021021   Kannan R;Rabert M;Sathiyamoorthi R (Statistics Dep, Annamalai Univ, Annamalainagar-608 002, Email: statkannan@yahoo.co.in) : Estimation of expected time to cross the antigenic diversity threshold of HIV infected using mixed exponential distribution. Biosci Res Bull 2012, 28(1), 21-32.

Focuses on the study of stochastic model for predicting the expected time to cross the antigenic diversity threshold of HIV infected using the intercontact times between the successive contacts are Poisson random variables. In the estimation of expected time to seroconversion, there is an important role for the inter-arrival times between successive contacts and it has a significant influence. The purpose of this study is to bringout the impact of the intercontact times and also the magnitude of contribution to antigenic diversity in successive contacts upon the time to seroconversion. The expected time to seroconversion and its variance are derived and numerical illustrations are provided using simulated data.

7 ref

021020   Kalanov T Z (NO, Home of Physical Problems, Pisatelskaya 6a, 100200 Tashkent, Uzbekistan, Email: tzk_uz@yahoo.com) : On rationalization of the foundations of differential calculus. Bull pure appl Sci 2012, 31(1), 1-7.

Logical analysis of differential calculus for the purpose of rationalization of the foundations of mathematics is proposed. Methodological basis for analysis is the unity of formal logic and rational dialectics. It is shown that the standard definitions of the concepts "variable quantity", "infinitesimal (infinitely diminishing) quantity", and "infinitely large (infinitely increasing) quantity" represent logical errors because these definitions are based on the concept of mathematical process. The correct definition of the concept "variable quantity" and the unified mathematical definition relating to both extreme cases of values of variable quantity (i.e. to the case of arbitrarily small values of the variable quantity and the case of arbitrarily large values of the variable quantity) and the case of arbitrary values of the variable quantity are proposed.

6 ref

021019   Kaladevi V;Selvarani P (Mathematics Dep, Seethalakshmi Ramaswami College, Tiruchirappalli-2, Email: kaladevi1956@gmail.com) : Detour sum and Wiener sum of chain diamond silicate network. Bull pure appl Sci 2012, 31(1), 67-72.

Let G(p,q) be a graph with p vertices and q edges. Let d(u,v) denote the distance between two vertices u, v ∈ V(G). The Wiener Polynomial of a graph G with q edges is denoted by W(G:q) and is defined as W(G, q) = Σq^d(u,v), where u, v ∈ V(G) and the sum is taken over all unordered distinct pairs of vertices u,v in V(G). The relation between Wiener Polynomial and Wiener Index is W(G) = W'(G:1) where ' denotes the first-order differentiation of W(G:q) with respect to q. Similar to Wiener Polynomial of a graph, a Detour polynomial is defined as D(G:q) = Σq^D(u,v), where D(u,v) is the detour distance between every unordered distinct pair of vertices u,v ∈ V(G). The Detour sum D(G) = D'(G:1) where ' denotes the first-order differentiation of D(G:q) with respect to q. In this paper, based on the above two definitions the Wiener Polynomial and the Detour polynomial of CHDS(n) is obtained.

5 illus, 8 ref

021018   Kaladevi V;Selvarani P (Mathematics Dep, Seethalakshmi Ramaswami College, Tiruchirappalli-2, Email: kaladevi1956@gmail.com) : Detour polynomial and Wiener polynomial of Y-tree and F-tree. Bull pure appl Sci 2012, 31(1), 9-13.

Let G(p,q) be a simple graph with p vertices and q edges. For any two vertices u and v in a connected graph G, the Detour Distance D(u,v) from u to v is defined as the length of a longest u-v path in G. The Detour Distance Polynomial or Detour Polynomial of G(p,q) is denoted by DDP(G:q) or DP(G:q) and defined as DP(G:q) = Σ^D(u,v), the sum is taken over all unordered distinct pairs of vertices u,v in V(G). The Detour sum D(G) = DP'(G:1) where ' denotes the first order differentiation of DP(G:q) with respect to q. Let d(u, v) denote the shortest distance between two vertices u,v ∈ V(G). The Wiener Polynomial of a graph G with q edges is denoted by W(G:q) and defined as W(G:q) = Σq^{d(u, v)}, where u,v ∈ V(G) and the sum is taken over all unordered distinct pairs of vertices u,v in V(G). In this paper, the Detour Polynomial and Wiener Polynomial of some special trees are obtained.

4 illus, 10 ref

021017   Kaladevi V;Dhevaki C (P.G. & Research Mathematics Dep, Seethalakshmi Ramaswami College, Trichy, Email: kaladevi1956@gmail.com) : m-Lucas numbers and m-(MY12)<. Bull pure appl Sci-Sect E 2012, 31(2), 233-41.

In this paper m-Lucas sequence is defined, which is the generalization of 2-Lucas sequence. In 2-Lucas sequence every term from third term, is a sum of previous two terms given the first number as 1 and the second number as 3. Further a new and special kind of sequence, which is the extension of m-Fibonacci and m-Lucas sequence is introduced and this is denoted by m-(MY12)^p sequence, where MY12 denotes Mathematics Year 2012. when p = 1, m-(MY12)¹ is a m-bonacci sequence and when p = 3, m-(MY12)³ is a m-Lucas sequence. The formulae for the sum of n-terms of m-Lucas sequence and m-(MY12)^p sequence, where p ∈ N, p ≠ 1, 2 are found out, similar to m-Bonacci sequence [1].

11 ref

021016   Kaladevi V;Dhevaki C (P.G. & Research Mathematics Dep, Seethalakshmi Ramaswami College, Trichy, Tamilnadu, Email: kaladevi1956@gmail.com) : Matrix modellinbg of 2-(MY)<. Bull pure appl Sci-Sect E 2012, 31(2), 175-9.

Matrix modelling of 2-Lucas sequence is discussed, inspired by the matrix modelling of Fibonacci sequence [2]. A new and special kind of sequence, which is the extension of 2-Fibonacci and 2-Lucas sequence is introduced and this is denoted by 2-(MY12)^p sequence, where MY12 denotes Mathematics Year 2012. The matrix modelling of 2-(MY12)^p sequence is also established.

5 ref

021015   Jagatheeshwari R;Lakshmi R (NO, P.S.G.R. Krishnammal College for Women, Coimbatore-641 004) : Fuzzy ideal of α₁ - near-rings. Res Highlight 2012, 22(4), 288-92.

3 ref

021014   Henry L;Selvaraj C;Sachithanantham S (Mathematics Dep, Periyar Arts College, Cuddalore-1) : Model for optimal base stock system for patient customers with lead time satisfying SCBZ property. Bull pure appl Sci 2012, 31(1), 119-28.

New type of Inventory model using the so-called setting the clock back to zero (SCBZ) property is analyzed. Base stock system for patient customers is a special type of ordering mechanism in inventory control theory. The inventory process begins with an initial inventory of B units. Whenever a customer order for V units is received, an inventory replenishment order of V units is replaced. Replenishment orders are filled after the lead time L. The customer order is filled as far as possible for the supply on hand. If the total unfilled Customer demand exceeds the supply on hand, then assume that the customer will not cancel the order but await the arrival of sufficient stock. It follows from our assumption that the sum of inventory on the ground and an order is constant in time and equal to B, known as base stock. In this problem it is assumed that the lead time is a random variable and it satisfies the SCBZ property. In the sense that before a truncation point, it has a distribution and after the truncation point, it undergoes a parametric change. Assuming that the truncation point itself a random variable, the optimal value of base stock is derived.

5 ref

021013   Hemasundar G V V (Mathematics Dep, S.I.W.S. College, 337, Sewree-Wadala Estate, Wadala, Mumbai-400 031, Email: gvvhemasundar@yahoo.co.in) : Proper holomorphic maps of plane domains of finite connectivity. J Ramanujan Mathl Soc 2012, 27(1), 41-9.

In this note, author give a proof of the fact that if Ω and Ω are domains of finite connectivity ≥ 3 in C, then the number of proper holomorphic maps from Ω to Ω is finite. As a special case we deduce a well known result that Aut(Ω) is finite for any domain Ω in C of finite connectivity ≥ 3.

2 illus, 8 ref

021012   Gupta N K;Mahto G (Mathematics Dep, S.K.M. College, Begusarai, Bihar, Email: nkgupta01beg@gmail.com) : Triangular equilibrium points in photogravitational restricted three body problem with poynting-robertson drag. Bull pure appl Sci 2012, 31(1), 95-100.

Found the equations of Motion of photogravitational restricted three body problem with poynting - Robertson Drag. We consider both primaries as radiating. We have found the position of triangular equilibrium points. The position of equilibrium points is affacted by radiation pressure and P-R Drag. All photogravitational and classical results of RTBP may be verified from this result.

8 ref

021011   Gupta N K (Mathematics Dep, S.K.M. College, Begusarai, P.O.- M. Bandwar, Dist.- Begusarai-851 129, Email: nkgupta01beg@gmail.com) : Comparative study of segregation behaviour of autotetraploid, autohexaploid and autooctaploid under selection in equilibrium state. Bull pure appl Sci-Sect E 2012, 31(2), 205-9.

Proposes the comparative study of segregation behaviour of a zygote remains unchanged if the alleles are interchanged in autotetraploid, autohexaploid and autooctaploid under selection in equilibrium state. Also discusses the optimization of gamete frequencies in a autohexaploid and autooctaploid population.

6 ref

021010   Getz J R (Mathematics and Statistics Dep, McGill Univ, Montreak, QC, H3A 2K6, Email: jgetz@math.mcgill.ca) : Approach to nonsolvable base change and descent. J Ramanujan Mathl Soc 2012, 27(2), 143-211.

Presents a collection of conjectural trace identities and explain why they are equivalent to base change and descent of automor-phic representations of GL_n(A_F) along nonsolvable extensions (under some simplifying hypotheses). The case n = 2 is treated in more detail and applications towards the Artin conjecture for icosahedral Galois representations are given.

56 ref

021009   Fasel J (NO, Mathematisches Institut der Munchen Univ, Theresienstr. 39, 8033, Munchen, Germany, Email: jean.fasel@gmail.com) : Degree map on unimodular rows. J Ramanujan Mathl Soc 2012, 27(1), 21-40.

Let k be a field and let (Aⁿ - 0) be the punctured affine space. We associate to any morphism g : (Aⁿ - 0) → (Aⁿ - 0) an element in the Witt group W(k) that we call the degree of g. We then use this degree map to give a negative answer to a question of M. V. Nori about unimodular rows.

22 ref

021008   Devasena G S;Sarma K L A P (Reader in Statistics, S.S.B.N. College, Anantapur-515 001) : Analytic solutions of a stochastic banking model with upper truncated amount of withdrawals. Bull pure appl Sci-Sect E 2012, 31(2), 267-74.

Stochastic Banking models (S.B.Ms) occupy an important place in modern research, dealing with cash flow analysis of a Banking System. Knowledge about the reserve level of a Banking system, play a vital role in many Fiscal policies of any economy. To have prospective and fruitful economic plans, one must have a prior knowledge about the cash reserve level available with the nation, without which the plans will be vague and ineffective. Hence in 1983 [3] proposed a stochastic banking model (S.B.M) with a critical reserve level (C ≥ 0) and obtain many results relating to the reserve level X(t) available with the system at any given time t ≥ 0, (vide Ref 2). Later in 1991, Sarma and Pushpanjali [5] Proposed a S.B.M.with general linear rate of inputs and obtained explicit expressions of M/G/1/FIFO/K and G/M/1/FIFO/K S.B.Ms. Further in 1995, Sarma and Sarma [6] obtained results of S.B.Ms where withdrawals or inter - withdrawals are assume to follow an Erlangian distribution. The application of this distribution to S.B.M.has more practical relevance because the service of a customer in a Bank consists of different phases like issuing of tokens, passing of the amount, making suitable entries and so on. Thus more and more practically relevant assumptions were brought in to the model, so that the S.B.M. suggested in 1983 is more and more closer to the reality. In this paper a practically valid and more essential assumption namely "Upper Truncation of Amount of Withdrawals" is incorporated into the Stochastic Banking Model in order to make the model more closer to reality and to increase the application potentiality of the model. An analytic solution of a M/M^a/1/FIFO/∞ Stochastic Banking Model (S.B.M) is obtained, Where M^a represents a upper truncated Law governing the random variable of amount of withdrawals.

7 ref

021007   Cooper S (Institute of Information and Mathematical Sciences, Massey Albany Univ, Private Bag-102 904, North Shore Mail Centre, Auckland, New Zealand, Email: s.cooper@massey.ac.nz) : Level 10 analogues of Ramanujan's series for 1/π. J Ramanujan Mathl Soc 2012, 27(1), 59-76.

Three general classes of series for 1/π are derived, one for each of the three index 2 subgroups lying between Γ₀(10) and its normalizer in SL₂(R).

23 ref

021006   Chaurasia V B L;Agnihotri M (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Application of two generalized H<. Int J latest Technol Mgmt appl Sci 2012, 1(3), 51-9.

Aim of the present paper is to apply the H^--function in solving a partial differential equation governing the forced vibration of a circular membrane.

5 ref

021005   Chaurasia V B I;Lata P (Mathematics Dep, University of Rajasthan, Jaipur-302 004) : Certain double integral relations involving the product of some transcedental functions. Int J latest Technol Mgmt appl Sci 2012, 1(3), 29-42.

Object of the present paper is to obtain few double integral relations involving the product of Fox's H-function, the multivariable H-function and the generalized polynomials. These integral relations are then applied to evaluate certain double integrals in terms of the multivariable H-function using Mellin Integral Transforms. Some interesting cases have also been discussed by proper choice of parameters.

13 ref

021004   Brion M (Grenoble 1 Univ, Institut Fourier, UMR 5582, BP 74, 38402 Saint-Martin d'Heres Cedex, France, Email: Michel.Brion@ujf-grenoble.fr) : Homogeneous bundles over Abelian varieties. J Ramanujan Mathl Soc 2012, 27(1), 91-118.

Obtained characterizations and structure results for homogeneous principal bundles over abelian varieties, that generalize work of Miyanishi and Mukai on homogeneous vector bundles. For this, we rely on notions and methods of algebraic transformation groups, especially observable subgroups and anti-affine groups.

31 ref

021003   Borkar V C (Mathematics & Statistics Dep, Yeshwant Mahavidyalaya, Nanded, Maharashtra-431 605, Email: borkarvc@gmail.com) : Decisive convergence spaces. Bull pure appl Sci-Sect E 2012, 31(2), 261-5.

Discusses definition and some basic properties of decisive convergence of ultrafilterin and decisive spaces.

6 ref

021002   Barreto S D (Mathematics Dep, Padre Conceicao College of Engineering, Verna, Goa-403 722, Email: sbarreto@pccegoa.org) : Uniqueness of equilibrium state for a quantum spin system on a graph. J Ramanujan Mathl Soc 2012, 27(2), 127-42.

Authors study a quantum spin glass [3,17] as a quantum spin system on an infinite graph. We construct the global dynamics for the quantum spin system on an infinite graph with deterministic nearest neighbour type of interactions. As expected, at a fixed temperature T, the equilibrium state [6,7,12] satisfies the kms [14,18,12] condition and is invariant under the action of the time evolution group. Furthermore, it is shown that the equilibrium state is unique if additional assumptions are made regarding the structure of the graph. Such results have been proved in the past mainly for translation invariant interactions on lattices, see [1,2,8,13]. More recently Matsui has established the uniqueness of the the Gibbs States for quantum spin models on lattices based on the ergodicity of Markov semigroups through the purification of quantum Gibbs states [10]. In our case the nearest neighbour type of interaction we have considered is more, general than similar type of interactions considered in some earlier works referred to above.

18 ref

021001   Bahan R;Pandey R N (Mathematics Dep, Patna Univ, Patna-800 005) : Pre-topological space. Bull pure appl Sci-Sect E 2012, 31(2), 257-9.

Author gave a modified definition of a pre-topological space which is a generalization of a topological space and give a few examples.

7 ref

021000   Apte H;Chattopadhyay P;Rao R A (NO, Bhaskaracharya Pratishthana, 56/14, Erandavane, Damle Path, Off Law College Road, Pune-411 004, Email: himanee200@gmail.com) : Local global theorem for extended ideals. J Ramanujan Mathl Soc 2012, 27(1), 1-20.

Established a relative version of Quillen's famous Local Global Principle for the elementary linear, symplectic and orthogonal groups acting on a unimodular row. Using this we deduce a symplectic analogue of a theorem of W. van der Kallen's Excision theorem for the action of the relative elementary linear group on the set of all relative unimodular rows.

22 ref

020999   Alshaery A A (Mathematics Dep, Faculty of Science, King Abdulaziz Univ, Jeddah, Saudi Arabia, Email: alshaary@hotmail.com) : Spatial circular restricted three-body problem (SCRTP) in sidereal cylindrical coordinates system. Bull pure appl Sci-Sect E 2012, 31(2), 153-61.

The equations of motion for the SCRTP in sidereal cylindrical coordinates system were established. Initial value procedure was given together with a numerical example and graphical representations of the variations of the two sidereal coordinate systems, Cartesian(x, y,z) and cylindrical (u₁,u₂,u₃). Many experimentations, show that, the usages of sidereal cylindrical coordinate system in the three body-problem lead to a wonderful property which is :the variations of the sidereal cylindrical coordinates during the orbital motion are very small in comparison to the corresponding variations of the Cartesian sidereal coordinates a property which produces more stable numerical integration procedures.

1 illus, 2 tables, 8 ref

017984   Wankhede-Barsagade M T;Meshram S A (Mathematics Dep, B.N. Bandodkar College of Science, Thane, Maharashtra, Email: minaltbw@gmail.com) : Use of elliptic curves in cryptography: an overview. Int J mathl Sci 2012, 11(3-4), 289-96.

Elliptic curve cryptography is based on deep mathematics involving elliptic curves in a finite field. It relies on the difficulty of solving the elliptic curve discrete logarithmic problems. Elliptic curve cryptography (ECC) is a public key encryption technique based on elliptic curve theory that can be used to create faster, smaller and more efficient cryptographic keys. ECC generates keys through the properties of the elliptic curve equation instead of the traditional method of generation as the product of very large prime numbers. The technology can be used in conjunction with most public key encryption methods, such as RSA. Many manufacturers including 3COM, Cylink, Motorola, Pitny, Bowes, Siemens, TRW and Verifone have included support for ECC in their products.

10 ref

017983   Waghmore H P;Tanuja A;Shilpa N (Mathematics Dep, Central College Campus, Bangalore Univ, Bangalore-560 001, Email: pree.tam@rediffmail.com) : Uniqueness and value-sharing of entire and meromporphic functions. Int J mathl Sci 2012, 11(3-4), 319-28.

Authors investigated the uniqueness problems on entire and meromorphic functions concerning differential polynomials sharing non-zero finite value and give some results. Obtains a number of theorems which generalize the results of R. S. Dyavanal and improve the results of S. S. Bhoosnurmath and R. S. Dyavanal and P. Sahoo.

7 ref

017982   Triolo S (Ingegneria Elettrica Dep, Elettronica e delle Telecomunicazioni, di Tecnologic Chimiche, Automatica e modelli Matematici (DIEETCAM), Palermo, Italy, Email: salvatore.triolo@unipa.it) : WQ- algebras of measurable operators. Indian J pure appl Math 2012, 43(6), 601-17.

Every C*-algebra 21 has a faithful *-representation π in a Hilbert space H. Consequently it is natural to pose the following question: under which conditions, the completion of a C*-algebra in a weaker than the given one topology, can be realized as a quasi *-algebra of operators? The present paper presents the possibility of extending the well known Gelfand - Naimark representation of C*-algebras to certain Banach C*-modules.

19 ref

017981   Singh K R;Shiva (Mathematics Dep, Meerut College, Meerut-250 001, Email: shiva.sdc@gmail.com) : Steady flow of a second-order fluid in a uniformly porous pipe. Int J mathl Sci 2012, 11(3-4), 329-36.

The unsteady flow of an incompressible second-order fluid through a uniformly porous pipe is considered. The flow function f(η) is expanded in powers of cross flow Reynolds number (assumed small). The variations of radial and axial velocities with the dimensionless radial variable η for different values of elastico-viscous parameter τ₁, cross viscous paramter τ₂ and Reynolds number R have been shown graphically. A complete description of the solution is presented and the mathematical expressions of the velocities are obtained. The radial shearing stress has also been obtained at the wall and center of the pipe.

7 ref

017980   Shiralashetti S C;Naregal S S;Veeresh B (Mathematics Dep, Karnatak Arts College, Dharwad-580 001, Email: shiralashettisc@yahoo.com) : Fast wavelet multigrid solution of the modified Reynolds equation of magnetohydrodynamic lubrication flow between rough plates. Int J mathl Sci 2012, 11(3-4), 353-64.

The effects of surface roughness on the squeeze film behaviour between two rectangular plates with electrically conducting fluid in the presence of transverse magnetic field are analysed. The modified Reynolds equation which incorporates randomized roughness structure with magnetic field is derived by assuming the roughness asperity heights to be small compared to the film thickness. Christensen stochastic theory is incorporated for modeling roughness. This equation is analyzed with Fast wavelet multigrid method. This method has the greatest advantage of minimizing errors using wavelet transforms in obtaining accurate solution as grid size tends to zero. It is found that, seven V-cycles are required to obtain a reasonably accurate solution in the multigrid scheme, whereas, only one modified V-cycle is required to obtain desired accuracy by Fast wavelet-multigrid method. Also, matrix of DWT acts as a natural preconditioner producing rapid convergence. Lubrication characteristics which are functions of roughness, Hartmann number and aspect ratio parameter are obtained. It is observed that effect of roughness and magnetic field is to provide significant load carrying capacity and ensure a delayed squeezing time compared with classical case.

5 illus, 16 ref

017979   Sharma P L;Kanwar R K (Mathematics Dep, Himachal Pradesh Univ, Shimla-171 005) : Adjoint of a Rhotrix and its basic properties. Int J mathl Sci 2012, 11(3-4), 337-43.

Describes the adjoint of a rhotrix, the scalar rhotrix and prove some related analogous theorems of matrices in the context of rhotrices.

7 ref

017978   Sharma P K;Bansal V (P.G. Mathematics Dep, D.A.V. College, Jalandhar City, Email: pksharma@davjalandhar.com) : On intuitionistic anti-fuzzy ideal in rings. Int J mathl Sci 2012, 11(3-4), 237-43.

Authors apply the Yuanli, Zhang, Quanma's idea of intuitionistic anti- fuzzy subgroups to subring and ideal of a ring. Introduces the notion of intuitionistic anti-fuzzy subring and intuitionistic anti-fuzzy ideal of rings, and investigate some related properties.

10 ref

017977   Sharma P K;Bahl A (P.G. Mathematics Dep, D.A.V. College, Jalandhar City, Punjab, Email: pksharma@davjalandhar.com) : Translates of intuitionistic fuzzy submodules. Int J mathl Sci 2012, 11(3-4), 277-87.

As an abstraction of the geometric notion of translation, first author has introduced two operators T_χ+ and T_χ- called the intuitionistic fuzzy translation operators on the intuitionistic fuzzy set and studied their properties and also investigate the action of these operators on the intuitionistic fuzzy subgroups of a group in [11] and on intuitionistic fuzzy subring and ideals of a ring in [12]. Authors discusses the action of these operators on the intuitionistic fuzzy submodules of a module.

13 ref

017976   Sharma P K (P.G. Mathematics Dep, D.A.V. College, Jalandhar City, Punjab, Email: pksharma@davjalandhar.com) : t-intuitionistic fuzzy subrings. Int J mathl Sci 2012, 11(3-4), 265-75.

The notion of f-intuitionistic fuzzy subring (normal subring and ideals) are defined and discussed. The homomorphic behavior of f-intuitionistic fuzzy subring (normal subring and ideals) and their inverse images has been obtained. Some related results have been derived.

13 ref

017975   Sharma N M;Gulhane P A (Mathematics Dep, H.V.P.M.'s College of Engg. and Technology, Amravati, Email: nidhimanish.sharma337@gmail.com) : Heaviside's unit step function based on fourier-stieltjes transform. Int J mathl Sci 2012, 11(3-4), 215-20.

Deals with distributional generalized Fourier Stieltjes (FS) transform of distributional function f in dual space of FS_{a, b} i.e. FS*_{a, b}. Discussed some properties of FS transform. Authors have also extended the properties for Heaviside' s unit step function on FS transform and discussed Fourier stieltjes transform of Selected Function.

3 ref

017974   Shakila Banu P (Mathematics Dep, Karpagam Univ, Coimbatore-641 021) : EP matrices over an incline. Int J mathl Sci 2012, 11(3-4), 175-82.

The characterization of EP matrices over an incline are developed with transpose-Tare obtained as a generalization and development of EP elements in a *-regular ring, EP elements in a reflexive semigroups. The results of this paper are generalization of the results available in the literature.

6 ref

017973   Sengupta S (NO, Delhi Public School, R.K.Puram, Email: shayonsengupta@gmail.com) : On the behavior of members and their stopping times in collatz sequences generated by variations in powers of two. Int J mathl Sci 2012, 11(3-4), 345-52.

Proposes some results that are related to the Collatz sequences generated by some variations in consecutive powers of two. Examineed these series from the perspective of strings, and match patterns and generate formulas that further prove the former claims. This paper further attempts to prove that the Collatz conjecture holds true for values greater than those which it has been computationally tested.

3 ref

017972   Sapkota B P (NO, Tribhuwan Univ, Nepal, Email: buddhisapkota@yahoo.com) : Mathematical modeling of indoor air pollutants distribution from biomass cook stoves in Nepal. Int J mathl Sci 2012, 11(3-4), 561-9.

30 ref

017971   Saini R K;Sangal A (NO, Mathematical Sciences and Computer Applications Dep, B.U. Jhansi) : Fixed point results on fuzzy metric space. Int J mathl Sci 2012, 11(3-4), 541-59.

Authors proved common fixed point theorems on fuzzy 2 and 3-metric spaces by introducing new Φ function. The theorem is an extension of result of Fisher, Sharma to fuzzy metric spaces.

35 ref

017970   Rama R;Badarla S;Mahalingam K;Yadav S K (Mathematics Dep, Indian Institute of Technology, Chennai, Email: ramar@iitm.ac.in) : Self-assembly of graphs of edges. Int J mathl Sci 2012, 11(3-4), 309-18.

Self-assembly is a process in which simple objects autonomously combine themselves into larger objects. Two simple connected graphs can be self assembled on edges. The decomposition of possibly self-assembled graphs given a set of generators of the given graph. A decomposition algorithm is given for this purpose which leads to a method of finding HPP in a given graph. If the given graph (possibly self-assembled) has HPP, then the base has HPP. Converse need not be true.

10 ref

017969   Pitchaimani M;Divya M (Ramanujan Institute for Advanced Study in Mathematics, Madras Univ, Chepauk, Chennai-600 005) : Homotopy perturbation method for solving HIV-1 infection model. Int J mathl Sci 2012, 11(3-4), 411-21.

Implemented Homotopy perturbation method to give approximate and analytical solutions of non-linear ordinary differential equation systems such as a model for HIV-1 infection. A modification of the homotopy perturbation method (HPM), based on the use of Pade approximants, is done. Some plots are presented to show the reliability and simplicity of the methods.

3 illus, 15 ref

017968   Pitcahimani M;Monica C (Ramanujan Institute for Advanced Study in Mathematics, Madras Univ, Chapauk, Chennai-600 005) : Stability analysis for HIV-1 infection dynamics using the matrix Lambert W function. Int J mathl Sci 2012, 11(3-4), 423-32.

Authors investigate the stability of the HIV-1 infection dynamical problem. An approach using the matrix Lambert W function for the analytical solution to system of delay differential equations is applied to this problem and compared with the result obtained using a bifurcation analysis.

27 ref

017967   Nawaz R (Mathematics Dep, Comsats Institute of Information Technology, Quaid Avenue, The Mall Wah Cantt., Pakistan, Email: rahi_qau@yahoo.com) : Acoustic difraction by an absorbing finite strip in a moving fluid. Indian J pure appl Math 2012, 43(6), 571-89.

The problem of cylindrical acoustic wave diffraction from an absorbing finite barrier in a moving fluid has been investigated in an improved form. The diffracted field in the far zone has already been discussed in [1], but due to some mathematical complications, the absorbing parameter was ignored in that study. In the present analysis the absorbing parameter is taken into account up to order one and presented in a better form solution. Moreover, the solution obtained in this analysis can be used to recover the results for the case of semi-infinite barrier [2] by taking an appropriate limit l → ∞. The results for still fluid can also be gathered by taking the value of Mach number to be zero. The integral transforms, Wiener-Hopf techniques and asymptotic expansions are used to acquire the diffracted field in the far zone. Finally, the solution is well supported by the graphical results showing the effects of various physical parameters on the separated field.

9 illus, 8 ref

017966   Nath D C;Bhattacharjee A;Singh H B (Statistics Dep, Gauhati Univ, Guwahati-781 014, Email: dilipc.nath@gmail.com) : Bayesian approach in structural equation modeling for human fertility in Manipur. Int J mathl Sci 2012, 11(3-4), 245-54.

The Structural Equation Modeling (SEM) is useful to deal with unobserved heterogeneity in the data. This paper is contributed with application of SEM through Bayesian approach to deal with unobserved heterogeneity effect in the fertility level of women residing in Manipur. It has been found that the high educational level is contributed for low fertility as compared to the low educational level. Also low income level has been observed as the contributing factor for the high fertility. The findings may be baseline information for future policy implication.

3 tables, 26 ref

017965   Mukwembi S;Dorothy S;Musekwa H (School of Mathematics Statistics and Computer Science, KwaZulu-Natal Univ, Westville Campus, South Africa, Email: mukwembi@ukzn.ac.za) : On bounds for the cutting number of a graph. Indian J pure appl Math 2012, 43(6), 637-49.

The cutting number of a vertex v of a finite graph G = (V, E) is a natural measure of the extent to which the removal of v disconnects the graph. Precisely, the cutting number c(v) of v is defined as the number of pairs of vertices {u,. w} of G such that u, w ≠ v and every u-w path contains v. The cutting number c(G) of G is the maximum value of c(v) over all vertices in V. We provide exact bounds on the cutting number of G in terms of order and diameter of the graph.

1 illus, 20 ref

017964   Mayil Vaganan B;Senthilkumaran M;Shanmuga Priya T (Applied Mathematics and Statistics Dep, Madurai Kamaraj Univ, Madurai-625 021) : Generalized cole-hopf transformation for a two-dimensional burgers equation with a variable coefficient. Indian J pure appl Math 2012, 43(6), 591-600.

Thr direct method is applied to the two dimensional Burgers equation with a variable coefficient (u_t + uu_x - u_xx)_x + s(t}u_yy = 0 is transformed into the Riccati equation H^t - 1/2 H² + (ρ/2 - 1) H = 0 via the ansatz u(x, y. t) = 1/<82>t H(ρ) + y/2√t ρ(x, y, t] = x/√t - y, provided that s(t) = t^-3/2. Further, a generalized Cole-Hopf transformations u(x.y,t) = y/2√r - 2/√t U_ρ (ρ, r)/U(ρ, r), ρ(x, y, t) = x/√t - y, r(t) - log t is derived to linearize (u_t + uu_x - u_xx)_x + t^-3/2 u_yy = 0 to the parabolic equation U_r. = U_{ρρ + (ρ/2 - 1) Uρ.}

13 ref

017963   Mallem S S (NO, , ) : Any number divisible by zero. Int J mathl Sci 2012, 11(3-4), 471-4.

017962   Mallem S S (NO, , ) : Any number multiplied by zero. Int J mathl Sci 2012, 11(3-4), 297-9.

017961   Lata Rani (NO, Singhania Univ, Pacheri Bari, Jhunjhunu, Rajestan) : Release policies based on cost and reliability criteria considering testing effort and efficiency. Int J mathl Sci 2012, 11(3-4), 525-40.

In this paper, authors discusses a model which integrates fault removal efficiency, failure rate and fault introduction rate into software reliability assessment. It considered imperfect debugging in the sense that not all faults can be removed completely, and new faults can be introduced while removing the existing ones. Secondly we give a brief review of a SRGM with generalized logistic testing effort function (TEF) which can be used to describe the actual consumption of resources during the software development process. Further, if software developers want to detect more faults in practice, it is advisable to introduce new test techniques, tools, or consultants, etc. Consequently, Discusses a software cost model that can be used to formulate realistic total software cost projects and diseoss the optimal release policy based on cost and reliability considering testing effort and efficiency.

6 ref

017960   Lakshmi S;Senbagavalli M (NO, Kunthavai Naachiar Govt. Arts College for Women, Thanjavur, Tamil Nadu) : Mathematical model for finding the steadystate and transient behavior of the secretion of vasopressin in hypertension cases. Int J mathl Sci 2012, 11(3-4), 393-9.

Impairment of humoral and neural regulation of blood pressure may contribute to preoperative and postoperative hypertension in coarctation of the aorta and may also affect the release of vasopressin. Because vasopressin has potent vasoactive effects, we measured plasma vasopressin before operation and after operation. Before operation, vasopressin levels correlated with systolic blood pressure. The inability to predict the hypertension and difficulty in applying the traditional valuation methods, induced to apply the results on both the steady state and transient behaviour of the model to study the size distribution of effects of vasopressin on hypertension. The application part is fitted with the mathematical model and conclusion is compared with medical report.

1 illus, 19 ref

017959   Lakshmi S;Saiva Raju N;Kavitha N (NO, K.N. Govt. Arts College for Women, Thanjavur) : Mathematical model for finding the secretion of salivary α-amylase and cortisol in children with asthma and healthy children and also with chronic stress. Int J mathl Sci 2012, 11(3-4), 453-61.

Birnbaum-Saunders distribution is a mixture, in equal proportions of an inverse Gaussian distribution and a reciprocal inverse Gaussian distribution. Desmond provided a more general derivation of this distribution based on a biological model. Birnbaum-Saunders derived maximum likelihood estimators for the parameters of the distribution. The survival function of the Birnbaum-Saunders distribution is used to find the function of the medical applications. Here the medical study examined whether chronic stress is related to daily life levels of salivary α-amylase, a marker for sympathetic activity and cortisol in healthy children versus children with asthma, which is well explained by the Mathematical results. Mathematical results are compared with medical results.

6 illus, 15 ref

017958   Lakshmi S;Manickam A (NO, K.N. Govt. Arts College for Women, Thanjavur, Tamilnadu, Email: lakshmi291082@yahoo.co.in ) : Mathematical MDDI model for differential orderliness of the GH release process in human and animals. Int J mathl Sci 2012, 11(3-4), 455-51.

Authors introduces the minimum dynamic discrimination information (MDDI) approach to probability modeling the results lead to MDDI characterizations of many well-known life time models and to the development of application part. Male and female specific modes of episodic growth hormone release are presumptively imposed by sex-steroid hormones are vividly distinguished contractively viva, a regularity statistic approximate entropy (ApEn), in both the rat and human. Investigates the orderliness of the growth hormone release process by the MDDI model relative to the exponential distribution which are monotonically concave downward functions.

1 illus, 19 ref