http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2013 , Hindawi Publishing Corporation . All rights reserved. Tue, 07 May 2013 14:55:00 +0000 http://www.hindawi.com/journals/ijmms/2013/689560/ We raise several elementary questions pertaining to various aspects of means. These questions refer to both known and newly introduced families of means, and include questions of characterizations of certain families, relations among certain families, comparability among the members of certain families, and concordance of certain sequences of means. They also include questions about internality tests for certain mean-looking functions and about certain triangle centers viewed as means of the vertices. The questions are accessible to people with no background in means, and it is also expected that these people can seriously investigate, and contribute to the solutions of, these problems. The solutions are expected to require no more than simple tools from analysis, algebra, functional equations, and geometry. Mowaffaq Hajja Copyright © 2013 Mowaffaq Hajja. All rights reserved. Mon, 29 Apr 2013 15:04:33 +0000 http://www.hindawi.com/journals/ijmms/2013/983607/ We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in and and in certain other groups. Our approach provides a justification for the use of the symbol denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider parallelism from an axiomatic perspective. Pentti Haukkanen, Mika Mattila, Jorma K. Merikoski, and Timo Tossavainen Copyright © 2013 Pentti Haukkanen et al. All rights reserved. Tue, 16 Apr 2013 13:08:10 +0000 http://www.hindawi.com/journals/ijmms/2013/265136/ Let be a graph on vertices and a collection of subgraphs of , one for each vertex, where is an orthogonal double cover (ODC) of if every edge of occurs in exactly two members of and any two members share an edge whenever the corresponding vertices are adjacent in and share no edges whenever the corresponding vertices are nonadjacent in . In this paper, we are concerned with the Cartesian product of symmetric starter vectors of orthogonal double covers of the complete bipartite graphs and using this method to construct ODCs by new disjoint unions of complete bipartite graphs. R. El Shanawany, M. Higazy, and A. El Mesady Copyright © 2013 R. El Shanawany et al. All rights reserved. Sun, 14 Apr 2013 12:22:47 +0000 http://www.hindawi.com/journals/ijmms/2013/929475/ In recent years, researchers have studied the size of different sets related to the dynamics of self-maps of an interval. In this note we investigate the sets of fixed points and periodic points of continuously differentiable functions and show that typically such functions have a finite set of fixed points and a countable set of periodic points. Aliasghar Alikhani-Koopaei Copyright © 2013 Aliasghar Alikhani-Koopaei. All rights reserved. Sun, 31 Mar 2013 18:00:41 +0000 http://www.hindawi.com/journals/ijmms/2013/504645/ A type of prolongation structure for several general systems is discussed. They are based on a set of one forms for which the underlying structure group of the integrability condition corresponds to the Lie algebra of , , and . Each will be considered in turn and the latter two systems represent larger cases. This geometric approach is applied to all of the three of these systems to obtain prolongation structures explicitly. In both cases, the prolongation structure is reduced to the situation of three smaller problems. Paul Bracken Copyright © 2013 Paul Bracken. All rights reserved. Sun, 31 Mar 2013 13:37:02 +0000 http://www.hindawi.com/journals/ijmms/2013/498159/ We consider meromorphic starlike univalent functions that are also bi-starlike and find Faber polynomial coefficient estimates for these types of functions. A function is said to be bi-starlike if both the function and its inverse are starlike univalent. Samaneh G. Hamidi, Suzeini Abd Halim, and Jay M. Jahangiri Copyright © 2013 Samaneh G. Hamidi et al. All rights reserved. Sun, 24 Mar 2013 09:17:34 +0000 http://www.hindawi.com/journals/ijmms/2013/769537/ Motivated by the familiar -hypergeometric functions, we introduce a new family of integral operators and obtain new sufficient conditions of univalence criteria. Several corollaries and consequences of the main results are also pointed out. Huda Aldweby and Maslina Darus Copyright © 2013 Huda Aldweby and Maslina Darus. All rights reserved. Sat, 23 Mar 2013 16:28:33 +0000 http://www.hindawi.com/journals/ijmms/2013/684757/ A stochastic Ramsey model is studied with the Cobb-Douglas production function maximizing the expected discounted utility of consumption. We transformed the Hamilton-Jacobi-Bellman (HJB) equation associated with the stochastic Ramsey model so as to transform the dimension of the state space by changing the variables. By the viscosity solution method, we established the existence of viscosity solution of the transformed Hamilton-Jacobi-Bellman equation associated with this model. Finally, the optimal consumption policy is derived from the optimality conditions in the HJB equation. Md. Azizul Baten and Anton Abdulbasah Kamil Copyright © 2013 Md. Azizul Baten and Anton Abdulbasah Kamil. All rights reserved. Thu, 21 Mar 2013 12:17:55 +0000 http://www.hindawi.com/journals/ijmms/2013/743734/ Following our paper [Linear Algebra Appl. 433(2010), 699–717], we present a framework and computational tools for the Coxeter spectral classification of finite posets . One of the main motivations for the study is an application of matrix representations of posets in representation theory explained by Drozd [Funct. Anal. Appl. 8(1974), 219–225]. We are mainly interested in a Coxeter spectral classification of posets such that the symmetric Gram matrix is positive semidefinite, where is the incidence matrix of . Following the idea of Drozd mentioned earlier, we associate to its Coxeter matrix , its Coxeter spectrum , a Coxeter polynomial , and a Coxeter number. In case is positive semi-definite, we also associate to a reduced Coxeter number , and the defect homomorphism . In this case, the Coxeter spectrum is a subset of the unit circle and consists of roots of unity. In case is positive semi-definite of corank one, we relate the Coxeter spectral properties of the posets with the Coxeter spectral properties of a simply laced Euclidean diagram associated with . Our aim of the Coxeter spectral analysis of such posets is to answer the question when the Coxeter type of determines its incidence matrix (and, hence, the poset ) uniquely, up to a -congruency. In connection with this question, we also discuss the problem studied by Horn and Sergeichuk [Linear Algebra Appl. 389(2004), 347–353], if for any -invertible matrix , there is such that and is the identity matrix. Daniel Simson and Katarzyna Zając Copyright © 2013 Daniel Simson and Katarzyna Zając. All rights reserved. Wed, 20 Mar 2013 17:15:39 +0000 http://www.hindawi.com/journals/ijmms/2013/109754/ We give an Ulam type stability result for the following functional equation: under a suitable condition. We also give a concrete stability result for the case taking up as a control function. Hiroyoshi Oda, Makoto Tsukada, Takeshi Miura, Yuji Kobayashi, and Sin-Ei Takahasi Copyright © 2013 Hiroyoshi Oda et al. All rights reserved. Thu, 14 Mar 2013 14:43:37 +0000 http://www.hindawi.com/journals/ijmms/2013/837080/ We classify the lattices of rank 16 over the Eisenstein integers which are even unimodular -lattices (of dimension 32). There are exactly 80 unitary isometry classes. Andreas Henn, Michael Hentschel, Aloys Krieg, and Gabriele Nebe Copyright © 2013 Andreas Henn et al. All rights reserved. Thu, 28 Feb 2013 08:08:23 +0000 http://www.hindawi.com/journals/ijmms/2013/705984/ Properties of asymmetric oscillator described by the equation (i), where and , are studied. A set of such that the problem (i), (ii), and (iii) have a nontrivial solution, is called α-spectrum. We give full description of α-spectra in terms of solution sets and solution surfaces. The exact number of nontrivial solutions of the two-parameter Dirichlet boundary value problem (i), and (ii) is given. Armands Gritsans and Felix Sadyrbaev Copyright © 2013 Armands Gritsans and Felix Sadyrbaev. All rights reserved. Thu, 21 Feb 2013 13:28:54 +0000 http://www.hindawi.com/journals/ijmms/2013/170749/ Let be a near ring. An additive mapping is said to be a right generalized (resp., left generalized) derivation with associated derivation on if (resp., ) for all . A mapping is said to be a generalized derivation with associated derivation on if is both a right generalized and a left generalized derivation with associated derivation on . The purpose of the present paper is to prove some theorems in the setting of a semigroup ideal of a 3-prime near ring admitting a generalized derivation, thereby extending some known results on derivations. Asma Ali, Howard E. Bell, and Phool Miyan Copyright © 2013 Asma Ali et al. All rights reserved. Tue, 19 Feb 2013 17:32:22 +0000 http://www.hindawi.com/journals/ijmms/2013/814587/ Diagonal updating scheme is among the cheapest Newton-like methods for solving system of nonlinear equations. Nevertheless, the method has some shortcomings. In this paper, we proposed an improved matrix-free secant updating scheme via line search strategies, by using the steps of backtracking in the Armijo-type line search as a step length predictor and Wolfe-Like condition as corrector. Our approach aims at improving the overall performance of diagonal secant updating scheme. Under mild assumptions, the global convergence results have been presented. Numerical experiments verify that the proposed approach is very promising. M. Y. Waziri and Z. A. Majid Copyright © 2013 M. Y. Waziri and Z. A. Majid. All rights reserved. Thu, 14 Feb 2013 16:08:09 +0000 http://www.hindawi.com/journals/ijmms/2013/753965/ We introduce a new class of mappings satisfying the “common limit range property” in symmetric spaces and utilize the same to establish common fixed point theorems for such mappings in symmetric spaces. Our results generalize and improve some recent results contained in the literature of metric fixed point theory. Some illustrative examples to highlight the realized improvements are also furnished. E. Karapınar, D. K. Patel, M. Imdad, and D. Gopal Copyright © 2013 E. Karapınar et al. All rights reserved. Wed, 13 Feb 2013 08:31:27 +0000 http://www.hindawi.com/journals/ijmms/2013/302628/ We study the Dirichlet problem for the equation in the exterior of nonclosed Lipschitz surfaces in . The Dirichlet problem for the Laplace equation is a particular case of our problem. Theorems on existence and uniqueness of a weak solution of the problem are proved. The integral representation for a solution is obtained in the form of single-layer potential. The density in the potential is defined as a solution of the operator (integral) equation, which is uniquely solvable. P. A. Krutitskii Copyright © 2013 P. A. Krutitskii. All rights reserved. Tue, 12 Feb 2013 09:34:39 +0000 http://www.hindawi.com/journals/ijmms/2013/283127/ We give a necessary and sufficient mean condition for the quotient of two Jensen functionals and define a new class of mean values where are continuously differentiable convex functions satisfying the relation ,  . Then we asked for a characterization of such that the inequalities or hold for each positive , where are the harmonic, arithmetic, logarithmic, and identric means, respectively. For a subclass of with , this problem is thoroughly solved. Slavko Simic Copyright © 2013 Slavko Simic. All rights reserved. Mon, 11 Feb 2013 08:56:42 +0000 http://www.hindawi.com/journals/ijmms/2013/653080/ We study the role of predation dynamics in oscillation of pest population in insect ecology. A two-dimensional pest control model (under the use of insecticides) with time delay in predation is considered in this paper. By the Hopf bifurcation theory, we prove the existence of the stable oscillation of the system. We also consider the economic viability of the control process. First we improve the Pontryagin maximum principle (PMP) where the delay in the system is sufficiently small and control function is linear, and then we apply the improved version of PMP to perform the optimal analysis of the pest control model as a special case. Samit Bhattacharyya and Suma Ghosh Copyright © 2013 Samit Bhattacharyya and Suma Ghosh. All rights reserved. Tue, 05 Feb 2013 11:21:02 +0000 http://www.hindawi.com/journals/ijmms/2013/190981/ Let be the generalized tempered distributions of -growth with restricted order , where the function grows faster than any linear functions as . We show the convergence of multiresolution expansions of in the test function space of . In addition, we show that the kernel of an integral operator provides approximation order in in the context of shift-invariant spaces. Byung Keun Sohn Copyright © 2013 Byung Keun Sohn. All rights reserved. Sun, 03 Feb 2013 09:14:28 +0000 http://www.hindawi.com/journals/ijmms/2013/376915/ We consider a partial action with enveloping action . In this work we extend α to a partial action on the ring and find its enveloping action . Finally, we introduce the concept of partial action of finite type to investigate the relationship between and . Jesús Ávila and João Lazzarin Copyright © 2013 Jesús Ávila and João Lazzarin. All rights reserved. Wed, 30 Jan 2013 18:27:53 +0000 http://www.hindawi.com/journals/ijmms/2013/918905/ Results on Colombeau product of distributions and are derived. They are obtained in Colombeau differential algebra of generalized functions that contains the space of Schwartz distributions as a subspace and has a notion of “association” that is a faithful generalization of the weak equality in . Biljana Jolevska-Tuneska and Tatjana Atanasova-Pacemska Copyright © 2013 Biljana Jolevska-Tuneska and Tatjana Atanasova-Pacemska. All rights reserved. Mon, 31 Dec 2012 14:26:05 +0000 http://www.hindawi.com/journals/ijmms/2012/395462/ We study canonical paracontact connection on a para-Sasakian manifold. We prove that a Ricci-flat para-Sasakian manifold with respect to canonical paracontact connection is an -Einstein manifold. We also investigate some properties of curvature tensor, conformal curvature tensor, -curvature tensor, concircular curvature tensor, projective curvature tensor, and pseudo-projective curvature tensor with respect to canonical paracontact connection on a para-Sasakian manifold. It is shown that a concircularly flat para-Sasakian manifold with respect to canonical paracontact connection is of constant scalar curvature. We give some characterizations for pseudo-projectively flat para-Sasakian manifolds. Bilal Eftal Acet, Erol Kılıç, and Selcen Yüksel Perktaş Copyright © 2012 Bilal Eftal Acet et al. All rights reserved. Thu, 27 Dec 2012 09:45:29 +0000 http://www.hindawi.com/journals/ijmms/2012/350183/ On a compact connected -dimensional Kähler manifold with Kähler form , given a smooth function and an integer , we want to solve uniquely in the equation , relying on the notion of -positivity for (the extreme cases are solved: by (Yau in 1978), and trivially). We solve by the continuity method the corresponding complex elliptic th Hessian equation, more difficult to solve than the Calabi-Yau equation (), under the assumption that the holomorphic bisectional curvature of the manifold is nonnegative, required here only to derive an a priori eigenvalues pinching. Asma Jbilou Copyright © 2012 Asma Jbilou. All rights reserved. Wed, 26 Dec 2012 11:12:32 +0000 http://www.hindawi.com/journals/ijmms/2012/481909/ We generalize r-costar module to r-costar pair of contravariant functors between abelian categories. S. Al-Nofayee Copyright © 2012 S. Al-Nofayee. All rights reserved. Tue, 25 Dec 2012 10:12:39 +0000 http://www.hindawi.com/journals/ijmms/2012/725270/ We show that the quantum family of all maps from a finite space to a finite-dimensional compact quantum semigroup has a canonical quantum semigroup structure. Maysam Maysami Sadr Copyright © 2012 Maysam Maysami Sadr. All rights reserved. Tue, 25 Dec 2012 09:59:20 +0000 http://www.hindawi.com/journals/ijmms/2012/368527/ We investigate the cyclic homology and free resolution effect of a commutative unital Banach algebra. Using the free resolution operator, we define the relative cyclic homology of commutative Banach algebras. Lemmas and theorems of this investigation are studied and proved. Finally, the relation between cyclic homology and relative cyclic homology of Banach algebra is deduced. Alaa Hassan Noreldeen Copyright © 2012 Alaa Hassan Noreldeen. All rights reserved. Mon, 24 Dec 2012 11:17:32 +0000 http://www.hindawi.com/journals/ijmms/2012/595076/ The aim of this paper is to introduce the space of roots to study the topological properties of the spaces of polynomials. Instead of identifying a monic complex polynomial with the vector of its coefficients, we identify it with the set of its roots. Viète's map gives a homeomorphism between the space of roots and the space of coefficients and it gives an explicit formula to relate both spaces. Using this viewpoint we establish that the space of monic (Schur or Hurwitz) aperiodic polynomials is contractible. Additionally we obtain a Boundary Theorem. Baltazar Aguirre-Hernández, José Luis Cisneros-Molina, and Martín-Eduardo Frías-Armenta Copyright © 2012 Baltazar Aguirre-Hernández et al. All rights reserved. Sat, 22 Dec 2012 09:18:18 +0000 http://www.hindawi.com/journals/ijmms/2012/318214/ We will extend the definition of antieigenvalue of an operator to antieigenvalue-type quantities, in the first section of this paper, in such a way that the relations between antieigenvalue-type quantities and their corresponding Kantorovich-type inequalities are analogous to those of antieigenvalue and Kantorovich inequality. In the second section, we approximate several antieigenvalue-type quantities for arbitrary accretive operators. Each antieigenvalue-type quantity is approximated in terms of the same quantity for normal matrices. In particular, we show that for an arbitrary accretive operator, each antieigenvalue-type quantity is the limit of the same quantity for a sequence of finite-dimensional normal matrices. Morteza Seddighin Copyright © 2012 Morteza Seddighin. All rights reserved. Tue, 11 Dec 2012 09:52:42 +0000 http://www.hindawi.com/journals/ijmms/2012/470293/ We show how a quantum formulation of financial economics can be derived from asymmetries with respect to Fisher information. Our approach leverages statistical derivations of quantum mechanics which provide a natural basis for interpreting quantum formulations of social sciences generally and of economics in particular. We illustrate the utility of this approach by deriving arbitrage-free derivative-security dynamics. Raymond J. Hawkins and B. Roy Frieden Copyright © 2012 Raymond J. Hawkins and B. Roy Frieden. All rights reserved. Mon, 10 Dec 2012 16:10:42 +0000 http://www.hindawi.com/journals/ijmms/2012/185346/ We prove that if is a 2-connect graph of size (the number of edges) and minimum degree with , where when and when , then each longest cycle in is a dominating cycle. The exact analog of this theorem for Hamilton cycles follows easily from two known results according to Dirac and Nash-Williams: each graph with is hamiltonian. Both results are sharp in all respects. Zh. G. Nikoghosyan Copyright © 2012 Zh. G. Nikoghosyan. All rights reserved.