024646   Meng-Zhu (NO, Coll of Fundamental Stud Shanghai Univ of Engng Sci, Shanghai-200. 006, P. R. China) : Convergence of the Ishikawa iteration process for the multi-valued uniformly Lipschitzian asymptotically pseudocontractive mappings in banacha spaces. Far East J mathl Sci 2006, 20(2), 173-8.

A new conception of the multi-valued uniformly Lipschitzian asymptotically pseudocontractive mappings is defined. The convergence of the Ishikawa iteration process for this mapping is dealt with. The results obtained generalize earlier results.

5 ref

024645   Maria Susai Manuel M;Thandapani E (Math Dep, Sacred Heart Coll, Tirupattur-635 601) : Theory of generalised difference operator and its applications. Far East J mathl Sci 2006, 20(2), 163-71.

The generalised difference operator <128><68>_l is introduced as Δ_l(y_k) = y_k+l -y_k and its relation with Δ and E, the usual difference and shift operators respectively are obtained. By defining its inverse, Δ^-1_l, some interesting results in number theory are obtained.

4 ref

024644   Maiti A;Samanta G P (Math Dep, Taki Govt Coll, P.O Taki, North 24-parganas-743 429, Email: alakesh_maity@hotmail.com) : Complex dynamics of a food chain model with mixed selection of functional responses. Bull Calcutta Mathl Soc 2005, 97(5), 393-412.

One approach to the study of an ecological community begins with an important object: its food web. Theoretical studies of food web must contend with the question of how to couple the large number of interacting species. One line of investigation assumes that the "building blocks" are species interacting in a pairwise fashion. The model describes a tritrophic food chain composed of logistic prey, a classical prey-dependent functional response for prey and predator, and a ratio dependent functional response for predator, and superpredator. Dynamical behaviours such as boundedness, stability, persistance, bifurcation et cetera of the model are studied critically. Finally it is discussed how these ideas illuminate some of the observed properties of real populations in the field, and explores practical implications.

6 illus, 33 ref

024643   Luca F;Shparlinski I E (NO, Instituto de Matematicas Universidad Nacional Autonoma de Mexico, C.P. 58089, Morelia, Michoacan, Mexico) : Arithmetic properties of the Ramanujan function. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 1-8.

Some arithmetic properties of the Ramanujan function τ (n), such as the largest prime divisor P (τ(n)) and the number of distinct prime divisors ω(τ(n)) of τ(n) for various sequences of n have been studied. In particular, it is shown that P (τ(n)) ≥ (log n)^33/31+o(1) for infinitely many n, and P(τ(p)τ(p²)τ(p<^ >3)) <62> (1 + o(1)) log log p log log log p/log log log log p for every prime p with τ (p) ≠0.

17 ref

024642   Li T;Huang T;Xu Y (Math Dep Sch of Sci, Southwest Jiaotong Univ, Chengdu 610031, P.R. China, Email: trili@swjtu.edu.cn) : On a mathematical relationship between the fixed point and the closed itemset in association rule mining. Int J Math Analysis 2006, 1(1), 69-79.

Association rule mining is an important research topic in knowledge discovery and data mining. Recent promising research on association rule mining. Recent promising research on association rule mining is however mainly to mine closed itemsets. A mathematical relationship between the fixed point and closed itemset in association rule mining has been discussed. To mine all requent closed itemsets is equal to build the fixed point lattice and mine its all points that satisfy support constraints. Further a new method for visualization of association rules based on the generalized association rule base has been proposed.

3 illus, 1 table, 30 ref

024641   Lakshmibal V L;Shukla P (Math Dep, Northeastern Univ, Boston, MA 02115, USA) : Standard monomial bases and geometric consequences for certain rings of invariants. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 9-36.

Consider the diagonal action of SL_n(K) on the affine space X = V^⊕m ⊕ (V^*)^⊕q where V = Kⁿ, K an algebraically closed field of arbirrary characteristic and m, q <62> n. A `standard monomial' basis for the ring of invariants K[X]^SLn(k). As a consequence, deduces that K[X]^SLn(K) is Cohen-Macaulay. Presents the first and second fundamental theorems for SL_n(K)-actions.

25 ref

024640   Kim D S (Dep of Math, Sogang Univ, Seoul 121-742, South Korea) : Sums for O<. Far East J mathl Sci 2005, 19(1), 71-107.

Let u,v:F_q→C be any functions. The sums Σ v(tr w) over w ∈O^-(2n,q) and over w ∈ SO^-(2n,q), and for char (F_q ≠ 2, also the sum Σ u(det w)v(tr w) over w∈O^-(2n,q) have been considered. It has been shown that all of them are polynomials in q with coefficients involving certain simple sums. In addition It has been shown that the number of elements w∈ SO^-(2n,q) with tr w =β(β ∈F_q) is equidistributed, as β varies over F_q.

13 ref

024639   Kemal U (Dep of Math Sci and Art Fac, The Univ of Selcuk Campus, Konya, Turkey, Email: kuslu@seluck.edu.tr) : Modified computation algorithm of second of discrete stability parameters of linear discrete systems with periodic coefficients. Far East J mathl Sci 2005, 19(1), 33-46.

In many sciences, one comes across the systems of first order linear discrete equations with periodic coefficients. It is important that these systems be discrete asymptotic stable and practical discrete asymptotic stability. There are various criteria determining discrete asymptotic stability of such systems in the literature. But all given algorithms for the calculation of eigenvalues of non-symmetric matrices are not well posed algorithms in the computers. For this reason, discrete stability parameters have been defined to determine the discrete asymptotic stability of such systems. Main goal of this study is to modify the algorithm given and to analyse whether such systems have been practical discrete asymptotic stable and discrete asymptotic stable or not. Furthermore an approximation of the second discrete stability parameter defined for these systems with periodic coefficients has been obtained.

5 ref

024638   Kar S K (Math Dep, Dinabandhu Mahavidyalaya, Bongaon, 24 Parganas (North)-743 235) : On some generating functions of confluent hypergeometric polynomials ₁F₁(n;α;x) from a view point of lie theory. Bull Calcutta Mathl Soc 2005, 97(5), 413-16.

New classes of generating functions are obtained by considering the irreducible representation ↑w;u of g(0,1).

4 ref

024637   Kar A;Kanoria M (Appl Math Dep, Univ of Calcutta, 92, A.P.C Road, Kolkata-700 009, Email: kar_avi@rediffmail.com) : A study of inverse unsteady state thermoelastic problem of a thin rectangular plate. Bull Calcutta Mathl Soc 2006, 98(2), 125-34.

The paper is concerned with the inverse unsteady state thermoelastic problem to determine the temperature, displacements and thermal stresses on the edge x = a of a thin rectangular plate occupying the region D: 0 ≤ x ≤ a, 0 ≤ y ≤ b when the interior temperatue is known. Finite fourier sine transform and Laplace transform techniques have been used. Numerical estimates for temperature, displacements and stresses on the boundary x = a have been obtained and depicted graphically.

5 illus, 5 ref

024636   Kamarujjama M (Appl Math Dep, Z.H. Coll of Engng and Technol Aligarh Muslim Univ, Aligarh-202 002) : A certain class of multiple generating functions. Int J Math Analysis 2006, 1(2), 229-40.

A certain class of multiple generating functions involving multiple series with essential arbitrary coeficients has been derived. By appropriately specializing these coefficients, a number of (known and new) multiple generating functions are obtained as special cases.

9 ref

024635   Jun Y B;Ozturk M A (Math Educ Dep, Gyeongsang Natn Univ, Chinju 660 701, Korea, Email: ybjun@gsnu.ac.kr) : Ideals of fuzzy implication algebras. Int J Math Analysis 2006, 1(1), 103-11.

The notion of ideals in fuzzy implication algebras is introduced. The ideal generated by a set is described.

5 ref

024634   Jaraden J J (Math and Statist Dep, Al-Hussein Bin Talal Univ, Maan, Jordan, Email: jjaradeen@yahoo.com) : Finite groups with tightly embedded subgroups. J appl Algebra Discrete Structs 2005, 3(3), 149-58.

A subgroup H of a group G is tightly embedded in G if |T : M| is a prime for every two subgroups M and T of G such that H ⊆ M ⊆ T and M is maximal subgroup in T. The purpose is to find the system of subgroups in the finite group G such that G is supersoluble if every subgroup H ∈ Σ is tightly embedded in G.

7 ref

024633   Janteng A;Halim S A;Darus M (Inst of Math Sci, Univ Malaya, 50603 Kuala Lumpur, Malaysia) : Coefficient inequality for certain subclasses of univalent functions. Far East J mathl Sci 2005, 19(1), 1-10.

Let f(z) = z + Σ^∞_n=2^α _nzⁿ be an analytic and univalent function in the unit disk D = {z:|z|<60>1}. The purpose of the paper is to introduce the functional |a₂a₄-μa²₃| when μ is real. Sharp upper bonds for |a₂a₄-μa²₃| for certain subclasses of univalent functions has been given. The results obtained are sharp.

10 ref

024632   Jain P K;Kaushik S K;Vashisht L K (Math Dep, Univ of Delhi, Delhi-110 007, Email: pawanujain@vsnl.net) : Bessel sequences and Banach frames in Banach spaces. Bull Calcutta Mathl Soc 2006, 98(1), 87-92.

Sufficient condition for a sequence to be a Banach frame, in terms of Banach Bessel sequence has been obtained. A condition for the stability of Banach Bessel sequences has also been given. Finally, a necessary and sufficient condition for a kind of Banach Bessel sequence to be a Banach frame has been given.

11 ref

024631   Ivic A (Katedra Matematike RGF-a, Universitet u Beogradu, Djusina 7 11000 Beograd, Serbia and Montenegro, Email: ivic@rgf.bg.ac.yu) : The laplace and mellin transforms of powers of the riemannn zeta-function. Int J Math Analysis 2006, 1(2), 113-40.

The paper gives a survey of known results concerning the Laplace transform L_k(s): <91>_o^∞ <157> ξ (1/2 + ix) <157>^2k e^-sx dx (k∈ N, ℜ e s <62> 0) and the (modified) Mellin transform (Z_k(s) : = <91> ₁^∞ <157> ξ(1/2 + ix) <157>^2k x^-s dx (k ∈ N), where the integral is absolutely convergent for ℜe s ≥ c(k) <62> 1. Also some new results on these integral transforms of <157> ξ (1/2 + ix) <157>^2k are given, which have important connections with power moments of the Riemann zeta-function ξ(s).

30 ref

024630   Iranmanesh A;Khosravi B (Pure Math Dep, Tarbiat Modarres Univ, P.O. Box-14115-137, Tehran, Iran) : A characterization of PSU (17, q). J appl Algebra Discrete Structs 2005, 3(3), 169-88.

Let G be a finite group. The order of G is the product of coprime positive integers which is called the order components of G. It was proved that some non-abelian simple groups are uniquely determined by their order components. As the main result of this paper. It has been show that the simple groups PSU (17, q) are also uniquely determined by their order components. As corollaries of this result, the validity of a conjeuture of J. G. Thompson and a conjecture of W Shi and J. Bi both on PSU (17,q) is obtained.

31 ref

024629   Hudzik H;Rajeev Kumar;Romesh Kumar (Fac of Math and Computer Sci, Adam Mickiewicz Univ, Umultowska 87, 61-614, Poznan, Poland) : Matrix multiplication operators on banach function spaces. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 71-81.

The matrix multiplication operators on Banach function spaces have been studied and their applications in semigroups have been discussed for solving the abstract cauchy problem.

24 ref

024628   Hazarika M (Math Sci Dep, Tezpur Univ, Napaam-784 028, Email: munmun@tezu.ernet.in) : On the spectrum of operator weighted shifts. Bull Calcutta Mathl Soc 2006, 98(1), 31-8.

The spectrum of an operator weigted shift on the space H² (K), where the weights are diagonal operators on the Hilbert space K has been described. Particular case studies are also being made for hyponormal operator weighted shifts.

4 ref

024627   Gunaltili I;Akca Z;Anapa P (Math Dep Fac of Sci and Arts, Univ of Osmangazi, Eskisehir-Turkey) : (0, 1)-conditional linear matrices with two consecutive column degrees. Int J Math Analysis 2006, 1(1), 23-35.

In this article, firstly a (0,1)-conditional linear matrix is defined. Then, the basic properties of a non-regular (0,1)-conditional linear matrix with two consecutive column degrees are determine. Finally, linear spaces represented by these matrices are classified.

8 ref

024626   Ghosh K (Math Dep, Dr. B.C. Roy Engng Coll, Jemua Road, Fuljhore, Durgapur-713 206, Email: koushikg123@yahoo.co.uk) : The collapse of rotating stellar cores in presence of magnetic field. Bull Calcutta Mathl Soc 2006, 98(1), 1-6.

An effort is made to investigate the collapse of the white dwarflike cores of rotating massive stars which are assumed to possess magnetic field at the end of their normal nuclear burning stage of evolution. The critical values for the dynamical collapse of the ratio β of rotational to gravitational energy and the ratio δ of magnetic to gravitational energy are obtained as the functions of the effective adiabatic exponent Γ of the matter at intermediate densities where this Γ is less than 4/3.

2 illus, 8 ref

024625   Ghosh H;Sunilkumar G;rajneshu (NO, Indian Agric Statist Res Inst, New Delhi) : Mixture nonlinear time-series analysis : modelling and forecasting. Calcutta Statist Ass Bull 2005, 57(225-226), 95-108.

Gaussian mixture transition distribution (GMTD) models and mixture autoregressive (MAR) models are generally employed to describe those data sets that depict sudden bursts, outliers and flat stretches at irregular time epochs. These two approaches are compared by considering weekly wholesale onion price data during April, 1998 to November, 2001. After eliminating trend, seasonal fluctuations are studied by fitting Box-Jenkins airline model to residual series. To this end, null hypothesis of presence of nonseasonal and seasonal stochastic trends is tested by using Osborn-Chui-Smith-Birchenhall (OCSB) auxiliary regression. Subsequently, appropriate filters in airline model for seasonal fluctuations are selected. Presence of autoregressive conditional heteroscedasticity (ARCH) is tested by Naive Lagrange multiplier (Nave- LM) test. Estimation of parameters is carried out using Expectation-Maximization (EM) algorithm and the best model is selected on the basis of Bayesian information criterion (BIG). Out-of-sample forecasting is performed for one-step and two-step ahead prediction by naive approach, proposed by Wong and Li (2000). It is concluded that, for data under consideration, a three-component MAR model performs the best.

1 table, 5 ref

024624   Ghaed M;Kulkarni S R (Math Dep, Univ of Pune, Pune-411 007, Email: Marzeich_Ghaedi@yahoo.com) : Note on certain subclasses on p-valently convex and starlike functions. Bull Calcutta Mathl Soc 2005, 97(5), 371-80.

Two subclasses GH A(α, p, n, λ) and GH B(α, p, n, λ) of p-valently analytic functions in the open unit disk U = {|z|:|z| <60> 1} are indtoduced. The object is to obtain several interesting properties of functions belonging to the subclasses GH A(λ, p, n, λ) and GH B (α p, n, λ).

6 ref

024623   Gauthier C (Math and Statist Dep, Universite de Moncton, Moncton, N.B., E1A 3E9 Canada) : Ternary operations on the set of real numbers. Math Educ 2005, 39(3), 131-7.

4 ref

024622   Gautam S S;Shanker K (Maths and Statist Dep, M.G.C.G.V., Chitrakoot (Satna), M.P.) : Power of a mixed model anova test procedure for nested classification with unequal subclass numbers - a theoretical investigation. Natn J Life Sci 2004, 1(2), 407-12.

Test procedure based on two preliminary tests of significance for a mixed model analysis of variance of three level nested classification with unequal subclass numbers was developed by Kripa Shanker (1990). The series formulae for different power components of the above test procedure are derived.

1 table, 10 ref

024621   Gao J;Guo W (Math Dep, Xuzhou Norm Univ, Xuzhou, 221116, PR China) : Completely c-permutable minimal subgroups. J appl Algebra Discrete Structs 2005, 3(3), 189-98.

A subgroup H of a group G is said to be completely conditionally pefmutable (or in brevity, completely c-permutable) in G it for every subgroup T of G there exists an element x ∈ (H, T) such that HT^x - T^xHA. Comp1etely c-permutable minimal subgroup is used to give come conditions under which a group belongs to a given formation of finite groups.

12 ref

024620   Ganguly A;Shinde S (Appl Math Dep, Shri G.S. Inst of Tehchnology and Sci, 23, Park Road, Indore-452 003) : Analysis of cylindrical imploding magneto-gasdynamic shock wave in non-homogeneous perfect gas with gravitation. Bull Calcutta Mathl Soc 2006, 98(2), 135-52.

The self-similar solution of magneto-gasdynamic equation of a strong cyclindrical converging shock wave in the presence of gravitation is derived analytically for perfect gas with specific heat ratio γ in non-uniform atmosphere. The equations of motion are reduced to more simplified form in x-y plane by using the reduced velocity transformation (Fujimoto and Mishkin 1978). The requirement of single maximum pressure leads to analytical determination of the self-similarity exponent a and values has been compared with values obtained by earlier authors in the absence of magnetic field and gravitation in a uniform medium. The variations of the flow parameters behind the imploding shock waves are shown in tables and respective influences of gravitational and the magnetic field and the non-homogeneous nature of the medium on the variation of the flow parameters have been studied.

1 illus, 12 tables, 7 ref

024619   Gajendra Singh (Math Dep, Simdega Coll, Simdega, Jharkhand-835 223) : QR-submanifold of a manifold with a Sasakian 3-structure. Bull Calcutta Mathl Soc 2006, 98(1), 79-86.

A Bejancu (1986) introduced the QR-submanifold of a Quaternian kaehler manifold which is based on the action of local basis {φ₁, φ₂, φ₃} are almost Hermitian structures.

6 ref

024618   Gajendra Singh (Math Dep, Simdega Coll, Simdega, Jharkhand-835 223) : Contact CR-products of Lorentzian Para Sasakian manifold. Bull Calcutta Mathl Soc 2006, 98(1), 71-8.

Contact CR-products have been studied by many authors. Kobayashi studied the contact CR-products of Sasakian manifolds. The contact CR-products of a Lorentzian para Sasakian manifolds have been studied and obtained in integrability conditions for the distributions D and D<94><255>. Some properties of contanct CR-products of Lorentzian Para Sasakian manifolds have also been studied.

17 ref

024617   Furkan H (Fen-Edebiyat Fakultesi, Sutcu Imam Universitesi 46100-Kahramanmaras, Turkey, Email: hasanfurkan@hotmail.com) : Convergence domain of infinite matrices and Knopps core theorem. Far East J mathl Sci 2005, 19(1), 109-19.

An extension of Knopps core theorem has been investigated by using the convergence domain of a normal matrix.

13 ref

024616   Ferrando J C;Amigo J M (Centro de Investigacion Operative, Universidad Miguel Hernandez, E - 03202 Elche (Alicante). Spain, Email: jc.ferrando@umh.es) : Complemented copies of l₁ in l_∞ ⊗<. Int J Math Analysis 2006, 1(1), 43-51.

If X is a real or complex Banach, it is not true in general that l_∞ ⊗^∧_{π X contains a complemented copy of l1 if and only if X does. It has been shown that l∞ ⊗^∧π X (as well as c0 ⊗^∧π X) contains a complemented copy of l1 if and only if x has a complemented copy of l1.}

7 ref

024615   Dutta T K;Kar S (Pure Math Dep, Univ of Calcutta, 35, Ballygunge Circular Road, Kolkata-700 019, Email: karsukhendu@yahoo.co.in) : On matrix ternary semirings. Int J Math Analysis 2006, 1(1), 81-95.

The notion of matrix sternary semiring has been introduced and some properties of ternary semiring which are invariants in matrix ternary semiring have been studied. Prime radical and Jacobson radical of a matrix ternary semiring M_n(S) have been characterized in terms of the corresponding radicals of the ternary semiring S.

11 ref

024614   Dutta T K;Kar S (Pure Math Dep, Univ of Culcutta, 35, Ballygunge Circular Road, Kolkata-700 019, Email: karsukhendu@yahoo.co.in) : On semiprime ideals and irreducible ideals of ternery semirings. Bull Calcutta Mathl Soc 2005, 97(5), 467-76.

Notations of semiprime ideal adn irreducible ideal have been introduced in a ternary semiring and study their different properties. Regular ternary semiring and has been studied semiprime k-ideals of the ternary semiring have been characterized.

11 ref

024613   Dutta T K;Kar S (Pure Math Dep, Univ of Calcutta, 35, Ballygunge Circular Road, Kolkata-700 019, Email: karsukhendu@yahoo.co.in) : On prime ideals and prime radical of ternary semirings. Bull Calcutta Mathl Soc 2005, 97(5), 445-54.

The notion of prime ideal and prime radical of a ternary semiring have been introduced and studied them. Prime ternary semiring and the prime ideals of the ternary semiring Z^-₀ have been studied.

8 ref

024612   Dube M;Rathee P (Dep of Statist, M. D. Univ, Rohtak-124 001) : Performance properties of a family of calibration estimators under non-normal errors. Int J agric statist Sci 2005, 1(1-2), 107-13.

The article studies the performance properties of various calibration estimators when the error distribution is not necessarily normal.

12 ref

024611   Datta S K (Math Dep, Krishnath Coll, Berhampore, Murshidabad-742 101) : On entire functions of L-bounded index and of non uniforma L-bounded index. Bull Calcutta Mathl Soc 2006, 98(1), 63-70.

The relation between a slowly changing function and the Nevanlinna characteristic function of composite entire functions whose right factors are of L- bounded index or of non uniform L-bounded index have been studied.

9 ref

024610   DasGupta R;Ghosh J K (NO, Indian Statistical Inst, Kolkata) : Optimal assembly problem of rotor blades : a heuristic approach. Calcutta Statist Ass Bull 2005, 57(225-226), 1-18.

Consider the optimal assembly problem of assigning blades of different but known momenta to fixed positions of a rotor of circular cross section used in hydroturbine. The assembly has to be such that the resultant imbalance of the rotor after assembly is a minimum and the momenta are more or less uniformly spread over the circular section. When the number of blades and consequently the number of possible permutations is also large, the optimal assembly is difficult to obtain. A few heuristic approaches for the assembly are suggested and the statistical properties for the assembly are studied under an appropriate data based model (for the distribution of momenta). The performance of the proposed techniques are compared with the optimal arrangement when the number of blades is small. It is also found that the imbalance arising out of the proposed assembly can be predicted with a high degree of accuracy, based only on first a few large momenta spacings when the blade momenta follow some standard distributions.

5 illus, 2 tables, 1 ref

024609   Daochun K Y S (Sch of Math Sci of South China Norm Univ, , Guangzhou, China 510631, Email: kongcoco@hotmail.com) : The growth of Laplace-Stieltjes transform convergent in the complex plane. Bull Calcutta Mathl Soc 2006, 98(2), 109-16.

The growth of Laplace-Stieltjes transform F(s) convergent in the whole plane is investigated. With the introduction of the Proximate order and the Type-function U(r), some results similar to Dirichlet series are obtained.

6 ref

024608   Danchev P V (NO, , 13, General kutuzov Street, Block 7, Floor 2, Flat 4, 4003 Plovdiv, Bulgaria) : Quasi-completeness of sylow p-subgroups in group algebras over special rings. Int J Math Analysis 2006, 1(1), 97-101.

Suppose G is an arbitrary multiplicative abelian group and R is an arbitrary unitary commutative ring of prime characteristic p. It is shown that if Rp^ω is with nilpotents, S (RG) is quasi-complete (in particular torsion complete) if and only if G is a bounded p-group. Thus a result due to Nachev as well as some resultsin this aspect published in Acta Math. Hungarica (1997), Ricerche di Matematica (2002) and Tamkang J. of mathematics (2003)have been generalised.

7 ref

024607   Daili N (Math Dep Fac of Sci, F. ABBAS Univ, 19000 Setif, Algeria, nourdaili_dz@yahoo.fr) : Analytic densities in number theory part, II: analytic densities of arithmetic functions. Int J Math Analysis 2006, 1(2), 205-27.

A detailed study on the analaytic density of arithmetic functions have been presented and some applications to classical number theory have been given. Some new results which generalize asymptotic density and analystic density in number theory have been given.

5 ref

024606   Daili N (Math Dep, F. Abbas Univ, 19000 Setif, Algeria, Email: nourdaili_dz@yahoo.fr) : Analytic densities in number theory. Part I. Analytic densities of subsets. Far East J mathl Sci 2006, 20(2), 219-40.

A detailed study of the analytic, conditional analytic and derived analytic densities are given and some applications to classical number theory has been presented. Some new existence criteria are established. Certain results obtained generalize those obtained earlier.

6 ref

024605   Corradi K;Szabo S (NO, , ) : Annihilators in a factorization. Int J Math Analysis 2006, 1(1), 1-22.

It is a conjecture that if a finite abelian group G is a direct product of its subsets A₁,...,A_n, then one of the annihilators of these factors must span the whole character group of G. The paper verifies this conjecture in four special cases.

9 ref

024604   Choi K S (Dep of Inf Security, Konyang Univ, Nonsan 320-800, Korea) : Weak convergence and norm convergence on Bergman space. Far East J mathl Sci 2005, 19(1), 25-32.

Measures μ related with weighted Bloch space B_q of D such g_n converges weakly to g in L^p_a (D,dA), then <207><207> g_n-g<207><207> L^p (D,dμ)^→0.

12 ref

024603   Chandra A;Mukherjee S P (NO, St. Xavier's Coll, Kolkata) : Some alternative methods of finding the optimal order quantity in inventory models. Calcutta Statist Ass Bull 2005, 57(225-226), 121-8.

A purchase inventory problem where both demand and supply have been taken to be random has been considered. Several possible ways of deriving the optimum order quantity based on the distribution of total cost have been proposed. Expressions for the optimum order quantity that minimizes the mode or exceedance probability of this distribution have been worked out for some particular demand and supply distributions.

1 ref

024602   Caldas M;Jafari S;Moshokoa S P;Noiri T (Matematica Aplicada Dep, Universidade Fedl Fluminense, Rua Mario Santos Braga, s/n 24020-140, Niteroi, RJ Brasil, Email: gmamccs@vm.uff.br) : A note on almost Moscow spaces. Far East J mathl Sci 2006, 20(2), 199-205.

Almost Moscow spaces as a new type of regularity are presented and studied.

12 ref

024601   Bhatt A G;Karandikar R L;Rao B V (NO, Indian Statistical Inst, 7, SJS Sansanwal Marg, New Delhi-110 016, Email: abhay@isid.ac.in) : On characterisation of Markov processes via martingale problems. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 83-96.

It is well-known that well-posedness of a martingale problem in the class of continuous (or r.c.1.1.) solutions enables one to construct the associated transition probability functions. The result is extended to the case when the martingale problem is well-posed in the class of solutions which are continuous in probability. This extension is used to improve of a criterion for a probability measure to be invariant for the semigroup associated with the Markov process. Examples of martingale problems that are well-posed in the class of solutions which are continuous in probability but for which non r. c.1.1 solution exists have been given.

13 ref

024600   Baskar S;Prasad P (Math Dep, Indian Inst of Sci, Bangalore-560 012, Email: prasad@math.iisc.ernet.in) : Formulation of the problem of sonic boom by a maneuvering aerofoil as a one-parameter family of Cauchy problems. Proc Indian Acad Sci-Mathl Sci 2006, 116(1), 97-119.

For the structure of a sonic boom produced by a simple aerofoil at a large distance from its source a physical model which consists of a leading shock (LS), a trailing shocck (TS) and a one-parameter family of nonlinear wavefronts in between the two shocks has been taken. Then a mathematical model it bas been and shown developed that according to this model the LS is governeed by a hyperbolic system of equations in conservation form and the system of equations governing the TS has a pair of complex eigenvalues. Similarly, it has been shown that a nonlinear wavefront originating from a point on the front part of the aerofoil is governed by a hyperbolic system of conservation laws and that originating from a point on the rear part is governed by a system of conservation laws, which is elliptic. Consequently, expect one the geometry of the TS to be kink-free and topologically different from the geometry of the LS. In the last section an evidence of kinks on the LS and kink-free TS from the numerical solution of the Euler's equations by Inoue, Sakai and Nishida has been pointed out.

11 illus, 13 ref

024599   Banerjee D (Math Dep, Visva-Bharati Univ, Santiniketan-731 235, Email: dibyendu192@rediffmail.com) : A note on relative order of meromorphic functions. Bull Calcutta Mathl Soc 2006, 98(1), 25-30.

Relative order of a meromorphic function with respect to another meromorphic function is considered and after proving some results, it is observed that the relative order of a transcendental meromorphic function with respect to a rational function is the same as that of its derivative.

5 ref

024598   Ballico E (NO, , , Email: ballico@science.unitn.it) : Brill-noether theory for vector bundles on curves defined over a finite field. Int J Math Analysis 2006, 1(2), 201-4.

Let X be a smooth and geometrically connected curve of genus g ≥ 2 defined over F_q. The existence of rank r geometrically stable vector bundles on X defined over F_q and with many sections.

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024597   Ballico E (Math Dep, Univ of Tarento, 38050 Povo (TN), Italy, Email: ballico@science.unitn.it) : Primitive linear series and primitive vector bundles on smooth projective curves. Int J Math Analysis 2006, 1(1), 37-41.

Let X be a smooth projective curve, E a vector bundle on X and t a non-negative integer, One will say that E is t-primitive if it is spanned and for every injective map j:E → F with F vector bundle, rank (F) = rank (E) and deg (F) = deg (E) + t one have h⁰ (X, F) = h⁰(X, E). This notion is explored here mainly when X is athe normalization of a plane curve.

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