International Journal of Mathematics and Mathematical Sciences http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2014 , Hindawi Publishing Corporation . All rights reserved. Interest of Boundary Kernel Density Techniques in Evaluating an Approximation Error of Queueing Systems Characteristics Thu, 14 Aug 2014 09:06:09 +0000 http://www.hindawi.com/journals/ijmms/2014/871357/ We show the interest of nonparametric methods taking into account the boundary correction techniques for a numerical evaluation of an approximation error between the stationary distributions of and queueing systems, when the density function of the general arrivals law in the system is unknown and defined on a bounded support. To compute this error, we use two kinds of norms: the norm and the weight norm. Numerical examples based on simulation studies are presented for the two cases of considered norms. A comparative study of the results has been provided. Aïcha Bareche and Djamil Aïssani Copyright © 2014 Aïcha Bareche and Djamil Aïssani. All rights reserved. Solving Fuzzy Multiproduct Aggregate Production Planning Problems Based on Extension Principle Sun, 03 Aug 2014 10:42:36 +0000 http://www.hindawi.com/journals/ijmms/2014/207839/ Aggregate production planning (APP) plays a critical role in supply chain management (SCM). This paper investigates multiproduct, multiperiod APP problems with several distinct types of fuzzy uncertainties. In contrast to the existing studies, the modelling in this work conserves the fuzziness such that the obtained APP is more effective. Based on Zadeh’s extension principle, the results obtained are fuzzy solutions described by membership functions, in contrast to results from previous studies. A pair of two-level parametric mathematical programs is formulated to calculate the lower and upper bounds of the optimum fuzzy performance measure. The membership function of the fuzzy total cost is constructed by enumerating various possibility levels. A case studied in previous research is investigated to demonstrate the validity of the proposed model and solution procedure. Because the optimal objective value and associated decision variables are expressed using fuzzy numbers rather than crisp values, the proposed approach is able to represent APP systems more accurately, and therefore, the results obtained can provide decision makers with more effective and informative APPs and more chance to achieve the optimal disaggregate plan. Shih-Pin Chen and Wen-Lung Huang Copyright © 2014 Shih-Pin Chen and Wen-Lung Huang. All rights reserved. On Harmonic Functions Defined by Differential Operator with Respect to -Symmetric Points Wed, 23 Jul 2014 08:25:04 +0000 http://www.hindawi.com/journals/ijmms/2014/628972/ We introduce new classes and of harmonic univalent functions with respect to -symmetric points defined by differential operator. We determine a sufficient coefficient condition, representation theorem, and distortion theorem. Afaf A. Ali Abubaker and Maslina Darus Copyright © 2014 Afaf A. Ali Abubaker and Maslina Darus. All rights reserved. Haar Wavelet Operational Matrix Method for Fractional Oscillation Equations Tue, 15 Jul 2014 13:11:05 +0000 http://www.hindawi.com/journals/ijmms/2014/174819/ We utilized the Haar wavelet operational matrix method for fractional order nonlinear oscillation equations and find the solutions of fractional order force-free and forced Duffing-Van der Pol oscillator and higher order fractional Duffing equation on large intervals. The results are compared with the results obtained by the other technique and with exact solution. Umer Saeed and Mujeeb ur Rehman Copyright © 2014 Umer Saeed and Mujeeb ur Rehman. All rights reserved. Applying GG-Convex Function to Hermite-Hadamard Inequalities Involving Hadamard Fractional Integrals Mon, 14 Jul 2014 11:21:04 +0000 http://www.hindawi.com/journals/ijmms/2014/136035/ By virtue of fractional integral identities, incomplete beta function, useful series, and inequalities, we apply the concept of GG-convex function to derive new type Hermite-Hadamard inequalities involving Hadamard fractional integrals. Finally, some applications to special means of real numbers are demonstrated. Zhi Zhang, JinRong Wang, and JianHua Deng Copyright © 2014 Zhi Zhang et al. All rights reserved. Proof of Some Conjectures of Melham Using Ramanujan's Formula Thu, 10 Jul 2014 12:10:06 +0000 http://www.hindawi.com/journals/ijmms/2014/738948/ We employ Ramanujan's formula to prove three conjectures of R. S. Melham on representation of an integer as sums of polygonal numbers. Bipul Kumar Sarmah Copyright © 2014 Bipul Kumar Sarmah. All rights reserved. Some Properties of Certain Class of Analytic Functions Thu, 10 Jul 2014 08:39:39 +0000 http://www.hindawi.com/journals/ijmms/2014/358467/ We obtain some properties related to the coefficient bounds for certain subclass of analytic functions. We also work on the differential subordination for a certain class of functions. Uzoamaka A. Ezeafulukwe and Maslina Darus Copyright © 2014 Uzoamaka A. Ezeafulukwe and Maslina Darus. All rights reserved. A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions Wed, 09 Jul 2014 08:04:19 +0000 http://www.hindawi.com/journals/ijmms/2014/374821/ We introduce a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically functions related to Cho-Kwon-Srivastava operator. A characterization property giving the coefficient bounds is obtained for this class of functions. The other related properties, which are investigated in this paper, include distortion and the radii of starlikeness and convexity. We also consider several applications of our main results to generalized hypergeometric functions. F. Ghanim and M. Darus Copyright © 2014 F. Ghanim and M. Darus. All rights reserved. A Note on the Warmth of Random Graphs with Given Expected Degrees Mon, 30 Jun 2014 11:27:36 +0000 http://www.hindawi.com/journals/ijmms/2014/749856/ We consider the random graph model for a given expected degree sequence . Warmth, introduced by Brightwell and Winkler in the context of combinatorial statistical mechanics, is a graph parameter related to lower bounds of chromatic number. We present new upper and lower bounds on warmth of . In particular, the minimum expected degree turns out to be an upper bound of warmth when it tends to infinity and the maximum expected degree with . Yilun Shang Copyright © 2014 Yilun Shang. All rights reserved. New Expansion Formulas for a Family of the -Generalized Hurwitz-Lerch Zeta Functions Thu, 26 Jun 2014 08:47:32 +0000 http://www.hindawi.com/journals/ijmms/2014/131067/ We derive several new expansion formulas for a new family of the λ-generalized Hurwitz-Lerch zeta functions which were introduced by Srivastava (2014). These expansion formulas are obtained by making use of some important fractional calculus theorems such as the generalized Leibniz rules, the Taylor-like expansions in terms of different functions, and the generalized chain rule. Several (known or new) special cases are also considered. H. M. Srivastava and Sébastien Gaboury Copyright © 2014 H. M. Srivastava and Sébastien Gaboury. All rights reserved. Folding Theory Applied to Residuated Lattices Wed, 25 Jun 2014 11:04:56 +0000 http://www.hindawi.com/journals/ijmms/2014/428940/ Residuated lattices play an important role in the study of fuzzy logic based on -norms. In this paper, we introduce some notions of -fold filters in residuated lattices, study the relations among them, and compare them with prime, maximal and primary, filters. This work generalizes existing results in BL-algebras and residuated lattices, most notably the works of Lele et al., Motamed et al., Haveski et al., Borzooei et al., Van Gasse et al., Kondo et al., Turunen et al., and Borumand Saeid et al., we draw diagrams summarizing the relations between different types of -fold filters and -fold residuated lattices. Albert Kadji, Celestin Lele, Jean B. Nganou, and Marcel Tonga Copyright © 2014 Albert Kadji et al. All rights reserved. Optimal Manufacturing-Remanufacturing Production Policy for a Closed-Loop Supply Chain under Fill Rate and Budget Constraint in Bifuzzy Environments Tue, 24 Jun 2014 12:16:32 +0000 http://www.hindawi.com/journals/ijmms/2014/690435/ We study a closed-loop supply chain involving a manufacturing facility and a remanufacturing facility. The manufacturer satisfies stochastic market demand by remanufacturing the used product into “as-new” one and producing new products from raw material in the remanufacturing facility and the manufacturing facility, respectively. The remanufacturing cost depends on the quality of used product. The problem is maximizing the manufacturer’s expected profit by jointly determining the collected quantity of used product and the ordered quantity of raw material. Following that we analyze the model with a fill rate constraint and a budget constraint separately and then with both the constraints. Next, to handle the imprecise nature of some parameters of the model, we develop the model with both constraints in bifuzzy environment. Finally numerical examples are presented to illustrate the models. The sensitivity analysis is also conducted to generate managerial insight. Soumita Kundu, Tripti Chakrabarti, and Dipak Kumar Jana Copyright © 2014 Soumita Kundu et al. All rights reserved. Legendre Wavelet Operational Matrix Method for Solution of Riccati Differential Equation Tue, 24 Jun 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2014/304745/ A Legendre wavelet operational matrix method (LWM) is presented for the solution of nonlinear fractional-order Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractional-order Riccati differential equations converted into a system of algebraic equations using Legendre wavelet operational matrix. Solutions given by the proposed scheme are more accurate and reliable and they are compared with recently developed numerical, analytical, and stochastic approaches. Comparison shows that the proposed LWM approach has a greater performance and less computational effort for getting accurate solutions. Further existence and uniqueness of the proposed problem are given and moreover the condition of convergence is verified. S. Balaji Copyright © 2014 S. Balaji. All rights reserved. On Some New Hermite-Hadamard Type Inequalities for s-Geometrically Convex Functions Thu, 19 Jun 2014 15:50:20 +0000 http://www.hindawi.com/journals/ijmms/2014/163901/ Some new integral inequalities of Hermite-Hadamard type related to the s-geometrically convex functions are established and some applications to special means of positive real numbers are also given. İmdat İşcan Copyright © 2014 İmdat İşcan. All rights reserved. Modified Decomposition Method with New Inverse Differential Operators for Solving Singular Nonlinear IVPs in First- and Second-Order PDEs Arising in Fluid Mechanics Thu, 19 Jun 2014 05:23:42 +0000 http://www.hindawi.com/journals/ijmms/2014/793685/ Singular nonlinear initial-value problems (IVPs) in first-order and second-order partial differential equations (PDEs) arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM) is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement. Nemat Dalir Copyright © 2014 Nemat Dalir. All rights reserved. Inversion Free Algorithms for Computing the Principal Square Root of a Matrix Wed, 18 Jun 2014 08:15:46 +0000 http://www.hindawi.com/journals/ijmms/2014/613840/ New algorithms are presented about the principal square root of an matrix . In particular, all the classical iterative algorithms require matrix inversion at every iteration. The proposed inversion free iterative algorithms are based on the Schulz iteration or the Bernoulli substitution as a special case of the continuous time Riccati equation. It is certified that the proposed algorithms are equivalent to the classical Newton method. An inversion free algebraic method, which is based on applying the Bernoulli substitution to a special case of the continuous time Riccati equation, is also proposed. Nicholas Assimakis and Maria Adam Copyright © 2014 Nicholas Assimakis and Maria Adam. All rights reserved. On the Equivalence of B-Rigidity and C-Rigidity for Quasitoric Manifolds Sun, 15 Jun 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2014/825850/ For quasitoric manifolds and moment-angle complexes which are central objects recently much studied in toric topology, there are several important notions of rigidity formulated in terms of cohomology rings. The aim of this paper is to show that, among other things, Buchstaber-rigidity (or B-rigidity) is equivalent to cohomological-rigidity (or C-rigidity) for simple convex polytopes supporting quasitoric manifolds. Jin Hong Kim Copyright © 2014 Jin Hong Kim. All rights reserved. Some New Transformation Properties of the Nielsen Generalized Polylogarithm Thu, 12 Jun 2014 11:18:22 +0000 http://www.hindawi.com/journals/ijmms/2014/210890/ Many of the properties of Nielsen generalized polylogarithm , for example, the special value and the transformation formulas, play important roles in the computation of higher order radiative corrections in quantum electrodynamics. In this paper, some transformation formulas of , and are obtained. In particular, the last three transformation formulas are new results so far in the literature. By use of these transformation formulas presented, new fast algorithms for Nielsen generalized polylogarithm can be designed. For , a new recurrence formula is also given. The identities and the calculation of and are also investigated. Nina Shang, Qinghua Feng, and Huizeng Qin Copyright © 2014 Nina Shang et al. All rights reserved. Somewhat Slightly Generalized Double Fuzzy Semicontinuous Functions Thu, 12 Jun 2014 09:33:51 +0000 http://www.hindawi.com/journals/ijmms/2014/756376/ The aim of this paper is to introduce the concepts of somewhat slightly generalized double fuzzy semicontinuous functions and somewhat slightly generalized double fuzzy semiopen functions in double fuzzy topological spaces. Some interesting properties and characterizations of these functions are introduced and discussed. Furthermore, the relationships among the new concepts are discussed with some necessary examples. Fatimah M. Mohammed, M. S. M. Noorani, and A. Ghareeb Copyright © 2014 Fatimah M. Mohammed et al. All rights reserved. On the Products of -Fibonacci Numbers and -Lucas Numbers Thu, 12 Jun 2014 07:15:20 +0000 http://www.hindawi.com/journals/ijmms/2014/505798/ In this paper we investigate some products of -Fibonacci and -Lucas numbers. We also present some generalized identities on the products of -Fibonacci and -Lucas numbers to establish connection formulas between them with the help of Binet's formula. Bijendra Singh, Kiran Sisodiya, and Farooq Ahmad Copyright © 2014 Bijendra Singh et al. All rights reserved. Generalized Derivations on Power Values of Lie Ideals in Prime and Semiprime Rings Tue, 03 Jun 2014 12:36:14 +0000 http://www.hindawi.com/journals/ijmms/2014/216039/ Let be a 2-torsion free ring and let be a noncentral Lie ideal of , and let and be two generalized derivations of . We will analyse the structure of in the following cases: (a) is prime and for all and fixed positive integers ; (b) is prime and for all and fixed integers ; (c) is semiprime and for all and fixed integer ; and (d) is semiprime and for all and fixed integer . Vincenzo De Filippis, Nadeem UR Rehman, and Abu Zaid Ansari Copyright © 2014 Vincenzo De Filippis et al. All rights reserved. Linear Relative -Widths for Linear Operators Preserving an Intersection of Cones Thu, 29 May 2014 13:15:15 +0000 http://www.hindawi.com/journals/ijmms/2014/409219/ We introduce the definition of linear relative -width and find estimates of linear relative -widths for linear operators preserving the intersection of cones of -monotonicity functions. S. P. Sidorov Copyright © 2014 S. P. Sidorov. All rights reserved. Some New Explicit Values of Quotients of Ramanujan’s Theta Functions and Continued Fractions Sun, 25 May 2014 10:59:06 +0000 http://www.hindawi.com/journals/ijmms/2014/534376/ We evaluate some new explicit values of quotients of Ramanujan’s theta functions and use them to find explicit values of Ramanujan’s continued fractions. Nipen Saikia Copyright © 2014 Nipen Saikia. All rights reserved. Compatible Deductive Systems of Pulexes Mon, 19 May 2014 00:00:00 +0000 http://www.hindawi.com/journals/ijmms/2014/606890/ The notion of (compatible) deductive system of a pulex is defined and some properties of deductive systems are investigated. We also define a congruence relation on a pulex and show that there is a bijective correspondence between the compatible deductive systems and the congruence relations. We define the quotient algebra induced by a compatible deductive system and study its properties. Shokoofeh Ghorbani Copyright © 2014 Shokoofeh Ghorbani. All rights reserved. Vector-Valued Inequalities in the Morrey Type Spaces Thu, 15 May 2014 09:55:36 +0000 http://www.hindawi.com/journals/ijmms/2014/738125/ We will obtain the strong type and weak type estimates for vector-valued analogues of classical Hardy-Littlewood maximal function, weighted maximal function, and singular integral operators in the weighted Morrey spaces when and , and in the generalized Morrey spaces for , where is a growth function on satisfying the doubling condition. Hua Wang Copyright © 2014 Hua Wang. All rights reserved. Explicit Design of Innovation Performance Metrics by Using Analytic Hierarchy Process Expansion Wed, 14 May 2014 06:46:53 +0000 http://www.hindawi.com/journals/ijmms/2014/125950/ The paper presents the explicit and objective measurement method for innovation performances by using the extensive version of Analytic Hierarchy Process (AHP). A hierarchical framework is constructed for the innovation performance criteria and giving the guideline for innovation performance of companies. By applying AHP Expansion framework, the innovation performance measurement factors can be prioritized and descending-order rank list of the performance factors can be made in order to select the best strategies to improve the innovativeness of companies. This new framework of innovation measurement is targeted for implementation at the actual analysis for innovation competitiveness of companies and expected to provide the milestones of measuring the innovation more effectively. Song-Kyoo Kim Copyright © 2014 Song-Kyoo Kim. All rights reserved. On the -Version of the Schwab-Borchardt Mean Tue, 13 May 2014 13:46:39 +0000 http://www.hindawi.com/journals/ijmms/2014/697643/ This paper deals with a one-parameter generalization of the Schwab-Borchardt mean. The new mean is defined in terms of the inverse functions of the generalized trigonometric and generalized hyperbolic functions. The four new bivariate means are introduced as particular cases of the -version of the Schwab-Borchardt mean. For the particular value of the parameter , these means become either the classical logarithmic mean or the Seiffert means or the Neuman-S├índor mean. Wilker- and Huygens-type inequalities involving inverse functions of the generalized trigonometric and the generalized hyperbolic functions are also established. Edward Neuman Copyright © 2014 Edward Neuman. All rights reserved. Bayesian Inference of Burr Type VIII Distribution Based on Censored Samples Tue, 13 May 2014 11:29:33 +0000 http://www.hindawi.com/journals/ijmms/2014/519469/ This paper is concerned with estimation of the parameter of Burr type VIII distribution under a Bayesian framework using censored samples. The Bayes estimators and associated risks have been derived under the assumption of five priors and three loss functions. The comparison among the performance of different estimators has been made in terms of posterior risks. A simulation study has been conducted in order to assess and compare the performance of different estimators. The study proposes the use of inverse Levy prior based on quadratic loss function for Bayes estimation of the said parameter. Navid Feroz Copyright © 2014 Navid Feroz. All rights reserved. Nonlinear Equations of Infinite Order Defined by an Elliptic Symbol Thu, 08 May 2014 13:46:15 +0000 http://www.hindawi.com/journals/ijmms/2014/656959/ The aim of this work is to show existence and regularity properties of equations of the form on , in which is a measurable function that satisfies some conditions of ellipticity and stands for the Laplace operator on . Here, we define the class of functions to which belongs and the Hilbert space in which we will find the solution to this equation. We also give the formal definition of explaining how to understand this operator. Mauricio Bravo Vera Copyright © 2014 Mauricio Bravo Vera. All rights reserved. The Behavior of Midsets When Repeatedly Taking the Midset of Two Lines in Geometry Thu, 08 May 2014 13:04:06 +0000 http://www.hindawi.com/journals/ijmms/2014/832647/ We study the outcome of taking midsets of two lines in geometry. We establish the algorithm for repeatedly finding these midsets and characterize the limiting midsets. We discuss the issue of angle measurement in Minkowski geometries, especially with respect to the limiting midsets. Joshua M. Fitzhugh and David L. Farnsworth Copyright © 2014 Joshua M. Fitzhugh and David L. Farnsworth. All rights reserved.