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A Note on Some Identities of Frobenius-Euler Numbers and Polynomials (2012)

J. Choi, D. S. Kim, T. Kim, and Y. H. Kim

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-16

Beschreibung: 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.

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Generalized Derivations in Semiprime Gamma Rings (2012)

Kalyan Kumar Dey, Akhil Chandra Paul, and Isamiddin S. Rakhimov

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-17

Beschreibung: 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.

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Polynomials in Control Theory Parametrized by Their Roots (2012)

Baltazar Aguirre-Hernández, José Luis Cisneros-Molina, and Martín-Eduardo Frías-Armenta

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-12-25

Beschreibung: 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.

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A Convolution Approach on Partial Sums of Certain Harmonic Univalent Functions (2012)

Saurabh Porwal

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-11-12

Beschreibung: The purpose of the present paper is to establish some new results giving the sharp bounds of the real parts of ratios of harmonic univalent functions to their sequences of partial sums by using convolution. Relevant connections of the results presented here with various known results are briefly indicated.

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Norm for Sums of Two Basic Elementary Operators (2012)

A. Bachir, F. Lombarkia, and A. Segres

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-12-09

Beschreibung: We give necessary and sufficient conditions under which the norm of basic elementary operators attains its optimal value in terms of the numerical range.

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Two Sufficient Conditions for Hamilton and Dominating Cycles (2012)

Zh. G. Nikoghosyan

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-12-11

Beschreibung: 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.

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Asymmetric Information and Quantization in Financial Economics (2012)

Raymond J. Hawkins and B. Roy Frieden

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-12-12

Beschreibung: 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.

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Solution of Fuzzy Matrix Equation System (2012)

Mahmood Otadi and Maryam Mosleh

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-26

Beschreibung: The main is to develop a method to solve an arbitrary fuzzy matrix equation system by using the embedding approach. Considering the existing solution to fuzzy matrix equation system is done. To illustrate the proposed model a numerical example is given, and obtained results are discussed.

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Fixed Point of -Hardy-Rogers Contractive Mappings in Partially Ordered Partial Metric Spaces (2012)

Mujahid Abbas, Hassen Aydi, and Stojan Radenović

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-29

Beschreibung: We prove some fixed point theorems for a T-Hardy-Rogers contraction in the setting of partially ordered partial metric spaces. We apply our results to study periodic point problems for such mappings. We also provide examples to illustrate the results presented herein.

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Subring Depth, Frobenius Extensions, and Towers (2012)

Lars Kadison

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-10-05

Beschreibung: The minimum depth

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11

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Fuzzy -Fold BCI-Positive Implicative Ideals in BCI-Algebras (2012)

S. F. Tebu, C. Lele, and J. B. Nganou

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-27

Beschreibung: We consider the notion of fuzzy -fold positive implicative ideals in BCI-algebras. We analyse many properties of fuzzy -fold positive implicative ideals. We also establish an extension properties for fuzzy n-fold positive implicative ideals in BCI-algberas. This work generalizes the corresponding results in the crisp case.

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On the Rational Approximation of Analytic Functions Having Generalized Types of Rate of Growth (2012)

Devendra Kumar

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-03

Beschreibung: The present paper is concerned with the rational approximation of functions holomorphic on a domain G⊂C, having generalized types of rates of growth. Moreover, we obtain the characterization of the rate of decay of product of the best approximation errors for functions f having fast and slow rates of growth of the maximum modulus.

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A Fixed Point Result for Boyd-Wong Cyclic Contractions in Partial Metric Spaces (2012)

Hassen Aydi and Erdal Karapinar

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-13

Beschreibung: A fixed point theorem involving Boyd-Wong-type cyclic contractions in partial metric spaces is proved. We also provide examples to support the concepts and results presented herein.

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Surfaces of Constant Curvature in the Pseudo-Galilean Space (2012)

Željka Milin Šipuš and Blaženka Divjak

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-10-16

Beschreibung: We develop the local theory of surfaces immersed in the pseudo-Galilean space, a special type of Cayley-Klein spaces. We define principal, Gaussian, and mean curvatures. By this, the general setting for study of surfaces of constant curvature in the pseudo-Galilean space is provided. We describe surfaces of revolution of constant curvature. We introduce special local coordinates for surfaces of constant curvature, so-called the Tchebyshev coordinates, and show that the angle between parametric curves satisfies the Klein-Gordon partial differential equation. We determine the Tchebyshev coordinates for surfaces of revolution and construct a surface with constant curvature from a particular solution of the Klein-Gordon equation.

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A Regularization of the Backward Problem for Nonlinear Parabolic Equation with Time-Dependent Coefficient (2012)

Pham Hoang Quan, Le Minh Triet, and Dang Duc Trong

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-10-18

Beschreibung: We study the backward problem with time-dependent coefficient which is a severely ill-posed problem. We regularize this problem by combining quasi-boundary value method and quasi-reversibility method and then obtain sharp error estimate between the exact solution and the regularized solution. A numerical experiment is given in order to illustrate our results.

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Existence and Uniqueness of Mild Solutions to Some Neutral Stochastic Partial Functional Integrodifferential Equations with Non-Lipschitz Coefficients (2012)

Mamadou Abdoul Diop, Khalil Ezzinbi, and Modou Lo

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-04-06

Beschreibung: 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.

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Spectral Properties of the Differential Operators of the Fourth-Order with Eigenvalue Parameter Dependent Boundary Condition (2012)

Ziyatkhan S. Aliyev and Nazim B. Kerimov

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-04-04

Beschreibung: 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.

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Pseudovaluations on WFI Algebras (2012)

Young Bae Jun, Min Su Kang, and Eun Hwan Roh

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-04-10

Beschreibung: 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.

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Fredholm Weighted Composition Operators on Dirichlet Space (2012)

Liankuo Zhao

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-27

Beschreibung: This paper characterizes bounded Fredholm, bounded invertible, and unitary weighted composition operators on Dirichlet space.

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Coefficient Bounds for Certain Subclasses of Analytic Functions Defined by Komatu Integral Operator (2012)

Serap Bulut

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-30

Beschreibung: We determine the coeffcient bounds for functions in certain subclasses of analytic functions of complex order, which are introduced here by means of a certain non-homogeneous Cauchy–Euler type differential equation of order m. Relevant connections of some of the results obtained with those in earlier works are also provided.

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A Second Order Characteristic Method for Approximating Incompressible Miscible Displacement in Porous Media (2012)

Tongjun Sun and Keying Ma

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-31

Beschreibung: An approximation scheme is defined for incompressible miscible displacement in porous media. This scheme is constructed by two methods. Under the regularity assumption for the pressure, cubic Hermite finite element method is used for the pressure equation, which ensures the approximation of the velocity smooth enough. A second order characteristic finite element method is presented to handle the material derivative term of the concentration equation. It is of second order accuracy in time increment, symmetric, and unconditionally stable. The optimal

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Generalization of a Quadratic Transformation Formula due to Gauss (2012)

Medhat A. Rakha

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-31

Beschreibung: The aim of this research paper is to obtain explicit expressions of (1−

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Ruifang Zhao

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-03

Beschreibung: Let

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A Rapid Numerical Algorithm to Compute Matrix Inversion (2012)

F. Soleymani

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-04

Beschreibung: The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.

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On a 4-Point Sixteenth-Order King Family of Iterative Methods for Solving Nonlinear Equations (2012)

Diyashvir Kreetee Rajiv Babajee and Rajinder Thukral

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-17

Beschreibung: A one-parameter 4-point sixteenth-order King-type family of iterative methods which satisfy the famous Kung-Traub conjecture is proposed. The convergence of the family is proved, and numerical experiments are carried out to find the best member of the family. In most experiments, the best member was found to be a sixteenth-order Ostrowski-type method.

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Multiple Positive Solutions for a Fractional Boundary Value Problem with Fractional Integral Deviating Argument (2012)

A. Guezane-Lakoud and R. Khaldi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-16

Beschreibung: This work is devoted to the existence of positive solutions for a fractional boundary value problem with fractional integral deviating argument. The proofs of the main results are based on Guo-Krasnoselskii fixed point theorem and Avery and Peterson fixed point theorem. Two examples are given to illustrate the obtained results, ending the paper.

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Tripled Coincidence Point Theorems for Nonlinear Contractions in Partially Ordered Metric Spaces (2012)

Binayak S. Choudhury, Erdal Karapınar, and Amaresh Kundu

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-20

Beschreibung: Tripled fixed points are extensions of the idea of coupled fixed points introduced in a recent paper by Berinde and Borcut, 2011. Here using a separate methodology we extend this result to a triple coincidence point theorem in partially ordered metric spaces. We have defined several concepts pertaining to our results. The main results have several corollaries and an illustrative example. The example shows that the extension proved here is actual and also the main theorem properly contains all its corollaries.

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Existence and Multiplicity of Solutions for Semipositone Problems Involving p-Laplacian (2012)

Guowei Dai and Chunfeng Yang

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-20

Beschreibung: We prove existence and multiplicity of positive solutions for semipositone problems involving p-Laplacian in a bounded smooth domain of ℝN under the cases of sublinear and superlinear nonlinearities term.

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Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces (2012)

Bashir Ali and G. C. Ugwunnadi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-23

Beschreibung: Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let 𝔍={T(t):t≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u,v:[0,∞)→[0,∞). Let F:=F(𝔍)=∩t≥0F(T(t))≠∅ and f:K→K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ+λ>1, let G:E→E be a δ-strongly accretive and λ-strictly pseudocontractive map. Let {tn} be an increasing sequence in [0,∞) with limn→∞tn=∞, and let {αn} and {βn} be sequences in (0,1] satisfying some conditions. Strong convergence of a viscosity iterative sequence to common fixed points of the family 𝔍 of uniformly asymptotically regular asymptotically nonexpansive semigroup, which also solves the variational inequality 〈(G-γf)p,j(p-x)〉≤0, for all x∈F, is proved in a framework of a real Banach space.

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On Double Summability of Double Conjugate Fourier Series (2012)

H. K. Nigam and Kusum Sharma

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-21

Beschreibung: For the first time, a theorem on double matrix summability of double conjugate Fourier series is established.

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A Note on Directional Wavelet Transform: Distributional Boundary Values and Analytic Wavefront Sets (2012)

Felipe A. Apolonio, Daniel H. T. Franco, and Fábio N. Fagundes

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-25

Beschreibung: By using a particular class of directional wavelets (namely, the conical wavelets, which are wavelets strictly supported in a proper convex cone in the k-space of frequencies), in this paper, it is shown that a tempered distribution is obtained as a finite sum of boundary values of analytic functions arising from the complexification of the translational parameter of the wavelet transform. Moreover, we show that for a given distribution f∈𝒮′(ℝn), the continuous wavelet transform of f with respect to a conical wavelet is defined in such a way that the directional wavelet transform of f yields a function on phase space whose high-frequency singularities are precisely the elements in the analytic wavefront set of f.

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Common Fixed Points of Generalized Meir-Keeler Type Condition and Nonexpansive Mappings (2012)

R. K. Bisht

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-17

Beschreibung: The aim of the present paper is to obtain common fixed point theorems by employing the recently introduced notion of weak reciprocal continuity. The new notion is a proper generalization of reciprocal continuity and is applicable to compatible mappings as well as noncompatible mappings. We demonstrate that weak reciprocal continuity ensures the existence of common fixed points under contractive conditions, which otherwise do not ensure the existence of fixed points. Our results generalize and extend Banach contraction principle and Meir-Keeler-type fixed point theorem.

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Bounds of Hankel Determinant for a Class of Univalent Functions (2012)

Sarika Verma, Sushma Gupta, and Sukhjit Singh

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-16

Beschreibung: The authors study the coefficient condition for the class ℌα defined as the family of analytic functions f,f(0)=0 and f′(0)=1, which satisfy ℜ[(1-α)f′(z)+α(1+(zf″(z))/(f′(z)))]>α, z∈E, where α is a real number.

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Index of Quasiconformally Symmetric Semi-Riemannian Manifolds (2012)

Mukut Mani Tripathi, Punam Gupta, and Jeong-Sik Kim

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-19

Beschreibung: We find the index of ∇˜-quasiconformally symmetric and ∇˜-concircularly symmetric semi-Riemannian manifolds, where ∇˜ is metric connection.

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Fourth-Order Four-Point Boundary Value Problem: A Solutions Funnel Approach (2012)

Panos K. Palamides and Alex P. Palamides

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-14

Beschreibung: We investigate the existence of positive or a negative solution of several classes of four-point boundary-value problems for fourth-order ordinary differential equations. Although these problems do not always admit a (positive) Green's function, the obtained solution is still of definite sign. Furthermore, we prove the existence of an entire continuum of solutions. Our technique relies on the continuum property (connectedness and compactness) of the solutions funnel (Kneser's Theorem), combined with the corresponding vector field.

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Some New Classes of Generalized Apostol-Euler and Apostol-Genocchi Polynomials (2012)

R. Tremblay, S. Gaboury, and B.-J. Fugère

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-14

Beschreibung: The main object of this paper is to introduce and investigate two new classes of generalized Apostol-Euler and Apostol-Genocchi polynomials. In particular, we obtain a new addition formula for the new class of the generalized Apostol-Euler polynomials. We also give an extension and some analogues of the Srivastava-Pintér addition theorem obtained in the works by Srivastava and Pintér (2004) and R. Tremblay, S. Gaboury, B.-J. Fugère, and Tremblay et al. (2011). for both classes.

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Optimized Steffensen-Type Methods with Eighth-Order Convergence and High Efficiency Index (2012)

F. Soleymani

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-09

Beschreibung: Steffensen-type methods are practical in solving nonlinear equations. Since, such schemes do not need derivative evaluation per iteration. Hence, this work contributes two new multistep classes of Steffensen-type methods for finding the solution of the nonlinear equation

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On Level p Siegel Cusp Forms of Degree Two (2012)

Hirotaka Kodama, Shoyu Nagaoka, and Yoshitsugu Nakamura

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-13

Beschreibung: We give a simple formula for the Fourier coefficients of some degree-two Siegel cusp form with level p.

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Noetherian and Artinian Lattices (2012)

Derya Keskin Tütüncü, Sultan Eylem Toksoy, and Rachid Tribak

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-20

Beschreibung: It is proved that if L is a complete modular lattice which is compactly generated, then Rad(L)/0 is Artinian if, and only if for every small element a of L, the sublattice a/0 is Artinian if, and only if L satisfies DCC on small elements.

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Optimal Control of Multiple Transmission of Water-Borne Diseases (2012)

G. Devipriya and K. Kalaivani

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-04

Beschreibung: A controlled SIWR model was considered which was an extension of the simple SIR model by adjoining a compartment (W) that tracks the pathogen concentration in the water. New infections arise both through exposure to contaminated water as well as by the classical SIR person-person transmission pathway. The controls represent an immune boosting and pathogen suppressing drugs. The objective function is based on a combination of minimizing the number of infected individuals and the cost of the drugs dose. The optimal control is obtained by solving the optimality system which was composed of four nonlinear ODEs with initial conditions and four nonlinear adjoint ODEs with transversality conditions. The results were analysed and interpreted numerically using MATLAB.

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Modular Identities and Explicit Evaluations of a Continued Fraction of Ramanujan (2012)

Nipen Saikia

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-11

Beschreibung: We study a new continued fraction of Ramanujan. We prove its modular identities and give some explicit evaluations.

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Morita Equivalence of Brandt Semigroup Algebras (2012)

Maysam Maysami Sadr

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-11

Beschreibung: We show that Banach semigroup algebras of any two Brandt semigroups over a fixed group are Morita equivalence with respect to the Morita theory of self-induced Banach algebras introduced by Grønbæk. As applications, we show that the bounded Hochschild (co)homology groups of Brandt semigroup algebras over amenable groups are trivial and prove that the notion of approximate amenability is not Morita invariant.

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Property P and Some Fixed Point Results on (ψ,ϕ)-Weakly Contractive G-Metric Spaces (2012)

Mona Khandaqji, Sharifa Al-Sharif, and Mohammad Al-Khaleel

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-12

Beschreibung: We prove some fixed point results for (ψ,ϕ)-weakly contractive maps in G-metric spaces, we show that these maps satisfy property P. The results presented in this paper generalize several well-known comparable results in the literature.

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End-Point Results for Multivalued Mappings in Partially Ordered Metric Spaces (2012)

Ismat Beg and Hemant Kumar Nashine

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-12

Beschreibung: The purpose of this paper is to prove end-point theorems for multivalued mappings satisfying comparatively a more general contractive condition in ordered complete metric spaces. Afterwards, we extend the results of previous sections and prove common end-point results for a pair of 𝒯-weakly isotone increasing multivalued mappings in the underlying spaces. Finally, we present common end point for a pair of 𝒯-weakly isotone increasing multivalued mappings satisfying weakly contractive condition.

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Localization and Perturbations of Roots to Systems of Polynomial Equations (2012)

Michael Gil'

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-04

Beschreibung: We establish estimates for the sums of absolute values of solutions of a zero-dimensional polynomial system. By these estimates, inequalities for the counting function of the roots are derived. In addition, bounds for the roots of perturbed systems are suggested.

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On Concircular ϕ-Recurrent K-Contact Manifold Admitting Semisymmetric Metric Connection (2012)

Venkatesha, K. T. Pradeep Kumar, C. S. Bagewadi, and Gurupadavva Ingalahalli

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-04

Beschreibung: In the present paper, we have studied ϕ-recurrent and concircular ϕ-recurrent K-contact manifold with respect to semisymmetric metric connection and obtained some interesting results.

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On a Third-Order Three-Point Boundary Value Problem (2012)

A. Guezane-Lakoud, N. Hamidane, and R. Khaldi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-04

Beschreibung: We consider a third-order three-point boundary value problem. We introduce a generalized polynomial growth condition to obtain the existence of a nontrivial solution by using Leray-Schauder nonlinear alternative, then we give an example to illustrate our results.

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Oscillation and Asymptotic Behavior of Higher-Order Nonlinear Differential Equations (2012)

J. Džurina and B. Baculíková

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-06

Beschreibung: The aim of this paper is to offer a generalization of the Philos and Staikos lemma. As a possible application of the lemma in the oscillation theory, we study the asymptotic properties and oscillation of the nth order delay differential equations (E)(r(t)[x(n−1)(t)]γ)′+q(t)xγ(τ(t))=0. The results obtained utilize also the comparison theorems.

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Taylor's Expansion Revisited: A General Formula for the Remainder (2012)

José Juan Rodríguez Cano and Enrique de Amo

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-10

Beschreibung: We give a new approach to Taylor's remainder formula, via a generalization of Cauchy's generalized mean value theorem, which allows us to include the well-known Schölomilch, Lebesgue, Cauchy, and the Euler classic types, as particular cases.

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Sheffer and Non-Sheffer Polynomial Families (2012)

G. Dattoli, B. Germano, M. R. Martinelli, and P. E. Ricci

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-09

Beschreibung: By using the integral transform method, we introduce some non-Sheffer polynomial sets. Furthermore, we show how to compute the connection coefficients for particular expressions of Appell polynomials.

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On Almost Orthogonal Frames (2012)

Virender, A. Zothansanga, and S. K. Kaushik

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-26

Beschreibung: Almost orthogonal frames have been introduced and studied. It has been proved that a bounded almost orthogonal frame satisfies Feichtinger conjecture. Also, we prove that a bounded almost orthogonal frame contains a Riesz basis.

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Neighborhoods of Certain Multivalently Analytic Functions (2012)

Serap Bulut

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-28

Beschreibung: We introduce and investigate two new general subclasses of multivalently analytic functions of complex order by making use of the familiar convolution structure of analytic functions. Among the various results obtained here for each of these function classes, we derive the coefficient bounds, distortion inequalities, and other interesting properties and characteristics for functions belonging to the classes introduced here.

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On the Modified Jump Problem for the Laplace Equation in the Exterior of Cracks in a Plane (2012)

P. A. Krutitskii and A. Sasamoto

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-28

Beschreibung: The boundary value problem for the Laplace equation outside several cracks in a plane is studied. The jump of the solution of the Laplace equation and the boundary condition containing the jump of its normal derivative are specified on the cracks. The problem has unique classical solution under certain conditions. The new integral representation for the unique solution of this problem is obtained. The problem is reduced to the uniquely solvable Fredholm equation of the second kind and index zero. The integral representation and integral equation are essentially simpler than those derived for this problem earlier. The singularities at the ends of the cracks are investigated.

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Translative Packing of Unit Squares into Squares (2012)

Janusz Januszewski

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-28

Beschreibung: Every collection of n (arbitrary-oriented) unit squares admits a translative packing into any square of side length 2.5·n.

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Generalization of Some Coupled Fixed Point Results on Partial Metric Spaces (2012)

Wasfi Shatanawi, Hemant Kumar Nashine, and Nedal Tahat

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-28

Beschreibung: Using the setting of partial metric spaces, we prove some coupled fixed point results. Our results generalize several well-known comparable results of H. Aydi (2011). Also, we introduce an example to support our results.

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Trigonometric Approximation of Signals (Functions) Belonging to W(Lr, ξ(t)) Class by Matrix (C1·Np) Operator (2012)

Uaday Singh, M. L. Mittal, and Smita Sonker

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-27

Beschreibung: Various investigators such as Khan (1974), Chandra (2002), and Liendler (2005) have determined the degree of approximation of 2π-periodic signals (functions) belonging to Lip(α,r) class of functions through trigonometric Fourier approximation using different summability matrices with monotone rows. Recently, Mittal et al. (2007 and 2011) have obtained the degree of approximation of signals belonging to Lip(α,r)- class by general summability matrix, which generalize some of the results of Chandra (2002) and results of Leindler (2005), respectively. In this paper, we determine the degree of approximation of functions belonging to Lip α and W(Lr, ξ(t)) classes by using Cesáro-Nörlund (C1·Np) summability without monotonicity condition on {pn}, which in turn generalizes the results of Lal (2009). We also note some errors appearing in the paper of Lal (2009) and rectify them in the light of observations of Rhoades et al. (2011).

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A Combinatorial Note for Harmonic Tensors (2012)

Zhankui Xiao

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-27

Beschreibung: We give another characterization of the annihilator of the space of (dual) harmonic tensors in the group algebra of symmetric group.

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Integrability for Solutions of Anisotropic Obstacle Problems (2012)

Hongya Gao, Yanjie Zhang, and Shuangli Li

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-29

Beschreibung: This paper deals with anisotropic obstacle problem for the 𝒜-harmonic equation ∑i=1nDi(ai(x,Du(x)))=0. An integrability result is given under suitable assumptions, which show higher integrability of the boundary datum, and the obstacle force solutions u have higher integrability as well.

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On a Subclass of Harmonic Convex Functions of Complex Order (2012)

N. Magesh and S. Mayilvaganan

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-30

Beschreibung: We introduce and study a subclass of harmonic convex functions of complex order. Coefficient bounds, extreme points, distortion bounds, convolution conditions, and convex combination are determined for functions in this class. Further, we obtain the closure property of this class under integral operator.

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Coincidence Points for Expansive Mappings under c-Distance in Cone Metric Spaces (2012)

Hassen Aydi, Erdal Karapinar, and Sirous Moradi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-07

Beschreibung: We establish some fixed (common fixed) and coincidence point results for mappings verifying some expansive type contractions in cone metric spaces with the help of the concept of a c-distance. Our results generalize, extend, and unify several well-known comparable results in the literature. Some examples are also presented.

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Iteration and Iterative Roots of Fractional Polynomial Function (2012)

Xiao-hua Liu

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-07

Beschreibung: Iteration is involved in the fields of dynamical systems and numerical computation and so forth. The computation of iteration is difficult for general functions (even for some simple functions such as linear fractional functions). In this paper, we discuss fractional polynomial function and use the method of conjugate similitude to obtain its expression of general iterate of order n under two different conditions. Furthermore, we also give iterative roots of order n for the function under two different conditions.

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Properties of Certain Subclass of Multivalent Functions with Negative Coefficients (2012)

Jingyu Yang and Shuhai Li

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-31

Beschreibung: Making use of a linear operator, which is defined by the Hadamard product, we introduce and study a subclass Ya,c+(A,B;p,λ,α) of the class A+(p). In this paper, we obtain the coefficient inequality, distortion theorem, radius of convexity and starlikeness, neighborhood property, modified convolution properties of this class. Furthermore, an application of fractional calculus operator is given. The results are presented here would provide extensions of some earlier works. Several new results are also obtained.

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Fixed Point Theorems for Asymptotically Contractive Multimappings (2012)

M. Djedidi and K. Nachi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-05

Beschreibung: We present fixed point theorems for a nonexpansive set-valued mapping from a closed convex subset of a reflexive Banach space into itself under some asymptotic contraction assumptions. Some existence results of coincidence points and eigenvalues for multimappings are given.

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On Prime-Gamma-Near-Rings with Generalized Derivations (2012)

Kalyan Kumar Dey, Akhil Chandra Paul, and Isamiddin S. Rakhimov

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-04

Beschreibung: Let N be a 2-torsion free prime Γ-near-ring with center Z(N). Let (f,d) and (g,h) be two generalized derivations on N. We prove the following results: (i) if f([x,y]α)=0 or f([x,y]α)=± [x,y]α or f2(x)∈Z(N) for all x,y∈N, α∈Γ, then N is a commutative Γ-ring. (ii) If a∈N and [f(x),a]α=0 for all x∈N, α∈Γ, then d(a)∈Z(N). (iii) If (fg,dh) acts as a generalized derivation on N, then f=0 or g=0.

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The Numerical Class of a Surface on a Toric Manifold (2012)

Hiroshi Sato

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-09

Beschreibung: 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.

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A Dengue Vaccination Model for Immigrants in a Two-Age-Class Population (2012)

Hengki Tasman, Asep K. Supriatna, Nuning Nuraini, and Edy Soewono

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-16

Beschreibung: 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.

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On BRK-Algebras (2012)

Ravi Kumar Bandaru

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-09

Beschreibung: 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.

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Normed Ordered and E-Metric Spaces (2012)

Ahmed Al-Rawashdeh, Wasfi Shatanawi, and Muna Khandaqji

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-11

Beschreibung: 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.

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Cusp Forms in S4(Γ0(47)) and the Number of Representations of Positive Integers by Some Direct Sum of Binary Quadratic Forms with Discriminant −47 (2012)

Barış Kendirli

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-02

Beschreibung: 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.

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Potential Symmetry Studies on a Rotating Fluid System (2012)

S. Y. Lou, Man Jia, F. Huang, and X. Y. Tang

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-07

Beschreibung: 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.

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Generalizations of the Simpson-Like Type Inequalities for Co-Ordinated s-Convex Mappings in the Second Sense (2012)

Jaekeun Park

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-29

Beschreibung: 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.

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Axisymmetric Vibration of Piezo-Lemv Composite Hollow Multilayer Cylinder (2012)

E. S. Nehru

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-29

Beschreibung: 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).

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Two-Point Boundary Value Problems for a Class of Second-Order Ordinary Differential Equations (2012)

Indranil Sen; Gupta and Maria C. Mariani

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-06

Beschreibung: 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.

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Transfer of the GPIT Property in Pullbacks (2012)

David E. Dobbs and Jay Shapiro

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-23

Beschreibung: 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).

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On Geometry of Submanifolds of (LCS)n-Manifolds (2012)

Mehmet Atceken

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-23

Beschreibung: 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.

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On Heat Conduction in Domains Containing Noncoaxial Cylinders (2012)

Dag Lukkassen and Annette Meidell

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-26

Beschreibung: 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.

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Properties of Carry Value Transformation (2012)

Suryakanta Pal, Sudhakar Sahoo, and Birendra Kumar Nayak

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-04-02

Beschreibung: 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.

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Multiple Positive Solutions for a Quasilinear Elliptic System Involving Concave-Convex Nonlinearities and Sign-Changing Weight Functions (2012)

Tsing-San Hsu

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-03-13

Beschreibung: 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.

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Approximation of the pth Roots of a Matrix by Using Trapezoid Rule (2012)

Amir Sadeghi and Ahmad Izani Md. Ismail

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-01-25

Beschreibung: 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.

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The Real and Complex Hermitian Solutions to a System of Quaternion Matrix Equations with Applications (2012)

Shao-Wen Yu

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-01-24

Beschreibung: 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.

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Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable (α,m)-Convex Mappings (2012)

Jaekeun Park

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-01-19

Beschreibung: 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.

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Discrete Mixed Petrov-Galerkin Finite Element Method for a Fourth-Order Two-Point Boundary Value Problem (2012)

L. Jones Tarcius Doss and A. P. Nandini

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-14

Beschreibung: 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.

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Some Coding Theorems for Nonadditive Generalized Mean-Value Entropies (2012)

Satish Kumar, Gurdas Ram, and Vishal Gupta

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-20

Beschreibung: 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.

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Graph of BCI-Algebras (2012)

Omid Zahiri and Rajab Ali Borzooei

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-02-16

Beschreibung: 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.

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Quasilinear Stochastic Cauchy Problem in Abstract Colombeau Spaces (2012)

Irina V. Melnikova and Uljana A. Alekseeva

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-10-10

Beschreibung: Generalized solutions to the abstract Cauchy problem for a quasilinear equation with the generator of an integrated semigroup and with terms reflecting nonlinear perturbations and white noise type perturbations are under consideration. An abstract stochastic Colombeau algebra is constructed, and solutions in the algebra are studied.

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On Properties of Third-Order Differential Equations via Comparison Principles (2012)

B. Baculíková and J. Džurina

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-27

Beschreibung: The objective of this paper is to offer sufficient conditions for certain asymptotic properties of the third-order functional differential equation [r(t)[x′(t)]γ]′′+p(t)x(τ(t))=0, where studied equation is in a canonical form, that is, ∫∞r-1/γ(s)ds=∞. Employing Trench theory of canonical operators, we deduce properties of the studied equations via new comparison theorems. The results obtained essentially improve and complement earlier ones.

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On Open-Open Games of Uncountable Length (2012)

Andrzej Kucharski

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-26

Beschreibung: The aim of this paper is to investigate the open-open game of uncountable length. We introduce a cardinal number μ(X), which says how long the Player I has to play to ensure a victory. It is proved that c(X)≤μ(X)≤c(X)+. We also introduce the class 𝒞κ of topological spaces that can be represented as the inverse limit of κ-complete system {Xσ,πρσ,Σ} with w(Xσ)≤κ and skeletal bonding maps. It is shown that product of spaces which belong to 𝒞κ also belongs to this class and μ(X)≤κ whenever X∈𝒞κ.

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Old and New Identities for Bernoulli Polynomials via Fourier Series (2012)

Luis M. Navas, Francisco J. Ruiz, and Juan L. Varona

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-13

Beschreibung: The Bernoulli polynomials Bk restricted to [0,1) and extended by periodicity have nth sine and cosine Fourier coefficients of the form Ck/nk. In general, the Fourier coefficients of any polynomial restricted to [0,1) are linear combinations of terms of the form 1/nk. If we can make this linear combination explicit for a specific family of polynomials, then by uniqueness of Fourier series, we get a relation between the given family and the Bernoulli polynomials. Using this idea, we give new and simpler proofs of some known identities involving Bernoulli, Euler, and Legendre polynomials. The method can also be applied to certain families of Gegenbauer polynomials. As a result, we obtain new identities for Bernoulli polynomials and Bernoulli numbers.

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Thema: Mathematik

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Semicontinuity of the Automorphism Groups of Domains with Rough Boundary (2012)

Steven G. Krantz

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-11-08

Beschreibung: Based on some ideas of Greene and Krantz, we study the semicontinuity of automorphism groups of domains in one and several complex variables. We show that semicontinuity fails for domains in , , with Lipschitz boundary, but it holds for domains in with Lipschitz boundary. Using the same ideas, we develop some other concepts related to mappings of Lipschitz domains. These include Bergman curvature, stability properties for the Bergman kernel, and also some ideas about equivariant embeddings.

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Diagonally Implicit Block Backward Differentiation Formulas for Solving Ordinary Differential Equations (2012)

I. S. M. Zawawi, Z. B. Ibrahim, F. Ismail, and Z. A. Majid

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-11-14

Beschreibung: This paper focuses on the derivation of diagonally implicit two-point block backward differentiation formulas (DI2BBDF) for solving first-order initial value problem (IVP) with two fixed points. The method approximates the solution at two points simultaneously. The implementation and the stability of the proposed method are also discussed. A performance of the DI2BBDF is compared with the existing methods.

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Variational Methods for NLEV Approximation Near a Bifurcation Point (2012)

Raffaele Chiappinelli

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-11-14

Beschreibung: We review some more and less recent results concerning bounds on nonlinear eigenvalues (NLEV) for gradient operators. In particular, we discuss the asymptotic behaviour of NLEV (as the norm of the eigenvector tends to zero) in bifurcation problems from the line of trivial solutions, considering perturbations of linear self-adjoint operators in a Hilbert space. The proofs are based on the Lusternik-Schnirelmann theory of critical points on one side and on the Lyapounov-Schmidt reduction to the relevant finite-dimensional kernel on the other side. The results are applied to some semilinear elliptic operators in bounded domains of . A section reviewing some general facts about eigenvalues of linear and nonlinear operators is included.

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On the Solvability of Discrete Nonlinear Two-Point Boundary Value Problems (2012)

Blaise Kone and Stanislas Ouaro

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-26

Beschreibung: We prove the existence and uniqueness of solutions for a family of discrete boundary value problems by using discrete's Wirtinger inequality. The boundary condition is a combination of Dirichlet and Neumann boundary conditions.

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Deterministic Kalman Filtering on Semi-Infinite Interval (2012)

L. Faybusovich and T. Mouktonglang

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-06-26

Beschreibung: We relate a deterministic Kalman filter on semi-infinite interval to linear-quadratic tracking control model with unfixed initial condition.

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The 2D Dirichlet Problem for the Propagative Helmholtz Equation in an Exterior Domain with Cracks and Singularities at the Edges (2012)

P. A. Krutitskii

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-02

Beschreibung: The Dirichlet problem for the 2D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution in the form of potentials is obtained. The problem is reduced to the Fredholm equation of the second kind and of index zero, which is uniquely solvable. The asymptotic formulae describing singularities of a solution gradient at the edges (endpoints) of the cracks are presented. The weak solution to the problem may not exist, since the problem is studied under such conditions that do not ensure existence of a weak solution.

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The Theory of Falling Shadows Applied to d-Ideals in d-Algebras (2012)

Young Bae Jun and Sun Shin Ahn

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-04-06

Beschreibung: 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.

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Examples of Rational Toral Rank Complex (2012)

Toshihiro Yamaguchi

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-05-22

Beschreibung: 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.

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Decomposition of Automorphisms of Certain Solvable Subalgebra of Symplectic Lie Algebra over Commutative Rings (2012)

Xing Tao Wang and Lei Zhang

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-07-31

Beschreibung: Let Cl+1(R) be the 2(l+1)×2(l+1) matrix symplectic Lie algebra over a commutative ring R with 2 invertible. Then tl+1CR = {m-1m-20-m-1T ∣ m̅1 is an l+1 upper triangular matrix, m̅2T=m̅2, over R} is the solvable subalgebra of Cl+1(R). In this paper, we give an explicit description of the automorphism group of tl+1(C)(R).

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Free-Boundary Seepage from Asymmetric Soil Channels (2012)

Adrian Carabineanu

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-08-01

Beschreibung: We present an inverse method for the study of the seepage from soil channels without lining. We give integral representations of the complex potential, velocity field, stream lines, free phreatic lines, and contour of the channel by means of Levi-Civitá's function ω. For different values of the Taylor coefficients of ω, we calculate numerically the contour of the channel, the phreatic lines, the seepage loss, the velocity field, the stream lines, and the equipotential lines. Examples are given for various symmetric or asymmetric channels, with smooth contours or with angular points.

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Positive Solutions for (k, n − k) Conjugate Multipoint Boundary Value Problems in Banach Spaces (2012)

Yulin Zhao

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-19

Beschreibung: By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem (-1)n-kun(t)=f(t,ut), 0

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The Nonlinear Analysis of Perturbation Solution for a Parabolic Differential System (2012)

Victor F. Dailyudenko

Hindawi

In: International Journal of Mathematics and Mathematical Sciences

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Publikationsdatum: 2012-09-07

Beschreibung: By investigation of perturbation solution for nonlinear reaction-diffusion system, we derive related differential model for perturbations that involves weak nonlinearities up to third order. For a first time, this model is shown to result in derivation of the system for amplitude distribution by means of nonlinear integration on orthogonal basis in spatial region. The obtained time-dependent system (TDS) contains all possible functional relations between the modes of wave train under consideration along with delayed relations, and after numerical simulation it provides some conclusions concerning the natural frequency of the investigated self-organization process in active medium. The related matrix and modulo operations which substantiate the derivation of the TDS are also considered.

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