On the Complexity of the Julia Sets of Rational Functions

ＯｎｔｈｅＣｏｍｐｌｅｘｉｔｙｏｆｔｈｅＪｕｌｉａＳｅｔｓｏｆＲａｔｉｏｎａｌＦｕｎｃｔｉｏｎｓＱｉａｏＪｉａｎｙｏｎｇ（乔建永）（ＩｎｓｔｉｔｕｔｅｏｆＭａｔｈｅｍａｔｉｃｓ，ＡｃａｄｅｍｉａＳｉｎｉｃａ，Ｂｅｉｊｉｎｇ，１０００８０）Ｃｏｍｍｕｎ...     

A Remark on the Intrinsic Rigidity of Compact Minimal Submanifolds in A Sphere

ＡＲｅｍａｒｋｏｎｔｈｅＩｎｔｒｉｎｓｉｃＲｉｇｉｄｉｔｙｏｆＣｏｍｐａｃｔＭｉｎｉｍａｌＳｕｂｍａｎｉｆｏｌｄｓｉｎＡＳｐｈｅｒｅ￥ＳｈｕＳｈｉｃｈａｎｇ（舒世昌）（ｉａＸｉｎｇｑｉｎ（贾兴琴）（ＸｉａｎｙａｎｇＴｅａｃｈｅｒｓ＇Ｃｏｌｌｅｇｅ，７...     

An Interpretation of the Poincare Morphism for Compact Toric Varieties

ＡｎＩｎｔｅｒｐｒｅｔａｔｉｏｎｏｆｔｈｅＰｏｉｎｃａｒéＭｏｒｐｈｉｓｍｆｏｒＣｏｍｐａｃｔＴｏｒｉｃＶａｒｉｅｔｉｅｓ￥Ｊｅａｎ－ＰａｕｌＢＲＡＳＳＥＬＥＴ（ＣＩＲＭ－Ｍａｒｓｅｉｌｌｅ－ＦｒａｎｃｅＳｉＧｍＡＣＮＲＳ，ＣＩＲＭＬｕｍｉｎｙＣａｓ...     

On the Average of Exponents

ＯｎｔｈｅＡｖｅｒａｇｅｏｆＥｘｐｏｎｅｎｔｓＣａｏＨｕｉｚｈｏｎｇ（曹惠中）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｈａｎｄｏｎｇＵｎｉｖｅｒｓｉｔｙ，Ｊｉｎａｎ２５０１００）Ａｂｓｔｒａｃｔ：Ｌｅｔｎ＞１ａｎｄｂｅｔｈｅｐｒｉｍｅｆａ...     

The Interpolation Problem on the Maximal Ideal Space of H~∞

ＴｈｅＩｎｔｅｒｐｏｌａｔｉｏｎＰｒｏｂｌｅｍｏｎｔｈｅＭａｘｉｍａｌＩｄｅａｌＳｐａｃｅｏｆＨ~∞￥ＧｕｏＫｕｎｇｕ（郭坤宇）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ，６１００６４）Ａｂｓ?..     

Reducing Subspaces of Certain Analytic Toeplitz Operators on the Bergman Space

ＲｅｄｕｃｉｎｇＳｕｂｓｐａｃｅｓｏｆＣｅｒｔａｉｎＡｎａｌｙｔｉｃＴｏｅｐｌｉｔｚＯｐｅｒａｔｏｒｓｏｎｔｈｅＢｅｒｇｍａｎＳｐａｃｅ＊）ＳｕｎＳｈａｎｌｉ（孙善利）ａｎｄＷａｎｇＹｕｅｊｉａｎ（王悦健）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉ...     

On the Integral Extension of Lattices

ＯｎｔｈｅＩｎｔｅｇｒａｌＥｘｔｅｎｓｉｏｎｏｆＬａｔｉｃｅｓＨａｎＳｈｉａｎ（韩士安）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＥａｓｔＣｈｉｎａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｓｈａｎｇｈａｉ，２０００６２）ＡｂｓｔｒａｃｔＩｎｔｈｉｓ...     

On the Construction of d-Continuous Modules over Some Special Rings

ＯｎｔｈｅＣｏｎｓｔｒｕｃｔｉｏｎｏｆｄ－ＣｏｎｔｉｎｕｏｕｓＭｏｄｕｌｅｓｏｖｅｒＳｏｍｅＳｐｅｃｉａｌＲｉｎｇｓ￥ＣｈｅｎＪｉｎｊｉａｎ（ＧｕａｎｇｄｏｎｇＮａｔｉｏｎａｌＩｎｓｔｉｔｕｔｅ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｅｐｅｐｅｒ，ｗｅｕｓｉｎｇ...     

Some Results Concerning the Consistency of Ls and LAD Estimates of Multiple Regression（I）

ＳｏｍｅＲｅｓｕｌｔｓＣｏｎｃｅｒｎｉｎｇｔｈｅＣｏｎｓｉｓｔｅｎｃｙｏｆＬｓａｎｄＬＡＤＥｓｔｉｍａｔｅｓｏｆＭｕｌｔｉｐｌｅＲｅｇｒｅｓｓｉｏｎ（Ｉ）ＪｉｎＭｉｎｇｚｈｏｎｇ（金明仲）（ＧｕｉｚｈｏｕＮａｔｉｏｎａｌＣｏｌｌｅｇｅ，Ｇｕｉｙａｎｇ...     

A New Characterization of the Analytic Radon-Nikodym Property for Bounded S

ＡＮｅｗＣｈａｒａｃｔｅｒｉｚａｔｉｏｎｏｆｔｈｅＡｎａｌｙｔｉｃＲａｄｏｎ－ＮｉｋｏｄｙｍＰｒｏｐｅｒｔｙｆｏｒＢｏｕｎｄｅｄＳｕｂｓｅｔｓＢｕＳｈａｎｇｑｕａｎ（步尚全）（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，Ｔｓｉｎｇｈ...     

中心对称与中心交错矩阵几何

应用对称(交错)矩阵几何基本定理,本文证明了域上中心对称(交错)矩阵几何基本定理.     

ZL-amenability and characters for the restricted direct products of finite groups

Let G   be a restricted direct product of finite groups _{Gi}i∈I${\{G_i\}}_{i\in I}$, and let Z?¹(G)${\mathrm{Z}?}^1(G)$ denote the centre of its group algebra. We show that Z?¹(G)${\mathrm{Z}?}^1(G)$ is amenable if and only if _Gi$G_i$ is abelian for all but finitely many i  , and characterize the maximal ideals of Z?¹(G)${\mathrm{Z}?}^1(G)$ which have bounded approximate identities. We also study when an algebra character of Z?¹(G)${\mathrm{Z}?}^1(G)$ belongs to _c0$c_0$ or ?^p${?}^p$ and provide a variety of examples.     

Asymptotic summation of perturbed linear difference systems in critical case

We propose an asymptotic summation method for certain class of linear difference systems. Both the ideas of the centre manifold theory and the averaging method are used to construct the asymptotics for solutions. We illustrate the asymptotic summation method by constructing the asymptotics for solutions of certain higher order scalar difference equation with an oscillatory decreasing coefficient.     

Stability of stationary solutions in models of the Calvin cycle

In this paper results are obtained concerning the number of positive stationary solutions in simple models of the Calvin cycle of photosynthesis and the stability of these solutions. It is proved that there are open sets of parameters in the model of Zhu et al. (2009) for which there exist two positive stationary solutions. There are never more than two isolated positive stationary solutions but under certain explicit special conditions on the parameters there is a whole continuum of positive stationary solutions. It is also shown that in the set of parameter values for which two isolated positive stationary solutions exist there is an open subset where one of the solutions is asymptotically stable and the other is unstable. In related models derived from the work of Grimbs et al. (2011), for which it was known that more than one positive stationary solution exists, it is proved that there are parameter values for which one of these solutions is asymptotically stable and the other unstable. A key technical aspect of the proofs is to exploit the fact that there is a bifurcation where the centre manifold is one-dimensional.     

Properties of the Michaelis-Menten mechanism in phase space

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity. To this end, we show that the slow manifold can be constructed as a centre manifold for a fixed point at infinity.     

Numerical analyses of the boundary effect of radial basis functions in 3D surface reconstruction

Surface reconstruction is very important for surface characterization and graph processing. Radial basis function has now become a popular method to reconstruct 3D surfaces from scattered data. However, it is relatively inaccurate at the boundary region. To solve this problem, a circle of new centres are added outside the domain of interest. The factors that influence the boundary behaviour are analyzed quantitatively via numerical experiments. It is demonstrated that if the new centres are properly located, the boundary problem can be effectively overcome whilst not reducing the accuracy at the interior area. A modified Graham scan technique is introduced to obtain the boundary points from a scattered point set. These boundary points are extended outside with an appropriate distance, and then uniformized to form the new auxiliary centres.      

Derivees logarithmiques pour une s-derivation algebrique

We use the results on the minimal basis of the centre of an Iwahori–Hecke algebra from our earlier work, as well as some additional results on the minimal basis, to describe the image and kernel of the Brauer homomorphism for Iwahori–Hecke algebras defined by L. Jones (Jones, L. Centres of Generic Hecke Algebras; Ph.D. Thesis; University of Virginia, 1987.).

     

Asymptotic Behaviour of Solutions of a Multidimensional Moving Boundary Problem Modeling Tumor Growth

We study a moving boundary problem modeling the growth of multicellular spheroids or in vitro tumors. This model consists of two elliptic equations describing the concentration of a nutrient and the distribution of the internal pressure in the tumor's body, respectively. The driving mechanism of the evolution of the tumor surface is governed by Darcy's law. Finally surface tension effects on the moving boundary are taken into account which are considered to counterbalance the internal pressure. To put our analysis on a solid basis, we first state a local well-posedness result for general initial data. However, the main purpose of our study is the investigation of the asymptotic behaviour of solutions as time goes to infinity. As a result of a centre manifold analysis, we prove that if the initial domain is sufficiently close to a Euclidean ball in the C ^m+μ-norm with m ≥ 3 and μ ∈ (0,1), then the solution exists globally and the corresponding domains converge exponentially fast to some (possibly shifted) ball, provided the surface tension coefficient γ is larger than a positive threshold value γ_*. In the case 0 < γ < γ_* the radially symmetric equilibrium is unstable.     

Restrictions and unfolding of double Hopf bifurcation in functional differential equations

The normal form of a vector field generated by scalar delay-differential equations at nonresonant double Hopf bifurcation points is investigated. Using the methods developed by Faria and Magalhães (J. Differential Equations 122 (1995) 181) we show that (1) there exists linearly independent unfolding parameters of classes of delay-differential equations for a double Hopf point which generically map to linearly independent unfolding parameters of the normal form equations (ordinary differential equations), (2) there are generically no restrictions on the possible flows near a double Hopf point for both general and -symmetric first-order scalar equations with two delays in the nonlinearity, and (3) there always are restrictions on the possible flows near a double Hopf point for first-order scalar delay-differential equations with one delay in the nonlinearity, and in nth-order scalar delay-differential equations (n?2) with one delay feedback.     

Modelling dispersion in laminar and turbulent flows in an open channel based on centre manifolds using 1D-IRBFN method

Centre manifold method is an accurate approach for analytically constructing an advection–diffusion equation (and even more accurate equations involving higher-order derivatives) for the depth-averaged concentration of substances in channels. This paper presents a direct numerical verification of this method with examples of the dispersion in laminar and turbulent flows in an open channel with a smooth bottom. The one-dimensional integrated radial basis function network (1D-IRBFN) method is used as a numerical approach to obtain a numerical solution for the original two-dimensional (2-D) advection–diffusion equation. The 2-D solution is depth-averaged and compared with the solution of the 1-D equation derived using the centre manifolds. The numerical results show that the 2-D and 1-D solutions are in good agreement both for the laminar flow and turbulent flow. The maximum depth-averaged concentrations for the 1-D and 2-D models gradually converge to each other, with their velocities becoming practically equal. The obtained numerical results also demonstrate that the longitudinal diffusion can be neglected compared to the advection.