International Journal of Mathematics and Mathematical Sciences
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© 2014 , Hindawi Publishing Corporation . All rights reserved.

ComplexityBased Modeling of Scientific Capital: An Outline of Mathematical Theory
Thu, 30 Oct 2014 11:17:56 +0000
http://www.hindawi.com/journals/ijmms/2014/785058/
The paper intends to contribute to a better understanding of the phenomenon of scientific capital. Scientific capital is a wellknown concept for
measuring and assessing the accumulated recognition and the specific scientific power. The concept of scientific capital developed by Bourdieu is used in international social science research to explain a set of scholarly properties and practices. Mathematical modeling is applied as a lens through which the scientific capital is addressed. The principal contribution of this paper is an axiomatic characterization of scientific capital in terms of natural axioms. The application of the axiomatic method to scientific capital reveals novel insights into problem still not covered by mathematical modeling. Proposed model embraces the interrelations between separate sociological variables, providing a unified sociological view of science. Suggested microvariational principle is based upon postulate, which affirms that (under suitable conditions) the observed state of the agent in scientific field maximizes scientific capital. Its value can be roughly imagined as a volume of social differences. According to the considered macrovariational principle, the actual state of scientific field makes socalled energy functional (which is associated with the distribution of scientific capital) minimal.
Yurij L. Katchanov and Natalia A. Shmatko
Copyright © 2014 Yurij L. Katchanov and Natalia A. Shmatko. All rights reserved.

Some Condition for Scalar and Vector Measure Games to Be Lipschitz
Wed, 01 Oct 2014 07:53:11 +0000
http://www.hindawi.com/journals/ijmms/2014/849685/
We provide a characterization for vector measure games in , with vector of nonatomic probability measures, analogous to the one of Tauman for games in , and also provide a necessary and sufficient condition for a particular class of vector measure games to belong to .
F. Centrone and A. Martellotti
Copyright © 2014 F. Centrone and A. Martellotti. All rights reserved.

Erratum to “The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications”
Tue, 30 Sep 2014 12:14:47 +0000
http://www.hindawi.com/journals/ijmms/2014/151753/
ShaoWen Yu
Copyright © 2014 ShaoWen Yu. All rights reserved.

On Maps of Period 2 on Prime and Semiprime Rings
Mon, 22 Sep 2014 08:47:39 +0000
http://www.hindawi.com/journals/ijmms/2014/140790/
A map f of the ring R into itself is of period 2 if for all ; involutions are much studied examples. We present some commutativity results for semiprime and prime rings with involution, and we study the existence of derivations and generalized derivations of period 2 on prime and semiprime rings.
H. E. Bell and M. N. Daif
Copyright © 2014 H. E. Bell and M. N. Daif. All rights reserved.

When an Extension of Nagata Rings Has Only Finitely Many Intermediate Rings, Each of Those Is a Nagata Ring
Tue, 02 Sep 2014 11:24:08 +0000
http://www.hindawi.com/journals/ijmms/2014/315919/
Let be an extension of commutative rings, with X an indeterminate, such that the extension of Nagata rings has FIP (i.e., has only finitely many subalgebras). Then, the number of subalgebras of equals the number of Rsubalgebras of S. In fact, the function from the set of Rsubalgebras of S to the set of subalgebras of given by is an orderisomorphism.
David E. Dobbs, Gabriel Picavet, and Martine PicavetL’Hermitte
Copyright © 2014 David E. Dobbs et al. 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 twolevel 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.
ShihPin Chen and WenLung Huang
Copyright © 2014 ShihPin Chen and WenLung 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 forcefree and forced DuffingVan 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 GGConvex Function to HermiteHadamard 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 GGconvex function to derive new type HermiteHadamard 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 ChoKwonSrivastava 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 ChoKwonSrivastava 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 HurwitzLerch 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 λgeneralized HurwitzLerch 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 Taylorlike 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 BLalgebras 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 ManufacturingRemanufacturing Production Policy for a ClosedLoop 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 closedloop supply chain involving a manufacturing facility and a remanufacturing facility. The manufacturer satisfies stochastic market demand by remanufacturing the used product into “asnew” 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 fractionalorder Riccati differential equations, having variety of applications in quantum chemistry and quantum mechanics. The fractionalorder 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 HermiteHadamard Type Inequalities for sGeometrically Convex Functions
Thu, 19 Jun 2014 15:50:20 +0000
http://www.hindawi.com/journals/ijmms/2014/163901/
Some new integral inequalities of HermiteHadamard
type related to the sgeometrically 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 SecondOrder PDEs Arising in Fluid Mechanics
Thu, 19 Jun 2014 05:23:42 +0000
http://www.hindawi.com/journals/ijmms/2014/793685/
Singular nonlinear initialvalue problems (IVPs) in firstorder and secondorder 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 secondorder 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 BRigidity and CRigidity for Quasitoric Manifolds
Sun, 15 Jun 2014 00:00:00 +0000
http://www.hindawi.com/journals/ijmms/2014/825850/
For quasitoric manifolds and momentangle 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, Buchstaberrigidity (or Brigidity) is equivalent to cohomologicalrigidity (or Crigidity) 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 2torsion 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.

VectorValued 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 vectorvalued analogues of classical HardyLittlewood 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.