International Journal of Mathematics and Mathematical Sciences
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The latest articles from Hindawi Publishing Corporation
© 2016 , Hindawi Publishing Corporation . All rights reserved.

On ShiftDependent Cumulative Entropy Measures
Tue, 07 Jun 2016 06:02:35 +0000
http://www.hindawi.com/journals/ijmms/2016/7213285/
Measures of cumulative residual entropy (CRE) and cumulative entropy (CE) about predictability of failure time of a system have been introduced in the studies of reliability and life testing. In this paper, cumulative distribution and survival function are used to develop weighted forms of CRE and CE. These new measures are denominated as weighted cumulative residual entropy (WCRE) and weighted cumulative entropy (WCE) and the connections of these new measures with hazard and reversed hazard rates are assessed. These informationtheoretic uncertainty measures are shiftdependent and various properties of these measures are studied, including their connections with CRE, CE, mean residual lifetime, and mean inactivity time. The notions of weighted mean residual lifetime (WMRL) and weighted mean inactivity time (WMIT) are defined. The connections of weighted cumulative uncertainties with WMRL and WMIT are used to calculate the cumulative entropies of some wellknown distributions. The joint versions of WCE and WCRE are defined which have the additive properties similar to those of Shannon entropy for two independent random lifetimes. The upper boundaries of newly introduced measures and the effect of linear transformations on them are considered. Finally, empirical WCRE and WCE are proposed by virtue of sample mean, sample variance, and order statistics to estimate the new measures of uncertainty. The consistency of these estimators is studied under specific choices of distributions.
Farsam Misagh
Copyright © 2016 Farsam Misagh. All rights reserved.

Quantum Difference Langevin System with Nonlocal Derivative Conditions
Sun, 05 Jun 2016 14:33:02 +0000
http://www.hindawi.com/journals/ijmms/2016/4928314/
We introduce a new class of boundary value problems for Langevin quantum difference systems. Some new existence and uniqueness results for coupled systems are obtained by using fixed point theorems. The existence and uniqueness of solutions are established by Banach’s contraction mapping principle, while the existence of solutions is derived by using LeraySchauder’s alternative. The obtained results are well illustrated with the aid of examples.
Surang Sitho, Sorasak Laoprasittichok, Sotiris K. Ntouyas, and Jessada Tariboon
Copyright © 2016 Surang Sitho et al. All rights reserved.

More of Dedekind: His Series Test in Normed Spaces
Tue, 31 May 2016 11:36:58 +0000
http://www.hindawi.com/journals/ijmms/2016/2508172/
Dedekind’s test for infinite series has a canonical interpretation in the context of normed spaces. It is shown that his test holds in a normed space precisely when the space is complete.
Robert Kantrowitz and Michael M. Neumann
Copyright © 2016 Robert Kantrowitz and Michael M. Neumann. All rights reserved.

A Note on Primitivity of Ideals in Skew Polynomial Rings of Automorphism Type
Mon, 30 May 2016 15:47:37 +0000
http://www.hindawi.com/journals/ijmms/2016/7159180/
We extend results about primitive ideals in polynomial rings over nil rings originally proved by Smoktunowicz (2005) for primitive ideals in skew polynomial rings of automorphism type.
Edilson Soares Miranda
Copyright © 2016 Edilson Soares Miranda. All rights reserved.

General QuadraticAdditive Type Functional Equation and Its Stability
Sun, 22 May 2016 06:21:26 +0000
http://www.hindawi.com/journals/ijmms/2016/1793065/
We investigate the general functional equation of the form − − , whose solutions are quadraticadditive mappings in connection with stability problems.
YangHi Lee and SoonMo Jung
Copyright © 2016 YangHi Lee and SoonMo Jung. All rights reserved.

The Agreement between the Generalized Value and Bayesian Evidence in the OneSided Testing Problem
Mon, 16 May 2016 11:54:31 +0000
http://www.hindawi.com/journals/ijmms/2016/8656909/
In the problem of testing onesided hypotheses, a frequentist may measure evidence against the null hypothesis by the value, while a Bayesian may measure it by the posterior probability that the null hypothesis is true. In this paper, we consider the relationship between the generalized value and the Bayesian evidence in testing onesided hypotheses in the presence of nuisance parameters. The sufficient conditions for the agreement between these two kinds of evidence are given. Some examples are provided to show the agreement of Bayesian and frequentist evidence in many classical testing problems. This is an illustration of reconcilability of evidence in a general framework where the nuisance parameters are present.
Yuliang Yin and Bingbing Wang
Copyright © 2016 Yuliang Yin and Bingbing Wang. All rights reserved.

A Tauberian Theorem for Double Cesàro Summability Method
Thu, 12 May 2016 17:15:35 +0000
http://www.hindawi.com/journals/ijmms/2016/2431010/
We have generalized Littlewood Tauberian theorems for summability of double sequences by using oscillating behavior and de la ValléePoussin mean. Further, the generalization of summability from summability is given as corollaries which were earlier established by the authors.
Bidu Bhusan Jena, Susanta Kumar Paikray, and Umakanta Misra
Copyright © 2016 Bidu Bhusan Jena et al. All rights reserved.

Derivations of Algebra
Thu, 28 Apr 2016 11:45:07 +0000
http://www.hindawi.com/journals/ijmms/2016/9276096/
We introduce the notion of derivation as a new derivation of algebra. For an endomorphism map of any algebra we show that at least one derivation of exists. Moreover, for such a map, we show that a selfmap of is derivation of if is an associative medial algebra. For a medial algebra , is derivation of if is an outside derivation of . Finally, we show that if is the identity endomorphism of then the composition of two derivations of is a derivation. Moreover, we give a condition to get a commutative composition.
Deena AlKadi
Copyright © 2016 Deena AlKadi. All rights reserved.

The Noncentral Version of the Whitney Numbers: A Comprehensive Study
Thu, 07 Apr 2016 10:59:45 +0000
http://www.hindawi.com/journals/ijmms/2016/6206207/
This paper is a comprehensive study of a certain generalization of Whitneytype and Stirlingtype numbers which unifies the classical Whitney numbers, the translated Whitney numbers, the classical Stirling numbers, and the noncentral Stirling (or Stirling) numbers. Several identities, applications, and occurrences are also presented.
Mahid M. Mangontarum, Omar I. Cauntongan, and Amila P. MacodiRingia
Copyright © 2016 Mahid M. Mangontarum et al. All rights reserved.

An Optimal Treatment Control of TBHIV Coinfection
Wed, 30 Mar 2016 14:45:34 +0000
http://www.hindawi.com/journals/ijmms/2016/8261208/
An optimal control on the treatment of the transmission of tuberculosisHIV coinfection model is proposed in this paper. We use two treatments, that is, antiTB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TBHIV coinfection model. The model exhibits four equilibria, namely, the diseasefree, the HIVfree, the TBfree, and the coinfection equilibria. We further obtain two basic reproduction ratios corresponding to TB and HIV infections. These ratios determine the existence and stability of the equilibria of the model. The optimal control theory is then derived analytically by applying the Pontryagin Maximum Principle. The optimality system is performed numerically to illustrate the effectiveness of the treatments.
Fatmawati and Hengki Tasman
Copyright © 2016 Fatmawati and Hengki Tasman. All rights reserved.

Characterization and Enumeration of Good Punctured Polynomials over Finite Fields
Mon, 21 Mar 2016 12:07:52 +0000
http://www.hindawi.com/journals/ijmms/2016/6093219/
A family of good punctured polynomials is introduced. The complete characterization and enumeration of such polynomials are given over the binary field . Over a nonbinary finite field , the set of good punctured polynomials of degree less than or equal to are completely determined. For , constructive lower bounds of the number of good punctured polynomials of degree over are given.
Somphong Jitman, Aunyarut Bunyawat, Supanut Meesawat, Arithat Thanakulitthirat, and Napat Thumwanit
Copyright © 2016 Somphong Jitman et al. All rights reserved.

Null Controllability of a Nonlinear Dissipative System and Application to the Detection of the Incomplete Parameter for a Nonlinear Population Dynamics Model
Thu, 03 Mar 2016 11:13:10 +0000
http://www.hindawi.com/journals/ijmms/2016/2820613/
We first prove a null controllability result for a nonlinear system derived from a nonlinear population dynamics model. In order to tackle the controllability problem we use an adapted Carleman inequality. Next we consider the nonlinear population dynamics model with a source term called the pollution term. In order to obtain information on the pollution term we use the method of sentinel.
Yacouba Simporé and Oumar Traoré
Copyright © 2016 Yacouba Simporé and Oumar Traoré. All rights reserved.

Existence Results for Some Equilibrium Problems Involving Monotone Bifunction
Wed, 03 Feb 2016 13:20:03 +0000
http://www.hindawi.com/journals/ijmms/2016/2093026/
This paper deals with some existence results of equilibrium problems on convex and closed sets (either bounded or unbounded) in Banach spaces. Moreover, an application to the existence of solution for a differential inclusion is given.
Ayed E. Hashoosh, Mohsen Alimohammady, and M. K. Kalleji
Copyright © 2016 Ayed E. Hashoosh et al. All rights reserved.

On Graphs of the Cone Decompositions for the MinCut and MaxCut Problems
Mon, 01 Feb 2016 14:02:35 +0000
http://www.hindawi.com/journals/ijmms/2016/7863650/
We consider maximum and minimum cut problems with nonnegative weights of edges. We define the graphs of the cone decompositions and find a linear clique number for the mincut problem and a superpolynomial clique number for the maxcut problem. These values characterize the time complexity in a broad class of algorithms based on linear comparisons.
Vladimir Bondarenko and Andrei Nikolaev
Copyright © 2016 Vladimir Bondarenko and Andrei Nikolaev. All rights reserved.

Characterizations of Regular Ordered Semirings by Ordered QuasiIdeals
Mon, 18 Jan 2016 06:44:38 +0000
http://www.hindawi.com/journals/ijmms/2016/4272451/
We introduce the notion of an ordered quasiideal of an ordered semiring and show that ordered quasiideals and ordered biideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duosemirings, and left (right) regular ordered semirings by their ordered quasiideals.
Pakorn Palakawong na Ayutthaya and Bundit Pibaljommee
Copyright © 2016 Pakorn Palakawong na Ayutthaya and Bundit Pibaljommee. All rights reserved.

Homotopic Chain Maps Have Equal Homology and Homology
Tue, 05 Jan 2016 13:18:53 +0000
http://www.hindawi.com/journals/ijmms/2016/5647548/
The homotopy of chain maps on preabelian categories is investigated and the equality of standard homologies and homologies of homotopic chain maps is established. As a special case, if and are the same homotopy type, then their th homology modules are isomorphic, and if is a contractible space, then its th homology modules for are trivial.
M. Z. KazemiBaneh
Copyright © 2016 M. Z. KazemiBaneh. All rights reserved.

Digit Benford Converges to Benford
Tue, 29 Dec 2015 12:46:24 +0000
http://www.hindawi.com/journals/ijmms/2015/123816/
Using the sum invariance property of Benford random variables, we prove that an digit Benford variable converges to a Benford variable as approaches infinity.
Azar Khosravani and Constantin Rasinariu
Copyright © 2015 Azar Khosravani and Constantin Rasinariu. All rights reserved.

Metrics on the Sets of Nonsupersingular Elliptic Curves in Simplified Weierstrass Form over Finite Fields of Characteristic Two
Mon, 28 Dec 2015 12:43:18 +0000
http://www.hindawi.com/journals/ijmms/2015/597849/
Elliptic curves have a wide variety of applications in computational number theory such as elliptic curve cryptography, pairing based cryptography, primality tests, and integer factorization. Mishra and Gupta (2008) have found an interesting property of the sets of elliptic curves in simplified Weierstrass form (or short Weierstrass form) over prime fields. The property is that one can induce metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. Later, Vetro (2011) has found some other metrics on the sets of elliptic curves in simplified Weierstrass form over prime fields of characteristic greater than three. However, to our knowledge, no analogous result is known in the characteristic two case. In this paper, we will prove that one can induce metrics on the sets of nonsupersingular elliptic curves in simplified Weierstrass form over finite fields of characteristic two.
Keisuke Hakuta
Copyright © 2015 Keisuke Hakuta. All rights reserved.

On Generalized Semiderivations of Prime Near Rings
Sun, 08 Nov 2015 06:43:00 +0000
http://www.hindawi.com/journals/ijmms/2015/867923/
Let be a near ring. An additive mapping is said to be a generalized semiderivation on if there exists a semiderivation associated with a function such that and for all . In this paper we prove that prime near rings satisfying identities involving semiderivations are commutative rings, thereby extending some known results on derivations, semiderivations, and generalized derivations. We also prove that there exist no nontrivial generalized semiderivations which act as a homomorphism or as an antihomomorphism on a 3prime near ring .
Abdelkarim Boua, A. Raji, Asma Ali, and Farhat Ali
Copyright © 2015 Abdelkarim Boua et al. All rights reserved.

Certain Bound for Starlike and Convex Functions with respect to Symmetric Points
Thu, 29 Oct 2015 07:54:58 +0000
http://www.hindawi.com/journals/ijmms/2015/205682/
The aim of this paper is to establish the coefficient estimates for the subclasses of starlike and convex functions with respect to symmetric points involving difference operator. Also certain applications based on these results for subclasses of univalent functions defined by convolution are given.
C. Ramachandran, D. Kavitha, and T. Soupramanien
Copyright © 2015 C. Ramachandran et al. All rights reserved.

The Hankel Transform of Noncentral Bell Numbers
Wed, 28 Oct 2015 07:28:59 +0000
http://www.hindawi.com/journals/ijmms/2015/417327/
We define two forms of analogue of noncentral Stirling numbers of the second kind and obtain some properties parallel to those of noncentral Stirling numbers. Certain combinatorial interpretation is given for the second form of the analogue in the context of 01 tableaux which, consequently, yields certain additive identity and some convolutiontype formulas. Finally, a analogue of noncentral Bell numbers is defined and its Hankel transform is established.
Cristina B. Corcino, Roberto B. Corcino, Jay M. Ontolan, Charrymae M. PerezFernandez, and Ednelyn R. Cantallopez
Copyright © 2015 Cristina B. Corcino et al. All rights reserved.

Recent Trends in Special Numbers and Special Functions and Polynomials
Tue, 20 Oct 2015 06:27:02 +0000
http://www.hindawi.com/journals/ijmms/2015/573893/
Serkan Araci, Mehmet Acikgoz, Cenap Özel, H. M. Srivastava, and Toka Diagana
Copyright © 2015 Serkan Araci et al. All rights reserved.

The Peak of Noncentral Stirling Numbers of the First Kind
Mon, 12 Oct 2015 08:26:59 +0000
http://www.hindawi.com/journals/ijmms/2015/982812/
We locate the peak of the distribution of noncentral Stirling numbers of the first kind
by determining the value of the index corresponding to the maximum value of the distribution.
Roberto B. Corcino, Cristina B. Corcino, and Peter John B. Aranas
Copyright © 2015 Roberto B. Corcino et al. All rights reserved.

A DomainSpecific Architecture for Elementary Function Evaluation
Sun, 11 Oct 2015 11:36:15 +0000
http://www.hindawi.com/journals/ijmms/2015/843851/
We propose a DomainSpecific Architecture for elementary function computation to improve throughput while reducing power consumption as a model for more general applications: support finegrained parallelism by eliminating branches, and eliminate the duplication required by coprocessors by decomposing computation into instructions which fit existing pipelined execution models and standard register files. Our example instruction architecture (ISA) extension supports scalar and vector/SIMD implementations of tablebased methods of calculating all common special functions, with the aim of improving throughput by (1) eliminating the need for tables in memory, (2) eliminating all branches for special cases, and (3) reducing the total number of instructions. Two new instructions are required, a table lookup instruction and an extendedprecision floatingpoint multiplyadd instruction with special treatment for exceptional inputs. To estimate the performance impact of these instructions, we implemented them in a modified Cell/B.E. SPU simulator and observed an average throughput improvement of 2.5 times for optimized loops mapping single functions over long vectors.
Anuroop Sharma and Christopher Kumar Anand
Copyright © 2015 Anuroop Sharma and Christopher Kumar Anand. All rights reserved.

Explicit Formulas for Meixner Polynomials
Sun, 11 Oct 2015 09:51:32 +0000
http://www.hindawi.com/journals/ijmms/2015/620569/
Using notions of composita and composition of generating functions, we show an easy way to obtain explicit formulas for some current polynomials. Particularly, we consider the Meixner polynomials of the first and second kinds.
Dmitry V. Kruchinin and Yuriy V. Shablya
Copyright © 2015 Dmitry V. Kruchinin and Yuriy V. Shablya. All rights reserved.

Analytic Solutions of a SecondOrder Functional Differential Equation with a State Derivative Dependent Delay
Mon, 05 Oct 2015 12:25:29 +0000
http://www.hindawi.com/journals/ijmms/2015/904679/
We investigate an analytic solution of the secondorder differential equation with a state derivative dependent delay of the form . Considering a convergent power series of an auxiliary equation with the relation , we obtain an analytic solution . Furthermore, we characterize a polynomial solution when is a polynomial.
Jiraphorn Somsuwan and Keaitsuda Maneeruk Nakprasit
Copyright © 2015 Jiraphorn Somsuwan and Keaitsuda Maneeruk Nakprasit. All rights reserved.

Faber Polynomial Coefficients of Classes of Meromorphic Bistarlike Functions
Sun, 04 Oct 2015 09:08:38 +0000
http://www.hindawi.com/journals/ijmms/2015/161723/
Applying the Faber polynomial coefficient expansions to certain classes of meromorphic bistarlike functions,
we demonstrate the unpredictability of their early coefficients and also obtain general coefficient estimates for
such functions subject to a given gap series condition. Our results improve some of the coefficient bounds
published earlier.
Jay M. Jahangiri and Samaneh G. Hamidi
Copyright © 2015 Jay M. Jahangiri and Samaneh G. Hamidi. All rights reserved.

Generalized Lacunary Statistical Difference Sequence Spaces of Fractional Order
Sun, 04 Oct 2015 08:50:49 +0000
http://www.hindawi.com/journals/ijmms/2015/984283/
We generalize the lacunary statistical convergence by introducing the generalized difference operator of fractional order, where is a proper fraction and is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator and investigate the topological structures of related sequence spaces. Furthermore, we introduce some properties of the strongly Cesaro difference sequence spaces of fractional order involving lacunary sequences and examine various inclusion relations of these spaces. We also determine the relationship between lacunary statistical and strong Cesaro difference sequence spaces of fractional order.
Ugur Kadak
Copyright © 2015 Ugur Kadak. All rights reserved.

Green’s Function for a Slice of the Korányi Ball in the Heisenberg Group
Sun, 04 Oct 2015 06:18:11 +0000
http://www.hindawi.com/journals/ijmms/2015/460461/
We give a representation formula for solution of the inhomogeneous Dirichlet problem on the upper half Korányi ball and for the slice of the Korányi ball in the Heisenberg group by obtaining explicit expressions of Greenlike kernel when the given data has certain radial symmetry.
Shivani Dubey, Ajay Kumar, and Mukund Madhav Mishra
Copyright © 2015 Shivani Dubey et al. All rights reserved.

On the Local Minima of the Order of Appearance Function
Thu, 01 Oct 2015 16:11:41 +0000
http://www.hindawi.com/journals/ijmms/2015/823973/
The order of appearance of the positive integer is the smallest positive integer such that divides , the th member of the Fibonacci sequence. In this paper, we improve upon some results from (Marques, 2011) concerning local minima of .
Florian Luca and Thato Mosima
Copyright © 2015 Florian Luca and Thato Mosima. All rights reserved.