019508   Chandrasekhar P;Natarajan R;Yadavalli V S S; Malada A (Statist Dep, Loyola Coll, Chennai-600 034) : An n unit system operating in a random environment. Opsearch 2005, 42(3), 280-7.

An n unit system operating in a random environment is considered. The environment determines the number of units required for the satisfactory performance of the system. Assuming that a unit in standby can fail and that the environment is described by a Markov Process, we obtain expressions for (1) the distribution and the moments of the time to the first disappointment and (2) the expected number of disappointments over an arbitrary interval (o,t).

6 ref

019507   Brunel E;Comte F (Mathematiques Appliquees - Paris 5 UMR CNRS 8145, Universite Rene Descartes, 45 Rue Des Saints-Peres 75270 Paris Cedex 06, France) : Penalized contrast estimation of density and hazard rate with censored data. Sankhya 2005, 67(3), 441-75.

Considers projection estimator methods for the estimation of density and hazard rate functions based on randomly right-censored data. Two types of adaptive hazard estimators are considered. The first one is a two-step estimator defined as the ratio of a penzlized contrast estimator of the subdensity and of the empirical survival function of the data. The second estimator is built by using another penalized projection contrast. Both estimators are proved to achieve automatically the standard optimal rate associated with the unknown regularity of the hazard function, but with some restriction for the "ratio" estimator. In the examples studied, the ratio estimator seems to be slightly better than the direct estimator.

3 illus, 2 tables, 28 ref

019506   Bhavani V;Sundara Murthy M (Math Dep, S.V.U. Coll of Engng, Tirupati-517 502) : Time-dependent travelling salesman problem. Opsearch 2005, 42(3), 199-227.

Time-Dependent Travelling Sales Man Problem is a 3-dimensional travelling sales man problem where the cost matrix C (i, j, k) is the cost of the sales man visiting from city i to city j at time (facility) k. The cost matrix C (i, j, k) (i, j, k = 1,2, ---n) is given. The problem is to find a tour for n cities for the travelling sales man with the restriction that he visits only one pair of cities at each point of time (facility), i.e. at a particular time he has to travel from one city to another city only. The objective is to find the feasible tour to the sales man such that the total cost is minimum. For this problem a computer programme is developed for the algorithm and is tested. It is observed that it takes less time for solving fairly higher dimension problems also. For tis problem the definition, notation and algorithm are illustrated with the help of a numerical example.

8 tables, 14 ref

019505   Bathul S (JNTU Coll of Engng, , Hyderabad-500 072) : Heat transfer in three dimensional viscous flow over a porous plate moving with harmonic disturbances. Bull pure appl Sci-Sect E 2005, 24(1), 69-97.

The effect of periodic suction velocity transverse to the main direction of motion of the plate moving with velocity U along with weak vibrations U₀ Cos nt, U₀ Sin nt along and perpendicular to the main direction of motion. The effect of these weak disturbances on the motion of the plate has been considered in the presence of cross suction velocity perpendicular to the main direction of flow. The plante as whole moves with a velocity whose component along and perpendicular to the main direction of motion are given by U + U₀₀ Sin nt. The results are valid for fairly large fluctuations in plate velocity.

6 illus, 4 ref

019504   Banerji P K;Loonker D;Al-Omari S K (Math Dep Fac of Sci, JNV Univ, Jodhipur-342 005, Email: banerjipk@yahoo.com) : Multipliers of a distributional hankel-type and schwartz-hankel integral transformations. J Indian Acad Math 2005, 27(1), 157-65.

Function space H_μυ being formed by infinitely differentiable functions on an interval (0, ∞), authors assigened a topology generated by certain family of seminorms which converts it to Hausdorff locally convex topological linear space and further its dual H'_{μ, υ} is defined. Having enumerated the properties of Hμ, υ and H'_{μ, υ} multipliers of H_{μ, υ} space are investigated along with that of H' _{μ, υ}. It is interesting to observe that the results are extended to Schwartz-Hankel transformation.

3 ref

019503   Ahmed S (Math Dep, Govt Degree Coll, Rajouri, Jammu & Kashmir) : On group integer topology. Bull pure appl Sci-Sect E 2005, 24(1), 153-7.

The concept of Group Interger Topology has been introduced and its various basic properties have been studied.

2 ref

019502   Acharyya S;Bagchi A (Vivekananda Coll, , Thakurpukur, Calcutta-700 063) : Constraint satisfaction methods for solving the staff transfer problem. Opsearch 2005, 42(3), 179-98.

The Staff Transfer Problem is concerned with the assignment of transfer postings to employees in large organizations. Staff transfers are an important issue in Human Resource Management in countries like India and China that have many large public sector undertakings. The Staff Transfer Problem can be viewed as a Constraint Satisfaction Problem, and methods such as Simulated Annealing, Genetic Algorithms, Satisfiability (GSAT), and Conflict Directed Backjumping can all be employed to solve randomly generated problem instances. Computer experimetns indicate that Simulated Annealing is the best method of solution. GSAT with a tabu list yields solutions of good quality but is unable to solve lage instances. Genetic Algorithms is also good, but it takes much more time than Simulated Annealing. Conflict Directed Backjumping, a deterministic search technique, is markedly inferior to the other methods. Thus for solving the Staff Transfer Problem, randomized approaches appear to be superior to deterministic ones.

16 ref

018460   Zonglao Z (Math Dep, Wenzhou Norm Coll, Wenzhou, Zhejiang 325 000, People's Republic of China, Email: zonglao@sohu.com) : Estimates and nonexistence of solutions of the scalar curvature equation on noncompact manifolds. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 309-18.

The conformal scalar curvature equation on complete noncompact Riemannian manifold of nonpositive curvature has been studied. Some estimates and properties of supersolutions of the scalar curvature equation have been derived and some nonexistence results have been obtained for complete solutions of scalar curvature equations.

9 ref

018459   Yang Q X (Math Dep, Wuhan Univ, 430 072 Hubei, China, Email: yangqu99@public.wh.hb.cn) : Wavelet characterization of Hormander symbol class S<. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 347-68.

The symbol in Hormander symbol class S^m_{ρ, ε} (m ∈ R, ρ,ε≥0) has been characterised by its wavelet coefficents. Consequently, the kernel distribution property for the symbol in th esymbol class S^m_ρ, ε (m ∈ R, ρ <60> 0, δ ≥0) which is more general than known results has analysed; for non-regular symbol operators, sharp L²-continuity which is better than Calderon and Caillancourt's result, and establish L^p (1 ≤ p ≤ ∞) continuit which is new and sharp have been established. The new idea is to analyse the symbol operators in phase space with relative wavelets, and to establish the kernel distribution property and the operator's continuity on the basis fo the wavelets coefficients in phase space.

19 ref

018458   Sridhara D (NO, Institut fur Mathematik Universitat Zurich, Zurich, Email: sridhara@math.unizh.ch) : Efficient coding of information : Huffman coding. Resonance 2006, 11(2), 51-73.

In his classic paper of 1948, Claude Shannon considered the problem of efficiently describing a source that outputs a sequence of symbols, each associated with a probabililty of occurrence, and provided the theoretical limits of achievable performance. In 1951, David Huffman presented a technique that attains this performance. Brief overview of some of their results has been discussed.

6 illus, 6 ref

018457   Siweya H J (Math Dep, Univ of Limpopo, Private Bag X1106, Sovenga, 0727, South Africa) : Localic spreads of the Banaschewski-Hong type. J appl mathl Analysis Applic 2005, 1(1), 47-53.

A (localic) spread is a frame homomorphism h : L → M between locally connected frames such that the collection {X ∈ M X is a component of h(u), for u ∈L} is a basis for M. How to construct a spread (h_* ° ƒ)^{° : L → N from a spread ƒ : L→ M beteen locally connected regular frames and a dense onto frame homomorphism h: N → M where M is locally connected relative to h has been shown.}

6 ref

018456   Singh S N;Tiwari R (Math and Statist Dep, Dr. Ram Manohar Lohia Avadh Univ, Faizabad-224 001) : Certain properties of M_n/G/1 queuing system relevant to inventory process. Natn Acad Sci Lett 2005, 28(7-8), 271-2.

Obtains certain properties of a single server queuing model under the assumption that there is a stationary optimal policy of the form: "Turn the server on when n customers are present and turn it off when the system is empty."

^ssc1 ref

018455   Shobha G;Sharma S C (NO, R.V. Coll of Engng, Mysore Road, Bangalore, Email: shobhatilak@rediffmail.com) : Prediction of census data base using artificial neural network. J appl mathl Analysis Applic 2005, 1(1), 77-85.

A technique for extracting, meaningful and economical knowledge from data source, which is derived from the current population survey conducted by the United States has been investigated. The survery is conducted based on demographic and economical aspects. The proposed model is a stand-alone application, which is used to predict the income of an individual based on his demographic and work related characteristics. The prediction module is developed using backpropogation multilayer perceptron (MLP) neural networks, a comparative study is also provided for prediction of income for different learning rates. The experimental results show that the designed system achieves an acceptable level of performance.

6 illus, 2 tables, 8 ref

018454   Santhosh G (Math Dep, T.K.M.M. Coll, Nangiarkulangara, Alappuzha-690 513) : Sequential coronations of graphs. Natn Acad Sci Lett 2005, 28(7-8), 269-70.

A labeling of a graph G is an assignment ƒ of labels to the vertices of G that induces for each edge xy a label depending on the vertex labels ƒ (x) and ƒ (y). Studies the sequential labeling of the graphs C_n odot P₄.

^ssc1 illus, 6 ref

018453   Ryoo C S;Kim T;Agarwal R P (Math Dep, Hannam Univ, Daejeon 306-791, Korea) : Restudying of the generalized Bernoulli polynomials. J appl mathl Analysis Applic 2005, 1(1), 35-45.

In the 21st century, the computing environment would make more and more rapid progress. Over the years, there has been increasing interest in solving mathematical problems with the aid of computers. Recently, the generalised Bernoulli polynomials are defined and studied by many authors. These generalised Bernoulli polynomials' structure has been investigated by using computer. The distribution and structure of the zeros of the generalised Bernoulli polynomials B_n,χ(X)for values of the index n have been described by using computer.

5 illus, 4 tables, 8 ref

018452   Ryoo C S (Math Dep, Hannam Univ, Daejeon 306-791, Korea, Email: ryoocs@hannam.ac.kr) : q-Bernoulli polynomials. J appl mathl Analysis Applic 2005, 1(1), 25-33.

Reports of the q-Bernoulli polynomials β_n,q^r (X) for values of the index n by using computer have been investigated.

3 illus, 2 tables, 11 ref

018451   Rosales J C (Departamento De Algeb, Universidad De Granada, E-18071 Granada, Spain, Email: jrosales@ugr.es) : Modular diophantine inequalities and some of their invariants. Indian J pure appl Math 2005, 36(8), 417-29.

Given two positive integers a and b, a mod b denotes the remainder of the division of a by b. A modular diophantine inequality is an expression of the form ax mod b ≤ x for some positive integers a and b. The set S (a, b) of integer solutions of this inequality is a numerical semigroup, that is, it is a subset of IN (IN denotes the set of nonnegative integers) closed under addition, 0 ε S (a, b) and its complement in IN has finitely many elements. It is well known that every numerical semigroup is finitely generalted, and thus there exist positive integers n₁,..., n_e such that S (a,b) = <6057>n₁..., N_e)<60> = {a₁n_n + ... + a₂n_e <157> a₁,..., a_e ε IN}. The paper continues the study of modular Diophantine inequalities an algorithmic procedure to compute a finite system of generators of S (a,b) has been described. The key result of this section associates to S (a,b) a full affine semigroup A (a, b) so that for any system of generators {(x₁, y₁),..., (x_e, y_e)} one has that {x₁ + y₁,..., x_e + y_e} is a system of generators of S (a, b). These facts together with the concept of modular permutation allows one to calculate a minimal system of generators for A (a, b) and consequently an upper bound for the embedding dimension of S (a, b).

11 ref

018450   Qi W J (NO, Zhangzhou Norm Univ, 363000, Fujian, People's Republic of China) : On p-modulus and p-capacity equalities in metric measure spaces. Indian J pure appl Math 2005, 36(8), 451-66.

Suppose X is a non-conpact metric measure space, E and F are two disjoint closed subsets of X and the boundary of E is also compact. By means of the Alexandroff compactification X of X some sufficient conditions for the equalities of p-modulus mod_p (E, F, X) and p-capacities with continuous or locally lipschitz test-functions have been obtained. The conclusions partly answer the open question on p-modulus ad p-capacity posed by Heinonen and Koskela.

15 ref

018449   Pilehrood K H;Pilehrood T H (NO, Inst for Stud in Theoretical Phys and Math (IPM), Tehran, Iran, Email: hessamik@ipm.in) : On the diophantine equation x<. Indian J pure appl Math 2005, 36(8), 431-9.

Let p be an old prime such that p - 3 is not a perfect square. It has been proved that the equation x² + 3 = py^p-1 has no solutions in rational numbers x, y. The proof depends on the unique factorization in the ring of algebraic integers of Q (√-3) and on certain congruence arguments. Furthermore, the equations x² + 3 = py^p-1/2 and x² + 3 = py⁶ in rationals x, y are also considered.

8 ref

018448   Padmavathamma;Chandrashekara B M;Raghavendra R (Stud in Math Dep, Univ of Mysore, Manasagangotri, Mysore-570 006) : Bijective proof of a partition theorem of M.V. Subbarao. J appl mathl Analysis Applic 2005, 1(1), 87-124.

The theorem "the number of partitions of n, in which each part appers two, three, or five times equals the number of partitions of n into parts congruent to 2, 3, 6, 9 or 10 modulo 12", was first stated by M.V. Subbarao. He gave an analytic proof. A bijective proof of this result has been given.

4 ref

018447   Ozturk M;Yalcin S (Math Dep Fac of Sci, Uludag Univ, Bursa 16059, Turkey, Email: ometin@uludag.edu.tr) : On harmonic bloch and normal functions. Indian J pure appl Math 2005, 36(8), 407-16.

Let ƒ=h+^-g be a harmonic univalent and sense preserving function of the unit disk, where h and g are analytic. Definition of a normal harmonic function is given. The necessary and sufficient conditions for ƒ=h + g^- to be Bloch or normal are determined. The sharp upper bound for <157>f(z)<157> is obtained whenever ƒ=h + g^- is a Bloch function. Sharp estimates for the normality order of ƒ when ƒ maps the unit disk onto the unity disk have been obtained.

9 ref

018446   Kulli V R;Janakiram B (Math Dep, Gulbarga Univ, Gulbarga-585 106) : Global nonsplit domination in graphs. Natn Acad Sci Lett 2005, 28(11-12), 389-92.

Let both G and G be connected graphs. A set D of vertices in a graph G=(V,E) is said to be a global nonsplit dominating set if D is a nonsplit dominating set of both G and G. The global nonsplit domination number γ_gns (G) of G is the minimum cardinality of a global nonsplit dominating set. Beside bounds on γ_gns, its relationship with other domination parameters is investigated. Also, some properties of global nonsplit dominating sets are given.

^ssc9 ref

018445   Kim M S;Kim T;Son J W (Math Dep, Kyungnam Univ, Masan 631-701, Korea, Email: mskim@kyungnam.ac.kr) : On Kummer-type congruences for the coefficients of p-adic formal series. J appl mathl Analysis Applic 2005, 1(1), 7-23.

Using p-adic valued measures and p-adic integrals on Zⁿ_p, some new congruences for the coefficients of the formal series of ƒ ∈θ [[T-1]] have been established. These generalise the Kummer-type congruences for modified higher order Bernoulli numbers which were originally given by Young and are closely related to the analogues of the Kummer type congruences for the ordinary Bernoulli numbers. Some examples and arithmetic properties have also been given.

19 ref

018444   Jung S M (Math Sect, Coll of Sci and Technol, Hong-1k University, Email: smjung@wow.hongik.ac.kr) : On the quadratic functional equation modulo a subgroup. Indian J pure appl Math 2005, 36(8), 441-50.

Let x be a topological vector space, let Y be a topological Abelian group, and let K be a discrete subgroup of Y. Assunme that a function ƒ : X → y satisfies (2) for all x, y ε X. It has been proved that if ƒ is continuous at the origin, then there exists a quadratic function allowed to deviate from ƒ(x) - ƒ(0) with K.

15 ref

018443   Jeyalakshmi P (Math Dep, Avinashilingam Deemed Univ, Coimbatore - 641 043) : Fuzzy separation axioms and finite approximations. Res Highlight 2006, 16(2), 79-83.

5 ref

018442   Jang L C;Kim Y H;Park D W;Ro Y S (Math and Computer Sci Dep, KonKuk Univ, Chungju 380-701, S. Korea) : Non archimedean integration associated with Euler numbers. J appl mathl Analysis Applic 2005, 1(1), 1-6.

Some properties of non-Archimedean integration which is defined by T. Kim, have been investigated. By using the results one can give an answer of the problems which is remained by I.-C. Huang and S-Y. Huang.

10 ref

018441   Jacob J;George S;Mathai A M (Statist Dep, St. Thomas Coll, Arunapuram P.O., Palai, Kottayam 686 574, Email: jjstc@sancharnet.in) : Some properties of complex matric-variate generalized dirichlet integrals. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 241-9.

Dirichlet integrals and the associated Dirichlet statistical densities are widely used in various areas. Generalizations of Dirichlet integrals and Dirichlet modesls to matrix-variate cases, when the matrices are real symmetric positive definite or hermitain positive definite, are availabale. Real scalar variables case of the Dirichlet models are generalized in various directions. One such generalization of thetype-2 or inverted Dirichlet is looked into. Matrix-variate analogue, when the matrices are hermitian positive definite, are worked out along with some properties which are mathematically and statistically interesting.

6 ref

018440   Gordji M E;Hosseiniun S A R (Math Dep, Fac of Sci Semnan Univ, Iran) : Ideal amenability of banach algebras on locally compact groups. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 319-25.

Studies ideal amenability of Banach algebras. Let A be a Banach algebra and let I be a closed tow-sided ideal in A, A is I-weakly amenable if H¹ (A, I) = {0}. Further, A is ideally amenable if A is I-weakly amenable for every closed two-sided ideal I in A. A continuous homomorphic image of an amenable Banach algebra is again amenable. It has been shown that for ideal amenability the homomorphism property for suitable direct summands is true similar to weak amenability and this result is applied for ideal amenability of Banach algebras on locally compact groups.

11 ref

018439   Gor R;Shah N H (Math Dep, Smt. D.J.Shah Parivar Sci Coll, Mithikui, Dholka-387810) : Lot-size model with variable deterioration rate under supplier credits. J appl mathl Analysis Applic 2005, 1(1), 65-76.

A mathematical model is developed to determine the optimal ordering policy for variable deterioration of the units in an inventory system under permissible delay in payments. Different scenarios of permissible delay in payments are discussed and the results are demonstrated with an illustrative example.

10 ref

018438   Ghaffari A;Medghalchi A R (Math Dep, Semnan Univ, Semnan, Iran, Email: ghaffari 1380@yahoo.com) : Saocle and finite dimensionality of some banach algebras. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 327-30.

Some algebraic conditions on a Banach algebra which force it to be finite dimensional have been described. For a locally compact group G, G is compact if there exists a measure μ in Soc (L¹ (G)) such that μ (G) μ 0. It is also proved that G is finite if Soc (M (G)) is closed and every nonzero left ideal in M(G) contains a minimal left ideal.

13 ref

018437   Gadgil S;Pancholi D (Stat Math Unit, Indian Statistical Inst, Bangalore-560 059, Email: gadgil@isibang.ac.in) : Homeomorphisms and the homology of non-orientable surfaces. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 251-7.

It has been shown that, for a closed non-orientable surface F, an automorphism of H₁ (F, Z) is induced by a homeomorphism of F if and only if it preserves the (mod 2) intersection pairing. Also the corresponding result for punctured surfaces has been proved.

1 illus, 4 ref

018436   David Kumar R (Collegiate Educzation Dep Government of Andhra Pradesh, , Hyderbad-500 001, Email: rdkumar 1729@yahoo.com) : Higher order Hessian structures on manifolds. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 259-77.

nth order Hessian structures have been defined and studied on manifolds. For n = 3, a detailed study is made a one-to-one correspondence between third-order Hessian structures and a certain class of connections on the second-order tangent bundle of a manifold is established. Further, it is shown that a connection on the tangent bundle of a manifold induces a connection on the second-order tangent bundle. Also second-order geodesics of special second-order connection whcih gives a geometric characterization of symmetric third-order Hessian structures have been defined.

17 ref

018435   Datta B;Upadhyay A K (Math Dep, Indian Inst of Sci, Bangalore-560 012, Email: dattab@math.iisc.ernet.in) : Degree-regular triangulations of torus and klein bottle. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 279-307.

A triangulation of a connected closed surface is called weakly regular if the action of its automorphism group on its vertices is transitive. A triangulation of a connected closed surface is called degree-regular if each of its vertices have the same degree. Clearly, a weakly regular triangulation is degree-regular. Lutz has classified all the weakly regular triangulations on at most 15 vertices. Data and Nilakantan have classified all the degree-regular triangulations of closed surfaces on at most 11 vertices. It has been proved that any degree-regular triangulation of the torus is weakly regular. There exists an n-vertex degree-regular triangulation of the Klein bottle if and only if n is a composite number ≥ 9. Two distinct n-vertex weakly regular triangulations of the torus have been constructed for each n ≥ 12 and a (4m + 2)-vertex weakly regular triangulation of the Klein bottle for each m ≥ 2. For 12 ≤ 15, All the n-vertex degree-reular triangulations of the torus and the Klein bottle have been classified. There are exactly 19 such triangulations, 12 of which are triangulations of the torus and remaining 7 are triangulations of the Klein bottle. Among the last 7, only one is weakly regular.

12 ref

018434   Chahal J S (NO, Brigham Young Univ, USA, Email: jasbir@math.byu.edu) : Foundation of basic arithmetic. Resonance 2006, 11(1), 8-20.

Outlines the early evolution of numerals as currently known.

7 illus, 3 ref

018433   Chahal J (NO, Brigham Young Univ, USA, Email: jasbir@math.byu.edu) : Foundation of basic arithmetic. Resonance 2006, 11(2), 6-16.

Utility of the place value system of representing numbers has been demonstrated.

1 ref

018432   Bhatnagar S (Math Dep, Panjab Univ, Chandigarh-160 014, Email: bhsavita@pu.ac.in) : Multipliers of A_p ((0, ∞)) with order convolution. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 331-8.

Multipliers from A_r (1) to A_p) (I), r ∞ p, where I = (0, ∞) is the locally compact topological semigroup with multiplication max and usual topology and A_r (I) = {ƒ ∈ L₁ (I) : ƒ^{^} ∈ L_r (I)] with norm <157><157><157> ƒ <157><157><157>_r = <157><157> ƒ <157><157>₁ + <157><157> ƒ ^{^} <157><157>_r. have been studied.

9 ref

018431   Agarwal R P;Kim J K;O'Regan D (Math Sci Dep, Fla Inst of Technol, Melbourene, Florida 32901-6975, USA) : Fixed point theory for composite maps on almost dominating extension spaces. Proc Indian Acad Sci-Mathl Sci 2005, 115(3), 339-45.

New fixed point results are presented for U^k_c (X, X) maps in extension type spaces.

11 ref

018430   Adiga C;Anitha N;Kim T (Stud in Math Dep, Univ of Mysore, Manasagangotri, Mysore-570 006, Email: c_adiga@hotmail.com ) : Transformation of Ramanujan's summation formula and its applications. J appl mathl Analysis Applic 2005, 1(1), 55-64.

Some new transformation formulas for Ramanujan's ₁ψ₁ summation formula have been obtained and some eta-function identities have been established. A q-Gamma function identity, an q-integral and some interesting series representations for π^3/2 / 2<206>2Γ²(3/4) and the beta function B (x,y) have been established.

8 ref

018429    (NO, , ) : PHI - The divine proportion, in Nature- Exactitude to the ratio of "1.618:1". Bionotes 2005, 7(4), 111-12.

017437   Zheng N G;Zhang X M (NO, Huzhou Broadcast and TV Univ, Huzhou, Zhejiang-313 000) : Some monotonic functions involving geometrically convex functions. J Analysis Computn 2005, 1(1), 39-45.

8 ref

017436   Zhang Z H;Lokesha V;Xiao Z G (Zixing Educ Res Sect, , Chenzhou, Human-423 400, China, Email: zxzh1234@163.com ) : The weighted heron mean in n variables. J Analysis Computn 2005, 1(1), 57-69.

A definition of the weighted Heron mean in n variables is given, its monotonicity is proved and an identity relating to the same mean is obtained.

5 ref

017435   Warade R W;Deshmukh K C (Math Dep, G.S. Coll, Khamgaon Dist Buldana-444 303) : On the quasi-static thermal deflection in a thin clamped circular plate. Ganita 2005, 56(1), 27-32.

Deals with the determination of thermal deflection of a thin clamped circular plate subjected to arbitrary initial temperature on the upper face, with lower face at zero temperature and the fixed circular edge theermally insulated. The results are obtained in a series form in terms of Bessel functions and illustrated graphically.

6 illus, 7 ref

017434   Waghamore H P (Math Dep, Cent Coll Campus Bangalore Univ, Bangalore-560 001) : Slowly changing functions and associated exceptional values of entire and meromorphic functions and their derivatives. J Analysis Computn 2005, 1(2), 95-100.

The notion of slowly changing function and their properties have been intoduced and studied earlier. In a natural way, slowly changing function leads to a new type of exceptional value called evG for entire and meromorphic functions.

6 ref

017433   Waghamore H P (Math Dep, Cent Coll Campus Bangalore Univ, Bangalore-560 001) : On classes of slowly changing functions and associated exceptional values of entire and meromorphic functions. J Analysis Computn 2005, 1(2), 83-93.

The notion of generalised slowly changing functions and their properties has been introduced. Slowly changing functions allow one to define a new type of exceptional value for entire and meromorphic functions. Introducing the notion of order of multiplicity of a - points. The study of such exceptional values have been further continued.

6 ref

017432   Verma S;Bansal P;Aziz S (Appl Math & Computationala Sci Dep, SGS Inst of Technol & Sci, 23 Park Road, Indore-452 003) : Asymptotic limit and threshold limit for the expenditure. Ultra Scient phys Sci 2005, 17(3M), 443-8.

Highlights the threshold limit and asymptotic limit for each of the five basic commodities, which are: Cooking gas, food ration, pertrol, electricity and communication media. With the help of given data income elasticities for these five basic commodities are calculated. Also highlights on economic aspects i.e., the threshold limit up to which any particular level of income group people can purchase.

4 ref

017431   Tiwari S;Dalela A K (Appl Math Dep, Hitkarini Engng Coll, Jabalpur-482 001) : Summability of fourier - Jacobi series. Res Link 2006, 4(8), 117-8.

Generalize the theorem of Choudhary replacing the condition (3.5) and (3.6) by a still weaker condition (3.7).

5 ref

017430   Thakur R S;Jain R C (Master in Computer Applic Dep, Govt. Geetanjali Girl Coll, Bhopal, Email: ramthakur2000@yahoo.com) : Frequent pattern mining. Ultra Scient phys Sci 2005, 17(3M), 401-8.

Mining frequent patterns from large databases play an aessential role in many data mining tasks and have broad application. There are many methods available for mining frequents patterns from large databases: most of them adopt Aprior-like candidate-generation-and-test approach. Some of algorithm adopts a divide-and-conquer approach. Studies such type of algorithms, and find their serious challenges. These challenges provide new opportunities to researches for future to generate efficient and minimum database scan algorithms.

21 ref

017429   Srivastava B (Math Dep, Lucknow Univ, Lucknow) : A generalization of a continued fraction of ramanujan, its n<. J Analysis Computn 2005, 1(2), 109-15.

A generalization of a continued fraction of Ramanujan and its n^th convergents, using partitions has been given.

4 ref

017428   Srivastava A C;Agarwal M;Saxena P (Math & Astr Dep, Univ of Luckow, Lucknow-226 007) : Flow of a viscous fluid through a porous circular pipe and its surrounding porous medium. Ganita 2005, 56(1), 1-8.

The flow of a viscous fluid through a circular pipe and its surrounding porous medium has been discussed when (i) the surrounding medium extends to a large distance (ii) it is bounded by an impervious co-axial circular cylinder. It is assumed that the flow inside the pipe is governed by Navier-Strokes equation and that outside it by Brinkman equation. Flows in two regions are matched by assuming that at the interface, the velocity is continuous but there is a jump in the shearing stress which is proportional to the velocity. It is found that due to surrounding porous medium, the velocity and the flux through the pipe in the clear flow region increase. In the case of unbounded porous medium, there is a boundary layer formation at the interface in the porous region which is governed by Brinkman equation and there is a slow seepage flow far away from the interface given by Darcy law. The case when the porous medium is confined between the interface and another impervious co-axial cylinder works as a viscometer for determining the response coefficients like viscosity of the fluid and permeability of the porous medium.

1 illus, 2 tables, 10 ref

017427   Srinivas S;Muthuraj R (Math Dep, Vellore Inst of Technol (Deemed Univ, Vellore0-632 014, Email: srinusuripeddi@hotmail.com) : Flow of a thermoviscous fluid in a radially non-symmetric constricted tube. Ultra Scient phys Sci 2005, 17(3M), 437-42.

Approximate solution for the problem of fluid flow through a rigid tube with a mild constriction is given. It is assumed that the fluid is thermoviscous and constriction is non-symmetric with respect to the radial distance. Analytical solutions for velocity and temperature field have been obtained. The effect of various parameters entering into the problem is discussed with the help of graphs.

5 illus, 10 ref