022018   Pandey K P;Goyal A;Tiwari B (NO, Madhav Proudyogiki Mahavidyalaya Zirnia, Narsinghgarh Road, Bhopal-462 030, Email: pandeykamleshwar@yahoo.com) : Study of (ε)- almost paracontact metric manifold-1. Ultra Scient phys Sci-Sect A 2012, 24(1), 171-6.

The object of the present paper is to studies of special (∈)-para Sasakian manifold and its properties. We have shown that a recurrent special (∈)- para Sasakian manifold with η, as 1-form of recurrence is Einstein manifold. Among others.

15 ref

022017   Nithyanantha Jothi S;Thangavelu P (Mathematics Dep, Aditanar College, Tiruchendur-628 216, Email: nithananthajothi@gmail.com) : On binary continuity and binary separation axioms. Ultra Scient phys Sci-Sect A 2012, 24(1), 121-6.

Recently the authors introduced the concept of binary topology between two sets and investigate its basic properties where a binary topology from X to Y is a binary structure satisfying certain axioms that are analogous to the axioms of topology. In this paper we introduce and study binary-T₀, binary-Ti and binary-T2 axioms that are analogous to the separation axioms of topology. Binary continuity is also characterized.

3 ref

022016   Mishra R K;Choudhary S;Shrivastava R (Mathematics Dep, BERI, Bhopal) : Common fixed point theorem for four mappings in fuzzy metric space. Ultra Scient phys Sci-Sect A 2012, 24(1), 240-4.

Authors prove common fixed point theorem for four mappings using new condition in fuzzy metric spaces.

21 ref

022015   Mishra R K;Choudhary S;Shrivastava R (Mathematics Dep, BERI., Bhopal, M.P.) : Common fixed point theorems for two mappings in fuzzy metric space. Ultra Scient phys Sci-Sect A 2012, 24(1), 15-18.

The concept of fuzzy sets was introduced initially by Zadeh in 1965. Georgeand Veeramani modified the concept of fuzzy metric space introduced. Fisher, Aliouche and Fisher, Telci proved some related fixedpoint theorems in compact metric spaces. Recently, Rao et. al. proved some fixed point theorems in sequentially compact fuzzy metric spaces. Motivated by a work due to Popa, we have observed that proving fixed point theorems using an implicit relation is a good idea since it covers several contractive conditions rather than one contractive condition.

10 ref

022014   Mangal I K;Singh J R;Sankle R (NO, Madhav Science College, Ujjain, Email: jrsinghstat@gmail.com) : Effect of measurement error on the control chart for mean under known coefficient of variation. Ultra Scient phys Sci-Sect A 2012, 24(1), 219-26.

Authors investigated the effect of measurement error on the mean ( X ) chart with known coefficient of variation (CV). Described the operating characteristic (OC) curve of the X chart where both the process average and CV changes.

4 tables, 6 ref

022013   Mangal I K;Singh J R;Sankle R (NO, Madhav Science College, Ujjain, Email: jrsinghstat@gmail.com) : Effect of measurement error on sampling plan under known coefficient of variation. Ultra Scient phys Sci-Sect A 2012, 24(1), 213-8.

Authors investigated that in what way the operating characteristic (OC) function of the usual variables sampling inspection plans with known coefficient of variation (CV) based on the assumption of normality, error free case and independent observation, are effected when the characteristic of an item possesses a measurement error.

2 tables, 4 ref

022012   Magesh N;Balaji M K;Sattanathan R (Mathematics Dep, Government Arts College (Men), Krishnagiri-635 001, Email: nmagi_2000@yahoo.co.in) : Subordination properties for certain subclasses of prestarlike functions. Ultra Scient phys Sci-Sect A 2012, 24(1), 99-110.

Making use of Salagean derivation operator in this paper, we define a generalized class of star like functions with negative coefficients and obtain subordination result, partial sums, integral transform for this class. Further internal means and square root transformation result are discussed.

11 ref

022011   Kavitha K;David N G (Mathematics Dep, Madras Christian College, Chennai-600 059, Email: kavitha.matha@yahoo.com ) : Split and non-split dominator chromatic numbers. Ultra Scient phys Sci-Sect A 2012, 24(1), 246-8.

Graph coloring and graph domination are two major research areas in the field of graph theory. Authors introduce the concept of split and non-split dominator coloring, which combine the concept of domination and coloring and prove some interesting results.

3 ref

022010   Jindal N;Sharma A;Agrawal V (NO, Chartered Institute of Technology, AbuRoad, Rajasthan, Email: er.neerajjindal@yahoo.com) : RSA: the mathematical approach. Engng Technol India 2012, 1(7), 51-3.

RSA is an important cryptographic technology that is widely used to provide secure transmission of data. It's an application of number theory which uses principles of abstract algebra and modular arithmetic to encrypt and decrypt messages. RSA is named after Rivest, Shamir and Adleman, the individuals who first published the technique. It is very simple to multiply numbers together, especially with computers. But it can be very difficult to factor numbers. RSA was the first algorithm known to be suitable for signing as well as encryption and one of the first great advances in public key cryptography. RSA is widely used in electronic commerce protocols, and is believed to be secure given sufficiently long keys and the use of up-to-date implementations. The security of RSA lies under its large keys size because factoring is a hard problem for prime numbers. The security of relies on the fact it is difficult to factor sufficiently large numbers. No polynomial-time method for factoring large integers on a classical computer has been found yet. However, it has not been proven that none exists. As of November 8, 2005, the largest number factored by general purpose methods was 640 bits long (known as the RSA-640 number) which was a 193 digit number. This factorization was done on 80 CPU's working together and took approximately four and a half months, total. The prize that the German BSI team received for factoring this number was $20,000. Because of the different methods of factorization that are being used with the help of linked computers super-computers, the current recommendation for the product of primes, N, is for it to be is at least 2048 bits long. However, if quantum computing reaches a sufficient level, as it is predicted to be no earlier than 2015, it potentially can perform factorization in polynomial time, rendering RSA and related algorithms obsolete.

3 ref

022009   Gupta P;Hajam M S (School of Studies in Statistics, Vikram Univ, Ujjain-456 010) : Cost benefit analysis of 2-out of 3: G system with correlated failure and repair times. Ultra Scient phys Sci-Sect A 2012, 24(1), 157-64.

The paper analyses a stochastic model of a cold standby system consisting of three non identical units-A, B and C in which two units are operative at a time. A single repair facility is considered to repair a failed unit. The priority in operation is being given to unit A over to unit B and to unit B over unit C. In case of repair of failed units the priority is just reverse than operation. The failure and repair times of each unit are assumed to follow bivariate exponential distribution. Several measures of system effectiveness are obtained by using regenerative point technique.

1 illus, 8 ref

022008   Gnanachandra P;Thangavelu P (Mathematics Dep, Aditanar College, Tiruchendur-628 216, Email: pgchandra07@rediffmail.com) : Remarks on rg-closure, gpr-closure operators and gpr-separation axioms. Ultra Scient phys Sci-Sect A 2012, 24(1), 185-91.

Recently Jin Han Park et. al. studied rg-continuity and some preservation theorems using rg-closure operator and Gnanambal et.al. discussed gpr-continuous functions using gpr-closure operator. Quite Recently Balasubramanian et.al. discussed several types of gpr-separation axioms. The purpose of this paper is to investigate some properties of rg-closure operator, gpr-closure operator and gpr-separation axioms. The most important result that is proved in this paper is "In a topological space every singleton set is rg-open" that leads to the investigation of some of the results due to Jin Han Park et. al. Gnanambal et. al. and separation axioms due to Balasubramanian et. al.

14 ref

022007   Fernandez S;Sebastian S (Mathematics Dep, St. Albert's College, Kochi-682 018, Email: souriarsebasatian@gmail.com) : On pseudo fuzzy complements of fuzzy sets and the existence of equilibrium and dual points. Ultra Scient phys Sci-Sect A 2012, 24(1), 87-90.

Fuzzy sets are sets with boundaries that are not precise. Fuzzy complements are fuzzy sets on [0,1 ] satisfying two axioms, viz. boundary conditions and monotonicity. But the existence of an equilibrium point of a fuzzy complement depends on its continuity. Here we introduce a new concept: pseudo fuzzy complement and prove that all such complements have a unique equilibriumpoint and dual point.

4 ref

022006   Earnest Lazarus Piriyakumar J;Vasuky M (Mathematics Dep, Tranquebar Bishop Manickam Lutheran College, Porayar-609 307, Email: jelpriyakumar@yahoo.com) : On the existence of supremum and infimum of fuzzy random variables. Ultra Scient phys Sci-Sect A 2012, 24(1), 47-58.

Investigates upon the characteristics on the existence of supremum and infimum of fuzzy random variables. This paper provides an improved version of the supremum and infimum of fuzzy random variables which plays a crucial role in the theoretical framework of the same. Finally the existence of supremum and infimum of the level continuous fuzzy valued measurable functions on a closed interval is examined and a necessary and sufficient condition with which its supremum and infimum can be attained, is provided.

8 ref

022005   Dorsett C (NO, Texas A&M Univ-Commerce, Texas (USA)) : Finite sets, closed images, and separation axioms. Ultra Scient phys Sci-Sect A 2012, 24(1), 235-9.

Additional topological characterizations of finite sets are given using closed images and separation axioms.

3 ref

022004   Dhanasekar S;Harikumar K;Sattanathan R (NO, , S.R.M., Univ, Email: dhana17101975@gmail.com) : New approach for solving fuzzy assignment problem. Ultra Scient phys Sci-Sect A 2012, 24(1), 111-16.

Assignment problem is a well known topic and is used very often in solving problems of engineering and management sciences. If the cost is not deterministic, then the problem is said to be assignment problem with fuzzy costs. Proposes a new algorithm to solve this fuzzy assignment problem.

8 ref

022003   Das R K;Narendra Kumar (Maths P.G. Dep, S.K.M. Univ, Dumka-814 101) : Fuzzy relational maps between two disjoint units of association. Ultra Scient phys Sci-Sect A 2012, 24(1), 117-20.

The paper is addressed to the introduction of a new notion of fuzzy relational maps by dividing the casual association of fuzzy cognitive maps of Taber into two disjoint units respectively named as domain and range space, the number of elements in these spaces being not equal. Also determines the methods of determination of hidden pattern and combined fuzzy relational maps.

6 ref

022002   Chongdar A K;Bera C S (Mathematics Dep, Bengal Engineering and Science Univ, Shibpur. P.O. Botanic Garden, Howrah-711 103) : On bilateral generating functions involving modified Jacobi polynomials from the group - theoretic view point. Ultra Scient phys Sci-Sect A 2012, 24(1), 1-8.

In this note, authors have obtained some novel results on bilateral generating functions involving P^{(α+n, β}_n+k (x), a modified form of Jacobi Polynomials by group theoretic method. In fact, in section 1, we have introduced a linear partial differential operator R which do not seem to have appeared in the earlier investigations and then we have obtained the extended form of the group generated by R. Finally, in section 2, we have obtained a novel generating relation involving the polynomial under consideration with the help of which, we have proved a general theorem on bilateral generating relations of P^(α+n,β)_n+k (x). Some particular cases of interest are also discussed.

1 ref

022001   Bera C S;Chongdar A K (Mathematics Dep, Bengal Engineering and Science Univ, Shibpur. P.O. Botanic Garden, Howrah-711 103, Email: chongdarmath@yahoo.co.in) : On some generating functions of modified jacobi polynomials. Ultra Scient phys Sci-Sect A 2012, 24(1), 41-6.

Author have obtained a novel extension of a theorem on bilateral generating function of modified Jacobi polynomials from the existence of quasi - bilateral generating function by group theoretic method.

3 ref

022000   Baruah A K (Mathematics Dep, Dibrugarh Univ, Dibrugarh-786 004, Email: baruah_arun123@rediffmail.com) : Extrapolation method in multiparameter eigenvalue problems. Ultra Scient phys Sci-Sect A 2012, 24(1), 81-6.

In solving multiparameter eigenvalue problem in the form of ordinary differential equations satisfying certain boundary conditions by shooting method, good starting values of the eigenvalues to be determined are always in need. Unlike trial and error method, in this paper we present a numerical procedure based on extrapolation method to find the starting values.

20 ref

021999   Bali R;Swati (Mathematics Dep, Rajasthan Univ, Jaipur-302 004, Email: balir5@yahoo.co.in) : Bianchi type I inflationary cosmological model with cosmological constant A. Ultra Scient phys Sci-Sect A 2012, 24(1), 35-40.

Inflationary cosmological model with cosmological constant A in the structure of Bianchi Type I space-time is investigated. To get the deterministic model of the universe, it has been assumed that ABC = e^3Ht and V(φ) = constant, where A,B,C are metric potentials, H the Hubble constant, V the flat potential, φ the Higg's field. It is found that inflationary scenario exists in Bianchi Type I space-time, the Higg's field decreases with time, the cosmological constant decreases with time and A tends to constant quantity when t → ∞. Since shear a ≠ 0 for large values of t, hence anisotropy is maintained for large values of t. However, when a=0, d = 0 then the model isotropizes. The physical aspects of the model in context to inflationary scenario are also discussed.

19 ref

021998   Amal S J F K;Thivagar L (NO, Loyola College, Nungambakkam, Chennai-600 034, Email: kamalsj@gmail.com) : Fuzzy linguistic congnitive maps and its applications to psychological problems faced by rural students studying in Tamil Nadu city colleges. Ultra Scient phys Sci-Sect A 2012, 24(1), 192-8.

Authors for the first time introduce a new fuzzy dynamical System, viz. Fuzzy Linguistic Cognitive Maps (FLCM) model which works on 'min' and 'max' operations. We apply this new model to the problem of rural students in city colleges, especially taking/studying their psychological problems for it cannot be directly studied using supervised data. This paper has three sections. Section one introduces this new model. Section two applies this problem to the psychological problems faced by the rural students studying in city colleges. The final section gives the use as well as the advantages of using the model.

2 illus, 2 ref

021997   Amal S J F K;Thivagar L (NO, Loyola College, Chennai-34) : Analysis of the problems faced by poor rural students studying in Chennai city colleges using FCM models. Ultra Scient phys Sci-Sect A 2012, 24(1), 27-34.

Author study the problems faced by poor rural students studying in Chennai city colleges using Fuzzy Cognitive Maps (FCMs) model. This paper has four sections. In section, one the problems faced by these students as taken from data collected from them is described and justification for using FCMs is also given. Section two briefly describes the FCM model. Section three gives the two FCM models given by students and the teachers. The hidden pattern and the conclusions based on this study is given in the final section.

2 illus, 3 ref

021996   Ahluwalia K K;Ronghe A K (NO, Mata Gujri Mahila Mahavidyalaya, Jabalpur-482 001, Email: kulwant.ahluwalia34@gmail.com) : Fourier series expansions of ??H - function. Ultra Scient phys Sci-Sect A 2012, 24(1), 199-203.

Authors are evaluating sine and cosine series expansions of H -Function defined by Inayet Hussein⁴ and employ them to establish certain integral for H -Function.

6 ref

021048   Vijayan A;Binu Selin T (Mathematics Dep, Nesamony Memorial Christain College, Marthandam-629 165, Kanyakumari District, Tamil Nadu, Email: naacnmccm@gmail.com) : Introduction to geodetic polynomial of a graph. Bull pure appl Sci 2012, 31(1), 25-32.

Introduced a new geodetic polynomial of a graph G. The geodetic polynomial of a graph G of order n is the polynomial g(G, x) = Σⁿ_i=g(G) g_e(G,i)x', where g_e(G,i) is the number of geodetic sets of G of size i and g(G) is the geodetic number of G. Obtains some properties of g (G,x) and its coefficients. Also, computed the polynomial for some specific graphs.

2 illus, 8 ref

021047   Venkata Ramudu B;Bhagya Lakshmi M (Statistics Dep, SSBN Degree & P.G. College, Anantapur-515 001, Email: venkataramudussbn@gmail.com) : Optimal replacement problem using two monotone processes. Bull pure appl Sci-Sect E 2012, 31(2), 217-24.

This paper studies a simple repairable system assuming that the system after repair is not as good as new' and also the successive working times form a decreasing α-series process and exposing to exponential failure law while the successive repair times form an increasing geometric process and exposing to Weibull failure law. Under these assumptions we study an optimal replacement policy N under which we replace the system when the number of failures reaches N. We derive an explicit expression of the long-run average cost per unit time and determine an optimal repair replacement policy N* such that the long, run average cost per unit time is minimized. Numerical results are provided to support the theoretical results.

1 table, 13 ref

021046   Venkat Raman P;Chary C K N (NO, Alluri Institute of Management Science, Warangal, Email: asstram@yahoo.co.in) : Non-darcian MHD flow of a newtonian fluid through a uniform circular rotating porous tube. Bull pure appl Sci-Sect E 2012, 31(2), 193-203.

Examined MHD steady flow of a Newtonian slightly conducting fluid through a uniform circular rotating porous tube in the presence of pressure gradient under the influence of a uniform magnetic field acts perpendicular to the flow direction. The tube is subjected to the rotating with an angular velocity and the non-Darcian equation of the flow is applied to examine the flow in porous medium. The solutions for the velocity and angular velocity distributions of a Newtonian fluid flowing through a uniform circular tube are obtained. The effect of the permeability parameter on the angular velocity and the flow of the fluid in completely investigated and represented graphically.

3 illus, 19 ref

021045   Urkude G P;Jumale R K;Jumale J K;Thengane K D (NO, Eklavya Residential School, Khairi-Parsoda, Ramtek, Distt.- Nagpur-441 106, Email: gowrdhanpurkude@rediffmail.com) : Generalized plane wave-like solutions of field equations of Bonnor and Schrodinger's unified filed theory in V₅. Bull pure appl Sci 2012, 31(1), 33-42.

Pandey [8] has investigated plane wave-like solutions of Bonnor and Schrodinger's field equations in four dimensional generalized Peres space-time on the lines of Takeno [6]. In the present paper, the work of Pandey [8] has been extended to higher five dimension and obtained five dimensional generalized plane wave-like solutions of field equations of Bonnor and Schrodinger's non-symmetric unified field theory in generalized Peres-space-time. It is found that the field equations proposed by Schrodinger do not have any plane wave-like solution. It is pointed out that solution of Pandey [8] is a particular case of solution presented here.

12 ref

021044   Ubale P V (NO, G.S. Science, Arts, Commerce College, Khamgaon-444 303, Email: prafullaubale@hotmail.com) : Approach for the optimal solution of Milp problems. Bull pure appl Sci-Sect E 2012, 31(2), 169-73.

Describes an algorithm for finding solutions to optimization problems in which some of the variables must take integer values. The solution of discrete optimization problem to optimality is often an immense job requiring very efficient algorithm. Describes a Branch and Bound algorithm to solve MILP problems.

4 ref

021043   Thilakam K;Sumathi A (NO, Seethalakshmi Ramaswami College, Tiruchirappalli-620 002, Email: suma_shivasrc@yahoo.com ) : Wiener number of arbitary super subdivisions of wheel W and fan F_n. Bull pure appl Sci-Sect E 2012, 31(2), 211-16.

The Wiener index W(G) of a connected graph G is the sum of the distances between all (ordered) pairs of vertices of G. In this paper, we give theoretical results for calculating the Wiener index of arbitrary super subdivisions of Wheel, Fan. These formulas pave the way to demonstrate the Wiener number of some molecular structures in future.

6 ref

021042   Susiganeshkumar E;Elangovan R;Sathiyamoorthi R (Community Medicine Dep, Sri Venkateshwaraa Medical College Hospital and Research Centre, Ariyur, Pondicherry-605 102, Email: susijk@rediffmail.com) : Estimation of expected time to recruitment under two sources of depletion of manpower. Bull pure appl Sci 2012, 31(1), 73-84.

Attrition is a common phenomenon in many organisations. This leads to the depletion of manpower. Recruitment on every occasion of manpower is not possible. Hence the cumulative depletion of manpower is permitted till.'it reaches a level called the threshold. If the total loss of manpower crosses the threshold the activities will be affected and hence recruitment becomes necessary. In this paper it is assumed that the depletion of manpower occurs due to two reasons namely the depletion after every occasion of policy decisions regarding pay, perquisites and work target. The other reason for depletion is due to transfer of personnel to sister organizations. The expected time to recruitment is derived under the assumption that the threshold itself is a random variable. Numerical illustrations are also given.

5 illus, 4 tables, 15 ref

021041   Surya P;Sivakamasundari K (Mathematics Dep, Avinashilingam Institute for Home Science and Higher Education for Wo, Coimbatore-641 043) : Construction of g- semi closed sets and g_α- closed sets for given topologies. Res Highlight 2012, 22(3), 204-10.

7 ref

021040   Sreenivasulu Reddy P;Shobhalatha G (Mathematics Dep, Narayana Emgineering College, Nellore-524 004) : Semirings satisfying the identity a + 1 = 1 + a = a. Bull pure appl Sci 2012, 31(1), 63-6.

In this paper author presented some results on semirings which satisfying the identity a + 1 = 1 + a = a for all a in S.

3 ref

021039   Sivatski A S (NO, St. Petersburg Electrotechnical Univ, 197376, St. Petersburg, Russia, Email: alexander.sivatski@gmail.com) : Applications of conics to quadratic forms over the rational function fields. J Ramanujan Mathl Soc 2012, 27(2), 241-54.

It is shown that for any forms ϕ1 and ϕ2 over a field k of characteristic different from 2 and a ∈ k*, the anisotropic part of the form ϕ₁ ⊥ (t² - a)ϕ₂ over the rational function field k(t) is of the same type, i.e. there exist forms τ₁ and τ₂ over k such that (ϕ₁ ⊥ (t² - a)ϕ₂) an ≈ τ₁ ⊥ (t² - a)τ₂. Also we determine the structure of certain Pfister forms over k(t), and describe the behavior of quadratic forms under biquadratic extensions of k in terms of some related forms over the function field of the product of two conies over k(x), or k(x, y). The excellence property of the function field of a conic plays the central role throughout the paper.

10 ref

021038   Singh Y;Manish Kumar;Singh S (School of Mathematics Statistics and Computational Sciences, Central Rajasthan Univ, Kishangarh, Ajmer) : Statistical analysis of air pollution based on expected number of exceedances in Jaipur city. Int J Pharmac biol Sci 2011, 5(3), 81-5.

In order to protect the population from adverse health effect due to pollution many governments choose to set a standard. Such standard usually take the form of some stated upper limit which pollutant level should not exceed. Such standard is called deterministic or ideal standard. An ideal standard describe the overall global situation but ignores the uncertainty and variation to examine compliance with it. In this paper we discuss the air pollution standard based on the expected number of exceedancies and on the basis of these standards we analyze the air pollution level in Jaipur city.

1 table, 6 ref

021037   Sharma V (Mathematics Dep, N.A.S. (P.G.) College, Meerut, Uttar Pradesh) : Operational readiness of a multistage complex repairable system. Bull pure appl Sci 2012, 31(1), 47-55.

Author has considered a multi component system consisting of N units in series having multiple failures (short circuit failure, human error, programming error, open circuit, mechanical breakdown, self life failure, major failure). System subjected to these failure waits for repair.

4 ref

021036   Sharma P L;Kanwar R K (Mathematics Dep, Himachal Pradesh Univ, Summer Hill, Shimla-171 005) : On inner product space and bilinear forms over rhotrices. Bull pure appl Sci 2012, 31(1), 109-18.

Discusses the inner product space, norm and bilinear form in the context of rhotrices over reals.

10 ref

021035   Sharma A S;Singh M P;Chandramouli A B (NO, Ideal Institute of Technology, Ghaziabad, Uttar Pradesh, Email: sharma.as09@gmail.com) : Steady laminar plane poiseuille flow between teo parallel plates through porous medium under the influence of uniform transverse magnetic field. Bull pure appl Sci-Sect E 2012, 31(2), 163-8.

Investigated the steady Laminar plane poiseuille flow between two parallel plates through porous medium under the influence of uniform transverse* magnetic field. Investigated skin friction, average, maximum minimum velocities, the volumetric flow and energy losses in channels.

15 ref

021034   Sharma A S;Singh M P;Chandramouli A B (NO, Ideal Institute of Technology, Ghaziabad, Uttar Pradesh) : Steady laminar plane poiseuille flow between two parallel plates under the influence of uniform transverse magnetic field. Bull pure appl Sci 2012, 31(1), 57-62.

In this paper author have investigated the steady Laminar plane poiseuille flow between two parallel plates under the influence of uniform transverse magnetic field. Also investigated skin friction, average, maximum minimum velocities, the volumetric flow and energy losses in channels.

15 ref

021033   Pushpa (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: push1435@yahoo.in) : Systmes of nonlinear volterra integral equations. Bull pure appl Sci 2012, 31(1), 85-94.

In this paper, author considered a system of nonlinear Volterra integral equations of the form X(t)= A(t) - ∫^t₀ C(t,s)g(X(s))ds and it is shown that if A ∈ L^p then its solution X(t) ∈ If and if A' ∈ L^p then g(X(t)) ∈ L^p.

15 ref

021032   Patankar V M;Rajan C S (NO, Indian Statistical Institute c/o Society for Electronic Transactions a, MGR Knowledge City, C.I.T. Campus, Taramani, Chennai-600 113, Email: vijay.patankar@utoronto.ca) : Locally potentially equivalent Galois representations. J Ramanujan Mathl Soc 2012, 27(1), 77-90.

It is shown that show that if two continuous semi-simple l-adic Galois representations are locally potentially equivalent at a sufficiently large set of places then they are globaly potentially equivalent. Also prove an analogous result for arbitrarily varying powers of character values evaluated at the Frobenius conjugacy classes. In the context of modular forms, we prove: given two non-CM newforms f and g of weight at least two, such that a_p(f)ⁿp = a_p(g)ⁿ on a set of primes of positive upper density and for some set of natural numbers n_p, then f and g are twists of each other by a Dirichlet character.

9 ref

021031   Narayana Murthy B R;Akhtar P;Venkata Ramudu B (NO, S.V. Degree and P.G. College, Anantapur-515 001, Email: palagiriakhtar@rediffmail.com) : Optimization of CASP-CUSUM schemes based on truncated log-logistic distribution. Bull pure appl Sci-Sect E 2012, 31(2), 243-55.

Among several techniques to control the quality, acceptance sampling plans are introduced mainly to accept or reject the lots of finished products. Such type of techniques are involved in the product which are destructive where 100% inspection is not possible such as bullets, batteries, bulbs and so on. In this paper we consider CASP-CUSUM Schemes based on the assumption that the continuous variable under consideration follows a truncated Log-logistic Distribution. The Log-logistic Distribution plays a vital role in Statistical Quality Control, particularly in estimating reliability by considering its distribution. Optimum CASP-CUSUM Schemes are suggested based on numerical results obtained.

13 tables, 9 ref

021030   Mohammad N;Vijayakumar M;Maheedulla A (Mathematics Dep, Aljouf Univ, P.O. Box. 2014, Al-Jouf, Skaka, KSA, Email: alnizam.sir@gmail.com) : Banach steinhaus theorem and invariant mean of reflexivity. Bull pure appl Sci 2012, 31(1), 43-6.

Applying Banach stainhaus theorem, we show that if a generalized Banach Space x is not reflexive then the space of bounded function from z with values in x doesnot admit.

10 ref

021029   Modi A K;Chute A L (Mathematics Dep, J.M. Patel College, Bhandara-441 904) : Some commutativity results on semi-prime rings. Bull pure appl Sci-Sect E 2012, 31(2), 225-32.

5 ref

021028   Lee J J (NO, Yonsei Univ, Shinchon-dong, Seodaemun-gu, Seoul-120 749, South Korea, Email: jungjolee@gmail.com) : Ranks of jacobians of curves related to binary forms. J Ramanujan Mathl Soc 2012, 27(2), 119-26.

Rubin and Silverberg reformulated the question of whether the ranks of the quadratic twists of an elliptic curve over Q are bounded into the question of whether a certain infinite series converges. Dabrowski and Jedrzejak consider an analogue of this theorem for the family of Jacobian varieties of twisted Fermat curves x⁹ + y^p = m (p fixed odd prime), where m runs through pth power-free integers. In this paper, we consider the family of Jacobian varieties of curves f(x, y) = mzⁿ, where f(x, y) ∈ Z[x, y] is an irreducible binary form of degree n ≥ 3 and m is an nth power-free integer.

14 ref

021027   Lakshmi S;Gomathi Sundari P (NO, K.N. Govt. Arts College for Women, Thanjavur-613 005, Email: lakshmi291082@yahoo.co.in) : New Mathematical model in Weibull proportional hazards regression using Gaba_A. Bull pure appl Sci 2012, 31(1), 101-7.

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-To-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and applications, the lifetime of assets is influenced by different risk factors, which are called covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesize these models from biomedical fields. For example, Neurotransmitters can have both toxic and trophic functions in addition to their role in neural signaling. Surprisingly, chronic blockade of GABA_A receptor activity for 5-8 d in vitro enhanced survival, suggesting that GABA_A receptor overactivation may be neurotoxic. Potentiating GABA_A receptor activity by chronic treatment with the endogenous neurosteroid. Other potentiators of GABA_A receptors, including benzodiazepines, mimicked the cell loss, suggesting that potentiating endogenous GABA activity is sufficient to produce neuronal death. Neurosteroidtreated neurons had lower resting intracellular calcium levels than control cells and produced smaller calcium rises in response to depolarizing challenges. The results may have implications for the mechanisms of programmed cell death in the developing CNS as well as implications for the long-term consequences of chronic GABAmimetic drug: use during development.

9 ref

021026   Kundu A;Chakrabarti G M (Applied Mathematics Dep, Calcutta Univ, 92, A.P.C. Road, Kolkata-700 009, Email: antarapalai@gmail.com) : Two warehouse supply chain management model with stochastic demand, controllable lead time and fuzzy present value with budget constraint and surprise function. Int J Inf Comput Sci 2012, 15(2), 1-11.

Two warehouse inventory management policy is presented with stochastic demand, controllable lead time with budget constraint and surprise function. Here own warehouse (OW) with limited storage capacity is placed at the market place and rented warehouse (RW) with sufficient storage capacity is at some distance from the market place. A budget constraint is also added to this model. The optimization problem with budget constraint is then transformed into a multi-objective optimization problem with the help of fuzzy chance-constrained programming technique and surprise function. In our studies, we relax the assumption about the demand, lead time and demand during lead time that follows known distributions and then apply the minimax distribution free procedure to solve the problem. We have developed an algorithm procedure to find the optimal order quantity, optimal lead time and optimal value of the safety factor. Finally average cost functions are derived and solved using a gradient based non-linear optimization technique (LINGO). To illustrate the results and its significant features, a numerical example is given.

1 illus, 2 tables, 22 ref

021025   Korkmaz M;Efe E (Mathematics Dep, Art and Science Faculty, Kahramanmaras Sutcu Imam Univ, 46100 Kahramanmaras, turkey, Email: mkorkmaz52@yahoo.com) : Lagrange interpolation approach to experimental data. Bull pure appl Sci-Sect E 2012, 31(2), 181-91.

Interpolation is an estimate of the unknown inter values via the use of the known values. In this study, it is reported that Lagrange interpolation could be applied to the experimental data obtained from trials which has ratio or scale of levels of at least one factor. For example, with Lagrange interpolation, it is possible to form the following: the result values of any intermediate levels, the absolute and local maxima/minima, turning points, the intermediate level of a desired result value and the standard errors of all the estimated ones and a desired result value, confidence limits, the result value of a level outside the range, estimates of missing observations, as well as the response surface estimates for the value and results in the form of graphic interaction in three-dimensional surface. By using Lagrange interpolation, the investigator is shown to obtain new ideas and interpretations in addition to the information of the well-known classical analysis.

3 illus, 3 tables, 13 ref

021024   Knutsen A L (Mathematics Dep, Bergen Univ, Johannes Brunsgate 12, 5008 Bergen, Norway) : On the birationality of the adjunction mapping of projective varieties. J Ramanujan Mathl Soc 2012, 27(1), 51-8.

Let X be a smooth projective n-fold such that q (X) = 0 and L a globally generated, big line bundle on X such that h⁰(K_x + (n - 2)L) <62> 0. We give necessary and sufficient conditions for the adjoint systems |Kx + kL| to be birational for k ≥ n - 1. In particular, for Calabi-Yau n-folds we generalize and prove parts of a conjecture of Gallego and Purnaprajna.

12 ref

021023   Karthikeyan K;Sundaramurthy M;Khadar Babu S K;Rajesh Anand B (School of Advanced Sciences, VIT Univ, Vellore-632 014) : New iterative algorithms for minimization of unconstrained nonlinear functions. Bull pure appl Sci 2012, 31(1), 15-23.

Author presented new iterative numerical algorithms for minimization of unconstrained nonlinear functions which is based on modified homotopy perturbation method. Then comparative study is made between new algorithms and Newton's algorithms by means of examples.

3 illus, 25 ref

021022   Karolyi G;Pal A (Institute of Mathematics, Eotvos Univ, Pazmany P. setany 1/C, H-1117, Budapest, Hungary, Email: karolyi@cs.elte.hu) : Cyclomatic number of connected graphs without solvable orbits. J Ramanujan Mathl Soc 2012, 27(2), 213-40.

Author study the combinatorics of constructing non-singular geometrically irreducible projective curves that do not admit rational points over finite solvable extensions of the base field. A graph is without solvable orbits if its group of automorphisms acts on each of its orbits through a non-solvable quotient. We prove that there is a connected graph without solvable orbits of cyclomatic number c if and only if c is equal to 6, 8, 10, 11, 15, 16, 19, 20, 21, 22, or is at least 24. For these numbers there exist smooth geometrically irreducible projective curves without* solvable points whose genus equals c.

15 ref