Authors:Jun LIU; Dachun YANG; Wen YUAN Pages: 1 - 33 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Jun LIU, Dachun YANG, Wen YUAN Let p∈ (0,1], q ∈(0,∞] and A be a general expansive matrix on ℝ n . Let H A p , q ( ℝ n ) be the anisotropic Hardy-Lorentz spaces associated with A defined via the non-tangential grand maximal function. In this article, the authors characterize H A p , q ( ℝ n ) in terms of the Lusin-area function, the Littlewood-Paley g-function or the Littlewood-Paley g λ *-function via first establishing an anisotropic Fefferman-Stein vector-valued inequality in the Lorentz space L p,qℝ n . All these characterizations are new even for the classical isotropic Hardy-Lorentz spaces on ℝ n . Moreover, the range of λ in the g λ *-function characterization of H A p , q ( ℝ n ) coincides with the best known one in the classical Hardy space H p ( ℝ n ) or in the anisotropic Hardy space H A p ( ℝ n ) .

Authors:Jing ZHANG; Yongqian ZHANG Pages: 34 - 56 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Jing ZHANG, Yongqian ZHANG We study the initial-boundary value problem for the one dimensional Euler-Boltzmann equation with reflection boundary condition. For initial data with small total variation, we use a modified Glimm scheme to construct the global approximate solutions (UΔt,d, IΔt,d ) and prove that there is a subsequence of the approximate solutions which is convergent to the global solution.

Authors:Hangjin JIANG; Qiongli WU Pages: 57 - 72 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Hangjin JIANG, Qiongli WU In this paper, we proposed a new statistical dependency measure for two random vectors based on copula, called copula dependency coefficient (CDC). The CDC is proved to be robust to outliers and easy to be implemented. Especially, it is powerful and applicable to high-dimensional problems. All these properties make CDC practically important in related applications. Both experimental and application results show that CDC is a good robust dependence measure for association detecting.

Authors:Xian-jia WANG; Rui DONG; Lin CHEN Pages: 73 - 92 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Xian-jia WANG, Rui DONG, Lin CHEN Natural selection opposes the evolution of cooperation unless specific mechanisms are at work in Prisoner's Dilemma. By taking advantage of the modern control theory, the controller design is discussed and the optimal control is designed for promoting cooperation based on the recent advances in mechanisms for the evolution of cooperation. Two control strategies are proposed: compensation control strategy for the cooperator when playing against a defector and reward control strategy for cooperator when playing against a cooperator. The feasibility and effectiveness of these control strategies for promoting cooperation in different stages are analyzed. The reward for cooperation can't prevent defection from being evolutionary stable strategy (ESS). On the other hand, compensation for the cooperator can't prevent defection from emerging and sustaining. By considering the effect and the cost, an optimal control scheme with constraint on the admissible control set is put forward. By analyzing the special nonlinear system of replicator dynamics, the exact analytic solution of the optimal control scheme is obtained based on the maximum principle. Finally, the effectiveness of the proposed method is illustrated by examples.

Authors:Meiman SUN; Guozheng YAN Pages: 110 - 124 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Meiman SUN, Guozheng YAN In this paper we consider a kind of exterior transmission problem in which the refractive index n(x) is a piecewise positive constant. Through establishing an equivalent boundary integral system, we obtain that the set of exterior transmission eigenvalues is a discrete set. Furthermore, we prove that there does not exist a transmission eigenvalue under some conditions.

Authors:Yingbo LIU; Ingo WITT Pages: 125 - 150 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Yingbo LIU, Ingo WITT For the 2-D quasilinear wave equation ( ∂ t 2 - Δ x ) u + ∑ i , j = 0 2 g i j ( ∂ u ) ∂ i j u = 0 satisfying null condition or both null conditions, a blowup or global existence result has been shown by Alinhac. In this paper, we consider a more general 2-D quasilinear wave equation ( ∂ t 2 - Δ x ) u + ∑ i , j = 0 2 g i j ( u , ∂ u ) ∂ i j u = 0 satisfying null conditions with small initial data and the coefficients depending simultaneously on u and ∂u. Through construction of an approximate solution, combined with weighted energy integral method, a quasi-global or global existence solution are established by continuous induction.

Authors:Lixin CHENG; Sijie LUO Pages: 151 - 156 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Lixin CHENG, Sijie LUO In this paper, we show that if an Asplund space X is either a Banach lattice or a quotient space of C(K), then it can be equivalently renormed so that the set of norm-attaining functionals contains an infinite dimensional closed subspace of X * if and only if X * contains an infinite dimensional reflexive subspace, which gives a partial answer to a question of Bandyopadhyay and Godefroy.

Authors:Zhiming WANG Pages: 157 - 168 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Zhiming WANG For a stochastic differential equation with non-Lipschitz coefficients, we construct, by Euler scheme, a measurable flow of the solution, and we prove the solution is a Markov process.

Authors:Yashan ZHANG Pages: 169 - 176 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Yashan ZHANG We prove that, under a semi-ampleness type assumption on the twisted canonical line bundle, the conical Kähler-Ricci flow on a minimal elliptic Kähler surface converges in the sense of currents to a generalized conical Kähler-Einstein on its canonical model. Moreover, the convergence takes place smoothly outside the singular fibers and the chosen divisor.

Authors:Wei SONG; Lin LI Pages: 177 - 186 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Wei SONG, Lin LI Most known results on polynomial-like iterative equations are concentrated to increasing solutions. Without the uniformity of orientation and monotonicity, it becomes much more difficult for decreasing cases. In this paper, we prove the existence of decreasing solutions for a general iterative equation, which was proposed as an open problem in [J. Zhang, L. Yang, W. Zhang, Some advances on functional equations, Adv. Math. (China) 24 (1995) 385–405] (or [W. Zhang, J.A. Baker, Continuous solutions of a polynomial-like iterative equation with variable coefficients, Ann. Polon. Math. 73 (2000) 29–36]).

Authors:Chengzhi WANG; Mingshu ZHANG; Caidi ZHAO Pages: 187 - 202 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Chengzhi WANG, Mingshu ZHANG, Caidi ZHAO This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

Authors:Haiping NIU; Shu WANG Pages: 203 - 219 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Haiping NIU, Shu WANG We study the singular structure of a family of two dimensional non-self-similar global solutions and their interactions for quasilinear hyperbolic conservation laws. For the case when the initial discontinuity happens only on two disjoint unit circles and the initial data are two different constant states, global solutions are constructed and some new phenomena are discovered. In the analysis, we first construct the solution for 0 ≤ t < T *. Then, when T *≤ t < T', we get a new shock wave between two rarefactions, and then, when t>T', another shock wave between two shock waves occurs. Finally, we give the large time behavior of the solution when t→∞. The technique does not involve dimensional reduction or coordinate transformation.

Authors:Kuo-Shou CHIU Pages: 220 - 236 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Kuo-Shou CHIU In this paper, we investigate the existence, uniqueness and the asymptotic equivalence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type (DEPCAG). This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

Authors:Hairong LIU Pages: 237 - 247 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Hairong LIU In this paper, the author computes the dimension of space of homogeneous Grushin-harmonic functions, and give an orthogonal basis of them. Moreover, the author describes the nodal curves of these homogenous Grushin-harmonic basis. As an application of the orthogonal basis, the author proves a Liouville-type theorem for the Grushin operator, that is the Grushin-harmonic functions are homogeneous polynomials provided that the frequency of such a function is equal to some constant.

Authors:Xiaojuan DUAN Pages: 269 - 288 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Xiaojuan DUAN In this paper, we explicitly construct some rotationally symmetric gradient pseudo-Kähler-Ricci solitons which depend on some parameters, on some line bundles and other bundles over projective spaces. We also discuss the “phase change” phenomenon caused by the variation of parameters.

Authors:Zhaoxing YANG; Guobao ZHANG Pages: 289 - 302 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Zhaoxing YANG, Guobao ZHANG This paper is concerned with the stability of traveling wavefronts for a population dynamics model with time delay. Combining the weighted energy method and the comparison principle, the global exponential stability of noncritical traveling wavefronts (waves with speeds c>c *, where c=c * is the minimal speed) is established, when the initial perturbations around the wavefront decays to zero exponentially in space as x→ − ∞, but it can be allowed arbitrary large in other locations, which improves the results in [9, 18, 21].

Authors:Santhosh GEORGE; C.D. SREEDEEP Pages: 303 - 314 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Santhosh GEORGE, C.D. SREEDEEP In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general Hölder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter.

Authors:Qiang TU; Wenyi CHEN Pages: 315 - 332 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Qiang TU, Wenyi CHEN In this paper we study integer multiplicity rectifiable currents carried by the subgradient (subdifferential) graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.

Authors:Hassan Eltayeb GADAIN Pages: 333 - 346 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Hassan Eltayeb GADAIN In this paper, the modification of double Laplace decomposition method is proposed for the analytical approximation solution of a coupled system of pseudo-parabolic equation with initial conditions. Some examples are given to support our presented method. In addition, we prove the convergence of double Laplace transform decomposition method applied to our problems.

Authors:Yajuan XU; Guojing WANG Pages: 347 - 360 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Yajuan XU, Guojing WANG In this paper, we study the price of catastrophe options with counterparty credit risk in a reduced form model. We assume that the loss process is generated by a doubly stochastic Poisson process, the share price process is modeled through a jump-diffusion process which is correlated to the loss process, the interest rate process and the default intensity process are modeled through the Vasicek model. We derive the closed form formulae for pricing catastrophe options in a reduced form model. Furthermore, we make some numerical analysis on the explicit formulae.

Authors:Hongwei LIU; Yijun HU; Linxiao WEI Pages: 361 - 376 Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Hongwei LIU, Yijun HU, Linxiao WEI In this paper, from the viewpoint of the time value of money, we study the risk measures for portfolio vectors with discount factor. Cash subadditive risk measures for portfolio vectors are proposed. Representation results are given by two different methods which are convex analysis and enlarging space. Especially, the method of convex analysis make the line of reasoning and the representation result be simpler. Meanwhile, spot and forward risk measures for portfolio vectors are also introduced, and the relationships between them are investigated.

Authors:Junfeng LIU; Ciprian A. TUDOR Pages: 1545 - 1566 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Junfeng LIU, Ciprian A. TUDOR In this paper we study a fractional stochastic heat equation on R d ( d ≥ 1 ) with additive noise ∂ ∂ t u ( t , x ) = d δ _ α _ u ( t , x ) + b ( u ( t , x ) ) + W ˙ H ( t , x ) where d δ _ α _ is a nonlocal fractional differential operator and W ˙ H is a Gaussian-colored noise. We show the existence and the uniqueness of the mild solution for this equation. In addition, in the case of space dimension d=1, we prove the existence of the density for this solution and we establish lower and upper Gaussian bounds for the density by Malliavin calculus.

Authors:Samir KALLEL Pages: 1567 - 1593 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Samir KALLEL The aim of this paper is to prove duality and reflexivity of generalized Lipschitz spaces Λ α , p , q k ( R ) , α ∈ R and 1 ≤ p , q ≤ ∞ , in the context of Dunkl harmonic analysis.

Authors:Yanli HAN; Yan GAO Pages: 1594 - 1606 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Yanli HAN, Yan GAO This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points (extreme points) and the existing ones need to verify all points in the bounded polyhedron.

Authors:Xiang GAO; Jihua MA Pages: 1607 - 1618 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Xiang GAO, Jihua MA This paper is concerned with the Diophantine properties of the sequence { ξ θ n } , where 1 ≤ ξ < θ and θ is a rational or an algebraic integer. We establish a combinatorial proposition which can be used to study such two cases in the same manner. It is shown that the decay rate of the Fourier transforms of self-similar measures μ λ with λ = θ - 1 as the uniform contractive ratio is logarithmic. This generalizes some results of Kershner and Bufetov-Solomyak, who consider the case of Bernoulli convolutions. As an application, we prove that μ λ almost every x is normal to any base b ≥ 2, which implies that there exist infinitely many absolute normal numbers on the corresponding self-similar set. This can be seen as a complementary result of the well-known Cassels-Schmidt theorem.

Authors:Zi WANG; Yuwen WANG Pages: 1619 - 1631 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zi WANG, Yuwen WANG In this paper, we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is “the generalized Neumann lemma” which is quite different from the method in [12] where “the generalized Banach lemma” was used. By the method of the perturbation analysis of bounded linear operators, we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.

Authors:Zhensheng GAO; Zhong TAN Pages: 1632 - 1638 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zhensheng GAO, Zhong TAN In this paper, we consider the short time classical solution to a simplified hydrodynamic flow modeling incompressible, nematic liquid crystal materials in R 3 . We establish a criterion for possible breakdown of such solutions at a finite time. More precisely, if (u,d) is smooth up to time T provided that ∫ 0 T ∇ × u ( t , ⋅ ) B M O ( R 3 ) + ∇ d ( t , ⋅ ) L 4 ( R 3 ) 8 d t < ∞ .

Authors:Hua CHEN; Hongge CHEN; Yirui DUAN; Xin HU Pages: 1653 - 1664 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Hua CHEN, Hongge CHEN, Yirui DUAN, Xin HU Let Ω be a bounded open domain in R n with smooth boundary ∂Ω, X = ( X 1 , X 2 , ⋯ , X m ) be a system of real smooth vector fields defined on Ω and the boundary ∂Ω is non-characteristic for X. If X satisfies the Hörmander's condition, then the vector field is finitely degenerate and the sum of square operator Δ X = ∑ j = 1 m X j 2 is a finitely degenerate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators ΔX on Ω.

Authors:Zhiying DENG; Yisheng HUANG Pages: 1665 - 1684 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Zhiying DENG, Yisheng HUANG This paper is dedicated to studying the existence and multiplicity of symmetric solutions for a class of biharmonic elliptic systems with critical homogeneous nonlinearity in R N . By virtue of variational methods and the symmetric criticality principle of Palais, we establish several existence and multiplicity results of G-symmetric solutions under certain appropriate hypotheses on the parameters and the weighted functions.

Authors:Lingyun GAO; Manli LIU Pages: 1685 - 1694 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Lingyun GAO, Manli LIU By use of Nevanlinna value distribution theory, we will investigate the properties of meromorphic solutions of two types of systems of composite functional equations and obtain some results. One of the results we get is about both components of meromorphic solutions on the system of composite functional equations satisfying Riccati differential equation, the other one is property of meromorphic solutions of the other system of composite functional equations while restricting the growth.

Authors:Jongrak LEE Pages: 1695 - 1704 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Jongrak LEE In this paper we consider the block Toeplitz operators T Phi on the weighted Bergman space A α 2 ( D , C n ) and we give a necessary and sufficient condition for the hyponormality of block Toeplitz operators with symbol in the class of functions Φ = F + G * with matrix-valued polynomial functions F and G with degree 2.

Authors:Suiming SHANG; Yu TIAN; Yajing ZHANG Pages: 1705 - 1726 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Suiming SHANG, Yu TIAN, Yajing ZHANG In this paper, the stability and bifurcation behaviors of a predator-prey model with the piecewise constant arguments and time delay are investigated. Technical approach is fully based on Jury criterion and bifurcation theory. The interesting point is that the model will produce two different branches by limiting branch parameters of different intervals. Besides, image simulation is also given.

Authors:Iz-iddine EL-FASSI; Janusz BRZDĘK; Abdellatif CHAHBI; Samir KABBAJ Pages: 1727 - 1739 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Iz-iddine EL-FASSI, Janusz BRZDĘK, Abdellatif CHAHBI, Samir KABBAJ We present results on approximate solutions to the biadditive equation f ( x + y , z - w ) + f ( x - y , z + w ) = 2 f ( x , z ) - 2 f ( y , w ) on a restricted domain. The proof is based on a quite recent fixed point theorem in some function spaces. Our main results state that, under some weak natural assumptions, functions satisfying the equation approximately (in some sense) must be actually solutions to it. In this way we obtain inequalities characterizing biadditive mappings and inner product spaces. Our outcomes are connected with the well known issues of Ulam stability and hyperstability.

Authors:Tianyuan XU; Chunhua JIN; Shanming JI Pages: 1740 - 1760 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Tianyuan XU, Chunhua JIN, Shanming JI This paper deals with the existence and the asymptotic behavior of discontinuous traveling wave entropy solutions for a modified Allen-Cahn model, in which, the usual Ficken-based model for phase transition is replaced with a more physical model with nonlinear diffusive flux. The discontinuous traveling waves correspond to the discontinuous phase transition phenomena.

Authors:Dinghuai WANG; Jiang ZHOU; Wenyi CHEN Pages: 1761 - 1774 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Dinghuai WANG, Jiang ZHOU, Wenyi CHEN This manuscript addresses Muckenhoupt A p weight theory in connection to Morrey and BMO spaces. It is proved that ω belongs to Muckenhoupt A p class, if and only if Hardy-Littlewood maximal function M is bounded from weighted Lebesgue spaces L p(ω) to weighted Morrey spaces M q p ( ω ) for 1 < q < p < ∞. As a corollary, if M is (weak) bounded on M q p ( ω ) , then ω ∈ A p. The A p condition also characterizes the boundedness of the Riesz transform R j and convolution operators T ɛ on weighted Morrey spaces. Finally, we show that ω ∈ A p if and only if ω ∈ B M O p ′ ( ω ) for 1 ≤ p < ∞ and 1/p+1/p′=1.

Authors:Lijuan WANG Pages: 1775 - 1790 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Lijuan WANG The large time behavior of solutions to the two-dimensional perturbed Hasegawa-Mima equation with large initial data is studied in this paper. Based on the time-frequency decomposition and the method of Green function, we not only obtain the optimal decay rate but also establish the pointwise estimate of global classical solutions.

Authors:Shenlian LI; Xuejun ZHANG; Si XU Pages: 1791 - 1802 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Shenlian LI, Xuejun ZHANG, Si XU Let Ω be a bounded symmetric domain in Cn. The purpose of this article is to define and characterize the general function space F(p,q,s) on Ω. Characterizing functions in the F(p,q,s) space is a work of considerable interest nowadays. In this article, the authors give several equivalent descriptions of the functions in the F(p,q,s) space on Ω in terms of fractional differential operators. At the same time, the authors give the relationship between F(p,q,s) space and Bloch type space on Ω too.

Authors:Fanchao KONG; Zhiguo LUO Pages: 1803 - 1816 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Fanchao KONG, Zhiguo LUO This paper is concerned with the non-Newtonian filtration equations with nonlinear sources and a time-varying delay. By an extension of Mawhin's continuation theorem and some analysis methods, several sufficient conditions ensuring the existence of solitary wave and periodic wave solutions are obtained. Some corresponding results in the literature are improved and extended. An example is given to illustrate the effectiveness of our results.

Authors:Yanyan CUI; Chaojun WANG; Hao LIU Pages: 1817 - 1829 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Yanyan CUI, Chaojun WANG, Hao LIU In this paper, we extend the Roper-Suffridge extension operator in complex Banach space, and prove that the extended Roper-Suffridge operators preserve the properties of the subclasses of spirallike mappings on the unit ball in complex Banach spaces. Thereby, we promote the conclusions to the cases in complex Hilbert spaces. The conclusions provide new approaches to construct these subclasses of spirallike mappings in several complex variables.

Authors:Shuangting LAN; Zongxuan CHEN Pages: 1830 - 1840 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Shuangting LAN, Zongxuan CHEN In this paper, we investigate difference Painlevé IV equations, and obtain some results on Nevanlinna exceptional values of transcendental meromorphic solutions w(z) with finite order, their differences Δ w ( z ) = w ( z + 1 ) - w ( z ) and divided differences Δ w ( z ) w ( z ) .

Authors:Rong DONG; Dongsheng LI Pages: 1841 - 1860 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Rong DONG, Dongsheng LI In this paper, a type of nonlinear elliptic equations with rapidly oscillatory coefficients is investigated. By compactness methods, we show uniform Hölder estimates of solutions in a C 1 bounded domain.

Authors:Daochun SUN; Yingying HUO; Yinying KONG; Fujie CHAI Pages: 1861 - 1869 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Daochun SUN, Yingying HUO, Yinying KONG, Fujie CHAI In this paper, we introduce the integration of algebroidal functions on Riemann surfaces for the first time. Some properties of integration are obtained. By giving the definition of residues and integral function element, we obtain the condition that the integral is independent of path. At last, we prove that the integral of an irreducible algebroidal function is also an irreducible algebroidal function if all the residues at critical points are zeros.

Authors:Quanqing LI; Xian WU Pages: 1870 - 1880 Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Quanqing LI, Xian WU In this paper, we study the following generalized quasilinear Schrödinger equations with critical or supercritical growths - div ( g 2 ( u ) ∇ u ) + g ( u ) g ′ ( u ) ∇ u 2 + V ( x ) u = f ( x , u ) + λ u p - 2 u , x ∈ R N , where λ > 0 , N ≥ 3 , g : R → R + is a C 1 even function, g ( 0 ) = 1 , g ′ ( s ) ≥ 0 for all s ≥ 0 , lim s → + ∞ g ( s ) s α - 1 : β > 0 for some α ≥ 1 and ( α - 1 ) g ( s ) > g ′ ( s ) s for all s > 0 and p ≥ α2*. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ > 0 using a change of variables and variational method.

Authors:Hakho HONG; Teng WANG Pages: 1177 - 1208 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Hakho HONG, Teng WANG For the general gas including ideal polytropic gas, we study the zero dissipation limit problem of the full 1-D compressible Navier-Stokes equations toward the superposition of contact discontinuity and two rarefaction waves. In the case of both smooth and Riemann initial data, we show that if the solutions to the corresponding Euler system consist of the composite wave of two rarefaction wave and contact discontinuity, then there exist solutions to Navier-Stokes equations which converge to the Riemman solutions away from the initial layer with a decay rate in any fixed time interval as the viscosity and the heat-conductivity coefficients tend to zero. The proof is based on scaling arguments, the construction of the approximate profiles and delicate energy estimates. Notice that we have no need to restrict the strengths of the contact discontinuity and rarefaction waves to be small.

Authors:Mina DINARVAND Pages: 1209 - 1220 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Mina DINARVAND In this paper, we introduce a new geometric constant C N J ( p ) ( a , X ) of a Banach space X, which is closely related to the generalized von Neumann-Jordan constant and analyze some properties of the constant. Subsequently, we present several sufficient conditions for normal structure of a Banach space in terms of this new constant, the generalized James constant, the generalized García-Falset coefficient and the coefficient of weak orthogonality of Sims. Our main results of the paper generalize some known results in the recent literature.

Authors:Turdebek N. Bekjan Pages: 1221 - 1229 Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Turdebek N. Bekjan Let M be a σ-finite von Neumann algebra equipped with a normal faithful state φ, and let A be a maximal subdiagonal algebra of M. We proved a Szegö type factorization theorem for the Haagerup noncommutative Hp-spaces.

Authors:Kwok-Pun Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Kwok-Pun HO We introduce the martingale Morrey spaces built on Banach function spaces. We establish the Doob's inequality, the Burkholder-Gundy inequality and the boundedness of martingale transforms for our martingale Morrey spaces. We also introduce the martingale block spaces. By the Doob's inequality on martingale block spaces, we obtain the Davis' decompositions for martingale Morrey spaces.

Authors:ZHU Abstract: Publication date: January 2018 Source:Acta Mathematica Scientia, Volume 38, Issue 1 Author(s): Li ZHU In this paper we obtain the Plancherel formula for the spaces of L 2-sections of the line bundles over the pseudo-Riemannian symmetric space G/H where G = SL(n + 1, ℝ) and H = S(GL(1, ℝ) × GL(n 1, ℝ)). The Plancherel formula is given in an explicit form by means of spherical distributions associated with the character χλ of the subgroup H. We follow the method of Faraut, Kosters and van Dijk.

Authors:Justyna Abstract: Publication date: November 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 6 Author(s): Stanisław MIGÓRSKI, Justyna OGORZAŁY We study a new class of elliptic variational-hemivariational inequalities arising in the modelling of contact problems for elastic ideally locking materials. The contact is described by the Signorini unilateral contact condition and the friction is modelled by the nonmonotone multivalued subdifferential condition which depends on the slip. The problem is governed by a nonlinear elasticity operator, the subdifferential of the indicator function of a convex set which describes the locking constraints and a nonconvex locally Lipschitz friction potential. The result on existence and uniqueness of solution to the inequality is shown. The proof is based on a surjectivity result for maximal monotone and pseudomonotone operators combined with the application of the Banach contraction principle.

Authors:Feng Abstract: Publication date: September 2017 Source:Acta Mathematica Scientia, Volume 37, Issue 5 Author(s): Feng SU The theory of integration to mathematical analysis is so important that many mathematicians continue to develop new theory to enlarge the class of integrable functions and simplify the Lebesgue theory integration. In this paper, by slight modifying the definition of the Henstock integral which was introduced by Jaroslav Kurzweil and Ralph Henstock, we present a new definition of integral on fractal sets. Furthermore, its integrability has been discussed, and the relationship between differentiation and integral is also established. As an example, the integral of Cantor function on Cantor set is calculated.