Further discussion on Kato""s chaos in set-valued discrete systems

For a compact metric space $Y$ and a continuous map $g:Y\rightarrow Y$, the collective accessibility and collectively Kato chaotic of the dynamical system $(Y, g)$ were defined. The relations between topologically weakly mixing and collective accessibility, or strong accessibility, or strongly Kato chaos were studied. Some common properties of $g$ and $\overline{g}$ were given. Where $\overline{g}: \kappa(Y)\rightarrow \kappa(Y)$ is defined as $\overline{g}(B)=g(B)$ for any $B\in\kappa(Y)$, and $\kappa(Y)$ is the collection of all nonempty compact subsets of $Y$. Moreover, it is proved that $g$ is collectively accessible (or strongly accessible) if and only if $\overline{g}$ in $w^{e}$-topology is collectively accessible (or strongly accessible).     

可定向闭曲面上保定向的周期映射

讨论可定向闭曲面上保定向周期映射的共轭类分类问题.Kulkarni(1997)指出:亏格g大于3时,曲面上任意周期大于或等于4g的周期映射共轭于两类周期映射中某个映射的幂.之后Hirose(2010)得到:亏格g大于12时,曲面上任意周期大于或等于3g的周期映射共轭于4类周期映射中某个映射的幂.本文在此基础上研究了周期大于或等于3(g-1)的情形:当亏格g大于21时,得到了和Hirose相似的结论,且找出了更多不能被包含在前面所讲的4类周期映射中的情形.     

H~1-Estimates of the Littlewood-Paley and Lusin Functions for Jacobi Analysis Ⅱ

Let $({\Bbb R}_+,*,\Delta)$ be the Jacobi hypergroup. We introduce analogues of the Littlewood-Paley $g$ function and the Lusin area function for the Jacobi hypergroup and consider their $(H^1, L^1)$ boundedness. Although the $g$ operator for $({\Bbb R}_+,*,\Delta)$ possesses better property than the classical $g$ operator, the Lusin area operator has an obstacle arisen from a second convolution. Hence, in order to obtain the $(H^1, L^1)$ estimate for the Lusin area operator, a slight modification in its form is required.     

Equivalent conditions involving common fixed points for maps on the unit interval

Let be a continuous self-map of the unit interval . Equivalent conditions are given to ensure that has a common fixed point with every continuous map that commutes with on a suitable subset of . This extends a recent result of Gerald Jungck.

     

ON JENSEN’S INEQUALITY FOR g-EXPECTATION

Briand et al.gave a counterexample showing that given g, Jensen‘s inequality for g-expectation usually does not hold in general. This paper proves that Jensen‘s inequality for g-expectation holds in general if and only if the generator g(t,z) is super-homogeneous in z. In particular, g is not necessarily convex in z.     

生成元一致连续的多维倒向随机微分方程的$L^p$解

在生成元~$g$~的第~$i$~个分量~$g_i(t,y,z)$~仅仅依赖于矩阵~$z$~的第~$i$ 行的条件下, Hamad\`{e}ne于2003年证明了生成元一致连续的倒向随机微分 方程的~$L^2$~解的存在性, 其~$L^2$~解的唯一性由范胜君等于2010年得到. 本文进一步地证明了该类倒向随机微分 方程的~$L^p\ (p>1)$~解的存在唯一性.     

给定围长的三圈图的无符号拉普拉斯谱半径

A tricyclic graph G =（V（G）, E（G）） is a connected and simple graph such that｜E（G）｜ = ｜V（G）｜＋2. Let Tg nbe the set of all tricyclic graphs on n vertices with girth g. In this paper, we will show that there exists the unique graph which has the largest signless Laplacian spectral radius among all tricyclic graphs with girth g containing exactly three（resp., four）cycles. And at the same time, we also give an upper bound of the signless Laplacian spectral radius and the extremal graph having the largest signless Laplacian spectral radius in Tg n,where g is even.     

Generalized p(x)-elliptic system with nonlinear physical data

This paper considers the following Dirichlet problem of the form \[-\text{div}\,\big(\Phi(Du-\Theta(u)\big)=v(x)+f(x,u)+\text{div}\,\big(g(x,u)\big),\] which corresponds to a diffusion problem with a source $v$ in moving and dissolving substance, the motion is described by $g$ and the dissolution by $f$. By the theory of Young measure we will prove the existence result in variable exponent Sobolev spaces $W^{1,p(x)}_0(\Omega;\R^m)$.     

单位球加权伯格曼空间上托普里兹算子的乘积

We consider the question for what kind of square integrable holomorphic functions f,g on the unit ball the densely defined products TfTg-are invertible and Fredholm on the weighted Bergman space of the unit ball.We furthermore obtain necessary and sufficient conditions for bounded Haplitz products HfTg-,where f∈L2(Bn,dvα) and g is a square integrable holomorphic function.     

*-representations on Banach *-algebras

We study notions of -bounded linear functionals and represent-
able functionals on Banach *-algebras. An equivalence between these two is established for general Banach *-algebras. In particular, we characterize -bounded linear functionals on Banach *-algebras with approximate identity and isometric involution. In addition, we prove a result on representation of -bounded positive linear functionals in terms of cyclic vectors for the corresponding *-representation.

     

Existence of Solutions to a Class of Fractional Differential Equations

In this paper, the existence of solutions to a class of fractional differential equations $D_{0+}^{\alpha}u(t)=h(t)f(t, u(t), D_{0+}^{\theta}u(t))$ is obtained by an efficient and simple monotone iteration method. At first, the existence of a solution to the problem above is guaranteed by finding a bounded domain $D_M$ on functions $f$ and $g$. Then, sufficient conditions for the existence of monotone solution to the problem are established by applying monotone iteration method. Moreover, two efficient iterative schemes are proposed, and the convergence of the iterative process is proved by using the monotonicity assumption on $f$ and $g$. In particular, a new algorithm which combines Gauss-Kronrod quadrature method with cubic spline interpolation method is adopted to achieve the monotone iteration method in Matlab environment, and the high-precision approximate solution is obtained. Finally, the main results of the paper are illustrated by some numerical simulations, and the approximate solutions graphs are provided by using the iterative method.     

多元盘Bergman空间上可逆的Toeplitz算子乘积

We prove a reverse Hlder inequality by using the cartesian product of dyadic rectangles and the dyadic cartesian product maximal function on Bergman space of polydisk.Next,we further describe when for which square integrable analytic functions f and g on the polydisk the densely defined products Tf Tg are bounded invertible Toeplitz operators.     

All maps of type are boundary maps

Let be a continuous map of an interval into itself having periodic points of period for all and no other periods. It is shown that every neighborhood of contains a map such that the set of periods of the periodic points of is finite. This answers a question posed by L. S. Block and W. A. Coppel.

     

Asymptotic and convergent expansions for solutions of third-order linear differential equations with a large parameter

In previous papers [6-8,10], we derived convergent and asymptotic expansions of solutions of second order linear differential equations with a large parameter. In those papers we generalized and developed special cases not considered in Olver"s theory [Olver, 1974]. In this paper we go one step forward and consider linear differential equations of the third order: $y"+a\Lambda^2 y"+b\Lambda^3y=f(x)y"+g(x)y$, with $a,b\in\mathbb{C}$ fixed, $f"$ and $g$ continuous, and $\Lambda$ a large positive parameter. We propose two different techniques to handle the problem: (i) a generalization of Olver"s method and (ii) the transformation of the differential problem into a fixed point problem from which we construct an asymptotic sequence of functions that converges to the unique solution of the problem. Moreover, we show that this second technique may also be applied to nonlinear differential equations with a large parameter. As an application of the theory, we obtain new convergent and asymptotic expansions of the Pearcey integral $P(x,y)$ for large $|x|$.     

双圆盘上Hardy空间上Hankel 算子和Toeplitz 算子的交换性

In this paper, we characterize when the Toeplitz operator Tf and the Hankel operator Hg commute on the Hardy space of the bidisk. For certain types of bounded symbols f and g, we give a necessary and sufficient condition on the symbols to guarantee TfHg = HgTf.     

Corrected outer functions

Given and a strictly positive continuous function on the unit circle, we construct a bounded analytic function such that a.e., and is in the Besov space on the unit disc.

     

单位球上$\mu$-Bloch空间之间的广义Ces\`{a}ro算子

Let μ, v ∈ [0, 1） be normal functions and g be holomorphic function on the unit ball. In this paper, we prove that the generalized Cesaro operator Tg ：βμ→βv is bounded and compact.     

Real forms of a Riemann surface of even genus

Natanzon proved that a Riemann surface of genus has at most conjugacy classes of symmetries, and this bound is attained for infinitely many genera . The aim of this note is to prove that a Riemann surface of even genus has at most four conjugacy classes of symmetries and this bound is attained for an arbitrary even as well. An equivalent formulation in terms of algebraic curves is that a complex curve of an even genus has at most four real forms which are not birationally equivalent.

     

The Dedekind-Mertens lemma and the contents of polynomials

We prove a sharpening of the Dedekind-Mertens Lemma relating the contents of two polynomials to the content of their product. We show that for a polynomial the integer in the Dedekind-Mertens Lemma may be replaced by the number of local generators of the content of . We also raise a question concerning the converse.

     

Discrete Morse Flow for Yamabe Type Heat Flows

In this paper, we study the discrete Morse flow for either Yamabe type heat flow or nonlinear heat flow on a bounded regular domain in the whole space. We show that under suitable assumptions on the initial data $g$ one has a weak approximate discrete Morse flow for the Yamabe type heat flow on any time interval. This phenomenon is very different from the smooth Yamabe flow, where the finite time blow up may exist.