018019   Qu C;Cao Y (NO, School of Science, Dalian Nationalities Univ, Dalian-116 600, China, Email: mathcy@dlut.edu.cn) : Global existence of solutions for a viscous Cahn-Hilliard equation with gradient dependent potentials and sources. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 499-513.

Considered class of nonlinear viscous Cahn-Hilliard equations with gradient dependent potentials and sources. By a Galerkin approximation scheme combined with the potential well method, author proverd the global existence of weak solutions.

22 ref

018018   Ponnammal T;Eswara Prasad G;Ganesan V (Mathematics Dep, S.T. Hindu College, Nagercoli) : Markovian bulk size queue with optional service under vacation policy. Int J mathl Sci 2013, 12(3-4), 217-25.

Consider a single server bulk arrival Markovian queuing system with vacation policy. The server provides two kinds of services such as the first service is compulsory under general bulk service rule for all customers and the second service is optional under usual bulk service rule. Interarrival times and the service times for both kinds of services follow exponential distribution. The expressions for steady state probability generating functions average queue length and average waiting time have been derived. The numerical results are discussed for justifying the Mathematical expressions.

2 tables, 7 ref

018017   Philomena C F;Sunny Kuriakose A (Mathematics Dep, Little Flower College, Guruvayoor, Kerala-680 103, Email: srphilo.jees372gmail.com) : Product of fuzzy frame-groups. Far East J mathl Sci 2012, 65(1), 139-51.

Authors define the product of two fuzzy frame-groups and thence they generalize it to the infinite product.

7 ref

018016   Paul I;Neelima C A (Mathematics Dep, Centre for Post Graduate Studies and Research, Bharata Mata College Th, Kochi-682 021, Email: pibmct@gmail.com) : Rough subrings and their properties. Int J mathl Sci 2013, 12(3-4), 205-16.

In this paper, authors shall review the concept of rough ring, introduce the concept of rough subring, rough ring homomorphism and give some properties of them.

10 ref

018015   Park J S (Mathematics Education Dep, Chinju National Education Univ, Jinj-660 756, Korea, Email: parkjs@cue.ac.kr) : Some fixed points for generalized Kannan type mappings on intuitionistic fuzz metric space using implicit function. Far East J mathl Sci 2012, 65(1), 119-27.

Defines generalized Kannan type mapping and establish a unique fixed point for generalized Kannan type mappings defined on intuitionistic fuzzy metric space using implicit function.

11 ref

018014   Panich S (Engineering Faculty, Srinakharinwirot Univ, 114 Sukhumvit 23, Bangkok 10110, Thailand, Email: surachap@swu.ac.th) : Active motion for rehabilitation with leg-exoskeleton suit. Far East J mathl Sci 2012, 65(1), 129-38.

Rehabilitation is to restore the patient's physical, sensory, and mental capabilities due to injury, illness, or disease. Active motion is one important aspect of rehabilitation for increasing or maintaining joint function providing appropriate resistance to the muscles to increase endurance and strength. This rehabilitation motion is influenced by bone surfaces within the joint, joint capsule, ligaments, tendons, and muscles acting on the joint. The meaning of active motion for rehabilitation is movement of a joint by patient's effort. In this motion, there is no outside force from therapist to help in the movement. In this paper, the new hardware design is introduced and the possible motions of each joint are calculated. The relative positions of each joint are determined by Denavit-Hartenberg method. In the simulation, the revolute, speed and acceleration of each joint in left side are studied to construct the real hardware.

8 illus, 11 ref

018013   Paliogiannis F C (Mathematics Dep, St. Francis College, 180 Remsen Street, Brooklyn Heights, New York 11201, USA, Email: fpaliogiannis@sfc.edu) : Fuglede-putnam theorem. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 253-6.

Proved the following generalization of the Fuglede-Puntam theorem. Let N be an unbounded normal operator in the Hilbert space, and let A be an unbounded self-adjoint operator such that D(N) ⊆ D(A). Then, AN ⊆ N* A ⇒ AN* ⊆ N A.

6 ref

018012   Nanda S;Dutta S (NO, KIIT Univ, Bhubaneswar, Email: snanda@kiit.ac.in) : Almost <97>-dual of certain sequence spaces. Int J mathl Sci 2013, 12(3-4), 171-5.

Purpose of this paper is to determine the almost α-dual of l₁ and some other sequence spaces.

7 ref

018011   Min W K;Kim Y K (Mathematics Dep, Kangwon National Univ, Chuncheon-200 701, Korea) : γ- soft sets and applications. Far East J mathl Sci 2013, 73(2), 389-402.

The purpose of this paper is to introduce the notions of monotonic operations and γ-soft sets induced by a monotonic operation γ. Also introduce new operations (=i_γ, c_γ) induced by y-soft sets and investigate some properties for such notions.

19 ref

018010   Marin A M;Ortiz R D;Ceballos J A R (NO, Faculty of Exact and Natural Sciences, Cartagena Univ, Sede Piedra de Bolivar, Avenue of Consulado, Cartagenda de Indias, Bolivar, Colombia, Email: amarinr@unicartagena.edu.co) : Positive solutions of a nonlinear elliptic problem. Far East J mathl Sci 2013, 73(2), 243-59.

In this paper, author consider a nonlinear elliptic problem with zero Dirichlet boundary conditions on a bounded domain in Rⁿ, and establish a symmetry theorem. It is well known that there are solutions of this elliptic problem.

9 ref

018009   Malathi D;Muthulakshmi S (Mathematics Dep, Avinashilingam Institute for Home Science and Higher Education for Wo, Coimbatore-641 043) : Three level skip-lot sampling plan. Res Highlight 2013, 23(2), 115-20.

This three level skip-lot plan provides flexibility in using the plan according to the nature of the process submitting the product. This plan is economical and efficient in making decision.

3 tables, 5 ref

018008   Madhavan K;Vaidyanathan S (Mathematics Dep, Vel Tech Dr. RR and Dr. SR Technical Univ, <35>42, Avadi- Vel Tech Road, Avadi, Chennai-600 002) : Reduced-order linear functional observer design for large-scale discrete-time linear control systems. Far East J mathl Sci 2013, 73(2), 369-87.

In this paper, necessary and sufficient conditions have been derived for the reduced-order linear functional observer design for large-scale discrete-time linear control systems. Based on this characterization of the reduced-order linear functional observer, a simple algorithm has been provided for the design of reduced-order linear functional observer, which can be easily implemented in MATLAB. Also proved a separation principle for the implementation of an observer-based feedback stabilization scheme for large-scale discrete-time linear control systems. A numerical example has been provided for illustrating the results.

2 illus, 22 ref

018007   Liao Y H (Applied Mathematics Dep, National Pingtung Education Univ, Pingtung 900, Taiwan, Email: twincos@ms25.hinet.net) : Dividend approach for the P&Z shapley value. Far East J mathl Sci 2013, 73(2), 305-11.

Different from the potential approach, author introduces the dividend approaches for the P&Z Shapley value.

5 ref

018006   Lee M (Mathematics Dep, Mokwon Univ, Daejeon-302 729, Korea, Email: lmsds@mokwon.ac.kr) : Stably usual limit shadowing property and partially hyperbolic. Far East J mathl Sci 2012, 65(1), 47-54.

Let p be a hyperbolic periodic point of f, and let H_f-(p) be the homoclinic class of p. Authors prove that if f has the C¹-stably usual limit shadowing property on H_f(p), then H_f(p) admits a dominated splitting.

12 ref

018005   Laytimi F;Nahm W (NO, Mathematiques-bat. M2, Lille 1 Univ, F-59655 Villeneuve d'Ascq Cedex, France, Email: fatima.laytimi@math.univ-lille.1.fr) : General vanishing theorem. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 479-90.

Let E be a vector bundle and L be a line bundle over a smooth projective variety X. In this article, author give a condition for the vanishing of Dolbeault cohomology groups of the form H^p,q(X, S^α E ⊗ ∧^β E ⊗ L) when S^{α + β} E ⊗ L is ample. This condition is shown to be invariant under the interchange of p and q. The optimality of this condition is discussed for some parameter values.

14 ref

018004   Katz A A (Mathematics and Computer Science Dep, St. John's College of Liberal Arts and Sciences, St. John's Univ, 300 Howard Avenue, DaSilva Academic Center 314, Staten Island, NY 10301, U.S.A., Email: katza@stjohns.edu) : Uniqueness of involution in locally C*-algebras. Far East J mathl Sci 2012, 65(1), 1-9.

Authors show that the involution in locally C*-algebras is uniquely determined.

8 ref

018003   Juma A R S;Zirar H (Mathematics Dep, Anbar Univ, Ramadi, Iraq, Email: hazhazirar@yahoo.com) : New class of multivalent meromorphic starlike harmonic functions defined by linear operator. Int J pure appl Sci Technol 2013, 18(1), 81-92.

Used the linear operator HH f_p,q,s f to introduce a new class ∑_Hp (α₁;α) of multivalent meromorphic starlike harmonic functions in punctured open unit disc U = {z ∈ C:O<60>|z|<60>1} = U - {0}. Gives sufficient coefficient condition for this class. Also, this coefficient condition is shown to be necessary if the coefficients of the co-analytic part of the harmonic functions are negative. Furthermore, we determine the extreme points, distortion and covering theorems, convolution and convex combination conditions for these functions.

10 ref

018002   Jiang Q;Shao C (School of Mathematical Sciences, Jinan Univ, Shandong-250 022, China, Email: syjqh2001@163.com) : Conjugacy class sizes and solvability of finite groups. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 239-44.

Let G be a finite group and G* be the set of primary, biprimary and tripri-mary elements of G. We prove that if the conjugacy class sizes of G* are (1, in, n, inn) with positive coprime integers m and n, then G is solvable. This extends a recent result of Kong (Manatsh. Math. 168(2) (2012) 267-271).

8 ref

018001   Jemilohun V G;Lawal Y O;Adebara L (Statistics Dep, Afe Babalola Univ, Ado-Ekiti ABUAD, Nigeria, Email: vincelohun@yahoo.com) : Statistical analysis of insurance claims reserves in Nigeria. Int J pure appl Sci Technol 2013, 18(2), 9-22.

Insurance claims are demands made by policyholders for payment under insurance for a loss covered by that policy. This paper set out to analyze claims data adopting lognormal regression model. Traditional claims reserving techniques are based on run-off triangle containing: aggregate claim figures. Such a triangle provides a summary of an underlying data set with individual claim figures. In this paper authors explore the interpretation of the available individual data in the framework of longitudinal data analysis. Making use of the theory of linear mixed models, a flexible model for loss reserving is built. Both likelihood - based, as well as Bayesian approach is considered.

9 tables, 14 ref

018000   Jayakumar J;Kalyanasundaram M (Mathematics Dep, Pondicherry Engineering College, Pondicherry-605 014, Email: jjayakumar@pec.edu) : Generalized power means modification of Newton's method for simple roots of nonlinear equation. Int J pure appl Sci Technol 2013, 18(2), 45-51.

In this paper, a class of Newton-type methods known as generalized power means Newton method for solving nonlinear equations is proposed. The new method includes power means instead of arithmetic mean when trapezoidal integration rule is used, thus replacing f'(x) in the classical Newton method. Also, three arbitrary parameters are introduced to generalize the method and to obtain higher order convergence. Many known, variants can be regarded as particular cases of this method. The order of convergence of these methods is shown to be three and five for an additional condition. Numerical examples and their results are provided to show the efficiency of the new class of methods compared to Newton's method.

2 tables, 14 ref

017999   Ige S O;Obafemi O S;Ajao I O (Mathematics and Statistics Dep, The Federal Polytechnic, Ado Ekiti, Ekiti State, Nigeria, Email: isaacoluwaseyiajao@gmail.com) : Possible effect of loss of information in reducing scales of measurement. Int J pure appl Sci Technol 2013, 18(2), 30-8.

In medicine and social sciences, data are often collected in the form of nominal or ordinal scale of measurement. When data are collected in form of interval or ratio scale of measurement they are usually reduced into either nominal or ordinal form for easy analysis,; thus, this work considered the possible effect of loss of information in reducing scales of measurement when data in form of interval or ratio scale of measurement are collapsed into either nominal or ordinal scale of measurement. The Pearson product moment correlation coefficient for continuous variable X (the human body weight) and Y (the corresponding blood pressure) are computed and the 95% confidence interval (1 & 1) are estimated, the data were later collapsed into various CXC table of various sizes and corresponding Tau-Statistics (1 ors) were also estimated. It is observed that more than 95% of the time the Tau-Statistics (l ors) fells within the 95% confidence intervals for the Pearson product moment correlation coefficient (1 cs) i.e. the two coefficients (Tau-Statistics and correlation coefficient) compared very favourably showing that the analytical results obtained from both reduced and original data were: identical.

8 ref

017998   Ibrahim H Z (Mathematics Dep, Faculty of Science, Zakho Univ, Kurdistan-Region, Iraq, Email: hariwan_math@yahoo.com ) : γ-P_s-open sets and γ-P_s-continuous in topological spaces. Int J pure appl Sci Technol 2013, 15(2), 18-28.

Authors introduce a new class of sets called γ-P s-open sets. This class of sets lies strictly between the classes of δ-open and γ-p-open sets. Also study its fundamental properties and compare it with some other types of sets and we investigate further topological properties of sets and we introduce and investigate new class of continuous named γ-P_s-continuous.

21 ref

017997   Hooda D S;Saxena S (NO, Jaypee Institute of Engineering and Technology, A.B. Road, Raghogarh, Distt. Guna-473 226, Email: ds_hooda@rediffmail.com) : Generalized past residual entropies and characterization of life time distribution. Int J mathl Sci 2013, 12(3-4), 133-43.

In the present paper authors have defined two parametric generalized past residual entropies. Based on these measures authors have characterized past life time distribution for continuous and discrete random variables. Authors have also proved as corollaries that these entropies characterize uniform distribution.

5 ref

017996   Hazod W;Kosfeld K (Faculty of Mathematics, Technische Dortmund Univ, Vogelpothsweg 87, D-44227 Dortmund, Germany, Email: kosfeld@math.uni-dortmund.de) : Multiple decomposability of probabilities on contractible locally compact groups. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 257-81.

Operator decomposable probabilities on vector spaces - generalizing (semi-)stable and self-decomposable laws - are well known. Here authors are concerned with multiple decomposability on locally compact groups. In fact, as it turned out that contraction properties play an essential role, throughout. They concentrate on contractible locally compact groups.

35 ref

017995   Hakami A H (Mathematics Dep, King Khalid Univ, P.O. Box 9004, Abha, Postal Code: 61431, Saudi Arabia, Email: aalhakami@kku.edu.sa) : Small zeros of quadratic forms MOD P<. Int J mathl Sci 2013, 12(3-4), 145-53.

Let Q(x) = Q(x₁, x₂, ..., x_n) be a quadratic form over Z, p be an odd prime, and Δ = - (- 1)^n/2 det A_Q/p. A solution of the congruence Q(x) = 0 (mod p^m) is said to be a primitive solution if p x_i for some i. Authors prove that if this congruence has a primitive solution then it has a primitive solution with || x || ≤ max (6^1/n p^{m[(1/2)+(1/n)}], 2^2(n+1)/(n-2) 3^2/(n-2)}, provided that n is even, n <62> m and n ≥ 2.

16 ref

017994   Guo L;Leng G (Mathematics Dep, Shanghai Univ, Shanghai-200 444, China, Email: lujunguo0301@163.com) : Determination of star bodies from p-centroid bodies. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 577-86.

In this paper, author proved that an origin-symmetric star body is uniquely determined by its p-centroid body. Furthermore, using spherical harmonics, it is shown estab-lished a result for non-symmetric star bodies. As an application, it is shown that there is a unique member of Γ_p K) characterized by having larger volume than any other member, for all real p ≥ 1 that are not even natural numbers, where Γ_p (K) denotes the p-centroid equivalence class of the star body K.

28 ref

017993   Ghazali P L;Mohd I;Mamat M (NO, Jabatan Matematik, Fakulti Sains dan Teknologi, Malaysia Terengganu (U, 21030 Kuala Terengganu, Malaysia) : Integration model of education plan Takaful: a case study for Terengganu, Kelantan and Perlis, states in Malaysia. Far East J mathl Sci 2012, 65(1), 97-117.

Education Takaful is one of the product plans in Family Takaful. This plan is created to be a more reasonable plan for all categories of income earner. In order to know the acceptance of this product; we conduct a study by distributing the questionnaire to the respondent. The case studies included 410 of working respondents to find out if this amendment to the plan is acceptable to them. The collected data in this case study uses SPSS software to analyze whether the new mathematical model proposed for the plan is acceptable.

4 illus, 6 tables, 15 ref

017992   Ge B (Mathematics Dep, Harbin Engineering Univ, Harbin-150 001, People's Republic of China, Email: gebin04523080261@163.com) : Sign changing solutions of the p(x)-laplacian equation. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 515-24.

This paper deals with the variational and Nehari manifold method for the p(x)-Laplacian equations in a bounded domain or in the whole space. Proves existence of sign changing solutions under certain conditions.

22 ref

017991   Ganesh V;Subbiah M (Mathematics Dep, Sri Manakula Vinayagar Engineering College, Madagadipet, Pondicherry-605 107, Email: lectganesh@yahoo.co.in) : Series solutions and a perturbation formula for the extended Rayleigh problem of hydrodynamic stability. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 293-302.

Generalized Tollmien's solutions of the Rayleigh problem of hydrody-namic stability to the case of arbitrary channel cross sections, known as the extended Rayleigh problem. We prove the existence of a neutrally stable eigensolution with wave number k_s <62> 0; it is also shown that instability is possible only for 0 <60> k <60> k_s and not for k <62> k_s. Then we generalize the Tollmien-Lin perturbation formula for the behavior of c_i, the imaginary part of the phase velocity as the wave number k → k_s - to the extended Rayleigh problem and subsequently, we use this formula to demonstrate the instability of a particular shear flow.

9 ref

017990   Fadugba S E;Ajayi A O;Nwozo C R (Mathematical Sciences Dep, Ekiti State Univ, Ado Ekiti, Nigeria, Email: emmasfad2006@yahoo.com) : Effect of Volatility on binomial model for the valuation of American options. Int J pure appl Sci Technol 2013, 18(1), 43-53.

Presents the effect of volatility on binomial model for the valuation of American options. Volatility is a measure of the dispersion of an asset price about its mean level over a fixed time interval. Binomial model is a widespread numerical method of calculating the price of American options as it takes into consideration the possibilities of early exercise and other factors like dividends. The strength and weakness of volatility on the valuation of options were considered. Binomial model is computationally efficient, good for pricing American options but not adequate to price path dependent options.

3 illus, 1 table, 15 ref

017989   Elbatal I;Elgarhy M (Mathematical Statistics Dep, Institute of Statistical Studies and Research, Cairo Univ, Cairo, Email: i_elbatal@staff.cu.edu.eg) : Transmuted Quasi Lindley distribution: a generalization of the Quasi Lindley distribution. Int J pure appl Sci Technol 2013, 18(2), 59-70.

Lindley distribution is one of the important for studying stress-strength reliability modeling. Besides, some researchers have proposed new classes of distributions based on modifications of the quasi Lindley distribution. In this paper, a new generalized version of this distribution which is called the transmuted quasi Lindley (TQL) distribution is introduced. A comprehensive mathematical treatment of the TL distribution is provided. Derives the r^th moment and moment generating function this distribution. Moreover, we discuss the least squares, weighted least squares and the maximum likelihood estimation of this distribution.

16 ref

017988   El-Marouf S A A;Al-Rehaili A N (Mathematics Dep, Faculty of Science, Taibah Univ, Madinahmonwarah, Kingdom of Saudi Arabia) : Asymptotic behaviour of solutions of perturbed nonlinear systems. Far East J mathl Sci 2012, 65(1), 11-27.

Boundedness and different notions of stability of solutions of the perturbed nonlinear system of the type y' = f(t, y) + g(t, y, Ty) are discussed. Some new sufficient conditions are given. Examples on the results are introduced. The obtained results improve and generalize some of those given in the literature.

18 ref

017987   Dagli M C;Can M (Mathematics Dep, Akdeniz Univ, 07058-Antalya, Turkey, Email: mcihatdagli@akdeniz.edu.tr) : New generalization of Hardy-Berndt sums. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 177-92.

Authors construct a new generalization of Hardy-Berndt sums which are explicit extensions or Hardy-Berndt sums. They express these sums in terms of Dedekind sums s_r(h, k : x, y|λ|) with x = y = 0 and obtain corresponding reciprocity formulas.

20 ref

017986   Chitra S;Indhumathi B;Ramya S (Mathematics Dep, P.S.G.R Krishnammmal College for Women, Coimbatore, Tamil Nadu, Email: 3ugmaths@gmail.com) : Strong edge-magic total labelings of certain graphs. Int J mathl Sci 2013, 12(3-4), 195-203.

Aim of the paper is extending Strong edge- magic total labeling for, Cycles, Petersen, Harary, Star, Tietze's, 14-Cubic graphs, 28-Cubic graphs and Flower Snark which forms wonderful examples.

20 ref

017985   Chen Y;Chen G (NO, School of Mathematics and Statistics, Southwest Univ, Chongqing-400 715, People's Republic of China, Email: math_yan@126.com) : Finite groups with the set of the numbers of subgroups of possible order containing exactly two elements. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 491-8.

Let G be a finite group, and n(G) be the set of the number of subgroups of possible order of G. Investigated the structure of G satisfying that n(G) = {1, m] for any positive integer m. Proved that the nilpotent length of G is less than 2. Investigated nilpotent groups with m = p + 1 or p² + p + 1 (p is a prime), and get the classification of such kinds of group. Also investigated non-nilpotent groups with m = p + 1 and get the classification of the groups under consideration.

10 ref

017984   Chattopadhyay A;Sinha K B (NO, J.N. Centre for Advanced Scientific Research, Bangalore-560 064, Email: 2003arupchattopadhyay@gmail.com) : Third order trace formula. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 547-75.

Dykema and Skripka showed the existence of higher order spectral shift functions when the unperturbed self-adjoint operator is bounded and the perturbation is Hilbert-Schmidt. In this article, author give a different proof for the existence of spectral shift function for the third order when the unperturbed operator is self-adjoint (bounded or unbounded, but bounded below).

18 ref

017983   Changpuek T;Pongsumpun P;Tang I M (Mathematics Dep, Faculty of Science, King Mongkut's Institute of Technology Ladkrabang, Chalongkrung Road, Ladkrabang, Bangkok 10520, Thailand, Email: kppuntan@kmitl.ac.th) : Analysis of mathematical model for swine flu transmission by age group. Far East J mathl Sci 2013, 73(2), 201-29.

Effect of age group in the human population is considered for the transmission of swine flu. Susceptible-Exposed-Infected-Quarantined-Recovered (SEIQR) model is used for describing the transmission of this disease. From the swine flu data in Thailand, age of patients is influenced to the transmission of this disease. The human population is separated into three groups such as 1-10 years, 11-20 years, and more than 20 years, respectively. The transmission rates of the disease in all age groups are assumed to be different. Local stability analysis of this model is given. Four equilibrium states are found and the conditions for stability of these four equilibrium states are established. Numerical solutions are shown to confirm the analytical results. The bifurcation diagrams are shown. The basic reproductive number is found and the alternative way to control the disease is discussed.

9 illus, 31 ref

017982   Chakraborty K;Minamide M (NO, Harish-Chandra Research Institute, Chhatnag Road, Jhusi, Allahabad-211 019, Email: kalyan@hri.res.in) : Partial sums of a spectral analogue of the Mobius function. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 193-201.

Sankaranarayanan and Sengupta introduced the function μ*(n) corresponding to the Mobius function. This is defined by the coefficients of the Dirichlet series 1/L_f(s), where L_f(s) denotes the L-function attached to an even Maa β cusp form f. Authors will examined partial sums of μ*(n). The main result is ∑_n≤x μ*(n) = O(x exp(-A √log x)), where A is a positive constant. It seems to be the corresponding prime number theorem.

13 ref

017981   Chada A;Pibaljommee B (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khon Kaen 40002, Thailand, Email: valentine_at@hotmail.co.th) : Fuzzy identity filters and fuzzy subpseudovarieties. Far East J mathl Sci 2013, 73(2), 347-67.

Defines the concept of fuzzy identity filters on P(W_{τ(X)²) and show that the lattice of all identity filters IF(τ) can be embedded into the lattice of all fuzzy identity filters FIF(τ) and the lattice of all subpseudovarieties of V can be embedded into the lattice of all fuzzy subpseudovarieties of V. Using a Galois connection, we obtain the Birkhoff-type characterization, namely, every pseudovariety can be defined by a set of fuzzy identity filters. Considered weights over a pseudovariety V and show that the lattice of all weights over V and the lattice of all fuzzy subpseudovarieties of V are isomorphic.}

18 ref

017980   Biswas I;Sebastian R (NO, School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: indranil@math.tifr.res.in) : Rationality of moduli spaces of vector bundles on real hirzebruch surfaces. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 213-23.

Let X be a real form of a Hirzebruch surface. Let M_H(r, c₁, c₂) be the moduli space of vector bundles on X. Under some numerical conditions on r, c₁ and c₂, author identify those M_H(r, c₁, c₂) that are rational.

7 ref

017979   Bingjun L;Weijun L (Mathematics Dep, Hunan Institute of Humanities Science and Technology, Loudi City, Hunan-417 000, China, Email: ydlbj@yahoo.com.cn) : Smallest Randic index for trees. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 167-75.

General Randic index R_α (G) is the sum of the weight d(u)d(v)^α over all edges uv of a graph G, where α is a real number and d(u) is the degree of the vertex u of G. In this paper, for any real number α ≠ 0, the first three minimum general Randic indices among trees are determined, and the corresponding extremal trees are characterized.

7 illus, 1 table, 7 ref

017978   Bhaumik S (School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai-400 005, Email: saurav@math.tifr.res.in) : Characteristic classes for GO(2n) in etale cohomology. Proc Indian Acad Sci-Mathl Sci 2013, 123(2), 225-33.

Let GO (2n) be the general orthogonal group (the group of similitudes) over any algebraically closed field of characteristic ≠ 2. Authors determine the smooth-etale cohomology ring with F₂ coefficients of the algebraic stack BGO(2n). In the topological category, Holla and Nitsure determined the singular cohomology ring of the classifying space BGO (2n) of the complex Lie group GO (2n) in terms of explicit generators and relations. They extend their results to the algebraic category. The chief ingredients in this are: (i) an extension to etale cohomology of an idea of Totaro, originally used in the context of Chow groups, which allows us to approximate the classifying stack by quasi projective schemes; and (ii) construction of a Gysin sequence for the G_m-fibration BO (2n) → BGO(2n) of algebraic stacks.

8 ref

017977   Basu A (Mathematics Dep, Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya, Burdwan-713 407, Email: anin_iitkgp@yahoo.com ) : On |N, P_k| summable lacunary Orlicz sequence space. Int J pure appl Sci Technol 2013, 15(2), 43-53.

Aim is to introduce a new class of |N, p_k| summable lacunary sequence space |N_p|_θ (E,M,r,γ), where E is a Banach space, M - (M_i) is a sequence of ×rlicz functions, r - (r_k) is a bounded sequence of strictly positive real numbers, γ = (γ_i) is a multiplier sequence of scalars and θ = (k_r) is a lacunary sequence and investigate its topological structure and inclusion relations among various algebraic and topological properties. Further, a new type of lacunary statistical convergence |S|_θ|_NPk| has been studied for this space.

26 ref

017976   Azad S I;Husain I;Akhtar M S (General Studies Dep, Yanbu Industrial College, Yanbu, P.O. Box-30436, KSA-51000, Email: dr.ismailazad@gmail.com) : Generalization of summation theorems due to Ramanujan and their uses in finding some curious results. Int J pure appl Sci Technol 2013, 15(2), 68-72.

Aim of this paper to provide the simple way for the generalization of three summation due to Ramanujan and then to use them to find, some curious results by applying the theory of hvpergeometric function. The result is derived with the help of generalized Dixon theorem available in the literature. The results derived in this research note are simple, interesting, easily established and may be potentially useful.

9 ref

017975   Astuti M;Garminia H;Salman A N M;Irawati (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Bengkulu Univ, Jalan Raya Kandang Limun Bengkulu 38121, Indonesia, Email: assamulia@yahoo.com) : Integral complete r-uniform hypergraphs and sunflower hypergraphs. Far East J mathl Sci 2012, 65(1), 87-96.

Authors introduce some results on integral hypergraphs, previously investigated for graphs. A hypergraph is called integral if all the eigenvalues of its adjacency matrix are integers. Authors study two special classes of hypergraphs, namely, complete r-uniform hypergraphs and sunflower hypergraphs. Authors characterize the classes of hypergraphs to be integral. Shows that the complete r-uniform hypergraphs are integral and find a sufficient and necessary condition for sunflower hypergraphs to be integral.

13 ref

017974   Anitha Devi D;Roja E;Uma M K (Mathematics Dep, Shri Sakthikailassh Women's College, Salem-636 003, Email: amv_1982@rediffmail.com) : Fundamental theorem in smooth fuzzy centred system via G_δ - sets. Far East J mathl Sci 2013, 73(2), 231-42.

In this paper, author introduce maximal smooth fuzzy centred system, the smooth fuzzy space θ(R) via G_δ -sets. The concept of G_δ -absolute ω(R) of a smooth fuzzy topological space is studied.

9 ref

017973   Aggarwal S;Gupta C (Mathematics Dep, Miranda House, Delhi Univ, Delhi-110 007, Email: shashi60@gmail.com) : Bi-level multi-objective linear programming under intuitionistic fuzzy environment. Int J pure appl Sci Technol 2013, 17(2), 45-61.

In this paper, bi-level linear programming problem with multiple objectives at each level in intuitionistic fuzzy environment is studied and solved. In this problem, technological coefficients and resources are characterized by intuitionistic fuzzy numbers having linear membership and non-membership function. Intuitionistic fuzzy efficient solution is computed for the upper level by the proposed model. Finally, intuitionistic fuzzy optimization technique is used to obtain the satisfying solution of the given problem. An illustrative numerical example is solved to demonstrate the efficiency of the proposed approach.

3 illus, 15 ref

017972   Abtahi F (Mathematics Dep, Isfahan Univ, Isfahan, Iran, Email: f.abtahi@sci.ui.ac.ir) : Completely continuous and weakly completely continuous abstract segal algebras. Proc Indian Acad Sci-Mathl Sci 2013, 123(4), 539-46.

Let A be a Banach algebra. It is obtained a necessary and sufficient condition for the complete continuity and also weak complete continuity of symmetric abstract Segal algebras with respect to A, under the condition of the existence of an approximate identity for β, bounded in A. In addition, a necessary condition for the weak complete continuity of A is given. Moreover, the applications of these results about some group algebras on locally compact groups are obtained.

19 ref

017004   Sen M;Jain G K;Ranjan R (NO, RCERT, Sitapura, Jaipur, Rajasthan) : Study of genetic algorithm with optimization. Int J latest Technol Engng Mgmt appl Sci 2013, 2(2), 50-8.

The Genetic Algorithm (GA) and its many versions have been popular in the academy and the industry mainly because of their intuitiveness, ease of implementation, and the ability to effectively solve highly nonlinear, mixed integer optimization problems that are typical of complex engineering systems. The drawback of the GA is its expensive computational cost. Particle Swarm Optimization (PSO) is a relatively recent heuristic search method whose mechanics are inspired by the swarming or collaborative behavior of biological populations. PSO is similar to the GA as these two evolutionary heuristies are populations-based search methods. In other words, PSO and the GA move from a set of points (population) to another set of points in a single integration with likely improvement using a combination of deterministic and probabilistic rules. This paper attempts to examine the claim that PSO has the same effectiveness (finding the true global optimal solution) as the GA but with significantly better computational efficiency (less function evaluations) by implementing statistical analysis and formal hypothesis testing. The major objective of this paper is to compare the computational effectiveness and efficiency of the GA and PSO using a formal hypothesis testing approach.

6 ref

017003   Savitri;Hooda N (Mathematics Dep, DCR Science & Technology Univ, Murthal, Haryana, Email: savitrimalik1234@gmail.com) : On tripled fixed point theorem in partially ordered complete metric space. Int J pure appl Sci Technol 2014, 20(1), 111-6.

Authors prove a tripled fixed point theorem for the mapping having the mixed monotone property in partially ordered metric space. Also give an example in support of the result.

7 ref