023043   Nadarajah S;Kotz S (Statistics Dep, Nebraska Univ, Lincoln, NE-685 83, USA) : On the ratio of t and laplace random variables. Natn Acad Sci Lett 2006, 29(3-4), 111-6.

Distribution of the ratio |X/Y| is derived when X and Y are Student's t and Laplace random variables distributed independently of each other. Extensive tabulations of the associated percentage points are also given.

1 illus, 11 ref

023042   Muthucumaraswamy R;Chandrakala P;Antony Raj S (Information Technology Dep, Sri Venkateswara College of Engineering, Sriperumbudur-602 102, Email: msamy@svce.ac.in) : Thermal radiation effects on moving vertical plate with chemical reaction. Int Rev pure appl Math 2006, 2(1), 1-12.

An analysis is performed to study the effects of thermal radiation on unsteady free convective flow over a moving vertical plate with mass transfer in the presence of homogenous first order chemical reaction. The fluid considered here is a gray, absorbing-emitting radiation but a non-scattering medium. The temperature and concentration level near the plate are raised linearly with time. The dimensionless governing equations are solved using the Laplace transform technique. The velocity and skin-friction are studied for different parameters like the radiation parameter, chemical reaction parameter, Schmidt number, thermal Grashof number, mass Grashof number and time. It is observed that the velocity increases with decreasing radiation parameter or chemical reaction parameter.

1 table, 3 illus, 9 ref

023041   Murty M S N;Apparao B V (Appl Math Dep, Acharya Nagarjuna Univ Post Graduate Centre, Nuzvid-521 201) : Two-point boundary value problems for third order non-linear differential equations containing parameters. Bull Calcutta Mathl Soc 2006, 98(6), 497-506.

Paper presents criteria for the existence, uniqueness and continuous dependence on parameter of solutions of a class of non-linear two-point Boundary Value problems associated with third order differential equations. The approach to this problem is based on converting the boundary value problem as an integral equation by means of a Green's function and using a suitable version of Banach fixed point theorem.

7 ref

023040   Murthy S;Hemantha Kumar K G (NO, , ) : Prediction of era of epigraphical documents based on texture features-a statistical approach. J Analysis Computn 2006, 2(1), 1-8.

Image texture as a function of the spatial variation in pixel intensities is useful in categorizing images. This paper describes few textural features extracted based on co occurrence matrix which are used to predict the period of the given epigraphical script. These texture features are the functions of distance and angle. For the prediction of the period, the angularly dependent features are not used instead their averages are used which are invariant to rotation. The texture features for the various test characters are extracted and stored as a knowledge base. The texture features of the given epigraphical script are computed and compared with the table containing information about texture parameters versus the period and then the period of the given epigaraphical script is predicted.

9 tables, 1 illus, 13 ref

023039   Maurer B;Stuckrad J (Fakultat fur Mathematik und Informatik, Leipzig Univ, Augustus Platz 10/11, D-04109 Leipzig, Germany, Email: bmp@gmx.de) : Reducing system of parameters and the Cohen-Macaulay property. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 159-65.

Let R be a local ring and let (x₁,...,x_r) be part of a system of parameters of a finitely generated R-module M, where r<60> dim_r M. It has been shown that if (y₁...,y_r)is part of a reducing system of parameters of M with M=(x1,...,x_r)M then (x₁,..., x_r) is already reducing. Moreover, there is such a part of a reducing system of parameters of M iff for all primes P ∈ Supp M ∩ V_R (x₁,..., x_r) with dim_R R/P = dim_R M - r the localization M_p of M at P is an r-dimensional Cohen-Macaulay module over R_p. Furthermore, will show that M is a Cohen-Macaulay module iff y_d is a non zero divisor on M/(y₁,..., y_d-1)M, where (y₁,..., y_d) is a reducing system of parameters of M (d := dim_R, M).

3 ref

023038   Manjunath Aradhya V N;Hemantha Kumar G; Shivakumara P (Dep of Studies in Computer Sci, Mysore Univ, Mysore-570 006) : Skew detection technique for binary document images based on mathematical morphology and hough transform. J Analysis Computn 2006, 2(1), 85-96.

When a document is fed to a scanner either mechanically or by a human operator for digitization, it suffers from some degrees of skew or tilt. Skew angle detection is an important component of any Optical Character Recognition (OCR) and Document Analysis System. In this paper Authors present a novel skew estimation technique for document images. The method considers, some selected characters of the text which may be subjected mathematical morphology and Hough transform to estimate skew angle accurately. Experimental results are presented and compared with results on several other skew detection methods.

4 tables, 8 illus, 16 ref

023037   Manjaiah D H;Subramanya K N;Sharma S C (Dep of Post graduate Studies & Resin Computer Sci, Mangalore Univ, mangalore-574 199) : Graphical analysis of different kanban strategies. J Analysis Computn 2006, 2(1), 51-66.

In the manufacturing companies hottest competitive weapon is kanban, which will help in all aspects to reduce both work-in-process (WIP) & finished good inventory. Also eliminate non-value-added activities such as material handling and paperwork. It can help in an industry to increase responsiveness and on-time delivery to customers. Kanban is one of the primary tools for a just-in-time (JIT) system. More and more manufacturing companies have implemented new material logistics systems using Kanbans. This has enabled companies to not only simplify their operations, but also reduce inventory while improving to customers. It goes without saying that making a kanban system effective requires detailed contracts between customers and suppliers. These contracts include agreements on details such as quantities of parts represented by a kanban signal, frequency of signals, lead times, delivery conditions and points of contact. In this context work carried on different methods of kanban provide an effective resultant scope, which positively inspires and motivate the efficient operations in the manufacturing industry.

6 illus, 8 ref

023036   Mali P C (Math of Dep, Jadavpur Univ, Kolkata-700 032, Email: prakash19592000@yahoo.co.uk) : A model-based mopdification of the walsh-hadamard transform image coding. Bull Calcutta Mathl Soc 2006, 98(6), 531-46.

The Walsh-Hadamard transform (WHT) is modified to obtain a new transform for a first-order stationary Markov process (FOSMP) with high correlation. It is performancewise superior to the slant transform (ST) with the same computing complexity for the FOSMP. This modified version is obtained from the WHT via some rotation matrices. It should be noted that the modified transform is still performancewise inferior to the discrete cosine transform (DCT) excepting that they are equivalent when the order of the transform matrix is equal to 4. However, computationally, the DCT requires much higher time than that of the modified transform.

3 tables, 11 ref

023035   Mahata G C;Goswami A (Matematics Dep, Indian Institute of Technology, Kharagpur-721 302, Email: goswami@maths.iitkgp.ernet.in) : Production lot-size model with fuzzy production rate and fuzzy demand rate for deteriorating item under permissible delay in payments. Opsearch 2006, 43(4), 358-75.

Fuzzy production lot-size inventory model with a permissible delay in payments is developed by assuming that the demand rate and the production-rate are triangular fuzzy numbers and the items deteriorate at a constant rate θ. The expressions for the average inventory cost both in the crisp sense and fuzzy sense are derived. The fuzzy model is defuzzified using fuzzy extension principle and its optimization with respect to the decision variables is carried out. The computation procedure is explained with help of a numerical example. Sensitivity of the optimal solution to changes in parameter values is examined.

1 table, 19 ref

023034   Mahadeva Naika M S;Maheshkumar M C;Sushan Bairy K (Math Dep, Central College Campus, Bangalore Univ, Bangalore-560 001) : On some modular equations of degree three found in Ramanujan's second notebook. J Analysis Computn 2006, 2(1), 45-9.

In his second notebook, Ramanujan has recorded several modular equations of degree 3. In this paper, Authors establish Ramanujan's modular equations of degree 3 by using a transformation formula. Also established some new modular equations of degree 3 in the classical theory.

4 ref

023033   Kulli V R;Muddebihal M H (Mathematics Dep, Gulbarga Univ, Gulbarga-585 106) : Lict graph and litact graph of a graph. J Analysis Computn 2006, 2(1), 33-43.

Authors introduce the concepts of the lict graph and the litact graph of a graph. Obtained properties of these graphs. Also present characterizations of graphs whose lict graphs and litact graphs are planar, outerplanar and minimally nonouterplanar. In addition, a necessary and sufficient condition was also presented for graphs whose lict graphs and litact graphs have crossing number one.

3 illus, 4 ref

023032   Khosravi A;Khosravi B (Faculty of Mathematical Sciences and Computer Engineering, Teacher Education Univ, 599 Taleghani Ave, Tehran-156 14, Iran, Email: khosravi_amir@yahoo.com) : Frames and bases in tensor products of Hilbert spaces and Hilbert C - modules. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 1-12.

Tensor product of Hilbert C*-modules and Hilbert spaces has been studied. It has been shown that if E is a Hilbert A-module and F is a Hilbert B-module, then tensor product of frames (orthonormal bases) for E and F produce frames (orthonormal bases) for Hilbert A ⊗ B-module E ⊗ F, and give more results. For Hilbert spaces H and K. Tensor product of frames of subspaces for H and K, tensor product of resolutions of the identities of H and K, and tensor product of frame representations for H and K have been studied.

19 ref

023031   Kamath R (Systat Software Asia-Pacific Ltd., , Shankara Narayana Building, Block-I,4th, Floor, M. G. Road, Bangalore-560 001, Email: rajashree@systat.com) : Periodic review inventory model with emergency orders using Bayesian demand estimation. Opsearch 2006, 43(4), 389-403.

Authors consider a periodic review inventory model, with the option of placing regular orders at review time points, and emergency orders in continuous time. Demand uncertainty is modeled by considering the mean demand to be a random variable, and the resulting demand distribution is estimated using the Bayesian approach. The optimal inventory policy for regular as well as emergency ordering, is evaluated. A profit comparison is done to observe the improvement in profit by placing emergency orders. Also, a sensitivity analysis of the estimated model is performed to test the sensitivity of the optimal solution to the demand estimation.

3 tables, 13 ref

023030   Hossain N F;Banu H;Halder A (Math Dep, Bangladesh Univ of Engng & Technol, Dhaka, Bangladesh) : Effect of spin-orbit coupling on the zeros of the scattering amplitude. Bull Calcutta Mathl Soc 2006, 98(6), 507-16.

The formulae for zeros of the scattering amplitude expressed as a complex polynomial in y = eⁱθ are derived for a spin-dependent square-well potential. The four zero trajectories closest to the origin are then obtained and studied in the complex momentum transfer plane for a variety of potential strengths. An analysis of the zero trajectories shows that in the 140 Mev to 550 Mev range of energy, inclusion of spin does not contribute appreciably whereas in the high energy range it is essential to take account of spin in the model.

6 illus, 7 ref

023029   Haldar K (Physics and Applied Mathematics Unit Dep, Indian Statistical Institute, 203, B.T. Road, Kolkata-700 108) : Application of modified decomposition method to laplace equation in two dimensional polar co-ordinates. Bull Calcutta Mathl Soc 2006, 98(6), 571-82.

Present paper represents the development of decomposition method. This method is divided into four classes. These are regular decomposition method, double decomposition method, modified decomposition method and asymptotic decomposition method. Out of these four methods, author have given a brief description of the modified decomposition method for Laplace equation. For clear illustration, considered some physical problems for circular disc and also for circular annulus. These problems are quoted from Wazwaz (2002) and have been solved by modified decomposition method. The closed form solutions of all these problems are easily obtained by this method.

6 ref

023028   Guillen B L;Regan D O;Saadati R (De Estadistica y Matematica Aplicada Dep, De Almeria Univ, 04120 Almeria 04120, Spain, Email: blafuerz@ul.es) : Quotient probabilistic normed spaces and completeness results. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 61-70.

Concept of quotient in PN spaces has been described with some examples. Proved some theorems with regard to the completeness of a quotient.

9 ref

023027   Gowri Navada K (Mathematics Dep, Periyar Univ, Salem-636 011, Email: gnavada@yahoo.com) : Some further remarks on good sets. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 197-203.

It has been shown that in n-fold cartesian product, n ≥ 4, a related component need not be a full component. Also proved that when n ≥ 4, uniform boundedness of lengths of geodesics is not a necessary condition for boundedness of solutions of (1) for bounded function f.

5 ref

023026   Gor R;Shah N H (Mathematics Dep, Smt. D.J. Shah Parivar Science College, Mithikui, Dholka-387 810, Email: ravigor@hotmail.com) : EOQ model for deteriorating items with price dependent demand and permissible delay in payments under inflation. Opsearch 2006, 43(4), 376-88.

Inventory model in which the supplier provides the purchaser a permissible delay of payments is developed when units in inventory are subject to constant rate of deterioration and demand is selling price dependent. Shortages are not allowed and effect of the inflation rate is considered. The optimal solution is characterized to optimize the net profit. An easy-to-use algorithm is given to find the optimal selling price, the optimal order quantity and replenishment cycle time to maximize the net profit. At the end, a numerical example is given to illustrate the theoretical results and sensitivity analysis of parameters on the optimal solutions is carried out.

3 tables, 26 ref

023025   Golet I (Mathematics Dep, Politehnica Univ, 300004 Timisoara, Romania, Email: io-goro@yahoo.co.uk) : Approximation of random signals in probabilistic normed spaces. J Approximation Theor Applic 2006, 2(1), 57-67.

Considers random signals as functions with values in a probabilistic ϕ-normed space. So, the ramework of probabilistic normed spaces give us the possibility to study some propeties of random signals. The main results of the paper are the approximation theorems for random signals. States, by means of probabilistic analysis, a new point of view in the study of random signals.

19 ref

023024   Ghaffari A (Mathematics Dep, Semnan Univ, Semnan, Iran, Email: ghaffari1380@yahoo.com) : Ergodic theory of amenable semigroup actions. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 177-83.

Stated and prove the mean ergodic theorem for amenable semigroup algebras.

20 ref

023023   Garg M;Rao A (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: gargmridula@gmail.com) : Fractional extensions of some boundary value problems in oil strata. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 267-81.

Solved three boundary value problems related to the temperature field in oil strata - the fractional extensions of the incomplete lumped formulation and lumped formulation in the linear case and the fractional generalization of the incomplete lumped formulation in the radial case. By using the Caputo differintegral operator and the Laplace transform, the solutions are obtained in integral forms where the integrand is expressed in terms of the convolution of some auxiliary functions of Wright function type. A generalization of the Laplace transform convolution theorem, known as Efros' theorem is widely used.

11 ref

023022   Faiziev V A;Sahoo P K (Mathematics Dep, Louisville Univ, Louisville, KY-402 92, USA, Email: vfaiz@tvcom.ru) : On the stability of Jensen's functional equation on groups. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 31-48.

Established the stability of Jensen's functional equation on some classes of groups. It has been proved that Jensen equation is stable on noncommutative groups such as metabelian groups and T(2, K), where K is an arbitrary commutative field with characteristic different from two. It has been proved that any group A can be embedded into some group G such that the Jensen functional equation is stable on G.

22 ref

023021   Dutt P K;Kishore Kumar N;Upadhyay C S (Mathematics Dep, Indian Institute of Technology Kanpur, Kanpur-208 016) : Nonconforming h-p spectral element methods for elliptic problems. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 109-145.

It has been shown that a modified version of the h-p spectral element method proposed in [6,7,13,14] can be used to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood of the corners. With this mesh authors seek a solution which minimizes the sum of a weighted squared norm of the residuals in the partial differential equation and the squared norm of the residuals in the boundary conditions in fractional Sobolev spaces and enforce continuity by adding a term which measures the jump in the function and its derivatives at inter-element boundaries, in fractional Sobolev norms, to the functional being minimized. In the neighbourhood of the corners, modified polar coordinates are used and a global coordinate system elsewhere. A stability estimate is derived for the functional which is minimized based on the regularity estimate in [2]. Examined how to parallelize the method and show that the set of common boundary values consists of the values of the function at the corners of the polygonal domain. The method is faster than that proposed in [6,7,14] and the h-p finite element method and stronger error estimates are obtained.

14 ref

023020   Dhayal S S;Chaudhary R C (Mathematics Dep, Univ of Rajasthan, Jaipur-302 004, Email: rcchaudhary@rediffmail.com) : Three dimensional flow and heat transfer of a non-newtonian fluid along a porous horizontal plate. Bull Calcutta Mathl Soc 2006, 98(5), 401-16.

An analysis has been carried out to study the flow of a non-Newtonian fluid along an infinite porous horizontal plate with transverse sinusoidal suction in the presence of viscous dissipative heat. The effect of the non-Newtonian fluid parameters on the flow variable has been discussed numerically and illustrated by graphs. The analytical solutions are found for velocity field and temperature distribution. The expressions for shear stress and rate of heat transfer are obtained and examined in detail with the help of figures.

1 illus, 4 ref

023019   Demidenko G V (NO, Sobolev Institute of Mathematics, Pr. Koptyuga 4 Novosibirsk-630 090 Russia, Email: demidenk@math.nsc.ru) : On solvability of boundary value problems for quasi-elliptic systems in R<. J Analysis Applic 2006, 4(1), 1-11.

Authors consider boundary value problems in Rⁿ₊ for a class of quasi-elliptic systems C(D_x)U = F(x). The symbol of the differential operator C(D_x) is homogeneous with respect to a vector α. The Lopatinskii condition for the problems holds. We prove unique solvability in the Sobolev spaces W^l_p(Rⁿ₊) under restriction |α| <62> p'. This restriction is essential.

7 ref

023018   Dadashzadehi R;Nimse S B (NO, Faculty Member of Azad Univ of Boeb, Iran, Email: r-dadashzadh@yahoo.com) : On stability in multiobjective linlear programming problems with fuzzy parameters. J Approximation Theor Applic 2006, 2(1), 49-56.

Investigates the stability of solution in fuzzy multiobjective linear programming with symmertrical trapezoid fuzzy numbers with respect to change of fuzzy parameters.

10 ref

023017   Dadashzadeh R;Nimse S B (NO, The Faculty Member of Azad Univ of Bonab, Iran, Email: r-dadashzadh@yahoo.com) : Linear programming with fuzzy resources numbers. J Approximation Theor Applic 2006, 2(1), 17-24.

Investigates the linear programming problem with fuzzy resources numbers, uses the fuzzy linear equation systems theory and non-negative matrix theory, proposes a new approach to solve the fuzzy linear programming problems.

12 ref

023016   Dadashzadeh R;Nimse S B (Mathematics Dep, Bonab Islamic Azad Univ, Bonab, Iran, Email: r-dadashzadh@yahoo.com) : Fuzzy linear programming problems with linear membership functions. J Analysis Computn 2006, 2(1), 97-110.

Authors interpret fuzzy linear programming (FLP) problems with linear membership functions, Authors propose on three kinds of fuzzy linear programming problems: linear programming problems with fuzzy technological coefficients and fuzzy coefficients in objective function, linear programming problems with all fuzzy coefficients, and linear programming problems with fuzzy right-hand-side numbers and fuzzy coefficients in objective function. The symmetric method of Bellman and Zadeh is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are nonlinear and even non-convex in general. For solving these problems "modified subgradient method" suggested by Gasimov was used.

9 ref

023015   Cieplinski K (NO, Institute of Mathematics, Pedagogical Univ, Podchorazych 2 30-084 Krakow Poland, Email: kc@ap.krakow.pl) : On properties of monotone mappings of the circle. J Analysis Applic 2006, 4(3), 169-78.

Relation between monotone and continuous mappings of the unit circle S¹ and their lifts is studied. Furthermore, it has been shown that the notion of lift can be introduced for strictly monotone functions of S¹ as well as given a sufficient condition for the continuity of monotone mappings of the circle.

16 ref

023014   Chu J;Regan D O;Meirong Zhang (Mathematical Sciences Dep, Tsinghua Univ, Beijing-100 084, China) : Positive solutions and eigenvalue intervals for nonlinear systems. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 85-95.

(p(t)u'_i (t)))'+λh_i(t)g_i (u)=0, 0 <60>t<60>1, i=1,2....,n. The proof is based on a well-known fixed point theorem in cones.re u= (u₁,....u_n) and fⁱ, i=1,2..., n are continuous and nonnegative functions, p(t), q(t):[0,1]→ (0, ∞) are continuous functions. Moreover, we characterize the eigenvalue intervals for (q(t)φ

22 ref

023013   Chaudhuri P K;Ray S (Appl Math Dep, Univ Coll of Sci, 92, A.P.C. Road, Kolkata-700 009, Email: pkcha@vsnl.net) : Thermal stress in a nonhomogeneous transversely isotropic medium containing a penny-shaped crack. Bull Calcutta Mathl Soc 2006, 98(6), 547-70.

Thermoelastic problem in a nonhomogeneous transversely isotropic medium containing a pennyªshaped crack has been discussed. Elastic coefficients, the coefficient of thermal conductivity and the thermal expansion coefficients are assumed to vary along a particular direction. Integral transform technique has been applied and the solution to the problem has been reduced to that of a Fredholm integral equation, which may be resolved numerically. Finally, various comparative results have been shown graphically.

4 illus, 1 table, 37 ref

023012   Cetinkaya A;Ozalp N (Mathematics Dep, Faculty of Arts and Sciences, Ahi Evran Univ, 40100 Kirsehir, Turkey, Email: caysegul@gazi.edu.tr) : Solutions for a class of iterated singular equations. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 259-65.

Some fundamental solutions of radial type for a class of iterated elliptic singular equations including the iterated Euler equation are given.

6 ref

023011   Cai G H;Wu H (Mathematics Dep, Zhejiang Gongshang Univ, Hangzhou-310 035, People's Republic China, Email: cghju@163.com) : Law of iterated logarithm for NA sequences with non-identical distributions. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 213-18.

Based on a law of the iterated logarithm for independent random variables sequences, an iterated logarithm theorem for NA sequences with non-identical distributions is obtained. The proof is based on a Kolmogrov-type exponential inequality.

12 ref

023010   Bujurke N M;Salimath C S;Shiralashetti S C (Mathematics Dep, Karnatak Univ, Dharwad-580 006) : Application of single term HAAR wavelet series solution to non-linear stiff differential equations arising in chemical reactions. J Approximation Theor Applic 2006, 2(1), 25-42.

Single Term Haar Wavelet Series (STHWS) approach to the solution of nonlinear stiff differential equations arising in Chemical reactions. The properties of single term Haar wavelet series are given. The method of implementation is discussed. Numerical solutions of some model equations are investigated for their stiffness and stability and numerical solutions are obtained to demonstrate the suitability and applicability of the method. The results in the form of bloci-pulse and discrete solutions are given, for non-linear stiff systems. As compared with the TR BDF2 method of Shampine and Gill's metheod. The STHWS turns out to be more efective in its ability to solve systems ranging from mildly to highly stiff equations. The method works even when higher order numerical methods for stiff systems fail to give solutions. The novel feature of the scheme is development of an algorithm exclusively for solving systems of non-linear algebraic equations resulting from STHWS. It reduces the computational effort enormously, at the same time, meeting accuracy requirements. One can see that the STHWS method takes substantially fewer steps and is about three times faster than Gill's method.

3 illus, 3 tables, 17 ref

023009   Breaz D;Owa S (Mathematics Dep, "1 Decembrie 1918" Univ Alba Iulia, Romania, Email: dbreaz@uab.ro) : Convexity of an integral operator for certain analytic functions. J Approximation Theor Applic 2006, 2(1), 1-3.

Analytic functions f_j(z) in the open unit disk U, an integral operator F_n(z) is introduced. Object of the paper is to consider the convexity of the integral operator F_n(z).

1 ref

023008   Boutaghou A;Nouri F Z (De Mathematiques Dep, Universite De Jijel, B.P./98, Ouled Aissa, 18000, Jijel Algeria, Email: boutaghou_a@yahoo.com) : On finite spectral method for axisymmetric elliptic problem. J Analysis Applic 2006, 4(3), 149-68.

Spectral element method is described which enables Elliptic problem defined in regular finite rectangle Ω₂ to be solved as a set of ordinary differential equations, this is achieved by reducing the problem of three spaces variables to two spaces variables using the axisymmetric case, and reducing the latter to one space variable by using the orthogonal matrix.

4 illus, 8 ref

023007   Bhati S M;Pujar S S (Mathematics of Dep, B.R.E.S'S Coll of Engng, Kopargaon-423 603, Email: satishbhatil@rediffmail.com) : Theorem of isometry of Sasakian manifolds to sphere. Bull Calcutta Mathl Soc 2006, 98(5), 429-42.

Considers a closed Sasakian manifold of dimension n <62> 2 with constant scalar curvature R of M, and admitting one parameter group of conformal transformation X in M. Deduces an integral formula and study the application of the integral formula. Proves a Theorem which describes the isometry of Sasakian manifolds to spheres. Many special, cases in terms of corollaries to indicate the geometrical significance of the Theorem have been studied.

10 ref

023006   Bhat V K;Raina R (School of Applied Physics and Mathematics, Shri Mata Vaishno Devi Univ, P/o Kakryal, Udhampur, J & K-182 121, Email: vijaykumarbhat2000@yahoo.com) : Dimension theory and its analogue in algebra. Int Rev pure appl Math 2006, 2(1), 49-52.

ref

023005   Begehr H;Harutjunjan G (NO, Math Inst, FU Berlin, Arnimallee 3, D-14195, Berlin Germany, Email: begehr@math.fu_berlin.de) : Robin boundary value problem for the Poisson equation. J Analysis Applic 2006, 4(3), 201-13.

Aim of this paper is to give explicit representations for solutions of the Robin boundary value problem for the Poisson equation. Also investigates the corresponding higher order operators.

2 ref

023004   Basavanagoud B;Mathad V N (Mathematics Dep, Karnatak Univ, Dharwad-580 003, Email: bgouder1@yahoo.co.in) : Characterization of minimally nonplanar mass graphs. J Analysis Computn 2006, 2(1), 23-31.

Authors deduce a necessary and sufficient condition for graphs whose mass graphs have minimally nonplanar. Also obtained necessary and sufficient condition for mass graphs to have minimally nonplanar in terms of forbidden subgraphs.

6 illus, 5 ref

023003   Barua R;Maitra A (Stat-Math Div, Indian Statistical Institute, Kolkata-700 108) : Borel hierarchies in infinite products of Polish spaces. Proc Indian Acad Sci-Mathl Sci 2007, 117(2), 205-11.

Let H be a product of countably infinite number of copies of an uncountable Polish space X. Let ∑ξ (∑ξ) be the class of Borel sets of additive class ξ for the product of copies of the discrete topology on X (the Polish topology on X), and let β = ∪ξ<60>ω ₁ ∑ξ. Proved in the Levy-Solovay model that ∑ξ = ∑ξ ∩ β for 1 ≤ ξ <60> ω₁.

6 ref

023002   Banerji P K;Loonker D (Mathematics of Dep, Faculty of Science, J.N.V. Univ, Jodhpur-342 005, Email: banerjipk@yahoo.com) : Laplace transorm for integrable boehmians. Bull Calcutta Mathl Soc 2006, 98(5), 465-70.

Using the relation between the Laplace and the Fourier transforms, the Laplace transform and their properties for integrable Bochmians are investigated and an inversion theorem is proved.

5 ref

023001   Bagdatli H;Soyucok Z (Mathematics Dep, Marmara Univ, Istanbul, Turkey) : On the problem of isometry of a hypersurface preserving mean curvature. Proc Indian Acad Sci-Mathl Sci 2007, 117(1), 49-59.

Problem of determining the Bonnet hypersurfaces in Rⁿ⁺¹, for n <62> 1, is studied here. These hypersurfaces are by definition those that can be isometrically mapped to another hypersurface or to itself (as locus) by at least one nontrivial isometry preserving the mean curvature. The other hypersurface and/or (the locus of) itself is called Bonnet associate of the initial hypersurface. The orthogonal net which is called A-net is special and very important for the study and it is described on a hypersurface. It is proved that, non-minimal hypersur-face in Rⁿ⁺¹ with no umbilical points is a Bonnet hypersurface if and only if it has an A-net.

16 ref

023000   Ayoub N;Rahman Q I (De Mathematiques et de statistique Dep, De montreal Univ, C.P. 6128, succursale Centre-ville montreal, Quebec H3C 3J7 Canada, Email: ayoubn@hotmail.com) : Lp inequalities for polynomials and trigonometric polynomials. J Analysis Applic 2006, 4(1), 13-49.

Purpose of this article is to elaborate upon the contents of Ro-gosinski's paper, and also present some applications illustrating the scope of his findings.

16 ref

022999   Ahmad K;Abdullah (Mathematics Dep, , Jamia Millia Islamia, New Delhi-110 025, Email: khlil_ahmad49@yahoo.com) : Certain results on wavelet packets. J Analysis Applic 2006, 4(3), 179-99.

Deals with certain results on wavelet packets. These results are useful in the study of characterization of Lebesgue spaces L^p (R), Hardy space H¹(R) and Sobolev spaces L^p,s (R).

22 ref

022998   Aggarwal R;Taqvi Z A;Ahmad I (Mathematics Dep, , Jamia Millia Islamia, New Delhi-110 025) : Non-linear stability of L₄ in the restricted three body problem for radiated axes symmetric primaries with resonances. Bull Astr Soc India 2006, 34(4), 327-56.

Investigates the non-linear stability of the triangular libration point L₄ of the Restricted three body problem under the presence or the third and fourth order resonances, when the bigger primary is an oblate body and the smaller a triaxial body and both are source of radiation. It is found through Markeev's theorem that L₄ is always unstable in the third order resonance case and stable or unstable in the fourth order resonance case depending upon the values of the parameters A₁, A'₁, A'₂, P and P', where A₁, A'₁ and A'₂, depends upon the lengths of the semi axes of the primaries and P and P' are the radiation parameters.

15 ref

022997   Abdou M A;Khamis A K (Mathematics of Dep, Faculty of Education, Alexandria Univ, Egypt, Email: abdella-77@yahoo.com ) : Fredholm-Volterra integral equation with Carleman kernel. Bull Calcutta Mathl Soc 2006, 98(5), 471-80.

Solution of Fredholm-Volterra integral equation of the first kind with Carleman kernel has been established. The kernel of Fredholm integral term is measured with respect to position and belongs to the class C([<87><60> ∞. The general solution of the integral equation is discussed in L₂(Ω) x C[0,T].

13 ref

022108   Zimba K (School of Computational & Mathematical Sciences, University of Limpopo (Turflop Campus), Sovenga 0727, Polokwane, South Africa) : Sum of multi-nomial coefficient. Far East J mathl Sci 2006, 21(3), 355-61.

Combinatorial reasoning underlies all analyses of computer systems. It also plays a similar role in discrete operations research problems and in finite probability. Therefore, in these fields and not excluding pure mathematics, it would not be unusual to meet the following binomial result: Let n be a positive integer and k, 0 ≤ k ≤ n, be an integer. Then ∑_{k=0(mod 2)}(n/k)=2_n-1 where (n/k) is a binomial coefficient. The above result may be proved by using the binomial theorem. In this paper we give a result which generalizes (1). This general result could be derived algebraically, however here author gives a combinatorial proof.

7 ref

022107   Zhou Z;Shi Y (Mathematics Dep, Guangdon Ocean Univ, Zhanjiang, Guangdong-524 048 P R China) : Periodic solutions of a class of nonautonomous second-order systems under sub-linear condition. Far East J mathl Sci 2006, 21(3), 373-8.

Existence theorems are obtained for periodic solutions of a class of nonautonomous second-order systems with a potential which is a sub-linear function by using the saddle point theorem in Critical Point Theory.

9 ref

022106   Yadav B M;Jha K N (Mathematics Dep, L N Mithila Univ, Darbhanga-846 004) : On congruence lattice representations and its distributivity. Math Educ 2006, 40(1), 68-75.

Authors main aim here is to investigate the resemblance between "yeast graph" and con-gruence lattice representations of algebraic lattices, It is shown that all strongly representable lattices of all equivalence algebras which is isomorphic to L is a congruence lattice.

5 ref