http://www.hindawi.comThe latest articles from Hindawi Publishing Corporation© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/983132This paper gives some estimates of the essential norm for the difference of composition operators induced by φ and ψ acting on the space, H∞(Dn), of bounded analytic functions on the unit polydisc Dn, where φ and ψ are holomorphic self-maps of Dn. As a consequence, one obtains conditions in terms of the Carathéodory distance on Dn that characterizes those pairs of holomorphic self-maps of the polydisc for which the difference of two composition operators on H∞(Dn) is compact.Zhong-Shan Fang and Ze-Hua Zhou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/296159Recently, Choi et al. (2008) have studied the q-extensions of the Apostol-Bernoulli and the Apostol-Euler polynomials of order n and multiple Hurwitz zeta function. In this paper, we define Apostol's type q-Euler numbers En,q,ξ and q-Euler polynomials En,q,ξ(x). We obtain the generating functions of En,q,ξ and En,q,ξ(x), respectively. We also have the distribution relation for Apostol's type q-Euler polynomials. Finally, we obtain q-zeta function associated with Apostol's type q-Euler numbers and Hurwitz's type q-zeta function associated with Apostol's type q-Euler polynomials for negative integers.Young-Hee Kim, Wonjoo Kim, and Lee-Chae Jang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/538573This paper shows that if S is a bounded linear operator acting on the weighted Bergman spaces Aα2 on the unit ball in ℂn such that STzi=Tz¯iS (i=1,…,n), where Tzi=zif and Tz¯i=P(z¯if); and where P is the weighted Bergman projection, then S must be a Hankel operator.Yufeng Lu and Jun Yang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/854725The purpose of this paper is to study the extendability of equilibrium states of rodlike nematic polymers with the Maier-Saupe intermolecular potential. We formulate equilibrium states as solutions of a nonlinear system and calculate the determinant of the Jacobian matrix of the nonlinear system. It is found that the Jacobian matrix is nonsingular everywhere except at two equilibrium states. These two special equilibrium states correspond to two points in the phase diagram. One point is the folding point where the stable prolate branch folds into the unstable prolate branch; the other point is the intersection point of the nematic branch and the isotropic branch where the unstable prolate state becomes the unstable oblate state. Our result establishes the existence and uniqueness of equilibrium states in the presence of small perturbations away from these two special equilibrium states.Hongyun Wang and Hong Zhou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/395257A method is developed for solutions of two sets of triple integral equations involving associated Legendre functions of imaginary arguments. The solution of each set of triple integral equations involving associated Legendre functions is reduced to a Fredholm integral equation of the second kind which can be solved numerically.B. M. Singh, J. Rokne, and R. S. Dhaliwal© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/279691This paper finds some lower and upper bounds for the essential norm of the weighted composition operator from α-Bloch spaces to the weighted-type space Hμ∞ on the unit ball for the case α≥1.Stevo Stević© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/840387We establish two inequalities concerning the weakly convergent sequence coefficient and other parameters, which enable us to obtain some sufficient conditions for normal structure.Hongwei Jiao and Yunrui Guo© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/295307We will study a new q-analogue of Bernoulli polynomials associated with p-adic q-integrals. Furthermore, we examine the Hurwitz-type q-zeta functions, replacing p-adic rational integers x with a q-analogue [x]q for a p-adic number q with |q−1|p<1, which interpolate q-analogue of Bernoulli polynomials.Lee-Chae Jang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/914367Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively. However, they have not dealt with congruence properties for these numbers entirely. Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials. Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers. In this paper, we study the new symmetries of the q-Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results. By using our symmetries for the q-Bernoulli polynomials, we can obtain some interesting relationships between q-Bernoulli numbers and polynomials.Taekyun Kim© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/371632A stage-structured three-species predator-prey model with Beddington-DeAngelis and Holling II functional response is introduced. Based on the comparison theorem, sufficient and necessary conditions which guarantee the predator and the prey species to be permanent are obtained. An example is also presented to illustrate our main results.Can-Yun Huang, Min Zhao, and Hai-Feng Huo© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/793297We give the existence of multiple twisted p-adic q-Euler ζ-functions and l-functions, which are generalization of the twisted p-adic (h,q)-zeta functions and twisted p-adic (h,q)-Euler l-functions in the work of Ozden and Simsek (2008).Min-Soo Kim, Taekyun Kim, and Jin-Woo Son© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/898471The main purpose of this paper is to study the distribution of Genocchi polynomials. Finally, we construct the Genocchi zeta function which interpolates Genocchi polynomials at negative integers.Seog-Hoon Rim, Kyoung Ho Park, and Eun Jung Moon© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/672618Using the fixed point method, we prove the generalized Hyers-Ulam stability of C∗-algebra homomorphisms and of generalized derivations on C∗-algebras for the following functional equation of Apollonius type ∑i=1nf(z−xi)=−(1/n)∑1≤i<j≤nf(xi+xj)+nf(z−(1/n2)∑i=1nxi).Fridoun Moradlou, Hamid Vaezi, and Choonkil Park© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/136592The functional inequality ‖f(x)+2f(y)+2f(z)‖≤‖2f(x/2+y+z)‖+ϕ  (x,y,z) (x,y,z∈G) is investigated, where G is a group divisible by 2,f:G→X and ϕ:G3→[0,∞) are mappings, and X is a Banach space. The main result of the paper states that the assumptions above together with (1) ϕ(2x,−x,0)=0=ϕ(0,x,−x) (x∈G) and (2) limn→∞(1/2n)ϕ(2n+1x,2ny,2nz)=0, or limn→∞2nϕ(x/2n−1,y/2n,z/2n)=0  (x,y,z∈G), imply that f is additive. In addition, some stability theorems are proved.Jaiok Roh and Ick-Soon Chang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/404636This paper gives some sufficient conditions for an analytic function to belong to the space consisting of all analytic functions f on the unit disk such lim|a|→1∫ D|f′(z)|p(1−|z|2)qK(g(z,a))dA(z)=0.Xiaoge Meng© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/459310Let ℂ≥0:={s∈ℂ∣Re⁡(s)≥0}, and let 𝒲+ denote the ring of all functions f:ℂ≥0→ℂ such that f(s)=fa(s)+∑k=0∞fke−stk (s∈ℂ≥0), where fa∈L1(0,∞), (fk)k≥0∈ℓ1, and  0=t0<t1<t2<⋯ equipped with pointwise operations. (Here ⋅^ denotes the Laplace transform.) It is shown that the ring 𝒲+ is not coherent, answering a question of Alban Quadrat. In fact, we present two principal ideals in the domain 𝒲+ whose intersection is not finitely generated.Amol Sasane© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/632473We study the h-stability of dynamic equations on time scales, without the regressivity condition on the right-hand side of dynamic equations. This means that we can include noninvertible difference equations into our results.Sung Kyu Choi, Yoon Hoe Goo, and Namjip Koo© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/605807Let Bn be the unit ball of Cn, H(Bn) the space of all holomorphic functions in Bn. Let u∈H(Bn) and α be a holomorphic self-map of Bn. For f∈H(Bn), the weigthed composition operator uCα is defined by (uCαf)(z)=u(z)f(α(z)),z∈Bn. The boundedness and compactness of the weighted composition operator on some weighted spaces on the unit ball are studied in this paper.Xiaohong Fu and Xiangling Zhu© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/360517We prove that a two-variable p-adic lq-function has the series expansion lp,q(s,t,χ)=([2]q/[2]F)∑a=1,(p,a)=1F(−1)a(χ(a)qa/〈a+pt〉s)∑m=0∞(−sm)(F/〈a+pt〉)mEm,qF* which interpolates the values lp,q(−n,t,χ)=En,χn,q∗(pt)−pnχn(p)([2]q/[2]qp)En,χn,qp∗(t), whenever n is a nonpositive integer. The proof of this original construction is due to Kubota and Leopoldt in 1964, although the method given in this note is due to Washington.Min-Soo Kim, Taekyun Kim, D. K. Park, and Jin-Woo Son© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/135873Let δX(ϵ) and R(1,X) be the modulus of convexity and the Domínguez-Benavides coefficient, respectively. According to these two geometric parameters, we obtain a sufficient condition for normal structure, that is, a Banach space X has normal structure if 2δX(1+ϵ)>max{(R(1,x)-1)ϵ,1-(1-ϵ/R(1,X)-1)} for some ϵ∈[0,1] which generalizes the known result by Gao and Prus.Hongwei Jiao, Yunrui Guo, and Fenghui Wang© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/304539In 2008, Jang et al. constructed generating functions of the multiple twisted Carlitz's type q-Bernoulli polynomials and obtained the distribution relation for them. They also raised the following problem: “are there analytic multiple twisted Carlitz's type q-zeta functions which interpolate multiple twisted Carlitz's type q-Euler (Bernoulli) polynomials?” The aim of this paper is to give a partial answer to this problem. Furthermore we derive some interesting identities related to twisted q-extension of Euler polynomials and multiple twisted Carlitz's type q-Euler polynomials.Min-Soo Kim, Taekyun Kim, and Jin-Woo Son© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/578417We prove that the semilinear elliptic equation −Δu=f(u), in Ω, u=0, on ∂Ω has a positive solution when the nonlinearity f belongs to a class which satisfies μtq≤f(t)≤Ctp at infinity and behaves like tq near the origin, where 1<q<(N+2)/(N−2) if N≥3 and 1<q<+∞ if N=1,2. In our approach, we do not need the Ambrosetti-Rabinowitz condition, and the nonlinearity does not satisfy any hypotheses such those required by the blowup method. Furthermore, we do not impose any restriction on the growth of p.Claudianor O. Alves and Marco A. S. Souto© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/845724The authors introduce new classes of analytic functions in the open unit disc which are defined by using multiplier transformations. The properties of these classes will be studied by using techniques involving the Briot-Bouquet differential subordinations. Also an integral transform is established.Adriana Cătaş, Georgia Irina Oros, and Gheorghe Oros© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/742040We derive two sets of explicit homogeneous algebraic constraint-preserving boundary conditions for the second-order in time reduction of the linearized Baumgarte-Shapiro-Shibata-Nakamura (BSSN) system. Our second-order reduction involves components of the linearized extrinsic curvature only. An initial-boundary value problem for the original linearized BSSN system is formulated and the existence of the solution is proved using the properties of the reduced system. A treatment is proposed for the full nonlinear BSSN system to construct constraint-preserving boundary conditions without invoking the second order in time reduction. Energy estimates on the principal part of the BSSN system (which is first order in temporal and second order in spatial derivatives) are obtained. Generalizations to the case of nonhomogeneous boundary data are proposed.Alexander M. Alekseenko© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/792160The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain integral operators defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also considered.Oh Sang Kwon and Nak Eun Cho© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/241736A molecular motor utilizes chemical free energy to generate a unidirectional motion through the viscous fluid. In many experimental settings and biological settings, a molecular motor is elastically linked to a cargo. The stochastic motion of a molecular motor-cargo system is governed by a set of Langevin equations, each corresponding to an individual chemical occupancy state. The change of chemical occupancy state is modeled by a continuous time discrete space Markov process. The probability density of a motor-cargo system is governed by a two-dimensional Fokker-Planck equation. The operation of a molecular motor is dominated by high viscous friction and large thermal fluctuations from surrounding fluid. The instantaneous velocity of a molecular motor is highly stochastic: the past velocity is quickly damped by the viscous friction and the new velocity is quickly excited by bombardments of surrounding fluid molecules. Thus, the theory for macroscopic motors should not be applied directly to molecular motors without close examination. In particular, a molecular motor behaves differently working against a viscous drag than working against a conservative force. The Stokes efficiency was introduced to measure how efficiently a motor uses chemical free energy to drive against viscous drag. For a motor without cargo, it was proved that the Stokes efficiency is bounded by 100% [H. Wang and G. Oster, (2002)]. Here, we present a proof for the general motor-cargo system.Hongyun Wang and Hong Zhou© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/232187The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)∑l=0∞∑d0+d1+⋯+dk=k−1,di∈ℕ(−1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k.Leechae Jang and Taekyun Kim© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/581582For s∈ℂ, the Euler zeta function and the Hurwitz-type Euler zeta function are defined by ζE(s)=2∑n=1∞((−1)n/ns), and ζE(s,x)=2∑n=0∞((−1)n/(n+x)s). Thus, we note that the Euler zeta functions are entire functions in whole complex s-plane, and these zeta functions have the values of the Euler numbers or the Euler polynomials at negative integers. That is, ζE(−k)=Ek∗, and ζE(−k,x)=Ek∗(x). We give some interesting identities between the Euler numbers and the zeta functions. Finally, we will give the new values of the Euler zeta function at positive even integers.Taekyun Kim© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/962849We introduce a q-analogues of Wright function and its auxiliary functions as Barnes integral representations and series expansion. The relations between q-analogues of Wright function and some other functions are investigated.Moustafa El-Shahed and Ahmed Salem© 2009, Hindawi Publishing Corporation. All rights reserved.http://www.hindawi.com/GetArticle.aspx?doi=10.1155/2008/178534We are concerned with fully nonlinear uniformly elliptic operators with a superlinear gradient term. We look for local estimates, such as weak Harnack inequality and local maximum principle, and their extension up to the boundary. As applications, we deduce ABP-type estimates and weak maximum principles in general unbounded domains, a strong maximum principle, and a Liouville-type theorem.M. E. Amendola, L. Rossi, and A. Vitolo© 2009, Hindawi Publishing Corporation. All rights reserved.