mode and the rate equation for photons has been solved to obtain photon density. The operational mechanism of the device is fully understood using this tool by graphical representation of output characteristics. The current flow in the device is restricted to less distribution width due to self focusing effect for greater magnitude of current or operating voltage. The peak value of optical intensity value for 807 nanometer exactly lies at the centre of the active region, which confirms the optical confinement.

9illus, 1 table, 9 ref

002026   Panda J P;Das S S;Dash G C (Math Dep, Coll of Engng and Technol, OUAT, Bhubaneswar 751 003xm) : Unsteady free convection MHD flow and mass transfer in a rotating porous medium. Appl Sci Period 2004, 6(3), 165-78.

The unsteady free convection and mass transfer flow of a viscous incompressible electrically conducting fluid through a porous medium bounded by a vertical plane surface in a rotating frame of reference has been studied in presence of a transverse magnetic field. The flow phenomenon is considered for the case when the plane surface absorbs the fluid with a velocity which fluctuates with the same frequency as that of temperature and a constant suction. The analytical expressions for velocity, temperature and concentration are obtained and the effects of the pertinent parameters of the velocity field are discussed. The steady part of the velocity is observed to have three layer character namely, thermal layer, concentration layer and suction layer while the oscillatory part exhibits a multilayer character called modified suction layers. The problem is significantly relevant to the geothermal areas where ground water flows through a porous medium subject to the earth's rotation.

6 illus, 1 table, 15 ref

002025   Natarajan P N (Math Dep, Ramakrishna Mission Vivekananda Coll, Chennai-600 004) : Euler and taylor methods of summability in complete ultrametric fields. J Analysis 2003, 11, 33-41.

Euler and Taylor methods of summability in complete, non-trivially valued, ultrametric fields of characteristics 0 have been introduced and some of their properties have been proved.

4 ref

002024   Medghalchi A R (Inst of Math, Teacher Training Univ, , Tehran, Iran) : Amenability and weak amenability of L(X)**, M(X)**. J Analysis 2003, 11, 53-9.

If A is a Banach algebra and A^** is the second dual of A with first Arens product, it is known that if A^** is amenable, then A is amenable. If A is a left ideal in A^** and A^** is weakly amenable, than A is weakly amenable. The general result for this case is not known i.e., does the weak-amenability of A^** imply the weak amenability of A? For a locally compact group G, is it is known that L¹(G)^** is amenable if and only if G is finite. If L¹(G)^** is weakly amenable, then M(G) is weakly amenable. The amenability and weak amenability of (L(X)^**, M(X)^**, the second duals of L(X), (hypergroup algebra) and M(X) (hypergroup measure algebra) have been investigated. It has been shown that if L(X)^** is weakly amenable, than M(X) is weakly amenable.

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002023   Inc M;Isik M (Math Dep, Firat Univ, 23119 Elazig/Turkiye, Email: minc@firat.edu.tr) : Adomian decomposition method for three-demensional parabolic equation with non-classic boundary conditions. J Analysis 2003, 11, 43-51.

Adomian decomposition method is developed for solving an initial-boundary value problems for the three demensional parabolic partial differential equation with non-classic boundary conditions. The approximate solutions of this problem are calculated in the form of a series with easily computable components. The accuracy of the proposed numerical scheme is examined by comparison with analytical, approximate and numerical results. The method is more accurate than other numerical methods. Exact solutions have been obtained without using any transformation.

1 illus, 25 ref

002022   Grahl J (Math Inst Univ Wurzburg Am Hubland, , 97074 Wurzburg, Germany, Email: grahl@mathematik.uni.wuerzburg.de) : A short proff of miranda's theorem and some extensions using Zalcman's lemma. J Analysis 2003, 11, 105-13.

According to a well-known theorem of Miranda a family F of nonvanishing analytic functions in the unit disk D with f^(k)(z) ≠ 1 for all z ∈ D and all f ∈ F for a fixed k ≥ 1 is normal. Using Zalcman's Lemma a short (and almost completely elementary) proof of this result has been given and of an extension to more general differential polynomials instead of f^(k). This method essentially goes back to A. Ros who had proved Montel's Fundamental Normality Test in this way.

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002021   Ganapathy J (University of Wisconsin - Oshkosh, , Oshkosh, WI-54901, USA) : Weighted L<. J Analysis 2003, 11, 69-83.

Results by Chung, Hunt and Kurtz are generalized for the weighted Hardy-Littlewood Maximal function M_vf defined in section 1 below. These include necessary and sufficient conditions for weighted L^p,q inequalities involving M_vf.

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002020   Eswari Bai M;Subha M C S;Narayana Swamy G;Rao K C (Department of Chemistry, Department of Polymer Science and Technology, Sri Krishnadevaraya University, Anantapur-515 003) : Acoustical studies of molecular interactions in binary liquid mixtures of butoxy ethanol with some amines at 308.15 K. J pure appl Ultrasonics 2004, 26(2-3), 79-83.

Densities and ultrasonic velocities of binary mixtures of 2-butoxy ethanol (BEL) with n-butylamine (NBA), sec-butylamine (SBA), tert-butylamine (TBA), n-hexylamine (NHA), n-octylamine (NOA) and cyclohexylamine (CHA), at 308.15 K are measured. From these measured values, various acoustical parametes like ocoustic impedance (Z), isentropic compressibility (k_E), intermolecular free length (L) and relative association (R) have been computed. The various excess properties like excess acoustic impedance (Z^E), excess isentropic compressibility (K_s^E), and excess intermolecular free length (L_f^E) have also been computed from the values of densities and ultrasonic velocities. The results have been discussed in terms of various interactions present in these mixtures and self associations in the components.

1 illus, 2 tables, 10 ref

002019   Dethe C G;Wakde D G (Electronics Dep, Shri Sant Gajanan Maharaj College of Engng, Shegaon-444 203) : On the prediction of packet process in network traffic using FARIMA time-series model. J Indian Inst Sci 2004, 84(1-2), 31-9.

The simultaneous existence of short and long-range dependence in the network traffic has exposed the limitations of conventional traffic models. A fractionally integrated autoregressive moving average process (FARIMA) has been suggested to model the packet process observed in network traffic. Different levels of aggregations for computing differencing parameter `d'have been used. Complete procedure for modeling and obtaining the predictions for packet process in network traffic using the FARIMA (p,d,q model has been given.

9 illus, 4 tables, 16 ref

002018   Berland M (NO, , 8, rue Dupin, 75006 Paris (France)) : Convergence D'une certaine serie D'exponentielles. J Analysis 2003, 11, 61-7.

Some properties have been studied on the convergence of a class of exponential series a little more general than those introduced by the author where in the coefficients are entire functions of bounded index, in the meaning of B.Lepson, with at most, a finite number of zeros. Methods of M.Blambert R.Parvatham and Gerd H. Fricke which are relatives to the existence of entire functions of bounded Borelien orders and bounded index have been used.

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002017   Alimohammadi D;Ebadian A (Math Dep, Univ of Arak, Arak 879, I R Iran, Email: d-alimohammadi@araku.ac.ir) : Second dual of real Lipschitz algebras of complex functions. J Analysis 2003, 11, 85-103.

A compact matric space (K, d) has been considered, where α∈(0,1) and Δ ={(x,y) ∈ K x K : x = y}, V = (K x K) - Δ. W = KUV. In 1987, Bade, Curitis and Dales showed that there is an isometric linear map of the Lipschitz space (lip (K,α), <124><124>.<124><124>α) into the Banach space (C₀(W), <124><124><124>.<124><124><124>), where <124><124><124>h<124><124><124> = <124><124>h<124><124>_K + <124><124>h<124><124>_V∈ C_O(W)). Also, the second dual of (lip (K, α), <124><124>.<124><124>)α) is isometrically isomorphic to Lipschitz space (Lip(K, α), <124><124>.<124><124>α). Recently we have defined Earricr the real Banach algebra of all complex Lipschitz functions (Lip (K, τ,α), <124><124>.<124><124>α) and (lip(K,τ,α), <124><124>.<124><124>α), where τ is a d-isometry topological involution on K. It has been shown that there is a real linear isometry of the real Banach space (lip(K,τ,α), <124><124>.<124><124>α) into the real Banach space C₀(W,τ), <124><124><124>.<124><124><124>), where τ is the topological involution on W induced by τ. Also, the secon dual of (lip(K,τ,α), <124><124>.<124><124>α) is isometrically isomorphic to (Lip_R(K,τ,α), <124><124>.<124><124>α), Lip_R(K,τ,α) is the set of the real functions in Lip(K,τ,α)

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002016   Alice K V;Krishna Kumar V (Math Dep, Newman Coll, Thodupuzha, Kerala-685 585, Email: vellatkrishna@yahoo.com) : Two classes of second and third-order differential expressions in the limit-circle case. J Analysis 2003, 11, 115-45.

Two special classes of second and third-order formally symmetric differential expressions whose co-efficients are determined by a single function and two real parameters have been considered. Necessary and sufficient conditions on this function and the parameters for the expressions to be in the corresponding limit-circle cases at <108> have been obtained. It is interesting to note that the limit classifications depend on the relative values of the two parameters.

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001016   Zhan J;Tan Z (Dep of Math, Hubei Institute for Nationalities, , Enshi, Hubei Province 445000, People's Republic of China) : Finitely copresented and cogenerated dimensions. Indian J pure appl Math 2004, 35(6), 771-81.

Relations of the finitely copresented dimension of injective equivalent modules have been studied and a shifting theorem has been given. The co-herent rings have been characterized with the finitely copresented dimension and properties of finitely copresented dimension of co-coherent ICF-rings have been given. The concepts of finitely cogenerated dimension of modules and some properties have been introduced.

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001015   Yuksel N;Ozdemir M (Dep of Mathematics, Erciyes Univ, 38039 Kayseri, Turkey) : The six vertex theorem for closed planar curve which bounds and immersed surface. Indian J pure appl Math 2004, 35(6), 723-35.

It has been proved that the number of vertices is at least 6 for closed planar curve which bounds an immersed surface with non-zero genus.

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001014   Yazdanpanah T (Fac of Math Sci, Teacher Training Univ, 599, Taleghani Avenue, Tehran, 15614, Iran) : Amenability and weak amenability of module extension of Banach algebras by 2-cocycles. Far East J mathl Sci 2004, 13(3), 357-74.

Let A be a Banach algebra, X be a Banach A-module, and T be a 2-cocycle. Then A⊕_TX becomes a Banach algebra with products and the norm as follows: (a,x)(b,y)=(ab,ay+xb+T(a,b)). (a,x) = a+x (a,b∈ A, x,y ∈X). The amenability and weak amenability of this algebra have been studied.

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001013   Yang X X Q; (Math Dep, Chongqing Normal Univ, Chongqing 400 047) : Second order duality for nonlinear programming. Indian J pure appl Math 2004, 35(5), 699-708.

Four second-order dual models for nonlinear programming are introduced and their duality under generalized second-order F-convexity assumptions are discussed. These results generalize and improve corresponding first-order works of Chandra and Abha.

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001012   Xiaoyue L;Daqing J (School of Math & Statists, Notheast Normal Univ, Changchun 130 024) : Optimal existence theory for single and multiple positive solutions to second order Neumann boundary value problems. Indian J pure appl Math 2004, 35(5), 573-86.

A new optimal existence theory for single and multiple positive solutions to second order Neumann boundary value problems have been dealt with by employing the fixed point theorem in cones. Some previous results have been improved some new reults have been reported.

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001011   Venkatlaxmi A;Padmvathi B S;Amaranath T (Dep of Mathematics and Statistics, Univ of Hyderabad, Hyderabad 500 046) : Unsteady Stokes equations: some complete solutions. Proc Indian Acad Sci-Mathl Sci 2004, 114(2), 203-13.

The completeness of solutions of homogenous as well as non-homogeneous unsteady Stokes equations are examined. A necessary and suffcient condition for a divergence-free vector to represent the velocity field to possible unsteady Stokes flow in the absence of body forces is derived.

6 ref

001010   Vasantha W B;Paramasivam K (Dep of Mathematics, Indian Institute of Technology, Madras Chennai 600036) : The chromatic number of a commutative groupoid. Ultra Scient phys Sci 2004, 16(2), 111-8.

The coloring problem of a commutative groupoid has been studied and the chromatic number of commutative groupoid has been defined. A class of commutative groupoids using the set of all integers modulo n, on which different closed binary nonassociative operations are defined has been constructed and the following results for n= 2m, the chromatic number of the commutative groupoid Z_n is m; for n=p², the chromatic number of the commutative groupoid Z_n is p; for n=pq, where p,q are primes such that 2<60>p<60>q, the chromatic number of the commutative groupoid Z_n is p. have been proved.

3 illus, 7 ref

001009   Tripathy B C (Math Sci Div, Inst of Advanced Study in Sci and Tech, Khanapara, Guwahati 781 022) : On generalized difference paranormed statistically convergent sequences. Indian J pure appl Math 2004, 35(5), 655-63.

Generalized difference paranormed sequence spaces defined over a seminormed sequence spaces defined over a seminormed spaces (X,q) are introduced and their different properties studied. Some inclusion results are proved. Some errors appearing in the article of Tripathy and Sen are discussed in detail.

21 ref

001008   Tiwari B (Dep of Math, B R D P G College, Deoria-274 001) : On S4-like Finsler spaces with semi-T'-condition. Bull Calcutta Mathl Soc 2004, 96(5), 389-94.

Generalises the T-condition in a Finsler space and studies S4-like Finsler space satisfying T'condition.

7 ref

001007   Tandon P N;Bali R;Siddiqui S U;Shukla A K (Dep of Mathematics, Harcourt Butler Technological Institute, Kanpur 208 002) : A study of nutritional transport in pulsatile blood flows through time dependent stenotic tube. Ultra Scient phys Sci 2004, 16(2), 199-204.

Represeting blood by couple stress fluid and introducing m 1 d sym metric stenosis in a small diameter tube, a study of nutritional transport has been made. The govering equations have been solved by Picard's type iterative procedure. Variations of the local concentration with various parameters involved in the analysis has been presneted through graphs and discussed. It has been observed that the rheological parameters of the fluid model representing concentration and shape and size of suspended microstructures dominate the nutritional transport. In the stenotic region, the diffusional process hinders owing to the closure of pores and this, in turn, prevents proper nutritional supply to the cells in the deeper region in the tissue.

5 illus, 17 ref