002214   Chandrakala P (Mathematics Dep, Bharathi Women's College, No.34/2, Ramanujam Garden Street, Pattalam, Chennai-600 012, Email: pckala05@yahoo.com) : Chemical reaction and MHD effects on moving vertical plate with variable temperature and uniform mass diffusion. Int J appl mathl Analysis Applic 0000, 7(2), 177-83.

Numerical technique is employed to derive a solution to the transient natural convection flow of an incompressible viscous fluid past an impulsively started Infinite vertical plate with variable temperature and uniform mass diffusion in the presence of magnetic field and homogeneous chemical reaction of first order. The governing equations are solved using implicit finite-difference method. The effect of velocity, temperature and concentration for different parameters like magnetic field parameter, chemical reaction parameter, Prandtl number and Schmidt number are studied. It is observed that the fluid velocity decreases with increasing chemical reaction parameter and magnetic field parameter.

5 illus, 5 ref

002213   Chandrakala P (Mathematics Dep, Bharathi Women's College, No.34/2, Ramanujam Garden Street, Pattalam, Chennai-600 012, Email: pckala05@yahoo.com) : (NULL). Int J appl mathl Analysis Applic 0000, 7(2), 169-76.

Finite difference solution of the unsteady flow past an impulsively started infinite vertical plate with uniform heat flux and mass diffusion are presented here, taking into account the homogeneous chemical reaction of first orderThe effect of velocity, temperature and concentration for different parameters like chemical reaction parameter, Schmidt number, Prandtl number, thermal Grashof number, mass Grashof number and time are studied. It is observed that due to the presence of first order chemical reaction, the velocity increases during the generative reaction and decreases in destructive reaction. It is observed that the velocity decreases in the presence of magnetic field. as compared to its absence.

6 illus, 8 ref

001162   Tiwari S K;Bariwal C (School of Mathematics, Vikram Campus Univ, Ujjain, Madhya Pradesh-456 010, Email: skt_tiwari75@yahoo.co.in) : Degree of approximation of conjugates of almost Lipschitz functions by almost (C,1)(E,q) means. J Indian Acad Math 2012, 34(2), 497-504.

In this paper, a theorem on the degree of approximation of conjugates of functions in a certain generalized Lip α-class by the almost (C, 1)(E, q) product means of conjugate Fourier series has been established.

13 ref

001161   Thiripurasundari V;Murugesan S (Mathematics Dep, Sri S. Ramasamy naidu Memorial College, Sattur-626 203, Email: thiripurasund@gmail.com) : Intuitionistic fuzzy boundary and intuitionistic fuzzy continuous functions. J Indian Acad Math 2012, 34(2), 413-25.

In this paper intuitionistic fuzzy boundary is introduced and its properties are investigated. Intuitionistic fuzzy continuous functions are characterized via intuitionistic fuzzy boundary.

10 ref

001160   Thakur S S;Kar M (Applied Mathematics Dep, Government Engineering College, Jabalpur, Email: samajh_singh@rediffmail.com) : On QSI-irresolute mappings. J Indian Acad Math 2012, 34(2), 615-20.

In the present paper the concept of qsl-Irresolute mappings have been introduced and studied.

10 ref

001159   Thakur S S;Banafar A S (Applied Mathematics Dep, Jabalpur Engineering College, Jabalpur, Madhya Pradesh-482 011) : Fuzzy pre I-connectedness. J Indian Acad Math 2012, 34(2), 591-8.

In the present paper the concept of fuzzy pre 1-connectedness in fuzzy ideal topological spaces have been introduced and studied some of its properties and characterizations.

19 ref

001158   Thakur M;Thakur S S (Applied Mathematics Dep, Government Engineering College, Jabalpur, Madhya Pradesh-482 011) : Intuitionistic fuzzy set C-connected mappings. J Indian Acad Math 2012, 34(2), 487-95.

The aim of this paper is to introduce and study the concept of intuitionistic fuzzy set c-connected mappings in intuitionistic fuzzy topological spaces.

15 ref

001157   Sundar P;Suguna R (NO, , 320/9A-H, Pothanur Main Road, Paramathi Velur-638 182, Email: mydt972009@gmail.com) : Comparison and oscillation theorems for nonlinear second order difference equations and inequalities. J Indian Acad Math 2012, 34(2), 555-67.

In this paper, author established several results involving comparison of the solution of nonlinear second-order difference equations and inequalities, for the most part of the form Δ²y(n)+a(n)f(y(n)) ≥ 0. In section 1, the linear comparison theorem of Levin type is partially extended to nonlinear equation and inequalities of the form (*). Section 2 is devoted to a comparison theorem for equations or inequalities of the related form Δ² y(n) + p(n, u(n)) Δ² y(n) + g(n, y(n)) (y(n)) <60> 0, for suitable sequences p and g. Finally, establish an oscillation theorem by comparing the non-linear equation (*) with a suitable linear equation.

19 ref

001156   Srivastava A K (NO, , Chandra Kuti, Cooks Compound, Ghasiyari Mandi, Lucknow-226 001, Email: aks196806@rediffmail.com) : Certain continued fraction representations for functions associated with second and third order Mock Theta functions. J Indian Acad Math 2012, 34(2), 345-62.

In the present paper author have proved infinite and finite continued fraction representation for a function Σ^m_n=0 [(b/a)_n (-ax)ⁿq^n(n-1)/2]/(b,xq)_n which gives corresponding representations for mock theta functions of order two and three as special cases.

10 ref

001155   Singh L S;Singh Y M;Singh Y R (Mathematics Dep, D.M. College of Science, Imphal-795 001, Email: ishambhu2008@rediffmail.com) : Common fixed point theorems of weakly biased mappings of type (R_L) in normed space. J Indian Acad Math 2012, 34(2), 637-51.

In this paper author established a necessary and sufficient condition for a pair of self mappings to be biased' of type (R_L) which has been introduced recently. Author also use a generalised Gregus type and ϕp-type contractive mappings to prove common fixed point theorem for a pair and 2 pairs of mappings in normed space using the concept of biased mappings of the type (R_L).

16 ref

001154   Singh B;Sharma R K;Shrivastava S (NO, School of Studies, Vikram Univ, Ujjain, Madhya Pradesh, Email: bijendrasingh@yahoo.com) : Common fixed point of semi compatible maps in fuzzy metric space. J Indian Acad Math 2012, 34(2), 439-49.

Using the concept of semi compatible mappings and introducing the concept of weak compatibility of type(z) in the context of a fuzzy metric space we prove results on common fixed point of six self maps of a fuzzy metric space. Results generalize the results of Vasuki, Grabiec and Singh & Chauhan.

10 ref

001153   Shetty B S;Lokesha V;Bayad A;Ranjini P S (Mathematics Dep, Sri Krishna School of Engineering & Management, Ambedkar Nagar, Bangalore-35, Email: shwethu17@gmail.com) : Comparative study of topological indices and molecular weight of some carbohydrates. J Indian Acad Math 2012, 34(2), 627-36.

Topological index of a graph G is a numeric quantity related to G which is describe molecular graph. In this paper, we compute Randic index, Zagreb index, Geometric-arithmetic index, zero connectivity index and ABC indices of class of carbohydrate is computed and compared it with its molecular weight.

1 table, 14 ref

001152   Saxena R K;Ram J;Daiya J (Mathematics & Statistics Dep, Jai Narain Vyas Univ, Jodhpur, Email: ram.saxena@yahoo.com) : Generalized fractional calculus of generalized multi-index Mittag-Leffer functions. J Indian Acad Math 2012, 34(2), 373-85.

In this recent paper Saxena et al. derived the Dirichlet averges of generalized multi-index Mittag-leffler function. This paper deals with the derivation of the generalized fractional differentiation and generalized fractional integration of the generalized multi-index Mittag-Leffler function defined and studied by Saxena and Nishimoto. The results obtained provide an extension of the results given by Kilbas et al., Saxena et al. and Saxena and Saigo and other.

28 ref

001151   Samriti Rani (NO, , 96, Defence Colony, Hisar, Haryana) : Difference betweein partial differential equation and ordinary differential equation in various equation system. Int J Sci Engng Comput Technol 2013, 3(1-2), 35-7.

Differential equations containing partial derivatives with two or more independent variables are called partial differential equations (PDES). These equations are of fundamental scientific interest but are substantially more difficult to solve, both analytically and computationally, than odes.

1 illus, 3 ref

001150   Saluja G S (Mathematics and I.T. Dep, Govt. N.P.G. College of Science, Raipur-492 010, Email: saluja_1963@rediffmail.com) : Convergence theorems for asymptotically nonexpansive mappings in the intermediate sense in uniformly convex banach spaces. J Indian Acad Math 2012, 34(2), 451-67.

The purpose of this paper is to establish weak and strong convergence of three-step iteration process with errors to converge to common fixed points for non-Lipschitzian asymptotically nonexpansive mappings in the intermediate sense in the framework of uniformly convex Banach spaces. The results presented in this paper extend and improve the corresponding results of

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001149   Sahu R C;nayak B K;Misra S P (Mathematics Dep, K.S.U.B. College, Bhanjanagar-761 126, Odisha, Email: rcsahu2@rediffmail.com) : Cosmological false vacuum models in general relativity and its modified theory. J Indian Acad Math 2012, 34(2), 469-80.

The problem of spatially homogeneous Bianchi type-1 space time is considered in general relativity and its modified theory (proposed by Barber, when source of the gravitational field is a perfect fluid. Corresponding to "gamma law equation of state", it is shown that the homogeneous and isotropic false vacuum models of the universe exist in both the theories of gravitation. The models found are inflationary and de-Sitter universes. Some important physical and geometrical features of the models are discussed.

6 ref

001148   Saaban A;Piah A R M;Majid A A (UUM College of Arts and Sciences, Utara Malaysia Univ, 06010 Simtok, Kedah, Malaysia) : Performance of the triangulation-based methods of positivity-preserving scattered data interpolation. Far East J mathl Sci 2011, 57(1), 1-11.

Presents the result and accuracy comparison of generalized positivity-preserving schemes for triangular Bezier patches of C¹ and C2 scattered data interpolants that have been constructed. Compares three methods of C¹ schemes using cubic triangular Bezier patches and one C² scheme using quintic triangular Bezier patches. The test case consists of four sets of node/test function pairs, with node-count ranging from 26 to 100 data points. The absolute maximum and mean errors are computed using 33x33 evaluation points on a uniform rectangular grid.

3 illus, 5 tables, 11 ref

001147   Rana P K (Mathematics Dep, Berhampore Girl's College, Berhampore, West Bengal-742 102, Email: rana_pravanjan@yahoo.co.in) : Topology through recognizable sets. J Indian Acad Math 2012, 34(2), 431-8.

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001146   Ponraj R;Vijaya Xavier Parthipan J;Kala R (Mathematics Dep, Sri Paramakalyani College, Alwarkurichi-627 412, Email: ponrajmath@gmail.com) : Pair sum labeling of some trees. J Indian Acad Math 2012, 34(2), 387-402.

Let G be a (p, q) graph. An injective map f: V (G) → { ± 1, ± 2, ...., ± p) is called a pair sum labeling if the induced edge function. f_e: E(G)→ Z - {0) defined by f_e(uv) = f(u) + f(v) is one-one and f_e (E (G)) is either of the form { ± k₁, ± k₂ ..., ± K_q/2) or {± k₁, ± k₂. ..., ± k_(q-1)/2) ∪ {k_(q+1)/2 according as q is even or odd. A graph with a pair sum labeling is called a pair sum graph. Here we prove that some trees which are obtained from stars and bistars are pair sum. Also we show that all trees of order ≤ 8 are pair sum graphs.

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001145   Ponraj R;Sivakumar M;Sundaram M (Mathematics Dep, Sri Paramakalyani College, Alwarkurchi-627 412, Email: ponrajmaths@indiatimes.com) : 3-total product cordial labeling of union of some graphs. J Indian Acad Math 2012, 34(2), 511-30.

Let f be a map from V[G] to {0, 1, ... k - i) where k is an integer, 2 ≤ k ≤ |V(G)|. For each edge uv assign the label f(u)f(v)(modk).f is called a k- Total Product cordial labeling if |f(i)-f(j)|≤ 1, i,j ∈ (0, 1, ... k - 1), where f(x) denotes the total number of vertices and edges labelled with x(x = 0, 1, 2, ... k - 1). In this paper author investigate 3-Total Product cordial labeling behaviour of union of some standard graphs.

6 illus, 6 ref

001144   Padmanabhan T (IUCAA, Post Bag 4, Pune Campus Univ, Ganeshkhind, Pune-411 007, Email: paddy@iucaa.ernet.in) : Calculus is developed in Kerala. Resonance 2012, 17(2), 106-15.

Foundations of calculus were developed by a school of mathematicians in Kerala during 1400- 1600, years before similar developments took place in the west.

2 illus, 3 ref

001143   Mathews J (NO, , 2230 Hamilton Drive, Ames, IA 50014, USA, Email: mathews@iastate.edu) : From hipparchus to a helix ruler. Resonance 2012, 17(1), 44-52.

This paper gives a brief history of the chord function a precursor of the sine function - from the mathematics/astronomy of Hipparchus and Ptolemy to the early twentieth century.

4 illus, 8 ref

001142   Malgonde S P;Lakshmi Gorty V R (Mathematics Dep, Bract's Vishwakarma Institute of Technology, Bibwewadi, Pune-411 037, Maharashtra, Email: spmalgonde@rediffmail.com) : Two complex variants of generalized Hankel-Clifford transformation of generalized functions. J Indian Acad Math 2012, 34(2), 599-613.

In this paper we consider two variants of the generalized Hankel-Clifford transformation. Extend these transformations to certain spaces of generalized functions and prove several results on inversion, uniqueness, boundedness and analyticity in such a way that the work of Betancor appears then as a particular case. The operational calculus of these transformations is developed and then applied to solve certain class of partial differential equations of the Bessel-Clifford type differential operators.

6 ref

001141   Malgonde S P;Lakshmi Gorty V R (Mathematics Dep, Bract's, Vishwakarma Institute of Technology, Bibwewadi, Pune-411 037, Email: spmalgonde@rediffmail.com) : Algorithm for computing zero-order generalized Hankel-Clifford transforms. J Indian Acad Math 2012, 34(2), 403-12.

Postnikov in 2003, proposed an algorithm to compute the Hankel transforms of order zero and one by using Haar wavelets. But the proposed method faced problems in the evaluation of zero-order Hankel and Hankel-type transform. To overcome this problem and to obtain an efficient algorithm for evaluating Hankel transform of order zero by using rationalized Haar wavelets was done by 0. P. Singh. Exact analytical representation of the zero order generalized Hankel-Clifford transform as series of the Bessel functions multiplied by the wavelet coefficients of the input function, is obtained in this paper. Numerical computations as well graphs are demonstrated using MATLAB software to illustrate the proposed algorithm.

6 illus, 11 ref

001140   Kulosman H;Miller A (Mathematics Dep, Louisville Univ, Louisville, KY 40292, U.S.A., Email: h0kulo01@louisville.edu) : Zero-divisor graphs of some special semigroups. Far East J mathl Sci 2011, 57(1), 63-90.

Introduce the notion of special semigroups. They are commutative Boolean semigroups that can be built from a trivial semigroup in a finitely many steps, where in each step, an idempotent is adjoined in one of the three allowed ways. The ith step of the building process is completely described by an element a_i of the set {'id', 'ze', 0, 1, ..., i - 1) of i + 2 elements. The sequence a = a₀, a₁; ..., a_N, obtained in that way, is called a defining sequence of the semigroup. It follows that the special semigroups form a large class of semigroups each of which can be easily defined. They can be arbitrarily big, nevertheless checking of associativity is completely avoided. Because of that they can be useful for various purposes. We give the description of the zero-divisor graphs of special semigroups and prove various properties of them.

15 ref

001139   Kulkarni S S;Datar H G (Statistics Dep, Willingdon College, Sngli-416 415, Email: sujatasubhash@rediffmail.com) : On IBFS to unbalanced transportation problem. J Indian Acad Math 2012, 34(2), 369-72.

In this paper various methods of obtaining an Initial Basic Feasible Solution (IBFS) to an Unbalanced Transportation Problem are compared. The contention of Goyal that the method suggested by him often results in a lower cost initial solution is refuted. It is found that the method suggested by Kulkarni-Datar requires lesser number of iterations to reach the optimal solution, which should really be considered as a better criterion for a good method.

1 table, 4 ref

001138   Kulkarni S S (Statistics Dep, Willingdon College, Sangli-416 415, Email: sujatasubhash@rediffmail.com) : New methods for solving unbalanced assignment problem. J Indian Acad Math 2012, 34(2), 569-77.

In this paper, two new heuristic methods of solving an unbalanced assignment problem (UAP) are suggested. Given UAP is modified either by assigning the declined job, as an additional job, to a specifically selected facility out of the n-l facilities or by dividing the declined job into at most n-1 parts for assigning these parts to the n-1 facilities. The suggested algorithms are also illustrated with a suitable numerical example.

3 tables, 10 ref

001137   Koshy T (Mathematics Dep, Framingham State Univ, Framingham, MA 01701, USA, Email: tkoshy@framingham.edu) : Telescoping binomial sums with catalan dividends. J Indian Acad Math 2012, 34(2), 621-6.

Author developed several Catalan formulas using suitable telescoping sums of binomial coefficients; one of them involves Lobb numbers, which occur in Lobb's generalization of Catalan's paren-thesization problem.

7 ref

001136   Kannan R;Vanimalini R;Sathiyamoorthi R (Statistics Dep, Annamalai Univ, Annamalai Nagar-608 002, Email: statkannan@yahoo.co.in) : Stochastic model for the estimation of expected time to seroconversion when the inter arrival times of contacts form a geometric process. J Indian Acad Math 2012, 34(2), 539-54.

This study is based on stochastic model for estimating the expected time to seroconversion of HIV transmission using geometric process. In the estimation of expected time to seroconversion there is an important role for the inter-arrival times between successive contacts and has a significant influence. In this paper it is assumed that threshold follows mixed exponential distribution and inter-arrival times between contacts forms a geometric process. Numerical illustrations are provided to have a Comparative idea of the behavior the expected time to seroconversion and its variance for the different combination of parameters involved in this model.

5 illus, 5 tables, 7 ref

001135   Jain D K;Yadav P (Applied Mathematics Dep, Madhav Institute of Technology & Science, Gwalior-474 005, Email: jain_dkj@yahoo.co.in) : Some fractional integral involving product of I-function and hypergeometric function. J Indian Acad Math 2012, 34(2), 481-6.

Developed an integral involving the product of I-function and hypergeometric function. The aim of this paper is to establish a theorem giving the fractional integral involving the product of the I-function and hypergeometric function. Some particular cases have also been discussed.

10 ref

001134   Goud T R (Mathematics Dep, Osmania Univ, Hyderabad-500 007, Email: tamtamrkrishna@gmail.com) : Temperature distribution in a circular disk subjected to a rotating heat source. J Indian Acad Math 2012, 34(2), 363-7.

The subject of the heat transfer has a great impact on the energy problems covering a spectrum ranging from the routine task of heating or cooling to the more sophisticated problems associated with nuclear power generation. In this paper, we have discussed the problem of determination of Temperature distribution when a work piece in the form of a circular disk is subjected to machining, using integral transform technique, the temperature distribution is determined for small values of time.

7 ref

001133   Gehlot K S;Chena Ram (Mathematics Dep, Bangur P.G. College, Pali, Pali-Marwar, Rajasthan-306 401, Email: drksgehlot@rediffmail.com) : Generalized fractional derivatives of the product of hypergeometric function and H-function. J Indian Acad Math 2012, 34(2), 531-8.

The aim of this paper is to established a theorem giving the generalized fractional derivatives of the product of hypergeometric function and the H-function.

9 ref

001132   Dubey A K;Narayan A (Mathematics Dep, Bhilai Institute of Technology, Bhilai House, Durg-491 001, Email: anilkumardby@rediffmail.com) : On multivalued f-nonexpansive three maps. J Indian Acad Math 2012, 34(2), 427-30.

In this paper, authors extend the two main results of Rhoades for f-non-expansive three maps.

4 ref

001131   Chena Ram;Agarwal G (Mathematics and Statistics Dep, Jai Narain Vyas Univ, Jodhpur, Rajasthan, Email: crc2007@rediffmail.com) : Uniformly starlike and uniformly convex functions involving generalized hypergeometric functions. J Indian Acad Math 2012, 34(2), 579-89.

The sufficient condition for the function z{₂R₁(a, b;c;k;z)} belonging to the classes of uniformly starlike and uniformly convex functions are derived. Similar results using integral operator are also investigated.

15 ref

001130   Chakravorty K (NO, , 23/A Harisava Road, Nabagram, Dist. Hioogly, West Bengal-712 246) : Behaviour of a visco-elastic hollow cylinder with longitudinal slit uder no body force over the curved surface and with variable temperature distribution out side and inside of it. J Indian Acad Math 2012, 34(2), 653-61.

The nature of displacements of the faces along the slit of the visco-elastic tube with variable temperature and under no body force are studied and Mathematical calculations are shown with Laplace transfer technique.

2 illus, 6 ref

001129   Chailos G (Computer Science Dep, Nicosia Univ, Nicosia 1700, Cyprus, Email: chailos.g@unic.ac.cy) : Characterization of the 'near H₁' class of functions, using a generalized Cauchy-type integral. Far East J mathl Sci 2011, 57(1), 105-11.

Study is done to set D to be a simply connected domain and authors assume that D has a Jordan rectifiable boundary ∂ and M ⊂ ∂ to be an open analytic arc whose Lebesgue measure satisfies 0 <60> m(M) <60> m(∂). Provides a characterization of NH¹_M((D), which is the class of holomorphic functions in D which are represented by Carleman formulae on M ⊂ ∂D, via a generalized Cauchy-type integral. Furthermore, show that this Cauchy-type integral associated to … ∈ JH_1M(D) is an element of NH¹_M(D).

9 ref

001128   Camara M G;Sow D (Ecole Doctorale de Mathematiques et Informatique, Laboratoire d'Algebra, de Cryptologie, de Geometric Algebrique et Appl, BP:5005 Dakar Fann, Senegal, Email: ghouraissiou@yahoo.fr ) : Introduction to the arithmetic of the dual integers. Far East J mathl Sci 2011, 57(1), 13-39.

Arithmetic structures of the special rings are of major interests for researchers in various fields. But until now, researchers are mainly focused on the arithmetic of the Euclidean and Dedekind domains. In this paper, authors study the arithmetic of the set D = Z + εZ with ε² = 0 of dual integers which is not a domain because of the existence of divisors of zero. Introduces the notions of pseudo-factorial and pseudo-Euclidean ring. For dual integers, in general, the factorization and the remainder on pseudo-division are not unique because of the existence of zero divisors. Nevertheless, we have successfully exhibited an algorithm that output always the same remainder for pseudo-division. Hence many known algorithms on integers Z and on Gaussian integers Z[i] can be rewritten on dual integers D. Similar results are obtained for [D/pD](x), where p is a prime integer.

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001127   Budhi W S;Lindiarti J (Mathematics Dep, Bandung Institute of Technology, Jl. Ganesa 10 Bandung 40132, Indonesia, Email: wono@math.itb.ac.id) : Boundedness of multilinear generalized fractional integral operators in generalized Morrey space. Far East J mathl Sci 2011, 57(1), 91-104.

Authors establish the boundedness of generalized fractional integral operators in m-Cartesian product of Morrey spaces. Defines the multilinear fractional integral operator on Rⁿ instead of Cartesian product of Kⁿ. In order to achieve the goal, Discusses about the boundedness of multilinear version of the classical maximal function In second part of the paper, Discusses about two kinds of Olsen inequalities for multilinear fractional operator.

11 ref

001126   Bouzkoura K (Mathematics Dep, Faculty of Sciences-Agdal, P.O. Box 1014, 10000 Rabat, Morocco) : New in the theory of fixed point on hyperconvex ultrametric spaces. Far East J mathl Sci 2011, 57(1), 41-7.

Authors introduce the notion of hyperconvexity in generalized ultrametric spaces, i.e., where the distance has values in a partially ordered set. Then, we give a new fixed point theorem in these spaces for nonexpansive mappings which leads to some corollaries.

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001125   Bhandari K (Mathematics Dep, Jodhpur Institute of Engineering & Technology for Girls, JIET Universe, Mogra-Village, NH-65 Pali Road, Jodhpur, Email: kamlesh_b79@indiatimes.com ) : General class of generating functions involving modified Laguerre polynomials and modified Bessel polynomials. J Indian Acad Math 2012, 34(2), 505-9.

In this paper a general class of generating functions by Lie group theoretic method for the modified Laguerre polynomial L_n^(α-n) (x) and modified Bessel polynomial Y_m^(α+n) (u) are obtained.

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001124   Abel M;Abel M;Tammo P (2. Liivi Str., Room 615, Institute of Mathematics, Tartu Univ, 50409 Tartu, Estonia, Email: Mart.Abel@ut.ee) : On representations of topological algebras. Far East J mathl Sci 2011, 57(1), 49-61.

Let A and Q be topological algebras and I be a nonempty collection of two-sided ideals of A such that the algebra Q is isomorphic to all the quotient algebras A/I, where I ∈ I. Representing the algebra A as a subalgebra of C(I, Q), i.e., the algebra of continuous functions from I to Q, is studied.

9 ref

000115   Yao X;Gao G (Applied Mathematics Dep, Yuncheng Univ, Shanxi 044000, P. R. China, Email: yaoxiyan63@163.com) : Some properties of g-(M, μ)-frames in a Hilbert space. Far East J mathl Sci 2011, 53(2), 183-91.

Let (M, μ) be a measure space, and let U and V be Hilbert spaces. Introduce a g-(M, μ)-frame {Λ_m)_m∈M for U with respect to a family of subspaces {V_m}_m∈M of V and obtain basic properties of g-(M, μ)-frame. Finally, obtain necessary and sufficient conditions on g-(M, μ.)-frames Λ₁ and Λ₂ and operators L₁ L₂ on U so that {Λ₁ L₁+ Λ₂L₂) is a g-(M, μ) -frame for U.

11 ref

000114   Song B;Pan L (Mathematics Dep, Southeast Univ, Nanjing-210 096, P.R. China, Email: 66songbing@163.com) : Periodic solutions for high order differential equations with deviating arguments. Far East J mathl Sci 2011, 55(2), 129-45.

By employing the coincidence degree theory of Mawhin, we investigate the existence of periodic solutions for high order differential equations with deviating arguments x⁽ⁿ⁾(t) + cx(t) + f(t, x(t - τ₀(t), x'(t - τ₁(t)), ..., x^(n-1)(t - τ_n-1(t)))) = p(t). Some new results on the existence of periodic solutions of the equations are obtained. The theorems are related to not only c and f(t, x₀, x₁, ..., x_n-1) but also the deviating argument τ_i(t), i = 0, 1, ..., n-l.

14 ref

000113   Sitthiwirattham T (Mathematics Dep, Faculty of Applied Science, King Mongkut's Univ of Technology North Ba, Bangkok, 10800, Thailand) : Matching number, edge covering number and edge dominating number ono joined graphs. Far East J mathl Sci 2011, 53(2), 217-24.

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000112   Sharma S (Statistics Dep, D.A.V. (P.G.) College, Dehradun, Email: smita.sharma73@yahoo.in) : Test procedures based on one preliminary test of significance in incomletely specified models. Invertis J Sci Technol 2013, 6(3), 177-81.

This article considers three factors (A, 8, C) factorial experiment with mixed effect model. The effect of A has been taken as fixed effect and 8 and C are taken as random effects. The objective here is to test the hypothesis about the main effect A. The incompletely specified model has been induced to completely specified model subject to the outcome of the one preliminary test of hypothesis based on Bancroft theory and the test procedures using approximate F-statistics have been developed.

9 ref

000111   Shalini Kumar;Jha M (Mathematics P.G. Dep, T.M.B.U., Bhagalpur, Bihar, Email: thakurshalini2000@gmail.com) : Existence and stability of libration points of the restricted three body problem, when both the primaries are heterogeneous axes-symmetric bodies with N layers. Invertis J Sci Technol 2013, 6(3), 164-76.

Investigated the Existence and Stability of the libration points in the Restricted Three Body Problem when both the primaries are heterogeneous axes -symmetric bodies with N layers having different densities p, p_i axes (a_ib_ic_i) and (a_i, b_i,c_i), (i = 1,2,3,....N) respectively. It is observed that there exists five libration points L_i (i' = 1,2,3,4,5), three collinear along the line of sisgies and two non-collinear. The collinear libration points are unstable for all values of μ (mass parameter) and non-collinear libration points are stable for μ <60> μ_c, a critical value.

6 illus, 9 ref

000110   Ryoo C S (Mathematics Dep, Hannam Univ, Daejeon-306 791, Korea) : Note on the twisted (h, q)-euler numbers and polynomials with weight α. Far East J mathl Sci 2011, 55(2), 209-17.

Author constructed a new type of twisted q-Euler numbers E^{(α, h)}_n,q,w and polynomials E^(α,h)_n,q,w(x). Some interesting results and relationships are obtained.

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000109   Pukdeboon C (Mathematics Dep, Faculty of Applied Science, King Mongkut's Technology Univ, North Bangkok, Bangkok 10800, Thailand, Email: cpd@kmutnb.ac.th) : Inverse optimal control for nonlinear systems with an input constraint. Far East J mathl Sci 2011, 55(2), 111-28.

This paper studies the inverse optimal control problem for nonlinear system with an input constraint. Based on the control Lyapunov function (CLF), the proposed controller is designed such that the small control property (SCP) is satisfied. This implies the existence of a smooth CLF and then a smooth stabilizing feedback control providing global asymptotical stability of the closed-loop system is designed. Using the inverse approach, a robust optimal controller is developed to minimize a derived performance index and make the system globally asymptotically stable. Moreover, some relations between the resulting controller and sliding mode controller are given. An example is presented and simulation results are included to verify the usefulness of the developed controller.

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000108   Phuapong S;Leeratanavalee S (Mathematics Dep, Faculty of Science Chiang Mai Univ, Chiang Mai-50200, Thailand, Email: phuapong.sa@hotmail.com) : Preserving of ideals on generalized induced algebras. Far East J mathl Sci 2011, 55(2), 197-208.

Substituting for the fundamental operations of an algebra term operations, we get a new algebra of the same type, called a generalized derived algebra. Such substitutions are called generalized hypersubstitutions. Generalized hypersubstitutions can also be applied to every equation of a fully invariant equational theory. The equational theory generated by the resulting set of the equations induces on every algebra of the type under consideration a fully invariant congruence relation. Factorized the generalized derived algebra by this fully invariant congruence relation, and will obtaind an algebra which is called a generalized induced algebra. In this paper, authors used a generalization of the concept of an ideal to a universal algebra and ask for the properties of I^σ = {[b]_θ A/σ|b ∈ I} in the algebra ^σ induced by the generalized hypersubstitution σ.

000107   Park J S (Mathematics Education and Institute of Mathematics Education Dep, Chinju National Education Univ, Jinju-660 756, South Korea, Email: parkjs@cue.ac.kr) : Fixed point for weak compatible mappings of type(α) in intuitionistic fuzzy metric space. Far East J mathl Sci 2011, 55(2), 147-54.

In this paper, we prove common fixed point theorem for four mappings satisfying weak compatible of type(a) in intuitionistic fuzzy metric space.

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