International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. More of Dedekind: His Series Test in Normed Spaces Tue, 31 May 2016 11:36:58 +0000 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 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 Quadratic-Additive Type Functional Equation and Its Stability Sun, 22 May 2016 06:21:26 +0000 We investigate the general functional equation of the form − − , whose solutions are quadratic-additive mappings in connection with stability problems. Yang-Hi Lee and Soon-Mo Jung Copyright © 2016 Yang-Hi Lee and Soon-Mo Jung. All rights reserved. The Agreement between the Generalized Value and Bayesian Evidence in the One-Sided Testing Problem Mon, 16 May 2016 11:54:31 +0000 In the problem of testing one-sided 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 one-sided 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 We have generalized Littlewood Tauberian theorems for summability of double sequences by using oscillating behavior and de la Vallée-Poussin 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 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 self-map 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 Al-Kadi Copyright © 2016 Deena Al-Kadi. All rights reserved. The Noncentral Version of the Whitney Numbers: A Comprehensive Study Thu, 07 Apr 2016 10:59:45 +0000 This paper is a comprehensive study of a certain generalization of Whitney-type and Stirling-type 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. Macodi-Ringia Copyright © 2016 Mahid M. Mangontarum et al. All rights reserved. An Optimal Treatment Control of TB-HIV Coinfection Wed, 30 Mar 2016 14:45:34 +0000 An optimal control on the treatment of the transmission of tuberculosis-HIV coinfection model is proposed in this paper. We use two treatments, that is, anti-TB and antiretroviral, to control the spread of TB and HIV infections, respectively. We first present an uncontrolled TB-HIV coinfection model. The model exhibits four equilibria, namely, the disease-free, the HIV-free, the TB-free, 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 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 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 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 Min-Cut and Max-Cut Problems Mon, 01 Feb 2016 14:02:35 +0000 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 min-cut problem and a superpolynomial clique number for the max-cut 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 Quasi-Ideals Mon, 18 Jan 2016 06:44:38 +0000 We introduce the notion of an ordered quasi-ideal of an ordered semiring and show that ordered quasi-ideals and ordered bi-ideals coincide in regular ordered semirings. Then we give characterizations of regular ordered semirings, regular ordered duo-semirings, and left (right) regular ordered semirings by their ordered quasi-ideals. 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 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. Kazemi-Baneh Copyright © 2016 M. Z. Kazemi-Baneh. All rights reserved. -Digit Benford Converges to Benford Tue, 29 Dec 2015 12:46:24 +0000 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 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 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 3-prime 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 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 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 0-1 tableaux which, consequently, yields certain additive identity and some convolution-type 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. Perez-Fernandez, 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 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 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 Domain-Specific Architecture for Elementary Function Evaluation Sun, 11 Oct 2015 11:36:15 +0000 We propose a Domain-Specific Architecture for elementary function computation to improve throughput while reducing power consumption as a model for more general applications: support fine-grained 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 table-based 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 extended-precision floating-point multiply-add 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 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 Second-Order Functional Differential Equation with a State Derivative Dependent Delay Mon, 05 Oct 2015 12:25:29 +0000 We investigate an analytic solution of the second-order 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 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 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 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 Green-like 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 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. Fuzzy -Fold Filters of Pseudoresiduated Lattices Thu, 01 Oct 2015 08:28:37 +0000 Given a pseudoresiduated lattice and a lattice , we introduce and characterize the fuzzy versions of different -fold implicative (resp., obstinate, Boolean, normal, and extended involutive) filters of . Moreover, we study some relationships between these different types of fuzzy -fold filters. Albert Kadji, Celestin Lele, and Marcel Tonga Copyright © 2015 Albert Kadji et al. All rights reserved. A Derivative-Free Conjugate Gradient Method and Its Global Convergence for Solving Symmetric Nonlinear Equations Thu, 03 Sep 2015 08:56:02 +0000 We suggest a conjugate gradient (CG) method for solving symmetric systems of nonlinear equations without computing Jacobian and gradient via the special structure of the underlying function. This derivative-free feature of the proposed method gives it advantage to solve relatively large-scale problems (500,000 variables) with lower storage requirement compared to some existing methods. Under appropriate conditions, the global convergence of our method is reported. Numerical results on some benchmark test problems show that the proposed method is practically effective. Mohammed Yusuf Waziri and Jamilu Sabi’u Copyright © 2015 Mohammed Yusuf Waziri and Jamilu Sabi’u. All rights reserved.