002008   Arvind Babu L R;Sameeullah A M;Palaniappan B (Information Technology Dep, CSE Wing, DDE, Annamalai Univ, Annamalai Nagar-608 002) : Complex algorithm for bounded variables. Acta Cienc Indica-Math 2007, 33(2), 633-6.

Linear Programming Problems are mathematical models used to represent real life situations in the form of linear objective function and constraints various methods are available to solve linear programming problems. One such proved and best method is revised simplex procedure is widely used. Revised simplex method is a univariate search technique and suffers the drawback of slow convergence with the tendency of variable popping in and out of the basis matrix. The numbers of iterations are more and increase in computational effort and time. This gives wide scope to a search of new algorithm. In the bounded complex algorithm a univariate search technique is adopted, but the entering variables are arranged not only based on the maximum contribution if that variable to the objective function but also on the type of the constraints. Once the priority arrangement of the promising variables is obtained the iterations are performed as in the Simplex Method by selecting a leaving variable based on bounds of the variables.

3 tables, 6 ref

002007   Arockiarani I;Janaki C (Mathematics Dep, Nirmala College for Women, Coimbatore-45) : πgα-closed sets and quasi-α-normal spaces. Acta Cienc Indica-Math 2007, 33(2), 657-66.

In this paper a new class of set called πgα-closed set is introduced and its properties are studied. Further author obtained characterization and preservation theorems for quasi-α-normal spaces.

21 ref

002006   Agney Kumar;Singh K K (Mathematics Dep, Agra College, Agra) : Numerical study of unsteady flow of viscous fluid down between two inclined parallel porous plates. Acta Cienc Indica-Math 2007, 33(2), 571-4.

The unsteady flow of viscous fluid down between two inclined parallel porous plates is studied. The velocity distribution for unsteady flow is obtained. The particular case for steady flow had also been deduced.

5 ref

002005   Agney Kumar;Singh K K (Mathematics Dep, Agra College, Agra) : Numerical study of effects of a magnetic field on unsteady blood flow through an indented tube with mild stenosis. Acta Cienc Indica-Math 2007, 33(2), 553-8.

In the present paper author studied a mathematical model on arterial unsteady blood flow with mild stenosis in the presence of magnetic field. The numerical solutions are given for velocity, volumetric flow rate, the shear stress at the surface of stenosis and wall shear stress of the fluid in the stenotic region.

9 ref

002004   Agney Kumar;Singh K K (Mathematics Dep, Agra College, Agra) : Investigation of back flow in generalized couette flow under influence of magnetic field and electric fields through porous media. Acta Cienc Indica-Math 2007, 33(2), 359-62.

The combined effects of magnetic and electric fields on separation tendency in generalized couette flow through porous media is studied.

1 table, 5 ref

002003   Agarwal V K (Mathematics Dep, Govt. Girls P.G. College, Hoshangabad-461 001) : Some fixed point theorems for multivalued mappings. Acta Cienc Indica-Math 2007, 33(2), 425-8.

Expand and generalize the results of Iseki [1,2], Reich [4], Sharma, Iseki and Rajput [6], Rus [5} and Wong [7] for multivalued mappings satisfying contractive type conditions.

7 ref

002002   Acharya D P;Pal A (NO, , 109/3, Kailash Roy Choudhury Road, Manirampur, Barrackpore, 24 Pgs(N)-700 120) : Effect of surface stress on the love wave propagation due to a point source in a water saturated porous layer over an inhomogeneous substratum. Acta Cienc Indica-Math 2007, 33(2), 255-73.

Investigates the propagation of Love waves in water saturated porous layer under the action of surface stress in presence of a point source of disturbance on the boundary surface of separation lying over an inhomogeneous semi-infinite substratum. The wave velocities have been derived in closed forms and numerical values of the same have been calculated for different cases. It has been pointed out by drawing graphs that the surface stress, inhomogeneity of the lower medium and porosity of the upper medium modulate the Love wave velocity to a considerable extent.

001082   Zihou Zhang;Zhu M (Mathematics Dep, Shanghai Univ, Shanghai, 200 444, P.R. China) : On the property p - k and property p* - k in Banach spaces. Far East J mathl Sci 2006, 23(3), 369-77.

Properties P - K and P* -- K (K = I, II, III, IV) are introduced. It has been shown that the properties P - K (K = 1, II, III, IV) are equivalent to strongly convex, nearly strongly convex, very convex, nearly very convex, respectively and the properties P* - K (K- = I, II, III, IV') are equivalent to Frechet differentiable, quasi-Frechet differentiable, very smooth, weakly very smooth, respectively. The dual relationship between the properties P-K and P* - K, and between their convexities and smoothnesses are also discussed.

9 ref

001081   Zhu X (Mathematics Dep, Central Michiger Univ, Mcrent Pleasent, MI 4 8859, USA, Email: zhulx@cmich.edu) : Generalization of Reid's pagoda technique. Far East J mathl Sci 2006, 23(3), 379-88.

Extended Reid's pagoda technique to a Calabi-Yau 3-fold which contains a rational curve that can be contracted to a cD₄ point.

4 ref

001080   Sudo T (NO, , ) : Stable rank of the reduced group C*-algebras of HNN extensions. Far East J mathl Sci 2006, 23(3), 417-20.

It has been shown that the stable rank of the reduced group C* -algebras of HNN extensions like Baumslag-Solitar groups is one or two.

8 ref

001079   Song Y (NO, , ) : Algebras in MC_n(k). Far East J mathl Sci 2006, 23(3), 435-43.

Let (R, J(R), k) be a local commutative k-subalgebra of M_n(k) with nilpotent maximal ideal J(R) and residue class field k. Classify maximal commutative k-:subalgebras of M_n(k) up to C₁-construction and C₂ -construction according to dim_k (J(R)/soc(R)).

10 ref

001078   Shanmugam T N;Sivasubramanian S;Darus M (Mathematics Dep, College of Engineering Anna Univ, Chennai-600 025, Email: shan@annauniv.edu) : On certain subclasses of functions involving a linear operator. Far East J mathl Sci 2006, 23(3), 329-39.

Derives certain subordination and superordmation results for certain normalized analytic functions in the open unit disk, involving Carlson-Shaffer operator. Relevant connections of the results, with various known results are also considered.

8 ref

001077   Sato I (NO, Oyama National College of Technology Oyama, Tochigi 323-0806, Japan, Email: isato@oyama-ct.ac.jp) : Coverings of digraphs. Far East J mathl Sci 2006, 23(3), 281-93.

Consider a finite covering (a regular covering) of a digraph D, and characterize a covering (a regular covering) of D by using a permutation group (a finite group). Furthermore, authors give a characterization for two coverings of D to be isomorphic (II-isomorphic) with respect to a subgroup II of the automorphism group Aut D, and show that two coverings of D are II-isomorphic if and only if two corresponding coverings of the symmetric digraph containing D as a spanning subdigraph is II-isomorphic. As an application, authors enumerate the isomorphism classes of coverings of D.

8 ref

001076   Padmavathamma M R;Kanna R;Chandrasshekara B M (Studies in Mathematics Dep, Mysore Univ, Manasagangotri, Mysore-570 006, Email: padma_vathamma@yahoo.com) : Bijective proof of the partition indentity C_2,r(n)= D_2,r(n) of M.V. subbarao. Far East J mathl Sci 2006, 23(3), 341-54.

Theorem "the number of partitions of n, in which each part appears 2, 2r and 2r + 1 times equals the number of partitions of n in which odd part is congruent to 2r + 1 (mod 4r + 2) and even part is congruent to 2 (mod 4) ", is a particular case of a result by M. V. Subbarao. Gives a bijective proof of this theorem.

5 ref

001075   Moslemi B (Mathematics Dep, The Ahvaz Univ, Iran, Email: bmoslemi2@yahoo.com) : On G-domains. Far East J mathl Sci 2006, 23(3), 355-9.

It is shown that domain R with k - dim R = 1 has infinite number of prime ideals (i.e., maximal ideals) if and only if the rank of every maximal ideal in R[x] is 2. Also extends the well-known characterization of Noetherian G-domains to G-domains with acc on radical ideals and dcc on prime ideals.

10 ref

001074   Manuel M M S;Xavier G B A;Thandapani E (Mathematics Dep, Sacred Heart Coll, Tirupattur-635 601, Email: manuelmsx-03@yahoo.com) : Qualitative properties of solutions of certain class of difference equations. Far East J mathl Sci 2006, 23(3), 295-304.

Defines rotatory solutions of generalised difference equations and discuss the rotatory and boundedness behavior of solutions of the generalised difserence equations p(k) u(k+l) p(k-l) u(k-l) + q(k) u(k), ken(t). Examples are provided to illustrate definitions and the main result.

6 ref

001073   Liu Z;Han Y;Shim S H;Kang S M (Mathematics Dep, Liaoning Normal Univ, P.O.Box 200, Dalian Liaoning 116 029, P.R. China, Email: zeqingliu@dl.cn) : Common fixed point theorems for a pair of contractive type densifying mappings. Far East J mathl Sci 2006, 23(3), 305-15.

Four common fixed point theorems involving a pair of contractive type densifying mappings are proved in complete metric spaces. The results presented generalize the corresponding results of Chatterjee, Fisher, Furi and Vignoli, Gungck, Leader, Liu, Ohta and Nikaido, and others.

ref

001072   Lee G Y;Seol H G (Mathematics Dep, Hanseo Univ, Seosan-356706, Korea) : k-Lucas numbers and completeness. Far East J mathl Sci 2006, 23(3), 421-33.

Considered the nth k-Lucas numbers and their completeness.

9 ref

001071   Efe H (Mathematics Dep, Faculty of Science and Arts, Gazi Univ, Teknikokullar, 06500 Ankara, Turkey, Email: hakanefe@gazi.edu.tr) : On t-uniformly continuous mappings in intuitionistic fuzzy metric spaces. Far East J mathl Sci 2006, 23(3), 317-28.

Gave some properties of t-uniformly continuous mapping. It has been been shown that every continuous mapping on the compact intuitionistic fuzzy metric spaces is t-uniformly continuous and characterize intuitionistic fuzzy metric spaces for which every real-valued continuous function is t-uniformly continuous. It is observe that every t-uniformly continuous mapping is uniformly continuous in the sense of Alaca et al., but converse does not hold in general. Nevertheless, It is shown that for each intuitionistic fuzzy metric space (X, M, N, *, <>) such that every real-valued continuous function is uniformly continuous there is an intuitionistic fuzzy metric on X compatible with the topology generated by (M, N) for which every real-valued continuous function is t-uniformly continuous.

18 ref

001070   Behravesh H;Ghaffarzadeh G (Mathematics Dep, Urima Univ, Urima, Iran, Email: h.behravesh@mail.urmia.ac.ir) : Quasi-permutation representations of 2-group of order ≤32. Far East J mathl Sci 2006, 23(3), 361-7.

Calculates c(G), q(G), p(G) for non-abelian 2-groups G, where <157> G <157> ≤32.

9 ref

001069   Afrouzi G A;Heidarkhani S (Mathematics Dep, Faculty of Basic Sciences Mazandaran Univ, Babolsar, Iran, Email: afrouzi@umz.ac.ir) : Existence of three solutions of a Dirichlet problem for elliptic equations involving the p-Laplacian. Far East J mathl Sci 2006, 23(3), 389-99.

6 ref

001068   Acikgoz A;Yuksel S (Mathematics Dep, Faculty of Arts and Sciences, Aksaray Univ, 68100 Aksaray, Turkey, Email: syuksel@selcuk.edu.tr) : Generalizations new class of A_I-R-sets. Far East J mathl Sci 2006, 23(3), 401-16.

Introduced and investigate new classes of generalizations of AI-R -sets and AI-R -continuous functions in ideal topological spaces and obtain some of their properties.

9 ref

000085   Sinha K (Epidemiology and Biostatistics Div, Illinois Univ, Chicago, USA) : Some aspects of diallel cross designs with correlated observations. Calcutta Statist Ass Bull 2006, 58(231-2), 243-61.

Purpose of this article is to present some theoretical results for analysis of diallet cross designs in blocked situations with a possible correlation structure within each block.

8 ref

000084   Sinha B K;Yimprayoon P;Tiensuwan M (Mathematics Faculty of Science Dep, Indian Statistical Institute, Kolkata) : Cohen's kappa statistic: a critical appraisal and some modifications. Calcutta Statist Ass Bull 2006, 58(231-2), 151-69.

Considered the problem of assessing agreement between two raters while the rating are given separately in 2 - point nominal scale and critically examine some features of Cohen's kappa statistic (KC) , widely and extensively used in this context. Author point out some undesirable features of KC and, in the process, propose two modified kappa statistics. Properties and features of these statistics are explained with illustrative examples.

5 tables, 20 ref

000083   Saharay R;Shah K R (Bayesian & Interdisciplinary Research Unit, Indian Statistical Institute, Kolkata) : Optimal crossover designs for comparing mixed carryover effects. Calcutta Statist Ass Bull 2006, 58(231-2), 223-42.

In this paper author consider a variant of the traditional non-circular model for crossover designs. Instead of assuming that each treatment applied to an experimental unit imparts the same carryover effect regardless of the treatment applied to the next period on the same unit, the model which assumes two types of carryover effects have been considred that extend from a period to the next period. One type is called self carryover effect when a treatment is followed by itself in the next period on the same unit and the other type is called mixed carryover effect when a treatment is followed by any other treatment in the next period. Such models are useful in sensory trials. Efficient estimation and testing of the direct treatment effects (imparted by the treatment itself on the experimental unit of application) as well as the carryover effects under different models are of interest to the practitioners from application and model building point of view and have been addressed by many researchers. In the present article the problem of identification of optimal designs for the estimation of the mixed carryover effects has been taken up. It is shown that under the self and mixed carryover model generalised Patterson's balanced designs (termed also totally balanced designs in the literature), which are known to be universally optimal for the estimation of the direct treatment effects are also universally optimal for the estimation of the mixed carryover effects provided that the number of periods exceeds two.

33 ref

000082   Nanda A K;Das S (Mathematics Dep, Indian Institute of Technology, Kharagpur) : R-norm residual entropy. Calcutta Statist Ass Bull 2006, 58(231-2), 197-207.

Stochastic order and an aging property have been defined based on R-norm residual entropy, and their properties have been studied. A few useful parametric distributions have been characterized with the help of this entropy. A couple of results have been developed for discrete random variables.

7 ref

000081   Maheria K;Chudasama U (Applied Chemistry Dep, Faculty of Technology and Engineering, Baroda The M.S. Univ, Vadodara-390 001, Email: uvcres@gmail.com) : Kinetics, thermodynamics and sorption characteristics of an inorganic ion exhanger-titanium phosphate towards Pb(II), Bi(III) and Th(IV). J Indian Inst Sci 2006, 86(5), 515-25.

Amorphous titanium phosphate (TiP), an inorganic ion exchanger of the class of tetravalent metal acid (tma) salts has been synthesized by sol-gel method. TiP has been characterized for elemental analysis (ICP-AES), spectral analysis (FT-IR), thermal analysis (TGA and DSC) and X-ray diffraction studies. Chemical resistivity of the material has been assessed in various media-acids, bases and organic solvents. The Na⁺ ion exchange capacity (IEC) has been determined and the effect of heating on IEC studied. The sorption/ion exchange behaviour of TiP towards Pb(II), Bi(III) and Th(IV) has been studied at different temperatures (313, 323 and 333 K). Kinetic parameters (overall rate constant k', equilibrium constant K_c, forward and reverse reaction rate constant k₁ and k₂, respectively) and thermodynamic parameters (standard free energy ΔG^<0>, standard enthalpy ΔH, and standard entropy ΔS⁰) have been evaluated and adsorption (Langmuir and Fruendlich) isotherms have been studied. Based on the above studies, the selectivity order is found to be Pb(II) <62> Th(IV) <62> Bi(III) at 333 K.

1 illus, 5 tables, 29 ref

000080   Gopalan M A;Devibala S (Math Dep, Natin Coll, Trichy, , , Email: devibala27@yahoo.com) : Equality of triangular numbers with special M-gonal numbers. Bull Allahabad Mathl Soc 2006, 21, 25-9.

Explicit formulas for the ranks of triangular numbers which are simultaneously equal to pentagonal, octagonal, decagonal and Dodecagonal numbers in turn are presented.

ref

000079   Franjic I;Pecaric J (Math Dep, FD Technol Biotechnol Faculty, Zagreb Univ, Pierottijeva 6,, , , Email: ifranjic@pbf.br) : On corrected Bullen-Simpson's inequality. Bull Allahabad Mathl Soc 2006, 21, 105-23.

The aim is paper is to derive correctet Bullen-Simpson's inequality, starting from corrected Simpson's and dual corrected Simpson's formula. By corrected mean formulae that approximate the integral not only with the values of the function in certain points but also with the value of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than formulae derived in [3].

11 ref

000078   Chattopadhyay A K;Gupta A (Statistics Dep, Calctta Univ, Kolkata) : Diffusion of rumours through epidemic models under non identical set up. Calcutta Statist Ass Bull 2006, 58(231-2), 263-80.

Spread of rumour can be modelled easily by using epidemic models because of the similarity in underlying processes. The present paper attempts to study diffusion of rumours through a simple epidemic model, taking the behavior of different persons involved under the process will be different and also the rate of spread will be time dependent the underlying variables will not be independent and identical. The process has been studied through simulation established theoretical result. The objective of the study is to predict the number of hearers at a particular time point by using the proposed model.

4 tables, 40 ref

000077   Bentley H L (Toledo Univ, Toledo, Ohio, USA, , ) : Motley merotopic spaces. Bull Allahabad Mathl Soc 2006, 21, 7-23.

Introduce a stronger form of the so called "union" axiom in mero-topic spaces. Author explore to what extent this property is preserved by the categorical constructions in Mer, the category of merotopic spaces. Finally, Author relate this class of spaces to the epireflective hull of the topological spaces in the category of nearness spaces.

16 ref

000076   Beg I (Cent Adv Study Math, Math Dep, Lahore Univ Mgmt Sci, 54792-Lahore, Pak, , , Email: ibeg@lums.edu) : Fuzzy multivalued functions. Bull Allahabad Mathl Soc 2006, 21, 41-104.

74 ref

000075   Basu A;Bhattacharjee A (Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, Kolkata) : Natural goodness-of-fit test for the exponental growth curve model based on the relative growth rate. Calcutta Statist Ass Bull 2006, 58(231-2), 211-21.

Natural goodness-of-fit test for the exponential growth curve model (EGCM) based on the property of finite differences.The EGCM has wide applications in various scientific fields such as biology, ecology, demography, population dynamics, finance, econometrics etc. Hill (1968,Biometrics, 4, 192-196) proposed a test for the polynomial growth curve model (PGCM) based on finite differences of the size variable. However, the PGCM has limited practical use and does not have any biologically interpretable parameters. In comparison, the exponential model is more realistic and biologically meaningful; a goodness-of-fit test for the EGCM has substantial practical value. Bhattacharya et. al. (2004) generalized Hill's approach to the case of the EGCM based on appropriate finite differences of functions of the size variable. Alternative test for the EGCM has been presented by directly modeling the relative growth rate (rather than the size variable itself) and hence avoid the assumptions necessary in Bhattacharya et al (2004). The performance of the theory developed is illustrated with several sets of real data and through simulation.

1 illus, 19 ref

000074   Aliouche A;Fisher B (Math Dep, Larbi Ben M'hid; Univ, Oum-EL-Bouaohi 04000, Alzeria, , , Email: alioucheabdelkrim@yahoo.fr) : Fixed point theorem for two set valued mappings on two complete metric spaces. Bull Allahabad Mathl Soc 2006, 21, 31-40.

Fixed point theorem for two set valued mappings on two complete metric spaces has been obtained.

7 ref

000073   Ahmed S E;An L;Nkurunziza S (Mathematics and Statistics Dep, Windsor Univ, Canada) : Improving the estimation of eigenvectors under quadratic loss. Calcutta Statist Ass Bull 2006, 58(231-2), 172-96.

Improved estimation of eigenvectors of a covariance matrix is considered under uncertain prior information (VPI] regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process. A very large gain in precision may be achieved by judiciously exploiting the information about the parameters which in practice wilt be available in any realistic problem. Several estimators based on preliminary test and the Stein-type shrinkage rules are constructed. The expressions for the bias and risk of the proposed estimators are derived and compared with the usual estimators. Author demonstrates how the classical large sample theory of the conventional estimator can be extended to shrinkage and preliminary test estimators for the eigenvector of a covariance matrix. It is established that shrinkage estimators are asymptotically superior to the usual sample estimators. For illustration purposes, the method is applied to three data sets.

3 illus, 34 ref

000072   Ahmed N;Sarma D;Barua D P (Math Dep, Gauhati Univ, Guwahati-781 014, , , Email: saheet-nazib@yahoo.com) : Three dimensional free convective flow and mass transfer along a porous vertical plate. Bull Allahabad Mathl Soc 2006, 21, 125-41.

Problem of three-dimensional free mass transfer flow of an incompressible viscous fluid along a vertical porous plate with trans verse sinusoidal suction velocity distribution and uniform free stream velocity is investigated. The governing equations are solved by regular perturbation technique. The expressions for the velocity field, the wall shear stress in the direction of the main flow and the rate of heat transfer and mass transfer from the plate to the fluid are obtained and some of them are demonstrated in graphs for different values of the parameters involved.

5 illus, 9 ref

000085   Sinha K (Epidemiology and Biostatistics Div, Illinois Univ, Chicago, USA) : Some aspects of diallel cross designs with correlated observations. Calcutta Statist Ass Bull 2006, 58(231-2), 243-61.

Purpose of this article is to present some theoretical results for analysis of diallet cross designs in blocked situations with a possible correlation structure within each block.

8 ref

000084   Sinha B K;Yimprayoon P;Tiensuwan M (Mathematics Faculty of Science Dep, Indian Statistical Institute, Kolkata) : Cohen's kappa statistic: a critical appraisal and some modifications. Calcutta Statist Ass Bull 2006, 58(231-2), 151-69.

Considered the problem of assessing agreement between two raters while the rating are given separately in 2 - point nominal scale and critically examine some features of Cohen's kappa statistic (KC) , widely and extensively used in this context. Author point out some undesirable features of KC and, in the process, propose two modified kappa statistics. Properties and features of these statistics are explained with illustrative examples.

5 tables, 20 ref

000083   Saharay R;Shah K R (Bayesian & Interdisciplinary Research Unit, Indian Statistical Institute, Kolkata) : Optimal crossover designs for comparing mixed carryover effects. Calcutta Statist Ass Bull 2006, 58(231-2), 223-42.

In this paper author consider a variant of the traditional non-circular model for crossover designs. Instead of assuming that each treatment applied to an experimental unit imparts the same carryover effect regardless of the treatment applied to the next period on the same unit, the model which assumes two types of carryover effects have been considred that extend from a period to the next period. One type is called self carryover effect when a treatment is followed by itself in the next period on the same unit and the other type is called mixed carryover effect when a treatment is followed by any other treatment in the next period. Such models are useful in sensory trials. Efficient estimation and testing of the direct treatment effects (imparted by the treatment itself on the experimental unit of application) as well as the carryover effects under different models are of interest to the practitioners from application and model building point of view and have been addressed by many researchers. In the present article the problem of identification of optimal designs for the estimation of the mixed carryover effects has been taken up. It is shown that under the self and mixed carryover model generalised Patterson's balanced designs (termed also totally balanced designs in the literature), which are known to be universally optimal for the estimation of the direct treatment effects are also universally optimal for the estimation of the mixed carryover effects provided that the number of periods exceeds two.

33 ref

000082   Nanda A K;Das S (Mathematics Dep, Indian Institute of Technology, Kharagpur) : R-norm residual entropy. Calcutta Statist Ass Bull 2006, 58(231-2), 197-207.

Stochastic order and an aging property have been defined based on R-norm residual entropy, and their properties have been studied. A few useful parametric distributions have been characterized with the help of this entropy. A couple of results have been developed for discrete random variables.

7 ref

000081   Maheria K;Chudasama U (Applied Chemistry Dep, Faculty of Technology and Engineering, Baroda The M.S. Univ, Vadodara-390 001, Email: uvcres@gmail.com) : Kinetics, thermodynamics and sorption characteristics of an inorganic ion exhanger-titanium phosphate towards Pb(II), Bi(III) and Th(IV). J Indian Inst Sci 2006, 86(5), 515-25.

Amorphous titanium phosphate (TiP), an inorganic ion exchanger of the class of tetravalent metal acid (tma) salts has been synthesized by sol-gel method. TiP has been characterized for elemental analysis (ICP-AES), spectral analysis (FT-IR), thermal analysis (TGA and DSC) and X-ray diffraction studies. Chemical resistivity of the material has been assessed in various media-acids, bases and organic solvents. The Na⁺ ion exchange capacity (IEC) has been determined and the effect of heating on IEC studied. The sorption/ion exchange behaviour of TiP towards Pb(II), Bi(III) and Th(IV) has been studied at different temperatures (313, 323 and 333 K). Kinetic parameters (overall rate constant k', equilibrium constant K_c, forward and reverse reaction rate constant k₁ and k₂, respectively) and thermodynamic parameters (standard free energy ΔG^<0>, standard enthalpy ΔH, and standard entropy ΔS⁰) have been evaluated and adsorption (Langmuir and Fruendlich) isotherms have been studied. Based on the above studies, the selectivity order is found to be Pb(II) <62> Th(IV) <62> Bi(III) at 333 K.

1 illus, 5 tables, 29 ref

000080   Gopalan M A;Devibala S (Math Dep, Natin Coll, Trichy, , , Email: devibala27@yahoo.com) : Equality of triangular numbers with special M-gonal numbers. Bull Allahabad Mathl Soc 2006, 21, 25-9.

Explicit formulas for the ranks of triangular numbers which are simultaneously equal to pentagonal, octagonal, decagonal and Dodecagonal numbers in turn are presented.

ref

000079   Franjic I;Pecaric J (Math Dep, FD Technol Biotechnol Faculty, Zagreb Univ, Pierottijeva 6,, , , Email: ifranjic@pbf.br) : On corrected Bullen-Simpson's inequality. Bull Allahabad Mathl Soc 2006, 21, 105-23.

The aim is paper is to derive correctet Bullen-Simpson's inequality, starting from corrected Simpson's and dual corrected Simpson's formula. By corrected mean formulae that approximate the integral not only with the values of the function in certain points but also with the value of the first derivative in end points of the interval. These formulae will have a higher degree of exactness than formulae derived in [3].

11 ref

000078   Chattopadhyay A K;Gupta A (Statistics Dep, Calctta Univ, Kolkata) : Diffusion of rumours through epidemic models under non identical set up. Calcutta Statist Ass Bull 2006, 58(231-2), 263-80.

Spread of rumour can be modelled easily by using epidemic models because of the similarity in underlying processes. The present paper attempts to study diffusion of rumours through a simple epidemic model, taking the behavior of different persons involved under the process will be different and also the rate of spread will be time dependent the underlying variables will not be independent and identical. The process has been studied through simulation established theoretical result. The objective of the study is to predict the number of hearers at a particular time point by using the proposed model.

4 tables, 40 ref

000077   Bentley H L (Toledo Univ, Toledo, Ohio, USA, , ) : Motley merotopic spaces. Bull Allahabad Mathl Soc 2006, 21, 7-23.

Introduce a stronger form of the so called "union" axiom in mero-topic spaces. Author explore to what extent this property is preserved by the categorical constructions in Mer, the category of merotopic spaces. Finally, Author relate this class of spaces to the epireflective hull of the topological spaces in the category of nearness spaces.

16 ref

000076   Beg I (Cent Adv Study Math, Math Dep, Lahore Univ Mgmt Sci, 54792-Lahore, Pak, , , Email: ibeg@lums.edu) : Fuzzy multivalued functions. Bull Allahabad Mathl Soc 2006, 21, 41-104.

74 ref

000075   Basu A;Bhattacharjee A (Bayesian and Interdisciplinary Research Unit, Indian Statistical Institute, Kolkata) : Natural goodness-of-fit test for the exponental growth curve model based on the relative growth rate. Calcutta Statist Ass Bull 2006, 58(231-2), 211-21.

Natural goodness-of-fit test for the exponential growth curve model (EGCM) based on the property of finite differences.The EGCM has wide applications in various scientific fields such as biology, ecology, demography, population dynamics, finance, econometrics etc. Hill (1968,Biometrics, 4, 192-196) proposed a test for the polynomial growth curve model (PGCM) based on finite differences of the size variable. However, the PGCM has limited practical use and does not have any biologically interpretable parameters. In comparison, the exponential model is more realistic and biologically meaningful; a goodness-of-fit test for the EGCM has substantial practical value. Bhattacharya et. al. (2004) generalized Hill's approach to the case of the EGCM based on appropriate finite differences of functions of the size variable. Alternative test for the EGCM has been presented by directly modeling the relative growth rate (rather than the size variable itself) and hence avoid the assumptions necessary in Bhattacharya et al (2004). The performance of the theory developed is illustrated with several sets of real data and through simulation.

1 illus, 19 ref

000074   Aliouche A;Fisher B (Math Dep, Larbi Ben M'hid; Univ, Oum-EL-Bouaohi 04000, Alzeria, , , Email: alioucheabdelkrim@yahoo.fr) : Fixed point theorem for two set valued mappings on two complete metric spaces. Bull Allahabad Mathl Soc 2006, 21, 31-40.

Fixed point theorem for two set valued mappings on two complete metric spaces has been obtained.

7 ref

000073   Ahmed S E;An L;Nkurunziza S (Mathematics and Statistics Dep, Windsor Univ, Canada) : Improving the estimation of eigenvectors under quadratic loss. Calcutta Statist Ass Bull 2006, 58(231-2), 172-96.

Improved estimation of eigenvectors of a covariance matrix is considered under uncertain prior information (VPI] regarding the parameter vector. Like statistical models underlying the statistical inferences to be made, the prior information will be susceptible to uncertainty and the practitioners may be reluctant to impose the additional information regarding parameters in the estimation process. A very large gain in precision may be achieved by judiciously exploiting the information about the parameters which in practice wilt be available in any realistic problem. Several estimators based on preliminary test and the Stein-type shrinkage rules are constructed. The expressions for the bias and risk of the proposed estimators are derived and compared with the usual estimators. Author demonstrates how the classical large sample theory of the conventional estimator can be extended to shrinkage and preliminary test estimators for the eigenvector of a covariance matrix. It is established that shrinkage estimators are asymptotically superior to the usual sample estimators. For illustration purposes, the method is applied to three data sets.

3 illus, 34 ref

000072   Ahmed N;Sarma D;Barua D P (Math Dep, Gauhati Univ, Guwahati-781 014, , , Email: saheet-nazib@yahoo.com) : Three dimensional free convective flow and mass transfer along a porous vertical plate. Bull Allahabad Mathl Soc 2006, 21, 125-41.

Problem of three-dimensional free mass transfer flow of an incompressible viscous fluid along a vertical porous plate with trans verse sinusoidal suction velocity distribution and uniform free stream velocity is investigated. The governing equations are solved by regular perturbation technique. The expressions for the velocity field, the wall shear stress in the direction of the main flow and the rate of heat transfer and mass transfer from the plate to the fluid are obtained and some of them are demonstrated in graphs for different values of the parameters involved.

5 illus, 9 ref