http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/634698/The computation of the roots of positive definite matrices arises in nuclear magnetic resonance, control theory, lattice quantum chromo-dynamics (QCD), and several other areas of applications. The Cauchy integral theorem which arises in complex analysis can be used for computing f(A), in particular the roots of A, where A is a square matrix. The Cauchy integral can be approximated by using the trapezoid rule. In this paper, we aim to give a brief overview of the computation of roots of positive definite matrices by employing integral representation. Some numerical experiments are given to illustrate the theoretical results.Amir Sadeghi and Ahmad Izani Md. IsmailCopyright © 2012 Amir Sadeghi and Ahmad Izani Md. Ismail. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/307036/We establish necessary and sufficient conditions for the existence of and the expressions for the general real and complex Hermitian solutions to the classical system of quaternion matrix equations A1X=C1,XB1=C2, and  A3XA3*=C3. Moreover, formulas of the maximal and minimal ranks of four real matrices X1,X2,X3, and X4 in solution X=X1+X2i+X3j+X4k to the system mentioned above are derived. As applications, we give necessary and sufficient conditions for the quaternion matrix equations A1X=C1,XB1=C2,A3XA3*=C3, and  A4XA4*=C4 to have real and complex Hermitian solutions.Shao-Wen YuCopyright © 2012 Shao-Wen Yu. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/809689/The author establish several Hermite-Hadamard and Simpson-like type inequalities for mappings whose first derivative in absolute value aroused to the qth (q≥1) power are (α,m)-convex. Some applications to special means of positive real numbers are also given.Jaekeun ParkCopyright © 2012 Jaekeun Park. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/842806/We investigate the Shintani functions attached to the spherical and nonspherical principal series representations of SL(3,R). We give the explicit formulas of the radial part of Shintani functions and evaluate the dimension of the space of Shintani functions.Keiju SonoCopyright © 2011 Keiju Sono. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/482840/We give some interesting identities on the twisted (h,q)-Genocchi numbers and polynomials associated with q-Bernstein polynomials.Seog-Hoon Rim and Sun-Jung LeeCopyright © 2011 Seog-Hoon Rim and Sun-Jung Lee. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/419341/We study the following quasilinear problem with nonlinear boundary condition -Δpu-λa(x)u|u|p-2=b(x)u|u|γ-2, in Ω and (1-α)|∇u|p-2(∂u/∂n)+αu|u|p-2=0, on ∂Ω, where Ω⊆RN is a connected bounded domain with smooth boundary ∂Ω, the outward unit normal to which is denoted by n. Δp is the p-Laplcian operator defined by Δpu=div⁡(|∇u|p-2∇u), the functions a and b are sign changing continuous functions in Ω, 1<p<γ<p*, where p*=Np/(N-p) if N>p and ∞ otherwise. The properties of the first eigenvalue λ1+(α) and the associated eigenvector of the related eigenvalue problem have been studied in (Khademloo, In press). In this paper, it is shown that if λ≤λ1+(α), the original problem admits at least one positive solution, while if λ1+(α)<λ<λ*, for a positive constant λ*, it admits at least two distinct positive solutions. Our approach is variational in character and our results extend those of Afrouzi and Khademloo (2007) in two aspects: the main part of our differential equation is the p-Laplacian, and the boundary condition in this paper also is nonlinear.S. KhademlooCopyright © 2011 S. Khademloo. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/970763/A discrete predator-prey model with Holling II and Beddington-DeAngelis functional responses is investigated. With the aid of differential equations with piecewise constant arguments, a discrete version of continuous nonautonomous delayed predator-prey model with Beddington-DeAngelis functional responses is proposed. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive solutions of the model are established.Changjin Xu and Maoxin LiaoCopyright © 2011 Changjin Xu and Maoxin Liao. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/342759/The limit set of a topological transformation group on S1 generated by two generators is proved to be totally disconnected (or thin) and perfect if the conditions (i–v) are satisfied. A concrete application to a Doubly Periodic Riccati equation is given.Keying Guan and Zuming ChenCopyright © 2011 Keying Guan and Zuming Chen. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/328197/An exponentially fitted explicit hybrid method for solving oscillatory problems is obtained. This method has four stages. The first three stages of the method integrate exactly differential systems whose solutions can be expressed as linear combinations of {1,x,exp(μx),exp(−μx)},μ∈C, while the last stage of this method integrates exactly systems whose solutions are linear combinations of {1,x,x2,x3,x4,exp(μx),exp(−μx)}. This method is implemented in variable step-size code basing on an embedding approach. The stability analysis is given. Numerical experiments that have been carried out show the efficiency of our method.F. Samat, F. Ismail, and M. B. SuleimanCopyright © 2011 F. Samat et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/969424/Recursive algebraic construction of two infinite families of polynomials in n variables is proposed as a uniform method applicable to every semisimple Lie group of rank n. Its result recognizes Chebyshev polynomials of the first and second kind as the special case of the simple group of type A1. The obtained not Laurent-type polynomials are equivalent to the partial cases of the Macdonald symmetric polynomials. Recurrence relations are shown for the Lie groups of types A1, A2, A3, C2, C3, G2, and B3 together with lowest polynomials.Maryna Nesterenko, Jiří Patera, and Agnieszka TereszkiewiczCopyright © 2011 Maryna Nesterenko et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/940839/In this paper with the help of the inverse function of the singular moduli we evaluate the Rogers-Ranmanujan continued fraction and its first derivative.Nikos BagisCopyright © 2011 Nikos Bagis. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/140259/We study characteristic r-lightlike submanifolds M tangent to the characteristic vector fields in an indefinite metric S-manifold, and we also discuss the existence of characteristic lightlike submanifolds of an indefinite S-space form under suitable hypotheses: (1) M is totally umbilical or (2) its screen distribution S(TM) is totally umbilical in M.Jae Won LeeCopyright © 2011 Jae Won Lee. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/686139/The aim of this paper is the variational study of the contact with adhesion between an elastic material and a rigid foundation in the quasistatic process where the deformations are supposed to be small. The behavior of this material is modelled by a nonlinear elastic law and the contact is modelled with Signorini's conditions and adhesion. The evolution of bonding field is described by a nonlinear differential equation. We derive a variational formulation of the mechanical problem, and we prove the existence and uniqueness of the weak solution using a theorem on variational inequalities, the theorem of Cauchy-Lipschitz, a lemma of Gronwall, as well as the fixed point of Banach.Boudjemaa Teniou and Sabrina BenferdiCopyright © 2011 Boudjemaa Teniou and Sabrina Benferdi. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/895273/Attribute data from high-quality processes can be monitored effectively by deciding on whether or not to stop at each time where r≥1 failures have occurred. The smaller the degree of change in failure rate during out of control one wants to be optimally protected against, the larger the r should be. Under homogeneity, the distribution involved is negative binomial. However, in health care monitoring, (groups of) patients will often belong to different risk categories. In the present paper, we will show how information about category membership can be used to adjust the basic negative binomial charts to the actual risk incurred. Attention is also devoted to comparing such conditional charts to their unconditional counterparts. The latter do take possible heterogeneity into account but refrain from risk-adjustment. Note that in the risk adjusted case several parameters are involved, which will all be typically unknown. Hence, the potentially considerable estimation effects of the new charts will be investigated as well.Willem AlbersCopyright © 2011 Willem Albers. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/356915/Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f(z)=zh(z)g(z)¯ defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, Slh*(A,B,α), with the functional zh(z) in the class of the generalized Janowski starlike functions, S*(A,B,α). By means of these functions, we obtained results on the generalized Janowski close-to-starlike log-harmonic mappings, CSTlh(A,B,α).Maisarah Haji Mohd and Maslina DarusCopyright © 2011 Maisarah Haji Mohd and Maslina Darus. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/976723/A Rademacher-type formula for the Fourier coefficients of the generating function for the partitions of n where no odd part is repeated is presented.Vyacheslav Kiria-KaiserbergCopyright © 2011 Vyacheslav Kiria-Kaiserberg. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/387429/We provide a new mathematical technique leading to the construction of the exact parametric or closed form solutions of the classes of Abel's nonlinear differential equations (ODEs) of the first kind. These solutions are given implicitly in terms of Bessel functions of the first and the second kind (Neumann functions), as well as of the free member of the considered ODE; the parameter ν being introduced furnishes the order of the above Bessel functions and defines also the desired solutions of the considered ODE as one-parameter family of surfaces. The nonlinear initial or boundary value problems are also investigated. Finally, introducing a relative mathematical methodology, we construct the exact parametric or closed form solutions for several degenerate Abel's equation of the first kind.Dimitrios E. Panayotounakos and Theodoros I. ZarmpoutisCopyright © 2011 Dimitrios E. Panayotounakos and Theodoros I. Zarmpoutis. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/504802/We investigate a fuzzy version of stability for the functional equation f(x+y+z+w) +2f(x)+2f(y)+2f(z)+2f(w)-f(x+y)-f(x+z)-f(x+w)-f(y+z)-f(y+w)-f(z+w)=0.Sun Sook Jin and Yang Hi LeeCopyright © 2011 Sun Sook Jin and Yang Hi Lee. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/506857/The paper deals with the existence of solutions of some generalized Stefan-type equation in the framework of Orlicz spaces.Mohammed Kbiri AlaouiCopyright © 2011 Mohammed Kbiri Alaoui. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/920737/Let X be an arbitrary nonempty set and L a lattice of subsets of X such that ∅, X∈L. A(L) denotes the algebra generated by L, and M(L) denotes those nonnegative, finite, finitely additive measures on A(L). In addition, I(L) denotes the subset of M(L) which consists of the nontrivial zero-one valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces, and products of a variety of measures.Carmen VladCopyright © 2011 Carmen Vlad. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/906846/Diffusion models have been used extensively in many applications. These models, such as those used in the financial engineering, usually contain unknown parameters which we wish to determine. One way is to use the maximum likelihood method with discrete samplings to devise statistics for unknown parameters. In general, the maximum likelihood functions for diffusion models are not available, hence it is difficult to derive the exact maximum likelihood estimator (MLE). There are many different approaches proposed by various authors over the past years, see, for example, the excellent books and Kutoyants (2004), Liptser and Shiryayev (1977), Kushner and Dupuis (2002), and Prakasa Rao (1999), and also the recent works by Aït-Sahalia (1999), (2004), (2002), and so forth. Shoji and Ozaki (1998; see also Shoji and Ozaki (1995) and Shoji and Ozaki (1997)) proposed a simple local linear approximation. In this paper, among other things, we show that Shoji's local linear Gaussian approximation indeed yields a good MLE.X. L. Duan, Z. M. Qian, and W. A. ZhengCopyright © 2011 X. L. Duan et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/838924/The stress induced in a loaded beam will not exceed some threshold, but also its maximum deflection, as for all the elastic systems, will be controlled. Nevertheless, the linear beam theory fails to describe the large deflections; highly flexible linear elements, namely, rods, typically found in aerospace or oil applications, may experience large displacements—but small strains, for not leaving the field of linear elasticity—so that geometric nonlinearities become significant. In this article, we provide analytical solutions to large deflections problem of a straight, cantilevered rod under different coplanar loadings. Our researches are led by means of the elliptic integrals, but the main achievement concerns the Lauricella FD(3) hypergeometric functions use for solving elasticity problems. Each of our analytic solutions has been individually validated by comparison with other tools, so that it can be used in turn as a benchmark, that is, for testing other methods based on the finite elements approximation.Giovanni Mingari Scarpello and Daniele RitelliCopyright © 2011 Giovanni Mingari Scarpello and Daniele Ritelli. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/245324/Wreath product constructions has been used to obtain for any positive integer n, solvable groups of derived length n, and commutator length at most equal to 2.Mehri Akhavan-MalayeriCopyright © 2011 Mehri Akhavan-Malayeri. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/324821/The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. In this paper, we investigate the concept of restricted positive definite functions and their relation with restricted representations of an inverse semigroup. We also introduce the restricted Fourier and Fourier-Stieltjes algebras of an inverse semigroup and study their relation with the corresponding algebras on the associated groupoid.Massoud Amini and Alireza MedghalchiCopyright © 2011 Massoud Amini and Alireza Medghalchi. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/679704/For α≥0, λ>0, we consider the M(α,λ)b of normalized analytic α-λ convex functions defined in the open unit disc U. In this paper, we investigate the class M(α,λ)b, that is, Re{(zfb′(z)/fb(z))[1-α+α(1-λ)(zfb′(z)/fb(z))+αλ(1+(zfb′′(z)/fb′(z)))]}>0, with fb is Koebe type, that is, fb(z):=z/(1-zn)b. The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class M(α,λ)b of n-fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.Saibah Siregar and Maslina DarusCopyright © 2011 Saibah Siregar and Maslina Darus. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/740816/In a quantum Markov chain, the temporal succession of states is modeled by the repeated action of a “bistochastic quantum operation” on the density matrix of a quantum system. Based on this conceptual framework, we derive some new results concerning the evolution of a quantum system, including its long-term behavior. Among our findings is the fact that the Cesàro limit of any quantum Markov chain always exists and equals the orthogonal projection of the initial state upon the eigenspace of the unit eigenvalue of the bistochastic quantum operation. Moreover, if the unit eigenvalue is the only eigenvalue on the unit circle, then the quantum Markov chain converges in the conventional sense to the said orthogonal projection. As a corollary, we offer a new derivation of the classic result describing limiting distributions of unitary quantum walks on finite graphs (Aharonov et al., 2001).Chaobin Liu and Nelson PetulanteCopyright © 2011 Chaobin Liu and Nelson Petulante. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/757134/Let G be a permutation group of degree n viewed as a subgroup of the symmetric group S≅Sn. We show that if the irreducible character of S corresponding to the partition of n into subsets of sizes n−2 and 2, that is, to say the character often denoted by χ(n−2,2), remains irreducible when restricted to G, then n = 4, 5 or 9 and G≅S3, A5, or PΣL2(8), respectively, or G is 4-transitive.S. Aldhafeeri and R. T. CurtisCopyright © 2011 S. Aldhafeeri and R. T. Curtis. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/164843/We study the problem of the boundedness and compactness of Tϕ when ϕ∈L2(Ω) and Ω is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of Tϕ.Roberto C. RaimondoCopyright © 2011 Roberto C. Raimondo. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/493531/The author obtained new generalizations and refinements of some inequalities based on differentiable s-convex mappings in the second sense. Also, some applications to special means of real numbers are given.Jaekeun ParkCopyright © 2011 Jaekeun Park. All rights reserved.http://www.hindawi.com/journals/ijmms/2011/609287/We prove that an operator is weak Dunford-Pettis if its adjoint is one but the converse is false in general, and we give some necessary and sufficient conditions under which each positive weak Dunford-Pettis operator has an adjoint which is weak Dunford-Pettis.Belmesnaoui Aqzzouz, Khalid Bouras, and Mohammed MoussaCopyright © 2011 Belmesnaoui Aqzzouz et al. All rights reserved.