018416   Charoenpol A;Ratanaprasert C (Mathematics Dep, Faculty of Science Silpakorn Univ, Nakhon Pathom, 73000 Thailand, Email: aveya.c@gmail.com) : All subdirectly irreducible BDLC-algebras. Far East J mathl Sci 2016, 100(3), 477-90.

In [1], we defined a BDLC-algebra to be a lattice-based algebra <193>A; ∨, ∧, f, 0, 1<209> whose <193>A; ∨, ∧, 0, 1<209> is a bounded distributive lattice and f is a connected 0-endomorphism. In this paper, we apply those results in [1] to characterize all subdirectly irreducible BDLC-algebras and show that every variety of BDLC-algebras can be generated by a single subdirectly irreducible algebra.

7 ref

018415   Charoenpol A;Ratanaprasert C (Mathematics Dep, Faculty of Science Silpakorn Univ, Nakhon Pathom, 73000 Thailand, Email: aveya.c@gmail.com) : Distributive lattice-based algebra: The BDLC. Far East J mathl Sci 2016, 100(1), 135-45.

Lattice-based algebras are extensively studied by several algebraist; especially those bounded distributive lattice-based algebras <193>A; F<209> whose F{∧, ∨, 0, 1} is a singleton set of a dual endomorphism on its lattice-based; for instance, Ockham algebras, Boolean algebras, De Morgan algebras, Stone algebras and Kleene algebras. In this paper, authors introduce a new bounded distributive lattice-based algebra which is named BDLC-algebra; it is an algebra A := <193>A; ∧, ∨, f, 0, 1<209> whose <193>A; ∧, ∨, 0, 1<193> is a bounded distributive - 18 - lattice and f is a connected 0-endomorphism. We show identities for varieties of BDLC-algebras and apply them to study algebraic properties of BDLC-algebras; especially, we characterize their minimal non-identical congruences.

9 ref

018414   Canadas A M;Vargas V C;Serna R J (Mathematics Dep, National Univ of Colombia Bogota, Colombia, Email: amorenoca@unal.edu.co) : Categorification via equipped graphs. Far East J mathl Sci 2016, 100(1), 19-30.

Indecomposable representations of the modular lattice ∠(A_n⁰, where A_n⁰ is an equipped Dynkin diagram, are used to give a categorification for Catalan numbers.

2 illus, 16 ref

018413   Brono A M;Ali A G K (Mathematics and Statistics Dep, Maiduguri Univ, Borno State, Nigeria) : Weighted cesaro C,_1.1-statistical convergence of double sequences. Far East J mathl Sci 2016, 100(3), 361-9.

Following the method of weighted statistical convergence for single sequences, we analogously define double weighted Ces ro statistical convergence and establish its relationship with N”rlund type transformations (N², β_n and Ces ro C, _1.1-summability.

28 ref

018412   Belyavskiy G;Misyura V;Puchkov E (NO, South Federal Univ, Rostov-on-Don, Russian Federation, Email: beliavsky@hotmail.com) : Prediction intervals for time series using neural networks based on wavelet-core. Far East J mathl Sci 2016, 100(3), 413-25.

For the prediction of the time series there are problems of the noise, the non-stationarity, and we do not have enough information to choose the financial market model. In this work, possibility of the time series prediction using a neural network model based on a wavelet-core is investigated. The problem of a confidential interval prediction is considered. The prediction of a confidential interval is more effective than the point prediction for decision making. One more feature is using the order statistics in addition to values of the time series in the training sample. The basic complexity of a problem lies in the training algorithm. The hybrid algorithm has been used. It combines the gradient method with the genetic algorithm. The prediction results show expediency and efficiency of the proposed method.

7 illus, 18 ref

018411   Aramaki J (Science Div, Faculty of Science and Engineering Tokyo Denki Univ, Hatoyama-Machi, Saitama 350-0394, Japan, Email: aramaki@mail.dendai.ac.jp) : Regularity of weak solution for a quasilinear parabolic type equation associated with the maxwell equation. Far East J mathl Sci 2016, 100(3), 505-20.

Authors consider a system of quasilinear parabolic type equations involving operator curl associated with the Maxwell equations which produces the intensive magnetic field depending on a function of the - 17 - time t and the magnetic field. We shall show the existence and uniqueness of the classical solution.

14 ref

017471   Yadolahi A;Ashtari A;Gumel A B (Electrical and Computer Engineering Dep, Manitoba Univ, Canada, Email: azadeh@ee.umanitoba.ca) : An O(h<. Int J appl mathl Analysis Applic 2017, 12(1), 61-74.

The paper presents a parallel and sequential algorithm, based on using the method of line semi-discretization for solving the second-order wave equation subject to time-dependent boundary conditions. In addition to being second-order in space and time, the method is shown to be L₀-stable. Numerical simulations are reported to illustrate the superior stability and computational efficiency of the method over corresponding methods based on the use of Pade approximation.

5 illus, 4 table, 16 ref

017470   Saurabh B (NO, Indian Statistical Institute, 7, SJSS Marg, New Delhi-110 016, Email: bipul9r@isid.ac.in) : Quantum quaternion spheres. Proc Math Sci 2017, 127(1), 133-64.

For the quantum symplectic group SP_q(2n), we describe the C*-algebra of continuous functions on the quotient space SP_q(2n)/SP_q(2n - 2) as an universal C*-algebra given by a finite set of generators and relations. The proof involves a careful analysis of the relations, and use of the branching rules for representations of the symplectic group due to Zhelobenko. We then exhibit a set of generators of the K-groups of this C*-algebra in terms of generators of the C*-algebra.

21 ref

017469   Noor M A;Noor K I;Mohyud-Din T (Mathematics Dep, COMSATS Institute of Information Technology, Islamabad, Pakistan, Email: noormaslam@hotmail.com) : Solving Burger's equations using HE's polynomials. Int J appl mathl Analysis Applic 2017, 12(1), 1-7.

In this paper, we applied He's polynomials, which are calculated from homotopy perturbation method (HPM) for solving Burger's and coupled Burger's equations. These equations arise in various problems related to engineering and applied sciences. It is observed that He's polynomials are compatible with Adomian's polynomials but are more user friendly and easier to evaluate than the Adomian's polynomials. Results obtained in this paper represent an improvement and refinement of the previously known results.

6 illus, 31 ref

017468   Noor M A;Noor K I (Mathematics Dep, COMSATS Institute of Information Technology, Islamabad, Pakistan, Email: noormaslam@hotmail.com) : Projection iterative methods for general variational inequalities. Int J appl mathl Analysis Applic 2017, 12(1), 29-36.

In this paper, we suggest and analyze some new three-step iterative methods for solving general variational inequalities using the projection and updating techniques. We also study the convergence criteria of these iterative methods under some mild conditions. Several special cases are also discussed. Results obtained in this paper represent some refinement and improvement of the previously known results.

28 ref

017467   Nemati H;Ghanbarpour M;Hajibabayi M; Hemmatnezhad M (Mechanical Engineering Dep, Mazandaran Univ, P.O. Box 484, Babol, Iran, Email: morteza.ghanbarpour@gmail.com) : Thin film flow of non-newtonian fluids on a vertical moving belt using homotopy analysis method. Int J appl mathl Analysis Applic 2017, 12(1), 9-17.

In this study, the problem of thin film flow of two non-Newtonian fluids namely, a Sisko fluid and an Oldroyd 6-constant fluid on a vertical moving belt that modeled by a system of nonlinear differential equations is studied. The system is solved using the Homotopy Analysis Method (HAM), which yields an analytic solution in the form of a rapidly convergent infinite series with easily computable terms. Homotopy analysis method contains the auxiliary - 38 - parameter h, which provides us with a simple way to adjust and control the convergence region of solution series. By suitable choice of the auxiliary parameter h, reasonable solutions for large modulus can be obtained.

8 illus, 30 ref

017466   Muthucumaraswamy R;Raj M S;Subramanian V S A (Applied Mathematics Dep, Sri Venkateswara College of Engineering, Sriperambudur, Email: msamy@svce.ac.in) : Heat and mass transfer effects on flow past an accelerated vertical plate with variable mass diffusion. Int J appl mathl Analysis Applic 2017, 12(1), 55-60.

An exact solution of unsteady flow past an uniformly accelerated infinite isothermal vertical plate has been presented in the presence of variable mass diffusion. The plate temperature is raised to T_w and species concentration level near the plate is made to rise linearly with time. The dimensionless governing equations are solved using Laplace-transform technique. The velocity profiles, temperature and concentration are studied for different physical parameters like thermal Grashof number, mass Grashof number, Schmidt number, Prandtl number and time. It is observed that the velocity increases with increasing values of thermal Grashof number or mass Grashof number. It is also observed that the velocity increases with decreasing values of the Schmidt number.

5 illus, 7 ref

017465   Mazouni A E;Laytimi F;Nagaraj D S (Laboratoire de Mathematiques de Lens EA 2462, Faculte des Sciences Jean Perrin Rue Jean Souvraz, SP18 F-62307 LENS Cedex, France) : Projections of veronese surface and morphisms from projective plane to grassmannian. Proc Math Sci 2017, 127(1), 59-67.

In this note, we describe the image of P² in Gr(2, C⁴) under a morphism given by a rank two vector bundle on P² with Chern classes (2,2).

10 ref

017464   Gras G (NO, , Villa la Gardette, chemin Chateau Gagniere, F-38520 Le Bourg d'Oisans, France, Email: g.mn.gras@wanadoo.fr) : Invariant generalized ideal classes - structure theorems for p-class groups in p-extensions. Proc Math Sci 2017, 127(1), 1-34.

Authors give, in sections 2 and 3, an english translation of: Classes generalislsees invariantes, J. Math. Soc. Japan, 46, 3 (1994), with some improvements and with notations and definitions in accordance with our book: Class Field Theory: From Theory to Practice, SMM, Springer-Verlag, 2nd corrected printing 2005. We recall, in section 4, some structure theorems for finite Z_p[G]-modules (G ≈ Z/pZ) obtained in: Sur les l-classes d'ideaux dans - 37 - les extensionscycliques relatives de degre premierl, Annales de I'lnstitut Fourier, 23, 3 (1973). Then we recall the algorithm of local normic computations which allows to obtain the order and (potentially) the structure of a p-class group in a cyclic extension of degree p. In section 5, we apply this to the study of the structure of relative p-class groups of Abelian extensions of prime to p degree, using the Thaine-Ribet-Mazur-Wiles-Kolyvagin 'principal theorem', and the notion of 'admissible sets of prime numbers' in a cyclic extension of degree p, from: Sur la structure des groupes de classes relatives, Annales de I'lnstitut Fourier, 43, 1 (1993). In conclusion, we suggest the study, in the same spirit, of some deep invariants attached to the p-ramification theory (as dual form of non-ramification theory) and which have become standard in a p-adic framework. Since some of these techniques have often been rediscovered, we give a substantial (but certainly incomplete) bibliography which may be used to have a broad view on the subject.

90 ref

017463   Gospavic R;Haque N;Popov V;Chen C S (NO, Wessex Institute of Technology Ashurst Lodge, Southampton, UK, Email: gospavic@wessex.ac.uk) : Extended method of fundamental solutions implemented with two different solvers. Int J appl mathl Analysis Applic 2017, 12(1), 19-27.

Two solvers are compared for solution of the system of equations obtained using the extended method of fundamental solutions. The method combines the method of fundamental solutions (MFS) and the dual reciprocity method (DRM). Two sets of bases functions are used, a fundamental solution for considered operator and a radial basis function (RBF) approximation of the particular solution. In this work the RBF used is the multiquadric (MQ) function. The stationary and non-stationary elliptic partial differential equations with variable coefficients are considered. For non-stationary case a finite difference time discretisation is used. A direct solver using a selected number of digits and indirect solver based on the truncated singular value decomposition (TSVD) were used and compared. The method is tested for different values of the shape parameter in the MQ basis functions.

3 illus, 3 table, 12 ref

017462   Gorgees H M;Hilal M M (Mathematics Dep, Baghdad Univ, College of Education for Pure Science Ibn-Al-Haitham, Baghdad, Iraq) : Effectiveness of multi-collinearity problem for estimating fuzzy linear regression parameters with application. Int J Sci Nat 2017, 8(2), 284-8.

Fatigue cracking or alligator cracking is a common type of distress in asphalt pavement. There are many reasons that cause the fatigue cracking in asphalt pavements such of asphalt mixtures which consist of asphalt, aggregate and mineral filler. Fatigue cracking distress in asphalt pavements most often instigated by failure of the surface due to traffic loading. However, it can be greatly influenced by environmental and other effects while traffic loading remains the direct cause. Frequently, overloading happens because the base or sub base inadequately support the surface layer and subsequently cannot handle loads that it would normally endure. In this research many factors were used to build a fuzzy linear regression model like fatigue life, initial flexural stiffness modulus, and initial tensile strain, stress level and air voids. The model had been analyzed by using the classical technique and our proposed procedure. The total spread error was used to compare the performance of the calculated procedures.

6 tables, 5 ref

017461   Filippis V D;Raza M A;Rehman N U (Faculty of Engineering, Messina Univ, Contrada Di Dio, 98166 Messina, Italy, Email: defilippis@unime.it) : Commutators with idempotent values on multilinear polynomials in prime rings. Proc Math Sci 2017, 127(1), 91-8.

Let R be a prime ring of characteristic different from 2, C its extended centroid, d a nonzero derivation of R, f(x₁, ..., x_n) a multilinear polynomial over C, Q a nonzero right ideal of R and m <62> 1 a fixed integer such that ([d(f(r₁, ..., r_n)), f(r₁, ..., r_n)])^m = [d(f(r₁, ..., r_n)), f(r₁, ..., r_n)] for all r₁, ..., r_n ∈ Q. Then either [f(x₁, ..., x_n), x_n+1]x_n+2 is an - 36 - identity for Q or d(Q)Q = 0.

18 ref

017460   Dukkipati A;Palimar S (Computer Science and Automation Dep, Indian Institute of Science, Bangalore-560 012, Email: ad@csa.iisc.ernet.in) : Primes of the form x<. Proc Math Sci 2017, 127(1), 35-43.

In this paper, we characterize primes of the form x² + dy² with x ≡ 0(mod N) or y ≡ 0(mod N) for positive integers N and d with d being square free.

13 ref

017459   Dubickas A;Siurys J (Mathematics and Informatics Dep, Vilnius Univ, Naugarduko 24, LT-03225 Vilnius, Lithuania, Email: arturas.dubickas@mif.vu.lt) : Some irreducibility and indecomposability results for truncated binomial polynomials of small degre. Proc Math Sci 2017, 127(1), 45-57.

In this paper, we show that the truncated binomial polynomials defined by P_n,k (x) = ∑_j=0^k (n/j)x^j are irreducible for each k ≤ 6 and every n ≥ k + 2. Under the same assumption n ≥ k + 2, we also show that the polynomial P_n,k cannot be expressed as a composition P_n,k(x) = g(h(x)) with g ∈ Q[x] of degree at least 2 and a quadratic polynomial h ∈ Q[x]. Finally, we show that for k ≥ 2 and m, n ≥ k + 1 the roots of the polynomial P_m,k cannot be obtained from the roots of P_n,k,, where m ≠ n, by a linear map.

7 tables, 12 ref

017458   Dabhi P A;Pandey M K (Mathematics Dep, Sardar Patel Univ, Vallabh Vidyanagar-388 120, Email: lightatinfinite@gmail.com) : Isometric multipliers of a vector valued beurling algebra ona discrete semigroup. Proc Math Sci 2017, 127(1), 109-16.

Let (S, ω) be a weighted abelian semigroup, let M_ω(S) be the semigroup of ω-bounded multipliers of S, and let A be a strictly convex commutative Banach algebra with identity. It is shown that T is an onto isometric multiplier of l¹ (S, ω, A) if and only if there exists an invertible σ ∈ M_ω(S), a unitary point a ∈ A, and a k <62> 0 such that T(f) = ka ∑_x∈S F(X) δσ(X)for each f = ∑_x∈S f(x)δ_x ∈ l¹(S, ω), A). It is also shown that an isomorphism from l¹ (S₁, ω₁, A) onto l¹ (S₂,ω₂, B) induces an isomorphism from M(l¹(S₁, ω₁, A)), the set of all multipliers of l¹ (S₁, ω₁, A), onto M(l¹(S₂, ω₂, B)).

6 ref

017457   Chandrashekar P;Roy S;Murthy A S V (NO, TIFR Center for Applicable Mathematics, Bangalore-560 065, Email: vasu@math.tifrbng.res.in) : Variational approach to estimate incompressible fluid flows. Proc Math Sci 2017, 127(1), 175-201.

A variational approach is used to recover fluid motion governed by Stokes and Navier-Stokes equations. Unlike previous approaches where optical flow method is used to track rigid body motion, this new framework aims at investigating incom-pressible flows using optical flow techniques. We formulate a minimization problem and determine conditions under which unique solution exists. Numerical results using finite element method not only support theoretical results but also show that Stokes flow forced by a potential are recovered almost exactly.

16 illus, 6 tables, 32 ref

017456   Bardakov V G;Bryukhanov O V;Gongopadhyay K (NO, Sobolev Institute of Mathematics, Novosibirsk State Univ, Novosibirsk 630090, Russia and Laboratory of Quantum Topology, Chelyabinsk State Univ, Brat'ev Kashirinykh Street 129,, Email: krishnendug@gmail.com) : Palindromic widths of nilpotent and wreath products. Proc Math Sci 2017, 127(1), 99-108.

We prove that the nilpotent product of a set of groups A₁, ..., A_s has finite palindromic width if and only if the palindromic widths of A_i, i = 1, ..., s, are finite. We give a new proof that the commutator width of F_n ? K is infinite, where F_n is a free group of rank n ≥ 2 and K is a finite group. This result, combining with a result of Fink [9] gives examples of groups with infinite commutator width but finite palindromic width with respect to some generating set.

21 ref

017455   Bakshi K C (NO, The Institute of Mathematical Sciences, Taramani, Chennai-600 113, Email: keshabcb@imsc.res.in) : On pimsner-popa bases. Proc Math Sci 2017, 127(1), 117-32.

In this paper, we examine bases for finite index inclusion of II₁ factors and connected inclusion of finite dimensional C*-algebras. These bases behave nicely with respect to basic construction towers. As applications we have studied automorphisms of the hyperfinite II₁ factor R which are 'compatible with respect to the Jones' tower of finite dimensional C*-algebras'. As a further application, in both cases we obtain a characterization, in terms of bases, of basic constructions. Finally we use these bases to describe the phenomenon of multistep basic constructions (in both the cases).

15 ref

017454   Athreya K B;Rajeev B (Mathematics and Statistics Dep, Iowa State Univ, Ames, Iowa 50011, USA, Email: kba@iastate.edu) : Weak convergence of the past and future of brownian motion given the present. Proc Math Sci 2017, 127(1), 165-74.

In this paper, we show that for t <62> 0, the joint distribution of the past [W_t-s : 0 ≤ s ≤ t] and the future (W_t+s : s ≥ 0] of a d-dimensional standard Brow-nian motion (W_s), conditioned on {W_t ∈ U}, where U is a bounded open set in R^d, converges weakly in C[0, ∞) x C[0, ∞) as t → ∞. The limiting distribution is that of a pair of coupled processes Y + B¹, Y + B² where Y, B¹, B² are independent, Y is uniformly distributed on U and B¹, B² are standard d-dimensional Brownian motions. Let σ_t, d_t be respectively, the last entrance time before time t into the set U and the first exit time after t from U. When the boundary of U is regular, we use the continuous - 34 - mapping theorem to show that the limiting distribution as t → ∞ of the four dimensional vector with components (W_σt, t - σ_t, W_dt, d_t - t), conditioned on {W_t ∈ U}, is the same as that of the four dimensional vector whose components are the place and time of first exit from U of the processes Y + B¹ and Y + B² respectively.

5 ref

017453   Anil Kumar C P (NO, Indian Statistical Institute, 8th Mile, Mysore Road, RVCE Post, Bangalore-560 059, Email: akcp1728@gmail.com) : Approximation of quadrilaterals by rational quadrilaterals in the plane. Proc Math Sci 2017, 127(1), 69-90.

Many questions about triangles and quadrilaterals with rational sides, diagonals and areas can be reduced to solving certain diophantine equations. We look at a number of such questions including the question of approximating arbitrary triangles and quadrilaterals by those with rational sides, diagonals and areas. We transform these problems into questions on the existence of infinitely many rational solutions on a two parameter family of quartic curves. This is further transformed to a two parameter family of elliptic curves to deduce our main result concerning density of points on a line which are at a rational distance from three collinear points (Theorem 4). We deduce from this a new proof of density of rational quadrilaterals in the space of all quadrilaterals (Theorem 39). The other main result (Theorem 3) of this article is on the density of rational triangles which is related to analyzing rational points on the unit circle. Interestingly, this enables us to deduce that parallelograms with rational sides and area are dense in the class of all parallelograms. We also give a criterion for density of certain sets in topological spaces using local product structure and prove the density Theorem 6 in the appendix section. An application of this proves the density of rational points as stated in Theorem 31.

28 ref

016521   Zakaria N N;Majid N A;Soon L L (Institute for Mathematical Research, Universiti Putra Malaysia, 43499 Serdang, Selangor, Malaysia) : Solution of boundary value problems using two-point direct block method with one-off step point. Far East J mathl Sci 2017, 101(2), 375-94.

In this paper, the two-point direct block method with one-off step is considered for solving boundary value problems (BVPs) with Dirichlet boundary conditions. The direct block method with one-off step is of type one-step method where it needs only one-point to start the next block. This method solves the second - 43 - order BVPs directly without reducing it into the system of first order equations. The solutions are calculated at two-steps simultaneously using constant step size. This method is implemented together with the shooting technique using Newton method to obtain the numerical solution. Numerical results are given to show the performance of this method compared to the existing methods.

1 illus, 4 tables, 13 ref

016520   Yamuna M;Karthika K (School of Advanced Sciences, VIT Univ, Vellore, Email: myamuna@vit.ac.in) : Domination subdivision stable trees. Far East J mathl Sci 2016, 99(5), 623-30.

Network behavior in the presence of fault can be analyzed, by determining the effect of graph operations that the underlying graph G has, on the fault tolerance criteria. It is important that the domination number of graph is not modified when G is modified. A tree is a smallest connected graph that can be used in such cases. In this paper, we provide a constructive characterization of domination subdivision stable trees.

11 ref

016519   Xavier G B A;Govindan B;Kumar S U V;Borg S J (Mathematics Dep, Sacred Heart College, Tirupattur-635 601, Email: brittoshc@gmail.com) : m(k)-Series solutions of generalized k-difference equation with variable coefficients. Far East J mathl Sci 2016, 99(5), 699-717.

In this paper, we obtain the summation solution called as -series, which is an extension of m-series of k-difference equation with variable coefficients using inverse of k-difference operator. Suitable examples provided and verified by MATLAB are obtained by equating summation solution and closed form solution of certain types of k-difference equation.

8 ref

016518   Wani S S (NO, Pillai College of Engineering, New Panvel, Navi Mumbai-410 206, Email: sachin.swani@gmail.com) : Modified crank nicolson type method for burgers equation. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 259-77.

In this paper a new finite difference scheme called Modified Crank Nicolson Type (MCNT)method is proposed to solve one dimensional non linear Burgers equation. The new scheme is obtained by discretizing the nonlinear term uu_x explicitly, u is approximated at t=t_n+1 and u_x by central difference at t = t_n. The stability and convergence of the scheme is analysed. The method is shown to be first order accurate in time and second order accurate inspace. The solutions of Burgers equation obtained by MCNT are compared with the exact and numerical solutionsof Burgers equation available in the literature. For comparisons of numerical solutions with existing methods three test problems are tested. The L₂ norm and L_∞ norm are used to compare the errors in the solutions. The solutions of Burgers equations are plotted at different time steps for different values of constant of diffusivity k.

6 illus, 14 tables, 29 ref

016517   Wagh S;Wagh D K (NO, G.S. Institute of Tech. and Sc., Indore, Madhya Pradesh, Email: swastiwagh@gmail.com) : Mathematical modeling of Friedreich's ataxia - a genetic neuro-muscular degenerative condition. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 66-70.

In this paper Authors propose a mathematical model of Friedreich's Ataxia (FA) - a genetic neuro-muscular degenerative condition which causes imbalance, in-coordination and jerky limb movements. These continue to increase till patient loses independence and becomes wheelchair bound. Currently Friedreich's Ataxia (FA) is not considered an important health problem because of its relatively low prevalence in the general population. However with improvement in health care diagnosis and delivery provisions, more and more people with Friedreich's Ataxia (FA) are being diagnosed and surviving. This means that its incidence and prevalence is bound to change. We have used a - 42 - mathematical model to estimate generational increase in the number of patients and carriers with FA. The results portray a scary picture and hence demand measures to take it more seriously by health care providers.

3 illus, 2 ref

016516   Venkatesh S H;Kulli V R;Goudar V M;Venkatesha (Sri Gauthama Research Centre, (Affiliated to Kuvempu Univ), Sri Siddhartha Institute of Technology, Tumkur, Karnataka, Email: sh1.venkatesh@gmail.com) : Results on accurate edge domination number in graphs. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 21-9.

A edge dominating set F of a graph G = (V, E) is an accurate edge dominating set, if <60> E - F <62> has no edge dominating set of cardinality | F |. The accurate edge domination number γ_ae (G) is the minimum cardinality of an accurate edge dominating set. We study the graph theoretic properties of γ_ae (G) and its exact values for some standard graphs. The relation between γ_ae (G) with other parameters are also investigated.

1 illus, 12 ref

016515   Vasantha Kandasamy W B;Thangaraj R (Mathematics Dep, Indian Institute of Technology, Chennai - 36, Email: vasanthakandasamy@gmail.com) : Operations on strict fuzzy graphs and dominant fuzzy graphs. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 46-51.

In this paper, the authors study the various properties enjoyed by strict and dominant fuzzy graphs introduced in3, by the authors. The usual operations on these fuzzy graphs are not extendable. For the first time such deviant nature is analysed.

1 illus, 3 ref

016514   Vasantha Kandasamy W B;Kandasamy I; Smarandache F (Mathematics Dep, IIT Madras, Chennai, Email: vasanthakandasamy@gmail.com) : The 3n ± p conjecture: A generalization of collatz conjecture. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 83-8.

The Collatz conjecture is an open conjecture in mathematics named so after Lothar Collatz who proposed it in 1937. It is also known as 3n +1 conjecture, the Ulam conjecture (after Stanislaw Ulam), Kakutanis problem (after Shizuo Kakutani) and so on. Several various generalization of the Collatz conjecture has been carried. In this paper a new generalization of the Collatz conjecture called as the 3n ± p conjecture; where p is a prime is proposed. It functions on 3n + p and 3n - p, and for any starting number n, its sequence eventually enters a finite cycle and there are finitely many such cycles. The 3n ± conjecture, is a special case of the 3n ± p conjecture when p is 1.

1 illus, 2 tables, 10 ref

016513   Vasantha Kandasamy W B;Ilanthenral K (Mathematics Dep, Indian Institute of Technology Madras, Chennai, Email: vasanthakandasamy@gmail.com) : MOD n-cognitive maps model. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 29-34.

In this paper the new notion of MOD natural neutrosophic numbers Cognitive Maps (MOD-n-CMs) model which is based on MOD natural neutrosophic numbers and Neutrosophic Cognitive Maps (NCMs) is introduced. This model will find it various applications in the fields of engineering and science where indeterminacy plays a role.

2 illus, 8 ref

016512   Tripathi A (Mathematics Dep, K.K. (P.G.) College, Etawah, Uttar Pradesh, Email: atkkdc@gmail.com) : Flow of A visco-elastic rivlin-ericksen (1955) fluid through porous medium in a long uniform rectangular duct due to an impulsive pressure gradient acting at the central part of a section. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 15-20.

The aim of the present paper is to study the unsteady flow of a visco-elastic Rivlin-Ericksen (1955) type fluid through porous medium in a long uniform rectangular duct under the influence of an impulsive pressure gradient acting at the central part of a section. The analytical expressions for velocity profile and flux have been determined by the application of transform technique. Some particular cases have been discussed in detail. The results for the flow of ordinary viscous fluid have also been deduced by taking parameter μ_1→0.

20 ref

016511   Tripathi A (Mathematics Dep, K.K.P.G. College, Etawah, Uttar Pradesh, Email: atkkdc@gmail.com) : Oscillatory flow of blood in a stenosed artery in the presence of magnetic field. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 245-50.

The purpose of this paper is to study the effect of magnetic field on oscillatory flow of blood in a rigid tube with a mild stenosis. Here I assumed that the blood behaves as a Newtonian fluid and the maximum height of the roughness is very small compared with the radius of the unconstructed tube. The expression are given for the instantaneous flow rate, resistive impedance and wall shear stress.

2 illus, 16 ref

016510   Toure I;Kangni K (NO, UFR de Mathematiques et Informatique Universite de Cocody-Abidjan, 22 BP 582 Abidjan 22, Cote D'Ivoire, Email: ibrahima.toure@univ-fhb.edu.ci) : Necessary condition for gelf and triples. Far East J mathl Sci 2016, 99(5), 735-42.

Let G be a locally compact group, K be a compact subgroup of Aut(G), the group of automorphisms of G and δ be a class of unitary irreducible representations of K. The triple (G, K, δ) is a Gelfand triple if the convolution algebra U_{c, δ}(G) of δ-radial functions is commutative. In this paper, we give some properties of these triples and obtain a necessary condition.

7 ref

016509   Tangkanchanawong C (Mathematics Dep, Faculty of Science, Khon Kaen Univ, Khin Kaen 40002, Thailand, Email: chitan@kku.ac.th) : A bound on poisson approximation of URN containing - 40 - at most k balls by stein's method. Far East J mathl Sci 2016, 99(5), 763-74.

In this paper, we give bound for approximation of the number of urns containing at most kballs by Poisson distribution via Stein-Chen coupling method.

14 ref

016508   Sung Y O (Applied Mathematics Dep, Kongju National Univ, 182 Sinkwandong, Kongju-city, 314-701, Korea) : Fuzzy difunctional relations under balanced mappings. Far East J mathl Sci 2016, 99(5), 631-9.

The images and preimages of fuzzy difunctional relations are studied under the balanced mappings.

6 ref

016507   Sun J (Mathematics Dep, Shanghai Univ, Shanghai 200444, P.R. China, Email: jcsun@shu.edu.cn) : Associating vertex algebras to certain affine lie algebras of krichever-novikov type. Far East J mathl Sci 2016, 99(5), 663-85.

We associate certain affine Lie algebras of Krichever-Novikov type with vertex C((z))-algebras and their modules in a certain category. In the course, we construct two families of Lie algebras closely related to certain affine Lie algebras of Krichever-Novikov type.

8 ref

016506   Srivastava M (Mathematics Dep, V.S.S.D.P.G. College, Kanpur, Email: manjarivssd@gmail.com) : Note on fuzzy pairwise R₀ bitopological spaces. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 367-9.

The purpose of this paper is to introduce the notion of fuzzy pairwise R0 axiom in fuzzy bitopological spaces and study some of its properties. Several interesting results have been obtained viz. it satisfy hereditary, good extension, productive and projective properties.

7 ref

016505   Siarez H;Reyes A (Escuela de Matematicas y Estadistica, Universidad Pedagogica y Tecnologica de Colombia Tunja, Colombia) : Generalized koszul property for skew PBW extensions. Far East J mathl Sci 2017, 101(2), 301-20.

Let R be a commutative algebra. In this paper, we show that constant skew PBW extensions of a generalized Koszul algebra R are also generalized Koszul. Let A be a semi-commutative skew PBW extension of R such that A is R-augmented. We show also that if R is augmented Koszul then A is R-augmented Koszul.

24 ref

016504   Sarkar M;Roy T K (Mathematics Dep, Indian Institute of Engineering Science and Technology, Shibpur P.O.-Botanic Garden, Howrah-711 103, Email: mridula.sarkar86@rediffmail.com ) : Truss design optimization with imprecise load and stress in intuitionistic fuzzy environment. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 12-23.

In this paper, Authors - 39 - have introduced a intuitionistic fuzzy mathematical programming with intuitionistic fuzzy number as co-efficient of objectives. Real world engineering problems are usually designed with imprecise parameter by the presence of many conflicting objectives. In this paper we develop an approach to solve multi-objective structural design using probabilistic operator. Here total integral values of triangular intuitionistic fuzzy number,and it has been used for imprecise applied load and material density in the test problem. In this paper we have considered a multi objective structural optimization model with weight and deflection as objectives and stress as constraint function. Here design variables are considered as cross sectional area of bars. This classical truss design example is presented here in to demonstrate the significance of our proposed optimization approach. Numerical example is given here to illustrate this structural model through this approximation method.

1 illus, 2 tables, 19 ref

016503   Sarkar M;Roy T K (Mathematics Dep, Indian Institute of Engineering Science and Technology, Shibpur. P.O.-Botanic Garden, Howrah-711 103, Email: mridula.sarkar86@yahoo.com) : Neutrosophic optimization technique and its application on structural design. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 309-21.

In this paper, Authors develop a neutrosophic optimization (NSO) approach for optimizing the design of plane truss structure with single objective subject to a specified set of constraints. In this optimum design formulation, weight of truss and deflection of loaded joint are the objective functions. The design variables and constraints are the cross-sectional areas and the stresses in members respectively. A classical truss optimization example is presented herein to demonstrate the efficiency of the neutrosophic optimization approach. The test problem includes a two-bar planar truss subjected to a single load condition. This single-objective structural optimization model is solved by fuzzy as well as neutrosophic optimization approach. Numerical example is given to illustrate our NSO approach. The result shows that the NSO technique plays a significant role in finding the best ever optimal solutions.

1 illus, 2 tables, 16 ref

016502   Santhini C;Gomathi R (Mathematics Dep, V.V. Vanniaperumal College for Women, Virudhunagar, Email: gomathiradha2@gmail.com) : New types of continuity via gpc-closed sets. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 176-82.

The aim of this paper is to introduce several continuous functions via gpc-closed sets in topological spaces namely gpc-continuous function, (gpc)*-continuous functions, minimal gpc-continuous function, maximal gpc-continuous function and study their properties. Furthermore, a decomposition of continuity is obtained.

10 ref

016501   Saeed A E M (Mathematics Dep, Alzaem Alazhari Univ, Sudan, Email: alikeria_math@yahoo.co.uk) : Limit cycle and non-homoclinic orbits for Fitzhugh-Nagumo system. Ultra Scient phys Sci-Sect A 2017, 29(1-4), 156-63.

In this paper Authors investigate the complete FitzHugh-Nagumo System with I ≠ 0. Based on the result in, we discuss the non-existence of homoclinic orbits of the system. Further, we prove that the system has unique limit cycle under the conditions of existence of homoclinic orbits.

1 illus, 22 ref

016500   Sachithanantham S;Jagatheesan R (NO, Arignar Anna Government Arts College, Viluppuram, Tamil Nadu, Email: rjm.maths@gmail.com) : Model for optimal reserve inventory between two machines with reference to truncation point of the repair time. Ultra Scient phys Sci-Sect B 2017, 29(1-4), 1-7.

In Inventory control theory, many suitable models for real life systems are constructed with the objective of determining the optimal inventory level. In a system where the machines are in series for producing the finished products. The reserve of semi-finished products between two - 38 - machines becomes unavoidable to minimize the idle time of machines in series. In this model the repair time of machines is assumed to be a random variable and it follows exponential distribution which satisfies the so called Setting the Clock Back to Zero (SCBZ) property. Also, the truncation point of the repair time distribution is itself a random variable and it follows mixed exponential distribution. Under this assumption an optimal reserve inventory is obtained.

6 ref

016499   Ravi K;Suresh S (Mathematics Dep, Sacred Heart College, Tamil Nadu, Email: shckravi@yahoo.co.in) : Fuzzy stability of a new mixed type additive and quadratic functional equation. Far East J mathl Sci 2016, 99(5), 641-62.

In this paper, we obtain the general solution and investigate the fuzzy stability of a new mixed type additive and quadratic functional equation f(2x+y) + f(2x-7) = 2[f(x+y) + f(x-7)] + 2[f(x) + f(-x)] - [f(y) + f(-y)].

31 ref

016498   Rao K S;Murali R (NO, Shri Pillappa College of Engineering, Bengaluru, Email: srinivas.dbpur@gmail.com) : Rainbow connection in modified brick product graphs. Far East J mathl Sci 2017, 101(2), 289-300.

Let G be a nontrivial connected graph on which is defined a coloring c: E(G) → {1, 2, 3, ..., k}, k ∈ N, of the edges of G, where adjacent edges may be colored the same. A path in Gis called a rainbow path if no two edges of it are colored the same. G is rainbow connected if G contains a rainbow u-v path for every two vertices uand vin it. The minimum kfor which there exists such a k-edge coloring is called the rainbow connection number of G, denoted by rc(G). The brick product of even cycles denoted by c(2n, m, r) was introduced by Alspach et al. [1] to study Hamiltonian laceability properties. In this paper, we determine rc(G) of the modified brick product graph C_M(2n, m, r) associated with even cycles for m = 1, r = 2, n ≥ 2 and for m = 1, r = 3, n ≥ 4.

7 illus, 10 ref

016497   Raju G;Siva Prasad R (Mathematics Dep, S.K. Univ, Anantapur, Andhra Pradesh, Email: rajumaths2010@gmail.com) : Hall effects on MHD convective flow of visco-elastic fluid through a rotating porous channel. Ultra Scient phys Sci-Sect A 2016, 28(5-7), 340-53.

In this paper, Authors consider hydromagnetic convective flow of an electrically conducting visco-elastic fluid through a rotating porous channel taking hall current into account. The governing equations are framed using Brinkman model. The exact solutions of the velocity and the temperature distributions are evaluated analytically using Laplace transform technique and which consist of the both steady and transient states. Thought is centered on the physical character of the solutions, and the construction of the various kinds of boundary layers outward appearance on the plates. The ultimate steady state velocity and temperature distributions are numerically discussed for various values of the flow parameters. The shear stresses and the Nusselt number are tabulated and discussed.

10 illus, 3 tables, 45 ref