014058   Ariyanti G;Suparwanto A;Surodjo B (Mathematics Education Dep, Widya Mandala Univ Madiun, East Java Indonesia, Email: ariyanti_gregoria@yahoo.com) : Necessary and sufficient conditions for the solution of the linear balanced systems in the symmetrized max plus algebra. Far East J mathl Sci 2015, 97(2), 253-66.

System max plus algebra does not have an additive inverse. Therefore, some equations do not have a solution. For example, the equation 3 c x = 2 has no solution, since there is no x such that max(3, x) = 2. One way of trying to solve this problem is to extend the max plus algebra to a larger system which will include additive inverse in the same way that the natural numbers were extended to the larger system of integers. The extended system that is larger than max plus means the symmetrize max plus algebra. This paper describes the necessary and sufficient condition for the solution of the balanced linear system, that is, the linear system over the symmetrized max plus algebra

5 ref

014057   An D;Rahman M (NO, Minnesota State Univ Mankato, MN 56001, USA, Email: dayeong.an@mnsu.edu) : Maximum likehood parameter estimation for beta inverse Weibull distribution. Far East J mathl Sci 2015, 97(2), 131-7.

Inverse Weibull distribution is the one of the widely applied distribution. In this paper, we are going to extend the study of the beta inverse Weibull distribution (BIW). The maximum likelihood estimation (MLE) procedure is implemented in the BIW distribution with three parameters. In computation, the Newton-Raphson method is applied and the simulation results are given. Finally, practical use of the model is demonstrated by dint of an application to real data. For the real data computation, using the. Fisher information matrix, the variance-covariance matrix is estimated.

3 tables, 3 ref

014056   Amara H;Khale S;Fateh E (NO, , Laboratory of Modeling and Applied Mathematics (LMAM), Univ 8 May 1945 B.P.401, Guelma 24000, Algeria, Email: amarahitta@gmail.com) : Strongly projective module in differentiable homology of lie groups. Far East J mathl Sci 2015, 97(1), 19-29.

Let G be a Lie group countable at infinity with a finite number of connected components. The purpose of this article is.to prove that the category C_G^{∞ of all differentiable Frechet G-modules has a strongly projective one by means of the vector distributions on G with compact supports. This represents a dual work of that of Hochschild and Mostow (cf. [13]) and expands the results established by Blanc and Wigner (cf. [1,2]).}

22 ref

014055   Alkaseasbeh M;Darus M (School of Mathematical Sciences, Faculty of Science and Technology Univ Kebangsaan, Malaysia-43600 UKM Bangi, Selangor, Malaysia, Email: zakariya.alkaseabeh@gmail.com) : On an operator defined by the combination of both generalized operators of Salagean and Ruscheweyh. Far East J mathl Sci 2015, 97(4), 443-55.

In this paper, an operator of the form of generalized Salagean and Ruscheweyh operators is introduced. Some properties of certain class containing this operator are investigated. Further, Fekete-Szego functional for this class is also given.

10 ref

014054   Albehbah M;Darus M (School of Mathematical Sciences, Faculty of Science and Technology Univ Kebangsaan Malaysia, Selangor, DE, Bangi, UKM-43600, Malaysia, Email: malbehbah@yahoo.com) : On new subclasses of meromorphic univalent functions with positive coefficients. Far East J mathl Sci 2015, 97(4), 481-93.

In this paper, a new class S^{θ_ω(k, α) of meromorphic univalent functions has been introduced and studied in D = {z : 0 <60> | z | <60> 1}. The aim of this work is to prove some properties for the class Sθ_ω(k, α).}

18 ref

014053   Albaidani M (Mathematics/Statistics Dep, Washington State Univ, Pullman, WA 99163, USA, Email: malbaidani@gmail.cpm ) : Explicit formula for a Bijective mapping from the set of distinct odd partitions into the set of self-conjugate partitions. Far East J mathl Sci 2015, 97(1), 95-100.

In this paper, we give a full explicitly defined bijective function from the set of self-conjugate partitions to the set of partitions into distinct odd parts. The bijection between these two sets is well known since Euler. However, to our knowledge an explicit formula for such mapping from the set of distinct odd partitions into the set of self-conjugate partitions has not been given until now.

3 ref

014052   Abashar A;Mamat M;Rivaie M;Fauzi M;Salleh Z (Faculty of Informatics and Computing, Univ Sultan Zainal Abidin (UniSZA) K. Terengganu, Malaysia, Email: tomcatkassala@yahoo.com) : Modified DPRP conjugate gradient method for unconstrained optimization. Far East J mathl Sci 2015, 97(1), 31-44.

Currently, Zhang [17] takes some modification of the Wei-Yao-Liu nonlinear conjugate gradient method suggested by Wei et al. [18] such that the modified method called NPRP method. Dai and Wen [19] make a simple modification to the NPRP called DPRP method. In this paper, we change denominator of DPRP method such that the modified DPRP method possesses global convergence under exact line search. Numerical results show that the proposed method is efficient for the given test functions when compared with classical formula and DPRP method.

2 illus, 1 table, 21 ref

012104   Zhang Z (School of Mathematics and Computer Science, Gannan Normal Univ, Ganzhou-341 000, Email: zhangzujin361@163.com) : Regularity criteria for the 3D magneto-micropolar fluid equations via the direction of the velocity. Proc Math Sci 2015, 125(1), 37-43.

Consider sufficient conditions to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations. It involves only the direction of the velocity and the magnetic field. Our result extends to the cases of Navier-Stokes and MHD equations.

19 ref

012103   Zhang M;Liu Q (The Attached Middle School, Fuyang Normal College, Fuyang Anhui-236 032, People's Republic of China, Email: zhmlqf@163.com) : An M/G/1 G-queue with server breakdown, working vacations and vacation interruption. Opsearch 2015, 52(2), 256-70.

In this paper, an M/G/I G-queue with server breakdowns, working vacations and vacation interruption is analyzed. A breakdown at busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. After repair the server is as good as new. Using the method of supplementary variable and the matrix-analytic method, the queue length distribution and the probability of service status at the arbitrary epoch under steady state conditions are obtained. Further, a special cases are presented. Finally, numerical illustrations are provided.

4 illus, 23 ref

012102   Wang J;Wang W (Mathematics Dep, China Three Gorges Univ, Yichang 443 002, China, Email: phone666888@163.com) : Lp-dual affine surface area forms of Busemann-Petty type problems. Proc Math Sci 2015, 125(1), 71-7.

Associated with the notion of L_p-intersection body which was defined by Haberl, we research L_p-dual affine surface area forms of Busemann-Petty type problems.

15 ref

012101   Tripathy A K (Mathematics Dep, Trident Academy of Technology, F2/A, Chandaka Industrial Estate, Bhubaneswar-751 024, Email: arun_tripathy06@rediffmail.com) : Higher order mixed type duality in nonsmooth multiobjective fractional programming involving generalized univex function. Opsearch 2015, 52(1), 108-33.

In this chapter, a new generalized class of higher order (F, α, p, d)-type 1 univex function is introduced with examples. KKT necessary and sufficient conditions for efficient solution for fractional programming with higher order (F, α, p, d)-type 1 univex function are established. Higher order mixed type duality for nonsmooth multiobjective fractional programming (MFP) is formulated and using the generalized higher order (F, α, p, d)-type 1 univexity assumption in the functions involved, the duality results are established. At the end, some special cases are discussed.

28 ref

012100   Tavasoli E;Salimi M;Yassemi S (Mathematics Dep, East tehran Branch, Islamic Azad Univ, Tehran, Iran, Email: elhamtavasoli@ipm.ir) : Reflexive modules with finite gorenstein dimension with respect to a semidualizing module. Proc Math Sci 2015, 125(1), 21-8.

Let R be a commutative Noetherian ring and let C be a semidualizing R-module. It is shown that a finitely generated R-module M with finite G_C-dimension is C-reflexive if and only if M_p is C_p-reflexive for p ∈ Spec (R) with depth (R_p) ≤ 1, and G_Cp - dim_Rp (M_p) ≤ depth (R_p) - 2 for p ∈ Spec (R) with depth (R_p) ≥ 2. As the ring R itself is a semidualizing module, this result gives a generalization of a natural setting for extension of results due to Serre and Samuel (see Czech. Math. J. 62(3) (2012) 663-672 and Beitrdge Algebra Geom. 50(2) (2009) 353-362). In addition, it is shown that over ring R with dim R ≤ n, where n ≥ 2 is an integer, G_D - dim_R (Hom_R (M, D)) ≤ n - 2 for every finitely generated R-module M and a dualizing R-module D.

12 ref

012099   Subburam S;Thangadurai R (NO, Institute of Mathematical Sciences, C.I.T. Campus, 4th Cross Street, Taramani, Chennai-600 113, Email: ssrammaths@gmail.com) : On Erdos-Wood's conjecture. Proc Math Sci 2015, 125(2), 139-47.

In this article, we prove that infinite number of integers satsify Erdos-Woods conjecture. Moreover, it follows that the number of natural numbers ≤ x satisfies Erdos-Woods conjecture with k = 2 is at least cx/(log x) for some positive constant c <62> 2.

7 ref

012098   Sinha P (NO, Operations Research/Management, 6, A J C Bose Road - Thakurpukur, Kolkata-700 063, Email: p_sinha@live.com) : Method for solving some optimization problems with bounds on variables. Opsearch 2015, 52(1), 186-93.

Author give a method to solve some quasi-convex programming instances having lower and upper bounds on the variables. In the method, instances without such bounds, or with less number of such bounds, are solved in different iterations. The method is a general one and may be combined with other suitable methods.

2 tables, 9 ref

012097   Sinha D;Sethi A (NO, South Asian Univ, Akbar Bhawan, Chanakyapuri, New Delhi-110 021) : Optimal algorithm to detect sign compatibility of a given sigraph. Natn Acad Sci Lett 2015, 38(3), 235-8.

A signed,graph (or sigraph in short) S is a graph G in which each edge x carries a value s(x) ∈ {+1,-1} called its sign denoted specially as S =(G,s). A sigraph S is sign-compatible if there exists a marking μ of its vertices such that the end vertices of every negative edge receive '-' signs in μ and no positive edge in S has both of its ends assigned '-' sign in μ. In this paper, we write algorithms to detect sign-compatibility of a given sigraph and obtain optimal algorithm with complexity O(n^2).

8 ref

012096   Singh N (Mathematics Dep, Indian Institute of Science, Bangalore-560 012, Email: nitin@math.iisc.ernet.in) : Strongly minimal triangulations of (S<. Proc Math Sci 2015, 125(1), 79-102.

Triangulated d-manifold K, satisfies the inequality (f_o(K)-d-1/2) ≥ [(D+2)/2]β₁ (K; Z₂) for d ≥ 3. The triangulated d-manifolds that meet the bound with equality are called tight neighbourly. In this paper, we present tight neighbourly trian-gulations of 4-manifolds on 15 vertices with Z₃ as an automorphism group. One such example was constructed by Bagchi and Datta (Discrete Math. 311 (2011) 986-995). We show that there are exactly 12 such triangulations up to isomorphism, 10 of which are orientable.

8 illus, 12 ref

012095   Sharma R;Saini R (Mathematics Dep, H P Univ, Shimla-171 005, Email: rajesh_hpu_math@yahoo.co.in) : Generalization of Samuleson's inequality and location of Eigenvalues. Proc Math Sci 2015, 125(1), 103-11.

Proves a generalization of Samuelson's inequality for higher order central moments. Bounds for the eigenvalues are obtained when a given complex n x n matrix has real eigenvalues. Likewise, we discuss bounds for the roots of polynomial equations.

14 ref

012094   Sharma R;Bhandari R;Saini R (Mathematics and Statistics Dep, Himachal Pradesh Univ, Shimla) : On Lower Bounds for varience and moments of unimodal distributions. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 1-14.

Authors provide an elementary proof of the lower bound for the variance of continuous unimodal distributions and obtain analogous bounds for the higher order central moments. A lower bound for the rth central moment of discrete distribution is given and compared favorably with a related bound for discrete unimodal distribution in literature.

12 ref

012093   Saxena V P (NO, Sagar Institute of Research, Technology and Science, Bhopal-462 041) : Trivial extension of Saxena's I-function. Natn Acad Sci Lett 2015, 38(3), 243-5.

In this communication it is shown that the so called generalization of Saxena's I-function, named as Aleph function, is nothing but another form of the I-function which is the subsequent generalization of Fox's H-function and last generalization of Hypergeometric functions. This implies that the said generalization in the form of Aleph function is redundant. Later on, other authors have also studied this so called generalization of I-function. All such studies are in fact, studies of the earlier function (I-function) unless or otherwise it indicates some new properties of both I-function and Aleph function. This later function does not reveal any significant change either in the definition or conditions of existence. The denominator of the complex integrand under contour integral, which is in the form of a finite summation, has an additional constant coefficient in each term. This coefficient can be expressed as a quotient of gamma functions. Hence the same can be absorbed in the definition of I-function.

12 ref

012092   Satheesh Kumar C;Unnikrishnan Nair B (Statistics Dep, Kerala Univ, Trivandrum-695 581, Email: drcsatheeshkumar@gmail.com) : On a class of hyper-poisson and alternative hyper-poisson distributions. Opsearch 2015, 52(1), 86-100.

Here we propose a class of hyper-Poisson and alternative hyper-Poisson distributions and study some of its important aspects by deriving expressions for its probability mass function, mean and variance and obtain conditions under which the distribution becomes under-dispersed or over-dispersed. Certain recurrence relations for probabilities, raw moments and factorial moments are also developed. Further, the estimation of the parameters of this class of hyper-Poisson distributions is attempted by various methods of estimation and shown that this new class of distribution gives better fit to certain rear life data sets compared to the existing models.

4 tables, 17 ref

012091   Sarkar A;Mukhopadhayaya A R;Ghosh S K (SQC & OR Unit, Indian Statistical Institute, Room No 320,Old C.G.O. Buildings, 110 Maharshi Karve Road, Munbai 400 020, Email: isiashok@gmail.com) : Productivity improvement by reduction of idle time throuh application of queuing theory. Opsearch 2015, 52(2), 195-211.

In Lean Six Sigma one of the primary objectives is to identify and eliminate the waiting or idle time for enhancing productivity and reducing production cost However, in some situations it is better to replace 'elimination' by 'optimization' due to the presence of conflicting requirements. Optimization techniques in the form of queuing models are quite useful to resolve this conflict. In an Indian textile manufacturing plant, the waiting (idle) time in the winding process is identified as a reason for high production cost. In this situation, it is to be determined as to how many machines are to be assigned to an operator for reducing waiting or idle time of both the operators and the machines leading to reduced production cost. The situation can be compared and contrasted to a machine repairman problem aiming for optimizing the number of machines per operator. The various process parameters have been estimated and suitably modified or derived to serve as inputs to the Queuing Model. Sensitivity analysis has been carried out to identify and control the significant factors. The objective of this paper is to demonstrate through an application of queuing models the procedure of optimizing the waiting or idle time. Consequently, the focus is on the application of optimization techniques like Queuing Theory and Simulation while implementing lean six sigma.

2 illus, 8 ref, 17 ref

012090   Samira A;Afrouzi G A;Niknam A (Mathematics Dep, Science and Research Branch, Islamic Azad Univ (IAU), Tehran, Iran, Email: ala_samira@yahoo.com) : Existence of positive weak solutions for (p, q)-laplacian nonlinear systems. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 537-44.

13 ref

012089   Sadhu V (Mathematics Dep, Indian Institute of Technology Bombay, Powai, Mumbai-400 076, Email: viveksadhu@math.iitb.ac.in) : Subintegrality, invertible modules and Laurent polynomial extensions. Proc Math Sci 2015, 125(2), 149-60.

Let A ⊆ B be a commutative ring extension. Let I(A, B) be the multiplicative group of invertible A-submodules of B. In this article, we extend a result of Sadhu and Singh by finding a necessary and sufficient condition on an integral birational extension A ⊆ B of integral domains with dim A ≤ 1, so that the natural map I(A, B) → I(A[X, X^{-1], B[X, X-1]) is an isomorphism. In the same situation, we show that if dim A ≥ 2, then the condition is necessary but not sufficient. Authors also discuss some properties of the cokernel of the natural map I(A, B) → I(A[X, X-1], B[X, X-1]) in the general case.}

10 ref

012088   Sadeghieh A;Ahmadidelir K (Yazd Branch, Islamic Azad Univ, Yazd, Iran, Email: sadeghieh@iauyazd.ac.ir) : n-th roots in finite polyhedral and centro-polyhedral groups. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 487-99.

The probability that a randomly chosen element in a non-abelian finite group has a square root, has been investigated by certain authors in recent years. In this paper, this probability will be generalized for the n-th roots when n ≥ 2 and it will be computed for every finite polyhedral group and all of the finite centro-polyhedral groups.

8 tables, 10 ref

012087   Rivaz S;Yaghoobi M A (Mathematics Dep, Faculty of Mathematics of Computer, Shahid Bahonar Univ of Kerman, Kerman, Iran, Email: sanazrivaz@math.uk.ac.ir) : Some results in interval multiobjective linear programming for recognizing different solutions. Opsearch 2015, 52(1), 75-85.

Based on the concepts of efficiency and weak efficiency, different solutions are defined to multiobjective linear programming problems with interval objective functions coefficients. This paper introduces a new solution concept namely necessarily weak efficient. Moreover, we propose some new results for recognizing different kinds of solutions by using some linear and nonlinear programming models. To illustrate the results, a numerical example is given.

2 illus, 23 ref

012086   Ranjan R;Chatterjee P;Chakraborty S (Production Engineering Dep, Jadavpur Univ, Kolkata-700 032, West Bengal, Email: s_chakraborty00@yahoo.co.in) : Evaluating performance of engineering department in an Indian University using DEMATEL and compromise ranking methodss. Opsearch 2015, 52(2), 307-28.

Performance efficiency of educational institutions should be constantly scrutinized and improved to make sure that competent manpower and researchers are produced proficiently in meeting the institutional standard of intellectuals. With a systematic performance evaluation system, resources can be directed satisfactorily and tasks may be completed effectively. Performance evaluation and ranking of engineering departments of technical institutions have received very limited attention due to complexity and difficulty in measuring the outputs. However, in today's global education system, performance evaluation of engineering departments is required to assess whether they meet the set objectives and foster an environment of continuous improvement. So, the objective of this paper is set to develop a multi-criteria decision-making framework for performance evaluation and ranking of 16 engineering departments in an Indian university which addresses the inter-relationships between the selection criteria with the aid of decision-making trial and evaluation laboratory (DEMATEL) method while building a relationship structure. Entropy method is used to determine the relative criteria weights, and finally, a compromise ranking method is applied to prioritize and rank those departments, It is observed that Electrical Engineering department emerges out as the best performer and Information Technology department lags behind in its performance. Based on analytical results, faculty/student ratio, infrastructural development, student results and international research publications are identified to play major roles in evaluating the performance of those departments. This integrated model can help practitioners to improve their decision-making process, especially when criteria are numerous and interrelated. Its relevance and implementation issues in context of Indian engineering education scenario are also discussed.

6 illus, 8 tables, 32 ref

012085   Rad N J;Krzywkowski M (Mathematics Dep, Shahrood Univ of Technology, Shahrood, Islamic Republic of Iran, Email: n.jafarirad@gmail.com) : Two-outer-independent domination in graphs. Natn Acad Sci Lett 2015, 38(3), 263-9.

We initiate the study of 2-outer-independent domination in graphs. A 2-outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of (V(G) {setminus} D) has at least two neighbors in D, and the set (V(G) {setminus} D) is independent. The 2-outer-independent domination number of a graph G is the minimum cardinality of a 2-outer-independent dominating set of G. We show that if a graph has minimum degree at least two, then its 2-outer-independent domination number equals the vertex cover number. Then we investigate the 2-outer-independent domination in graphs with minimum degree one.

12 ref

012084   Paul J;Thomas P Y (Statistics Dep, Keral Univ, Trivandrum) : Tsallis entropy properties of record values. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 47-60.

This paper provides Tsallis entropy of record values. Its important properties are analysed and a characterization theorem is established. Further we derived expressions for Tsallis entropy of concomitants of record values arising from the Farlie-Gumbel-Morgenstern family of distributions and for residual Tsallis entropy of record values are also derived.

15 ref

012083   Neirameh A (Mathematics Dep, Faculty of Sciences, Gonbad Univ, Kavoos, Gonbad, Iran, Email: a.neirameh@gonbad.ac.ir) : Soliton solutions of the generalized Sinh-Gordon equation by the binary (G' / G)-expansion method. Pramana J Phys 2015, 85(4), 739-45.

Aim of this paper is to extend the applications of (G' / G)-expansion method to solve a generalized sinh-Gordon equation. In fact, the binary (G'/G)-expansion method is introduced for finding different new exact solutions. It is shown that this method is a powerful mathematical tool for solving nonlinear evolution equations with time-dependent coefficients in mathematical physics.

18 ref

012082   Nair M T (Mathematics Dep, Indian Institute of Technology, Madras, Chennai-600 036, Email: mtnair@iitm.ac.in) : Morozov-type discrepancy principle for nonlinear ill-posed problems under η-condition. Proc Math Sci 2015, 125(2), 227-38.

For proving the existence of a regularization parameter under a Morozov-type discrepancy principle for Tikhonov regularization of nonlinear ill-posed problems, it is required to impose additional nonlinearity assumptions on the forward operator. Lipschitz continuity of the Freechet derivative and requirement of the Lipschitz constant to depend on a source condition is one such restriction (Ramlau P, Numer. Fund. Anal. Optim. 23(1&22) (2003) 147-172). Another nonlinearity condition considered by Scherzer (Computing, 51 (1993) 45-60) was by requiring the forward operator to be close to a linear operator in a restricted sense. A seemingly natural nonlinear assumption which appears in many applications which attracted attention in various contexts of the study of nonlinear problems is the so-called η-condition. However, a Morozov-type discrepancy principle together with η-condition does not seem to have been studied, except in a recent paper by the author (Bull. Aust. Math. Soc. 79 (2009) 337-342), where error estimates under a general source condition is derived, by assuming the existence of the parameter. In this paper, the existence of the parameter satisfying a Morozov-type discrepancy principle is proved under the η-condition on the forward operator, by assuming the source condition as in the papers of Scherzer (Computing, 51 (1993) 45-60) and Ramlau (Numer. Funct. Anal. Optim. 23(1&22) (2003) 147-172). This source condition is, in fact, a special case of the source condition in the author's paper (Bull. Aust. Math. Soc. 79 (2009) 337-342).

19 ref

012081   Mini Mol S M (Statistics Dep, Kerala Univ, Trivandrum) : On an extended past entropy measure and its properties. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 61-8.

In the present paper a new generalized entropy measure in the past lifetime known as extended past entropy measure is introduced and some properties of this measure is discussed. Further some characterization results using this measure is also proposed.

12 ref

012080   Matinfar M;Eslami M;Roshandel S (Mathematics Dep, Faculty of Mathematical Sciences, Mazandaran Univ, Babolsar, Iran, Email: mostafa.eslami@umz.ac.ir) : First integral method to study the (2+1)-dimensional Jaulent-Miodek equations. Pramana J Phys 2015, 85(4), 593-603.

In this paper, we have presented the applicability of the first integral method for constructing exact solutions of (2+1 )-dimensional Jaulent-Miodek equations. The first integral method is a powerful and effective method for solving nonlinear partial differential equations which can be applied to nonintegrable as well as integrable equations. The present paper confirms the significant features of the method employed and exact kink and soliton solutions are constructed through the established first integrals.

30 ref

012079   Matinfar M;Eslami M;Kordy M (Mathematics Dep, Faculty of Mathematical Sciences, Mazandaran Univ, Babolsar, Iran, Email: m_kordy_1391@yahoo.com) : Functional variable method for solving the fractional Korteweg-de Vries equations and the coupled Korteweg-de Vries equations. Pramana J Phys 2015, 85(4), 583-92.

This paper presents the exact solutions for the fractional Korteweg-de Vries equations and the coupled Korteweg-de Vries equations with time-fractional derivatives using the functional variable method. The fractional derivatives are described in the modified Riemann-Liouville derivative sense. It is demonstrated that the calculations involved in the functional variable method are extremely simple and straightforward and this method is very effective for handling nonlinear fractional equations.

39 ref

012078   Margaux B (NO, , Laboratoire de Recherche "Princess Stephanie", Monte Carlo 51840, Monaco, Email: benedictus.margaux@gmail.com) : Smoothness of limit functors. Proc Math Sci 2015, 125(2), 161-5.

Let S be a scheme. Assume that we are given an action of the one dimensional split torus G_m,S on a smooth affine S-scheme X. Authors consider the limit (also called attractor) subfunctor X_λ consisting of points whose orbit under the given action admits a limit at 0. Authors show that X_λ is representable by a smooth closed subscheme of X. This result generalizes a theorem of Conrad et al. (Pseudo-reductive groups (2010) Cambridge Univ. Press) where the case when X is an affine smooth group and G_{m, S}acts as a group automorphisms of X is considered. It also occurs as a special case of a recent result by Drinfeld on the action of G_{m, S} on algebraic spaces (Proposition 1.4.20 of Drinfeld V, On algebraic spaces with an action of B_m, preprint 2013) in case S is of finite type over a field.

8 ref

012077   Malinowska I A (Institute of Mathematics, Bialystok Univ, 15-245 Bialystok, Ciolkowskiego 1 M, Poland, Email: izabelam@math.uwb.edu.pl) : On p-supersolvability of finite groups. Proc Math Sci 2015, 125(2), 173-9.

Number of authors have studied the structure of a group G under the assumption that some subgroups of G are well located in G. We will obtain some new criteria of p-supersolvability and p-nilpotency of groups.

11 ref

012076   Maity H K;Pal M (Statistics Dep, Calcutta Univ, Kolkata) : Ordering policy for deteriorating items with hybrid demand under permissible delay in payment and price inflation. Calcutta Statist Ass Bull 2015, 67(Mar-Jun), 69-88.

The paper studies an inventory model for deteriorating items under price inflation and permissible delay in payment. The demand rate is assumed to be hybrid, which is observed for commodities like coffee, cotton, tin, copper, wristwatch, automobile, etc. The model is studied over a finite planning horizon with unequal cycle lengths. A solution procedure is indicated to determine the optimal number of replenishments, cycle times and optimal order quantities.

3 tables, 12 ref

012075   Lijing Z (School of Mathematics and Physics, Univ of South China, Hengyang, Hunan, People's Republic of China, Email: zhenglijing817@163.com) : Yoneda algebras of almost Koszul algebras. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 477-85.

Let k be an algebraically closed field, A a finite dimensional connected (p, q)-Koszul self-injective algebra with p, q ≥ 2. In this paper, authors prove that the Yoneda algebra of A is isomorphic to a twisted polynomial algebra A^{! [t; β] in one indeterminate t of degree q + 1 in which A is the quadratic dual of A, β is an automorphism of A!, and tb = β(b)t for each t ∈ A!, As a corollary, we recover Theorem 5.3 of [2].}

6 ref

012074   Laxmi P V;Suchitra V (Applied Mathematics Dep, Andhra Univ, Visakhapatnam-530 003, Email: vijaya_iit2003.co.in) : Discrete-time renewal input state dependent queue with working vacations and change over time. Opsearch 2015, 52(2), 285-306.

This paper considers a discrete-time renewal input state dependent queue with multiple working vacations and change over time. Using the supplementary variable and recursive techniques, the steady state system length distributions at different time epochs have been derived. Based on the system length distributions, some performance measures of the model have been discussed. The optimum values of service rates have been found through quadratic fit search method under a given cost structure.

4 illus, 3 tables, 15 ref

012073   Laxmi P V;Soujanya M L (Applied Mathematics Dep, Andhra Univ, Visakhapatnam-530 003, Email: vijaya_iit2003@yahoo.com ) : Retrial inventory system with negative customes and service interuptions. Opsearch 2015, 52(2), 212-24.

In this paper, we consider a single server queueing system wherein demands arrive according to Poisson process, each demanding exactly one unit of inventory item. The operating policy is (s, S) policy in which an order is placed for a quantity up to S whenever the inventory level falls to s. The ordered items are received after a random time which is exponentially distributed. The service may be interrupted according to Poisson process in which case it restarts after an exponentially distributed time. The demands that occur during the server breakdown period or stock-out period may turn out to be ordinary or negative and they enter into the orbit of infinite size. These demands retry after a random time, which is again exponentially distributed. Matrix geometric solution is obtained for the steady state distribution of the model. Various performance measures and cost analysis are shown with numerical results.

3 illus, 1 table, 16 ref

012072   Kuo C C (Mathematics Dep, Fu Jen Univ, New Taipei City, Taiwan-242 05, Republick of China, Email: cckuo@math.fju.edu.tw) : Multiplicative pertubations of local C-semigroups. Proc Math Sci 2015, 125(1), 45-55.

In this paper, authors establish some left and right multiplicative perturbation theorems concerning local C-semigroups when the generator A of a perturbed local C-semigroup S(.) may not be densely defined and the perturbation operator B is a bounded linear operator from D(A) into R(C) such that CB = BC on D(A), which can be applied to obtain some additive perturbation theorems for local C-semigroups in which B is a bounded linear operator from [D(A)] into R(C) such that CB = BC on D(A). We also show that the perturbations of a (local) C-semigroup S(.) are exponentially bounded (resp., norm continuous, locally Lipschitz continuous, or exponentially Lipschitz continuous) if S(.) is.

14 ref

012071   Kharbanda P;Agarwal D;Sinha D (Centre for Mathematical Sciences, Banastahli Univ, Rajasthan, Email: pallavimath@yahoo.co.in) : Multiobjective programming under (ϕ, d)-v-type I univexity. Opsearch 2015, 52(1), 168-85.

In this paper, we have introduced a new class of (ϕ, d)-V-type I univex, quasi (ϕ, d)-V-type 1 univex, pseudo (ϕ), J)-V-type I univex, quasi-pseudo (ϕ, d)-V-type I univex and pseudo-quasi (ϕ, d)- V-type I univex functions in case of nonlinear multiobjective programming problem where functions involved are nondifferentiable and illustrated through non-trivial examples that this class extends some known classes in literature. Various Karush-Kuhn-Tucker type sufficient optimality conditions are obtained under this newly introduced class of functions. Also, for mixed type multiobjective dual program, we have established weak, strong, converse and strict converse duality results in order to relate the efficient and weak efficient solutions of primal and dual problem.

22 ref

012070   Khan S I;Khan U;Ahmed N;Jan S U;Waheed A; Mohyud-Din S T (NO, Comsats Institute of Information Technology, Univ Road, Abbottabad, Pakistan) : Effects of viscous dissipation and convective boundary conditions on Blasius and Sakiadis problems for casson fluid. Natn Acad Sci Lett 2015, 38(3), 247-50.

In this article, two types of problems are investigated. The flow and heat transfer over: (1) a static flat plate (Blasius problem) and (2) a moving flat plate (Sakiadis problem) are considered. Convective boundary conditions are used to formulate the energy equation. Suitable similarity transform has been employed to reduce the governing nonlinear partial differential equations to a set of somewhat simpler nonlinear differential equations. These equations are then solved numerically by using sixth order Runge-Kutta method. Influences of different emerging parameters on both the problems are presented graphically coupled with comprehensive discussions.

23 ref

012069   Ke-Ang Fu;Qiu Y;Tong Y (School of Statistics and Mathematics, Zhejiang Gongshang Univ, Hangzhou 310018, China, Email: zjgsustat@163.com) : Limit law of the iterated logarithm for B-valued trimmed sums. Proc Math Sci 2015, 125(2), 221-5.

Given a sequence of i.i.d. random variables [X, X_n; n ≥ 1) taking values in a separable Banach space (B, ||.||) with topological dual B*, let X^{(r)_n = X_m if ||X_m|| is the r-th maximum of {||X_k||; 1 ≤ k ≤ n} and (r)S_n = S_n - (X(1)_n + ... + X(r)_n) be the trimmed sums when extreme terms are excluded, where S_n = ∑n_k=1 X_k. In this paper, it is stated that under some suitable conditions, lim_n→∞ 1/[√ log log n] max_{1 <131> k <131> n ||(r)Sk||/√k = σ(X) a.s., where σ2}(X) = sup_f∈B*1 Ef2(X) and B*₁ is the unit ball of B*.}

11 ref

012068   Kannan K;Rajalakshmi D (mathematics Dep, Srinivasa Ramanujan Centre, Sastra Univ, Kumbakonam-612 001) : Soft g-loclly closed sets. Natn Acad Sci Lett 2015, 38(3), 239-41.

Soft sets have many applications in various real time problems in the field of engineering, social science, medical science etc. Recently, the concept of soft topological space has been developed with the help of soft sets. In the present paper, we continue the study of soft generalized closed sets in soft topological spaces by introducing new concepts, namely soft g-locally closed sets, soft g-locally closed* sets, soft g-locally closed** sets.

6 ref

012067   Kamali Z;Yousefi B (Mathematics Dep, Shiraz Branch, Islamic Azad Univ, Shiraz Iran, Email: zkamali@shirazu.ac.in) : Disjoint hypercyclicity of weighted composition operators. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 559-67.

In this paper, we discuss about disjoint hypercyclicity of weighted composition operators on some function spaces of analytic functions on a plane domain.

15 ref

012066   Jiang Q;Shao C (School of Mathematical Sciences, Jinan Univ, 250022 Shandong, China, Email: syjqh2001@163.com) : New characterization of L₂(p) by NSE. Proc Indian Acad Sci-Mathl Sci 2015, 125(4), 507-10.

In this paper we give a new characterization of simple group L₂(p) with p a prime by both its order and nse(L₂(p)), the set of numbers of elements of L₂(p) with the same order.

9 ref

012065   Jain M;Bhagat A (Mathematics Dep, Indian Institute of Technology, Roorkee, Roorkee-247 667) : Transient analysis of finite F-Policy retrial queues with delayed repair and thershold recovery. Natn Acad Sci Lett 2015, 38(3), 257-61.

The transient analysis of F-policy retrial queue has been carried out using Runge-Kutta method of fourth order. The server is unreliable and may break down while providing service to the customers. The failed server is sent to the repair facility where after required setup time, the repair is done as per pre-specified rule known as 'threshold recovery policy' for the repair. The cost optimization of the system has been carried out and threshold parameters are computed.

8 ref

012064   Iyiola O S;Ojo G O (Mathematics and Statistics Dep, King Fahd Univ of Petroleum and Minerals, KFUPM, Dhahran, Saudi Arabia, Email: samuel@kfupm.edu.sa) : On the analytical solution of Fornberg-Whitham equation with the new fractional derivative. Pramana J Phys 2015, 85(4), 567-75.

Motivated by the simplicity, natural and efficient nature of the new fractional derivative introduced by R Khalil et al in J. Comput. Appl. Math. 264, 65 (2014), analytical solution of space-time fractional Fornberg-Whitham equation is obtained in series form using the relatively new method called q-homotopy analysis method (q-HAM). The new fractional derivative makes it possible to introduce fractional order in space to the Fornberg-Whitham equation and be able to obtain its solution. This work displays the elegant nature of the application of q-HAM to solve strongly nonlinear fractional differential equations. The presence of the auxiliary parameter h helps in an effective way to obtain better approximation comparable to exact solutions. The fraction-factor in this method gives it an edge over other existing analytical methods for nonlinear differential equations. Comparisons are made on the existence of exact solutions to these models. The analysis shows that our analytical solutions converge very rapidly to the exact solutions.

5 illus, 18 ref

012063   Herman A;Singh G (Mathematics and Statistics Dep, Regina Univ, Regina S4S 0A2, Canada, Email: allen.herman@uregina.ca ) : Revisiting the Zassenhaus conjecture on torsion units for the integral group rings of small groups. Proc Math Sci 2015, 125(2), 167-72.

In recent years several new restrictions on integral partial augmentations for torsion units of ZG have been introduced, which have improved the effectiveness of the Luthar-Passi method for checking the Zassenhaus conjecture for specific groups G. In this note, we report that the Luthar-Passi method with the new restrictions are sufficient to verify the Zassenhaus conjecture with a computer for all groups of order less than 96, except for one group of order 48 - the non-split covering group of S₄, and one of order 72 of isomorphism type (C₃ x C₃) x D₈. To verify the Zassenhaus conjecture for this group we give a new construction of normalized torsion units of QG that are not conjugate to elements of ZG.

7 ref

012062   Gumber D;Sharma M (School of Mathematics and Computer Applications, Thapar Univ, Patiala-147 004, Email: dkgumber@yahoo.com) : Class-preserving automorphisms of some finite p-groups. Proc Math Sci 2015, 125(2), 181-6.

Let G be a finite p-group of order p^{5, where p is a prime. We give necessary and sufficient conditions on G such that G has a non-inner class-preserving automorphism.}

13 ref