http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2012, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/867247/There is a CW complex T(X), which gives a rational homotopical classification of almost free toral actions on spaces in the rational homotopy type of X associated with rational toral ranks and also presents certain relations in them. We call it the rational toral rank complex of X. It represents a variety of toral actions. In this note, we will give effective 2-dimensional examples of it when X is a finite product of odd spheres. This is a combinatorial approach in rational homotopy theory.Toshihiro YamaguchiCopyright © 2012 Toshihiro Yamaguchi. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/236352/We develop a model of dengue transmission with some vaccination programs for immigrants. We classify the host population into child and adult classes, in regards to age structure, and into susceptible, infected and recovered compartments, in regards to disease status. Since migration plays important role in disease transmission, we include immigration and emigration factors into the model which are distributed in each compartment. Meanwhile, the vector population is divided into susceptible, exposed, and infectious compartments. In the case when there is no incoming infected immigrant, we obtain the basic reproduction ratio as a threshold parameter for existence and stability of disease-free and endemic equilibria. Meanwhile, in the case when there are some incoming infected immigrants, we obtain only endemic equilibrium. This indicates that screening for the immigrants is important to ensure the effectiveness of the disease control.Hengki Tasman, Asep K. Supriatna, Nuning Nuraini, and Edy SoewonoCopyright © 2012 Hengki Tasman et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/272137/In 2007, Haung and Zhang introduced the notion of cone metric spaces. In this paper, we define an ordered space E, and we discuss some properties and examples. Also, normed ordered space is introduced. We recall properties of ℝ, and we discuss their extension to E. We introduce the notion of E-metric spaces and characterize cone metric space. Afterwards, we get generalizations of notions of convergence and Cauchy theory. In particular, we get a fixed point theorem of a contractive mapping in E-metric spaces. Finally, by extending the notion of a contractive sequence in a real-valued metric space, we show that in E-metric spaces, a contractive sequence is Cauchy.Ahmed Al-Rawashdeh, Wasfi Shatanawi, and Muna KhandaqjiCopyright © 2012 Ahmed Al-Rawashdeh et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/952654/The notion of BRK-algebra is introduced which is a generalization of BCK/BCI/BCH/Q/QS/BM-algebras. The concepts of G-part, p-radical, medial of a BRK-algebra are introduced and studied their properties. We proved that the variety of all medial BRK-algebras is congruence permutable and showed that every associative BRK-algebra is a group.Ravi Kumar BandaruCopyright © 2012 Ravi Kumar Bandaru. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/536475/In this paper, we give a method to describe the numerical class of a torus invariant surface on a projective toric manifold. As applications, we can classify toric 2-Fano manifolds of the Picard number 2 or of dimension at most 4.Hiroshi SatoCopyright © 2012 Hiroshi Sato. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/748590/This paper presents the result on existence, uniqueness of mild solutions to neutral stochastic partial functional integrodifferential equations under the Carathéodory-type conditions on the coefficients. The results are obtained by using the method of successive approximation. An example is provided to illustrate the results of this work.Mamadou Abdoul Diop, Khalil Ezzinbi, and Modou LoCopyright © 2012 Mamadou Abdoul Diop et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/456517/We consider the fourth-order spectral problem y(4)(x)-(q(x)y'(x))′=λy(x),  x∈(0,l) with spectral parameter in the boundary condition. We associate this problem with a selfadjoint operator in Hilbert or Pontryagin space. Using this operator-theoretic formulation and analytic methods, we investigate locations (in complex plane) and multiplicities of the eigenvalues, the oscillation properties of the eigenfunctions, the basis properties in Lp(0,l), p∈(1,∞), of the system of root functions of this problem.Ziyatkhan S. Aliyev and Nazim B. KerimovCopyright © 2012 Ziyatkhan S. Aliyev and Nazim B. Kerimov. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/174372/Carry Value Transformation (CVT) is a model of discrete deterministic dynamical system. In the present study, it has been proved that (1) the sum of any two nonnegative integers is the same as the sum of their CVT and XOR values. (2) the number of iterations leading to either CVT=0 or XOR=0 does not exceed the maximum of the lengths of the two addenda expressed as binary strings. A similar process of addition of modified Carry Value Transformation (MCVT) and XOR requires a maximum of two iterations for MCVT to be zero. (3) an equivalence relation is shown to exist on Z×Z which divides the CV table into disjoint equivalence classes.Suryakanta Pal, Sudhakar Sahoo, and Birendra Kumar NayakCopyright © 2012 Suryakanta Pal et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/856927/We consider heat conduction in domains containing noncoaxial cylinders. In particular, we present some regularity results for the solution and consider criteria which ensure the single valueness of the corresponding complex potential. Examples are discussed. In addition, we present some classes of cases where the parameters describing the solution are rational. Alternative ways of calculating the heat flux are also discussed.Dag Lukkassen and Annette MeidellCopyright © 2012 Dag Lukkassen and Annette Meidell. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/861797/The purpose of this paper is to give some identities on the Frobenius-Euler numbers and polynomials by using the fermionic p-adic q-integral equation on ℤp.J. Choi, D. S. Kim, T. Kim, and Y. H. KimCopyright © 2012 J. Choi et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/109214/Let Ω∋0 be an-open bounded domain in RN(N≥3) and p*=(pN/(N-p)). We consider the following quasilinear elliptic system of two equations in W01,p(Ω)×W01,p(Ω): -Δpu=λf(x)|u|q-2u+(α/(α+β))h(x)|u|α-2u|v|β,-Δpv=μg(x)|v|q-2v+(β/(α+β))h(x)|u|α|v|β -2v, where λ,  μ>0, Δp denotes the p-Laplacian operator, 1≤q<p<N,α,β>1 satisfy p<α+β≤p*, and f,  g,  h are continuous functions on Ω¯ which are somewhere positive but which may change sign on Ω. We establish the existence and multiplicity results of positive solutions to (the above mentioned quasilinear elliptic system equations) by variational methods.Tsing-San HsuCopyright © 2012 Tsing-San Hsu. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/163689/A rotational fluid model which can be used to describe broad vortical flows ranging from large scale to the atmospheric mesoscale and the oceanic submesoscale is studied by the symmetry group theory. After introducing one scalar-, two vector-, and two tensor potentials, we find that the Lie symmetries of the extended system include many arbitrary functions of z and {z,t}. The obtained Lie symmetries are used to find some types of exact solutions. One of exact solutions can be used to qualitatively describe the three-dimensional structure of hurricanes.S. Y. Lou, Man Jia, F. Huang, and X. Y. TangCopyright © 2012 S. Y. Lou et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/794040/We study the general semilinear second-order ODE u′′+g(t,u,u′)=0 under different two-point boundary conditions. Using the method of upper and lower solutions, we obtain an existence result. Moreover, under a growth condition on g, we prove that the set of solutions of u′′+g(t,u,u′)=0 is homeomorphic to the two-dimensional real space.Indranil SenGupta and Maria C. MarianiCopyright © 2012 Indranil SenGupta and Maria C. Mariani. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/693090/On the basis of the theory of a falling shadow which was first formulated by Wang (1985), the notion of falling d∗-ideals in d-algebras is introduced, and related properties are investigated. Characterizations of a falling d∗-ideal are established. Relations among falling d∗-ideals, falling d-ideals, falling d#-ideals, falling d-subalgebras, and falling BCK-ideals are discussed.Young Bae Jun and Sun Shin AhnCopyright © 2012 Young Bae Jun and Sun Shin Ahn. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/303492/A basis of S4(Γ0(47)) is given and the formulas for the number of representations of positive integers by some direct sum of the quadratic forms x12+x1x2+12x22, 2x12±x1x2+6x22, 3x12±x1x2+4x22 are determined.Barış KendirliCopyright © 2012 Barış Kendirli. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/715751/A generalized identity for some partial differentiable mappings on a bidimensional interval is obtained, and, by using this result, the author establishes generalizations of Simpson-like type inequalities for coordinated s-convex mappings in the second sense.Jaekeun ParkCopyright © 2012 Jaekeun Park. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/406364/Axisymmetric vibration of an infinite piezolaminated multilayer hollow cylinder made of piezoelectric layers of 6 mm class and an isotropic LEMV (Linear Elastic Materials with Voids) layers is studied. The frequency equations are obtained for the traction free outer surface with continuity conditions at the interfaces. Numerical results are carried out for the inner, middle, and outer hollow piezoelectric layers bonded by LEMV (It is hypothetical material) layers and the dispersion curves are compared with that of a similar 3-layer model and of 3 and 5 layer models with inner, middle, and outer hollow piezoelectric layers bonded by CFRP (Carbon fiber reinforced plastics).E. S. NehruCopyright © 2012 E. S. Nehru. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/304647/We show geometrical properties of a submanifold of a (LCS)n-manifold. The properties of the induced structures on such a submanifold are also studied.Mehmet AtcekenCopyright © 2012 Mehmet Atceken. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/315686/We give an optimality characterization of nonadditive generalized mean-value entropies from suitable nonadditive and generalized mean-value properties of the measure of average length. The results obtained cover many results obtained by other authors as particular cases, as well as the ordinary length due to Shannon 1948. The main instrument is the l(ni) function of the word lengths in obtaining the average length of the code.Satish Kumar, Gurdas Ram, and Vishal GuptaCopyright © 2012 Satish Kumar et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/270132/Let M be a 2-torsion-free semiprime Γ-ring satisfying the condition aαbβc=aβbαc for all a,b,c∈M,  α,β∈Γ, and let D:M→M be an additive mapping such that D(xαx)=D(x)αx+xαd(x) for all x∈M,  α∈Γ and for some derivation d of M. We prove that D is a generalized derivation.Kalyan Kumar Dey, Akhil Chandra Paul, and Isamiddin S. RakhimovCopyright © 2012 Kalyan Kumar Dey et al. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/126835/We associate a graph to any subset Y of a BCI-algebra X and denote it by G(Y). Then we find the set of all connected components of G(X) and verify the relation between X and G(X), when X is commutative BCI-algebra or G(X) is complete graph or n-star graph. Finally, we attempt to investigate the relation between some operations on graph and some operations on BCI-algebras.Omid Zahiri and Rajab Ali BorzooeiCopyright © 2012 Omid Zahiri and Rajab Ali Borzooei. All rights reserved.http://www.hindawi.com/journals/ijmms/2012/962070/A quadrature-based mixed Petrov-Galerkin finite element method is applied to a fourth-order linear ordinary differential equation. After employing a splitting technique, a cubic spline trial space and a piecewise linear test space are considered in the method. The integrals are then replaced by the Gauss quadrature rule in the formulation itself. Optimal order a priori error estimates are obtained without any restriction on the mesh.L. Jones Tarcius Doss and A. P. NandiniCopyright © 2012 L. Jones Tarcius Doss and A. P. Nandini. 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/2012/743873/Let T be a commutative ring, I a prime ideal of T, D a subring of T/I, and R the pullback T×T/ID. Ascent and descent results are given for the transfer of the n-PIT and GPIT (generalized principal ideal theorem) properties between T and R. As a consequence, it follows that if I is a maximal ideal of both T and R, then R satisfies n-PIT (resp., GPIT) if and only if T satisfies n-PIT (resp., GPIT).David E. Dobbs and Jay ShapiroCopyright © 2012 David E. Dobbs and Jay Shapiro. 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/2012/274783/Using Buşneag's model, the notion of pseudovaluations (valuations) on a WFI algebra is introduced, and a pseudometric is induced by a pseudovaluation on WFI algebras. Given a valuation with additional condition, we show that the binary operation in WFI algebras is uniformly continuous.Young Bae Jun, Min Su Kang, and Eun Hwan RohCopyright © 2012 Young Bae Jun et al. All rights reserved.