023268   Petcharat K;Sukparungsee S (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's University of Technology North Bsangkok, 10800 Bangkok, Thailand, Email: yha99@hotmail.com) : Exact solution of average run length of ewma chart for MA(q) processes. Far East J mathl Sci 2013, 78(2), 291-300.

The main objective of this paper is to derive explicit formula of the Average Run Length (ARL) for Exponentially Weighted Moving Average (EWMA) chart by using the second kind Fredholm integral equation when observations are described by Moving Average order q (MA(q)) processes with exponential white noise. The results of ARL obtained from explicit formula and integral equation are in good agreement, and a computational time of former is much less than the latter approach. Meaningfully, the approached analytical formulas greatly reduced the computational times for evaluating ARL.

4 tables, 21 ref

023267   Nzimbi B M;Pokhariyal G P;Mondal S K (NO, School of Mathematics, College of Biological and Physical Sciences, N, P.O. Box 30197, Nairobi, Kenya, Email: nzimbi@uonbi.ac.ke) : Note on metric equivalence of some operators. Far East J mathl Sci 2013, 75(2), 301-18.

Authors study the metric equivalence relation and closely related relations on some classes of operators. They describe the spectral picture of metrically equivalent operators. We give some conditions when metric equivalence of operators implies unitary equivalence of operators.

11 ref

023266   Nurdin (Mathematics Dep, Faculty of Mathematics and Natural Sciences, Hasanuddin Univrsity, JI. Perintis Kemerdekaan Km. 10 Tamalanrea Makassar, Indonesia, Email: nurdin1701@gmail.com) : The total edge and vertex irregularity strength of nC₃-snake. Far East J mathl Sci 2013, 78(2), 205-10.

The total edge (vertex) irregular t-labeling of graph G + (V, E) is a function ƒ : V ∪ U → {1,2,3,...., t} such that the weights of all edges (vertices) of G are distinct. The weight of edge under a total t-labeling is the number labels of xy and the end vertices of xy and the weight of vertex x ε V under a total t-labeling is the number labels of x and the labels of edges incidence with x. The total edge (vertex) irregularity strength of G is the minimum positive natural number of t such that G has a total edge (vertex) irregular t-labeling. In this paper, we find the total edge (vertex) irregularity strength of a triangular snake.

5 ref

023265   Mubarki A M;El-Maghrabi A I (NO, , Mathematics Dep, Faculty of Science, Taibah Univ, Email: alimobarki@hotmail.com) : Generalization of nearly open sets in topological spaces. Int J pure appl Sci Technol 2013, 19(2), 35-47.

Aim of this paper is to introduce and study the notion of SnPm-open sets and S_nP_m- continuity such that n, -m ∈ {τ, δ, θ}. Also, some characterizations and several properties of these notions are presented. Finally we show that certain results of several publications on the concepts of weakness and strength of nearly open sets are considered as corollaries of the results of this research.

22 ref

023264   Matsuda K (Engineering Science Dep, Niihama National College of Technology, 7-1 Yagumo-chou, Niihama, Ehime, 792-8580, Japan, Email: matsuda@sci.niihama-nct.ac.jp) : Mixed sums of squares and triangular numbers. Far East J mathl Sci 2013, 75(2), 369-83.

3 ref

023263   Majeed A A;Lynch P (School of Education, University of Adelaide, Level 8, Nexus Building 10 Pulteney Street Adelaide SA 5000, Australia, Email: aysha.abdulmajeed@adelaide.edu.au) : Low achievement in mathematics-a survey. Far East J mathl Sci 2013, 78(2), 243-70.

In mathematics education low student achievement continues to remain a cause of concern and an impetus to reform efforts. Legislators, policy makers and the public, express dissatisfaction with students' ability to successfully acquire mathematical knowledge, skill, and the confidence they need to apply mathematics. Australia is one of the many countries reporting low levels of mathematics achievement in its student populations. In South Australia, the mean scores obtained by middle school students in mathematics in international surveys (PISA, 2009; TIMSS, 2007) and national standardised tests (NAPLAN, 2012) are not only below the national mean and those obtained by many other states but are consistently declining. Low achieving students are generally identified on the basis of performance on tests. In this article the low performance of South Australian middle school students in the national test (NAPLAN) and international surveys (TIMSS and PISA) will be outlined followed by a section on declining enrolment in advanced mathematics courses.

4 illus, 8 tables, 80 ref

023262   Magesh N;Prameela V (P.G. and Research Mathematics Dep, Government Arts College (Men), Krishnagiri-635 001, Email: nmagi_2000@yahoo.co.in) : Further properties on certain subclass of meromorphically starlike functions defined by LIU-Srivastava operator. Far East J mathl Sci 2013, 76(2), 255-71.

In this paper, author introduced and study a subclass M_p(α, η, k) of meromorphically univalent functions defined by generalized Liu-Srivastava operator. Obtained coefficient estimates, extreme points, growth and distortion bounds, radii of meromorphic starlikeness and merpmorphic convexity for the class M_p(α, λ, k, c) by fixing the second coefficient. Further, it is shown that the class M_p(α, λ, k, c) is closed under convex linear combination.

24 ref

023261   Li C;Xie Z;Guo F (Mathematics Dep, Sichuan Agriculture Univ, Yaan, Sichuan-625 014, P.R. China, Email: lichunhong200610@sina.com) : On integral solution of nonlocal fractional volterra integro-differential equation with hille-yosida operator. Far East J mathl Sci 2013, 76(2), 291-305.

This paper is concerned with the nonlocal fractional Volterra integro-differential equation with Hille-Yosida operator in Banach spaces. The existence and uniqueness of integral solution of the equation is obtained by using fractional calculus and fixed point theorems.

21 ref

023260   Lekkoksung S (Mathematics Dep, Faculty of Engineering, Rajamangala Technology Isan Univ, Khon Kaen Campus, Thailand, Email: lekkoksung_somsak@hotmail.com) : Characterizations of regular ordered semigroups in terms of Q-fuzzy subsets. Far East J mathl Sci 2013, 76(2), 273-90.

The concept of g-fuzzy generalized bi-ideals of an ordered semigroup is introduced. Regular ordered semigroups are characterized by means of Q-fuzzy left ideals, Q-fuzzy right ideals and Q-fuzzy (generalized) bi-ideals.

14 ref

023259   Kwon N (Mathematics Dep, Daegu University, Daegu 712-714, Korea, Email: nkwon@daegu.ac.kr) : On the radicals of the intersection pairings arising from homology representations. Far East J mathl Sci 2013, 78(2), 217-29.

Author explicitly calculate the radical of the intersection pairing defined on the Borel-Moore homology of certain Lagrangian varieties. As a by product, constructed geometrically non-degenerate contravariant bilinear forms on the irreducible representations of finite dimensional simple Lie algebras.

9 ref

023258   Ku C Y;Wong K B (Mathematics Dep, National Singapore Univ, 117543, Singapore, Email: matkcy@nus.edu.sg) : On r-cross intersecting families of sets. Far East J mathl Sci 2013, 75(2), 295-300.

21 ref

023257   Krapeedang M;Saengsura K (Mathematics Dep, Faculty of Science, Mahasarakham Univ, Mahasarakham-44150, Thailand, Email: kittisak.s@msu.ac.th) : Idempotent and regular elements of cohypersubstitutions of type τ = (2). Far East J mathl Sci 2013, 75(2), .

Mapping σ which assigns to every n-ary cooperation symbol f_i an n_i-ary coterm of type τ = (n_i)_i∈I= is said to be a cohypersubstitution of type T. The concepts of cohypersubstitutions were introduced in [3]. Every cohypersubstitution σ of type τ induces a mapping σ on the set of all coterms of type T. The set of all cohypersubstitutions of type τ under the binary operation o which is defined by σ ₁ o σ ₂ := σ ₁ ° σ₂ for all σ ₁, σ ₂ ∈ Cohyp(τ) forms a monoid and called monoid of cohypersubstitution of type T. In this research, authors characterize all idempotent arid regular elements of Cohyp(τ), where τ = (2).

5 ref

023256   Jong-Kwang Y;Rhee H J (Liberal Art and Science Dep, Chodang Univ, 419 sungnamri Muangun, Chonnam, Korea) : Algebraic spectral subspaces and invariant subspaces. Far East J mathl Sci 2013, 75(2), 319-36.

This paper examines the admissible operators on a complex Banach space and shows that if T ∈ L(X) is a super-decomposable operator on a complex Banach space X whose dimension is greater than 1 with ∩_λ∈C(<108> I - T)^PX = {0} for some integer p <62> 0, then Lat(T) is non-trivial.

19 ref

023255   Jayakumar T;Kanagarajan K;Indrakumar S (Mathematics Dep, Sri Ramakrishna Mission Vidyalaya College of Arts and Science, Coimbatore-641 020, Email: jayakumar.thippan68@gmail.com) : Numerical solution for hybrid fuzzy systems by runge-kutta heun method. Far East J mathl Sci 2013, 76(2), 205-22.

Author studied numerical methods for hybrid fuzzy differential equations by an application of the Runge-Kutta Heun method for, fuzzy differential equations. Proved a convergence result and gave numerical examples to illustrate the theory.

2 illus, 1 table, 28 ref

023254   Hasni R;Zainol N N (Mathematics Dep, Faculty of Science and Technology, University Malaysia Terengganu, 21030 Kuala Terengganu Terengganu, Malaysia, Email: hroslan@umt.edu.my) : Chromatic equivalence of K₄-homeomorphs with girth 11. Far East J mathl Sci 2013, 78(2), 181-96.

2 illus, 14 ref

023253   Gaimnazarov G;Narjigitov H;Gaimnazarov O G (NO, Gulistan State Univ, Gulistan City, Uzbekistan, Email: xusan1956@inbox.uz) : Some properties of functions associated with the derivative of fractional order in the space L_p (-∞, ∞). Far East J mathl Sci 2013, 76(2), 319-36.

In the present paper, authors study some properties of the function f(x) in the space L_p(-∞, ∞). We prove theorems on fractional derivative of the function f(x). Some inequalities are obtained for modulus of smoothness of fractional order based on the best approximations by entire functions Q_σ(x) ∈ L_p(-∞, ∞).

20 ref

023252   Fernandes C;Ramos P;Mexia J (ADM-Area Departamental de Matermatica, ISEL - Instituto Superior de Engenharia de Lisboa Lisboa, Portugal, , Email: cfernandes@adm.isel.pt) : Cobs and stair nesting - segregation and - 9 - crossing. Far East J mathl Sci 2013, 78(2), 301-8.

Stair nesting leads to very light models since the number of their treatments is additive on the numbers of observations in which only the level of one factor various. These groups of observations will be the steps of the design. In stair nested designs we work with fewer observations when compared with balanced nested designs and the amount of information for the different factors is more evenly distributed. We now integrate these models into a special class of models with orthogonal block structure for which there are interesting properties.

7 ref

023251   Farhane L (Mathematics Dep, Faculte des Sciences de Monastir, , 5019 Monastir, Tunisie, Email: lot.farhane@fsm.rnu.tn) : On the graduation of the real line with non-negative integer matrices. Far East J mathl Sci 2013, 78(2), 279-90.

8 ref

023250   Cho Y U (Mathematics Dep, College of Education Silla University, Pusan 617-736, Korea, Email: yucho@silla.ac.kr ) : On isomorphic property in Γ-near-rings II. Far East J mathl Sci 2013, 78(2), 221-16.

Paper concern with some concepts of near-rings and Γ-near-rings. Author already studied the isomorphic theorem of Γ near-rings. Investigated the second isomorphic theorem of Γ near-rings.

5 ref

023249   Chen S;Fang C (NO, Institute of Applied Mathematics,Chongqing University of Posts and Tel, Chongqing 400065, P.R. China, Email: chensl@cqupt.edu.cn) : A new extracgradient method for single-valued variational inequality. Far East J mathl Sci 2013, 78(2), 231-41.

Proposed a new extragradient method for the single-valued variational inequality problem. The method is proven to be globally convergent to a solution of the variational inequality problem, provided the mapping is continuous and pseudomonotone. Convergence analysis is also presented.

11 ref

023248   Changphas T (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khon Kaen-40002, Thailand, Email: thacha@kku.ac.th) : Complete ideals in ordered semigroups. Far East J mathl Sci 2013, 75(2), 225-32.

Authors introduce complete left ideals, complete right ideals and complete (two-sided) ideals of an ordered semigroup. Obtains relations between the complete left ideals and the set of all (0, 1) -regular elements of an ordered semigroup.

7 ref

023247   Boyadzhiev K N (Mathematics and Statistics Dep, Ohio Northern Univ, Ada, OH 45810, U.S.A., Email: k-boyadzhiev@onu.edu) : Evaluation of one exotic Furdui type series. Far East J mathl Sci 2013, 75(2), 359-67.

Authors present a closed form evaluation of one interesting alternating serieswhose value is a combination of three mathematical constants, π, In 2, and ζ(3). The paper contains also some additional results on integrals and series.

6 ref

023246   Barilla D;Caristi G;Puglisi A (S.E.A.M. Dep, University of Messina, Italy, Email: dbarilla@unime.it) : On a meromorphic-starlikeness-preserving property for an integral operator. Far East J mathl Sci 2013, 78(2), 271-8.

5 ref

023245   Bakery A A (Mathematics Dep, Faculty of Science and Arts, King Abdulaziz Univ (KAU), P.O. Box 80200, Code 21589 Khulais Saudi Arabia, Email: awad_bakery@yahoo.com) : New class of n-normed sequence related to the orlicz sequence space. Far East J mathl Sci 2013, 76(2), 245-54.

In this paper. author introduced a sequence space combining the sequence space introduced by Sargent and Orlicz function over n-normed spaces and examine some properties of the resulting sequence space like solidness, symmetricity, convergence-free, etc. Obtained some inclusion relations involving this sequence space.

16 ref

023244   Areepong Y;Sukparungse S (Applied Statistics Dep, Faculty of Applied Science, King Mongkut's Technology North Bangkok Un, 10800, Thailand, Email: yupaporna@kmutnb.ac.th) : Closed form formulas of average run length of moving average control chart for nonconforming for zero-inflated process. Far East J mathl Sci 2013, 75(2), 385-400.

Objective of this research is to study the performance of control charts for quickest detection of change in means with a moving average control chart (MA). The main characteristics of a control chart are the average run length (ARL₀) (mean of false alarm times) and the average delay time (ARL₁) (mean delay of true alarm times). The ARL₀ should be sufficiently large while the process is still in-control and the ARL₁ should be small when the process goes out-of-control. Explicit formulas of ARL₀ and ARL₁ for MA chart are presented when the probability of observing a defective product follows a zero-inflated Poisson (ZIP) distribution, i.e., a distribution that is similar to a Poisson distribution but with an excess number of zeros. We looked at processes in which there was no mean shift in amount of defectives and in which there was a mean shift. Based on the ARL measure, the performance of ZIP-MA chart was shown that for the shift increasing ZIP-MA performs better as the value of (w) decreases.

2 tables, 22 ref

023243   Alsadhan S A (Mathematical Sciences Dep, Dammam Univ, Saudi Arabia, Email: saalsadhan@ud.edu.sa) : Inclusion properties of certain classes of meromorphic functions associated wit cho-kwon-srivastava operator. Far East J mathl Sci 2013, 76(2), 307-17.

In this paper, author introduced and investigate some new classes of meromorphic univalent functions associated with Cho-Kwon-Srivastava operator. Several properties regarding inclusion relationships are proved.

7 ref

023242   Alkhal R (Mathematics Dep, Faculty of Science, Dammam Univ, P.O. Box 838, Dammam, Saudi Arabia, Email: ranaab@hotmail.com) : Certain classes of meromorphic harmonic functions defined by Dziok-Srivastava operator. Far East J mathl Sci 2013, 75(2), 233-44.

In this paper authors introduce and study new classes of meromorphic harmonic functions defined in the punctured unit disk U{0} = {z ∈ C : (0 <60> |z| <60> 1)} by using the Dziok-Srivastava operator. Coefficient inequalities, distortion bounds, convolution condition, convex combinations and neighborhood of such functions are considered.

6 ref

023241   Abbo B;Danna A;Youssouf P;Some B (Mathematiques et Informatique Dep, Faculte des Sciences Exactes et Appliquees, Ndjamena Univ, Chad, Email: bakariabbo@yahoo.fr) : Extension of the new iterative approach of Adomian algorithm to partial differential equations (PDE) strongly nonlinear with initial and boundary conditions. Far East J mathl Sci 2013, 75(2), 245-55.

In this previous articles [1-5], authors presented a new iterative approach in the algorithm of the Adomian method for solving nonlinear Cauchy ODE and PDE. They show the extension of the new technique to nonlinear PDE systems with initial and boundary conditions, thus generalizing a large number of biomathematics phenomena. Based on a combination of Adomian decomposed method and a notion of sequential approximations method, this new technique, contrary to the Adomian classical method, leads to quick converging algorithms and makes allowance for boundary conditions imposed to the PDE in the Adomian canonical form.

17 ref

022265   Sukklin R;Leerawat U (Mathematics Dep, Kasetsart Univ, Bangkok, Thailand, Email: rattana.nueng@gmail.com) : Fuzzy SU-subalgebras and fussy SU-ideals. Far East J mathl Sci 2013, 74(1), 191-200.

The notions of fuzzy SU-subalgebra and fuzzy SU-ideal in SU-algebra are introduced and some of their properties are investigated. Moreover, we have discussed the relations between fuzzy SU-subalgebras and fuzzy SU-ideals of SU-algebras.

7 ref

022264   Shin-Wook K;Park H (Mathematics Dep, Chonbuk National Univ, Chonju, Chonbuk-561 756, Korea) : Possible maximal rank of elliptic curve of the form y<. Far East J mathl Sci 2013, 74(1), 105-17.

Let y² = x³ pqx be an elliptic curve, where p and q are distinct odd primes such that p = 3 (mod 16) and q = 11 (mod 16). Then we treat the possible maximal rank of this curve.

7 ref

022263   Shin-Wook K;Park H (Mathematics Dep, Chonbuk National Univ, Chinju, Chinbuk-561 756, Korea) : Range of rank in an elliptic curve. Far East J mathl Sci 2013, 74(2), 379-88.

Elliptic curve as y² = x³ + px, where p is an odd prime. In this paper, author investigated the range of this form when p is an odd prime such that p = 13, 15 (mod 16).

5 ref

022262   Shanas Babu P;Thilagavathi K T (Mathematics Dep, National Institute of Technology, Calicut-673 601, Email: babushanas@gmail.com) : Acyclic colouring of some line graphs. Far East J mathl Sci 2013, 74(2), 333-9.

In this paper, authors discuss the acyclic vertex colouring and acyclic chromatic number of line graph of wheel graph and gear graph.

2 illus, 14 ref

022261   Sataprahm C;Luadsong A (Mathematics Dep, Faculty of Science, King Mongkut's Technology Thonburi Univ (KMUTT), 126 Pracha-utid Road, Bangmod, Toongkru, Bangkok-10140, Thailand, Email: chon52501409@gmail.com) : Numerical algorithm of MLPG method for solving Navier-stokes equations. Far East J mathl Sci 2013, 74(1), 53-72.

This article presents a numerical algorithm using the Meshless Local Petrov Galerkin (MLPG) method to solve Navier-Stokes equations. This method with the moving least square (MLS) approximation for trial function is used to solve pressure-correction equation. The local symmetric weak form (LSWF) with the improved Gaussian weight function and the local unsymmetric weak form (LUSWF) with the classical Gaussian weight function on both regular and irregular nodes are present in numerical example. The numerical algorithm is not complicated which works very well. Moreover, the numerical results are satisfied for all schemes.

5 illus, 4 tables, 14 ref

022260   Prakash J;Vaid K;Bala R (Mathematics and Statistics Dep, Himachal Pradesh Univ, Summer Hill, Shimla-171 005, Email: jpsmaths67@gmail.com) : Upper limits to the complex growth rates in triply diffusive convection. Proc Indian Natn Sci Acad 2014, 80(1), 115-22.

Paper mathematically establishes that the complex growth rate (p_r, p_i) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer with one of the components as heat with diffusivity K, must lie inside a semicircle in the right-half of the (p_r, p_i-plane whose centre is origin and radius equals √(R₁ + R₂) σ where, R₁ and R₂ are the Rayleigh numbers for the two concentration components with diffusivities κ₁ and κ₂ (with no loss of generality, κ <62> κ₁ <62> κ₂) and σ is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.

14 ref

022259   Pavic Z;Pavic V (NO, mechanical Engineering Faculty in Slavonski Brod, Osijek Univ, Trg Ivane Brlic Mazuranic 2, 35000 Slavonski Brod, Croatia, Email: zlatko.pavic@sfsb.hr) : Applications of convexity of quantities and inequalities. Far East J mathl Sci 2013, 74(2), 269-87.

Convex combinations supported by the geometrical images have been applied in determining the position of the center of physical and mathematical quantity. The main results of the paper include the presentation of the center (barycenter) of quantity in the integral form, and the application of the convexity on mathematical inequalities.

4 illus, 6 ref

022258   Nishimura H (NO, Institute of Mathematics, Tsukuba Univ, Tsukuba, Ibaraki, 305-8571, Japan) : Axiomatic differential geometry III-2- its landscape- chapter 2: model theory II. Far East J mathl Sci 2013, 74(1), 139-54.

Given a complete and (locally) cartesian closed category U, it is shown that the category of functors from the category of Weil algebras to the category U is (locally, resp.) cartesian closed. The corresponding axiomatization for differential geometry based upon Weil functors is then given.

31 ref

022257   Nishimura H (NO, Institute of Mathematics, Tsukuba Univ, Tsukuba, Ibaraki-305 8571) : Axiomatic differential geometry III-1- its landscape- chapter 1: model theory I. Far East J mathl Sci 2013, 74(1), 17-26.

A kind of model theory for our axiomatic differential geometry is proposed. It is claimed that smooth manifolds, which have occupied the center stage in differential geometry, may be replaced by functors on the category of Weil algebras. Our model theory is geometrically natural and conceptually motivated, while the model theory of synthetic differential geometry is highly artificial and exquisitely technical.

29 ref

022256   Namnak C (Mathematics Dep, Faculty of Science, Naresuan Univ, Phitsanulok, 65000, Thailand, Email: chaiwatn@nu.ac.th) : Regularity conditions on generalized linear transformation semigroups. Far East J mathl Sci 2013, 74(1), 179-90.

For a semigroup S, an element a of S is said to be regular if a = axa for some x ∈ S, left [right] regular if a = xa² [a = a²x] for some x ∈ S and completely regular if a = axa and ax = xa for some x ∈ S. In this paper, we give a necessary and sufficient conditions when elements of the transformation semigroup preserving equivalence to be regular, left regular, right regular and completely regular.

6 ref

022255   Mollin R A (Mathematics and Statistics Dep, Calgary Univ, Calgary, Alberta, T2N 1N4, Canada, Email: ramollin@ucalgary.ca) : New Class number one criteria for real - 31 - quadratic fields of Richaud-Degert type and prime-producing polynomials. Far East J mathl Sci 2013, 74(2), 201-47.

Presented new class number one criteria for real quadratic fields of Richaud-Degert (R-D) type-those with discriminant d = s² + r, where r | 4s -which subsumes all known such criteria in the literature. For values of narrow R-D types, those with |r| 4, authors provide an unconditional list. This extends and strengthens what Andrew Granville called the Rabinowitsch-Mollin-Williams criterion, and provides new class number one criteria in relation to prime-producing polynomials for general RD-types.

13 ref

022254   Mizere D;Nguessolta E;Kissita G;Makany R A (NO, Marien Ngouabi Univ, BP 69 Brazzaville, Congo) : Successive partial triadic analysis. Far East J mathl Sci 2013, 74(2), 341-60.

Partial triadic analysis, also called the STATIS method on tables, is a method which permits joint analysis of several data tables described by the same individuals (in rows) and the same variables (in columns). It makes a compromise defined by a linear combinational of all original tables. This method has been applied in ecology and in several other domains. But the partial triadic analysis has a major inconvenience. The (weighting) coefficients of the linear combination which defines the compromise do not always have the same sign, leading to misinterpretation. To avoid this difficulty, we propose a new procedure, called "successive partial triadic analysis (sPTA)". In the procedure, compromises having the same proprieties as the classic PTA compromises and axes of representation common to all the tables are constructed; and one can define the specific weights (inertia) necessary to study the stability between tables of the same case.

20 ref

022253   Lee J G (Electrical and Computer Engineering Dep, Seoul National Univ, Seoul-151 744, Korea) : Zeros of the Riemann zeta function. Far East J mathl Sci 2013, 74(1), 73-85.

Author present a short proof of the Riemann hypothesis. Authors show that zeros of the Riemann zeta function should be on the line with the real value 1/2, in the region where the real part of complex variable is between 0 and 1.

4 ref

022252   Kusmayadi T A;Sudibyo N A;Sri Kuntari (Mathematics Dep, Faculty of Mathematics and Natural Sciences Sebelas Maret Univ, Surakarta, 57126, Indonesia, Email: trikusma@uns.ac.id) : Eccentric digraph of (n,t)-kite graph. Far East J mathl Sci 2013, 74(2), 369-78.

Let G be a graph with a set of vertices V(G) and a set of edges E(G). The distance from vertex u to vertex v in G is the length of the shortest path from vertex u to v. The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertices of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph G is the digraph that has the same set of vertices as G, and there is an arc (directed edge) from u to v in ED(G) if and only if v is an eccentric vertex of u in G. In this paper authors determine the eccentric digraph of an (n,t)-kite graph.

1 illus, 7 ref

022251   Jitpattanakul A;Pukdeboon C (Mathematics Dep, Faculty of Applied Science, King Mongkut's Technology North Bangkok Un, 1518 Pibulsongkram Road, Bangsue, Email: anuchitj@kmutnb.ac.th) : Optimal attitude control for rigid spacecraft using successive approximation approach. Far East J mathl Sci 2013, 74(1), 37-52.

This paper studies a successive approximation approach (SAA) designing for attitude control systems of a rigid spacecraft. Based on the SAA, a nonlinear system with a standard quadratic cost functional is transformed into - 30 - a sequence of time-varying approximations for which the optimal control problem can be solved explicitly. An optimal controller which is designed based on an approximated system and sliding mode control (SMC) concepts is then applied to the nonlinear system. It is theoretically shown that the response of the approximating sequence of linear time-varying system converges to the response of the attitude tracking control system. An example of multiaxial attitude manoeuvres is presented and simulation results are given to verify the usefulness of the proposed controller.

4 illus, 14 ref

022250   Im M (Mathematics Education Dep, Hennam Univ, Daejeon-306 791, Korea, Email: mki@hannam.ac.kr) : Formulation of the generalized analytic Fourier-Feynman transform of the convolution product on abstract Wiener space. Far East J mathl Sci 2013, 74(1), 155-69.

Firstly, author defines a generalized analytic Fourier-Feynman transform of functionals defined on abstract Wiener space and investigate the properties of the inverse transform of it. Author second study various relations between the generalized analytic Fourier-Feynman transform and the convolutions. Then author have a formula of the generalized analytic Fourier-Feynman transform of the convolution product of certain functionals defined on abstract Wiener space.

9 ref

022249   Gong R;Xie P (NO, School of Mathematics and Information Science, Key Laboratory of Mathe, Guangzhou-510 006, P.R. China, Email: gongruming@163.com) : Estimates for multilinear singular integrals with non-smooth kernels on weighted morrey spaces. Far East J mathl Sci 2013, 74(2), 311-32.

In this paper, authors establish estimates for certain multilinear singular integrals on weighted Morrey spaces. They apply these results to prove the boundedness of multilinear commutators.

16 ref

022248   Fujita R (Mathematics and Statistics Premedical Sciences Div, Premedical Sciences Dokkyo Medical Univ, Kitakobayashi 880, Mibu, Tochigi, 321-0293, Japan, Email: fujita@dokkyomed.ac.jp) : On the Euler characteristic of a finite T₀- space. Far East J mathl Sci 2013, 74(1), 87-103.

Given a finite topological space, there exists an adjacency matrix for the graph associated to the topology, which is called a topogenous matrix of the finite topological space. In this paper, we show that the Euler characteristic of a finite T₀ -space is represented by the topogenous matrix.

2 illus, 8 ref

022247   Fisher P H (Mathematics Dep, Botswana Univ, Private bag 0704, Gaborone, Botswana, Email: paul.fisher@mopipi.ub.bw) : Remarks on minimal semi-symmetric 3-designs with a null polarity and their associated strongly regular graphs. Far East J mathl Sci 2013, 74(1), 171-7.

Authors investigate the possibility of certain classes of strongly regular graphs being equivalent to a class of semi-symmetric 3-designs, that contains a null polarity.

5 ref

022246   Eke B;Nkwanta A (Mathematics Dep, Morgan State Univ, 1700 E. Cold Spring Lane, Baltimore, M.D. 21251, U.S.A., Email: Boniface.eke@morgan.edu) : Canonical extensions and direct sums of fuzzy partially ordered sets. Far East J mathl Sci 2013, 74(2), 289-310.

Fuzzy relations are used to create partially ordered sets and lattices I contained in this paper. Extensions of partially ordered sets and lattices are examined. The extensions studied include what are called canonical extensions and direct sums. Among the results is one showing that every cover function for a finitary distributive lattice is also a cover function for some nonfinitary distributive lattice. This result shows the necessity of the condition "finitary" that is used in an earlier result to prove - 29 - the isomorphism of any two finitary distributive lattices which share a common cover function.

13 ref

022245   Dominic Y;Marudai M (Mathematics Dep, St. Joseph's College, Tiruchirappalli, Tamil Nadu, Email: dominic,yesu@gmail.com) : Some fixed point results in linear 2-banach spaces. Far East J mathl Sci 2013, 74(1), 1-15.

Authors prove the existence and uniqueness of fixed point for generalized (φ, Ψ) weak contraction in the setting of 2-Banach spaces.

7 ref

022244   Caristi G;Saitta E (S.E.A.M. Dep, Messina Univ, Italy, Email: gcaristi@gcaristi@unime.it) : Pareto minimum points of an inconsistent system. Far East J mathl Sci 2013, 74(2), 361-8.

Starting from the definition of the "Pareto minimum solution" of an inconsistent system, authors study some results concerning the last square solutions and we consider the best approximation of the solution of an inconsistent system.

3 ref