International Journal of Mathematics and Mathematical Sciences The latest articles from Hindawi Publishing Corporation © 2016 , Hindawi Publishing Corporation . All rights reserved. A 4-Point Block Method for Solving Higher Order Ordinary Differential Equations Directly Thu, 28 Jul 2016 14:57:28 +0000 An alternative block method for solving fifth-order initial value problems (IVPs) is proposed with an adaptive strategy of implementing variable step size. The derived method is designed to compute four solutions simultaneously without reducing the problem to a system of first-order IVPs. To validate the proposed method, the consistency and zero stability are also discussed. The improved performance of the developed method is demonstrated by comparing it with the existing methods and the results showed that the 4-point block method is suitable for solving fifth-order IVPs. Nazreen Waeleh and Zanariah Abdul Majid Copyright © 2016 Nazreen Waeleh and Zanariah Abdul Majid. All rights reserved. Real Hypersurfaces of Nonflat Complex Projective Planes Whose Jacobi Structure Operator Satisfies a Generalized Commutative Condition Wed, 27 Jul 2016 08:43:15 +0000 Real hypersurfaces satisfying the condition have been studied by many authors under at least one more condition, since the class of these hypersurfaces is quite tough to be classified. The aim of the present paper is the classification of real hypersurfaces in complex projective plane satisfying a generalization of under an additional restriction on a specific function. Theocharis Theofanidis Copyright © 2016 Theocharis Theofanidis. All rights reserved. Univalent and Starlike Properties for Generalized Struve Function Thu, 14 Jul 2016 12:15:11 +0000 We derive conditions on the parameters , , and so that the function where is the normalized form of generalized Struve function, belongs to the class Also, some sufficient conditions for the function to be in the class are obtained. Aaisha Farzana Habibullah, Adolf Stephen Bhaskaran, and Jeyaraman Muthusamy Palani Copyright © 2016 Aaisha Farzana Habibullah et al. All rights reserved. On the Commutative Rings with At Most Two Proper Subrings Thu, 14 Jul 2016 08:47:01 +0000 The commutative rings with exactly two proper (unital) subrings are characterized. An initial step involves the description of the commutative rings having only one proper subring. David E. Dobbs Copyright © 2016 David E. Dobbs. All rights reserved. Spatial Tail Dependence and Survival Stability in a Class of Archimedean Copulas Tue, 05 Jul 2016 06:39:02 +0000 This paper investigates properties of extensions of tail dependence of Archimax copulas to high dimensional analysis in a spatialized framework. Specifically, we propose a characterization of bivariate margins of spatial Archimax processes while spatial multivariate upper and lower tail dependence coefficients are modeled, respectively, for Archimedean copulas and Archimax ones. A property of stability is given using convex transformations of survival copulas in a spatialized Archimedean family. Diakarya Barro, Moumouni Diallo, and Remi Guillaume Bagré Copyright © 2016 Diakarya Barro et al. All rights reserved. On the Computation of Degenerate Hopf Bifurcations for -Dimensional Multiparameter Vector Fields Thu, 30 Jun 2016 11:31:33 +0000 The restriction of an -dimensional nonlinear parametric system on the center manifold is treated via a new proper symbolic form and analytical expressions of the involved quantities are obtained as functions of the parameters by lengthy algebraic manipulations combined with computer assisted calculations. Normal forms regarding degenerate Hopf bifurcations up to codimension 3, as well as the corresponding Lyapunov coefficients and bifurcation portraits, can be easily computed for any system under consideration. Michail P. Markakis and Panagiotis S. Douris Copyright © 2016 Michail P. Markakis and Panagiotis S. Douris. All rights reserved. On Shift-Dependent Cumulative Entropy Measures Tue, 07 Jun 2016 06:02:35 +0000 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 information-theoretic uncertainty measures are shift-dependent 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 well-known 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 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 Leray-Schauder’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 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.