抑制剂作用下肿瘤生长模型的参数识别

该文考虑抑制剂作用下肿瘤生长的模型. 假设肿瘤是球对称的, 其表面为运动边界, 用函数r=R(t)表示. 既然多细胞肿瘤扁球体(MTS)通常作为肿瘤生长的体外模型, 在实验室能够被观察和控制, 因此研究如下反问题: 根据观察到的MTS动态增长(即给定R(t)), 来确定抑制剂的参数. 运用极大值原理, 作者证明了该抛物反问题解的唯一性. 进一步, 用最优控制框架来重构模型中的抑制剂参数, 证明了最优控制问题解的存在性, 并推导了最优控制满足的最优性必要条件.     

求解非线性系统的有效集信赖域方法

该文给出了一个求解非线性系统的信赖域方法.主要思想是通过引入松弛变量,将问题等价地转化为带非负约束的最优化问题.作者利用有效集策略,在每次迭代中只需求解一个低维的信赖域子问题,该信赖域子问题是通过截断共轭梯度法来近似求解的.在较弱的条件下,获得了一个更一般的收敛性结果.     

Normality and Related Properties of Forcing Algebras

The authors present a sufficient condition for irreducibility of forcing algebras and study the (non)reducedness phenomenon. Furthermore, the authors prove a criterion for normality of forcing algebras over a polynomial base ring with coefficients in a perfect field. This gives over algebraically closed fields a geometrical normality criterion for algebraic (forcing) varieties. Besides, the authors examine in detail a specific (enlightening) example with several forcing equations. Finally, the authors compute explicitly the normalization of a particular forcing algebra by means of finding explicitly the generators of the ideal defining it as an affine ring.     

关于齐次四元Monge-Ampère方程的一些注记北大核心CSCD

本文考虑了四元数空间Hn中齐次四元Monge-Ampère方程的狄利克雷问题解的正则性.首先,当区域是边界为C1,1的强拟凸域时,作者给出了解的Lipschitz估计.其次,考虑了四元MongeAmpère算子的收敛性.最后,讨论了齐次四元Monge-Ampère方程的粘性次解与F-次调和函数之间的关系.     

ON MARKOV CHAINS IN SPACE-TIME RANDOM ENVIRONMENTS

In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...     

Quantitative Stability of the Brunn-Minkowski Inequality for Sets of Equal Volume

The authors prove a quantitative stability result for the Brunn-Minkowski inequality on sets of equal volume:If |A| =|B| ＞ 0 and |A + B|1/n =(2 + δ)|A|1/n for some small δ,then,up to a translation,both A and B are close (in terms of δ) to a convex set K.Although this result was already proved by the authors in a previous paper,the present paper provides a more elementary proof that the authors believe has its own interest.Also,the result here provides a stronger estimate for the stability exponent than the previous result of the authors.     

Fast Growth Entire Functions Whose Escaping Set Has Hausdorff Dimension Two

The authors study a family of transcendental entire functions which lie outside the Eremenko-Lyubich class in general and are of infinity growth order. Most importantly, the authors show that the intersection of Julia set and escaping set of these entire functions has full Hausdorff dimension. As a by-product of the result, the authors also obtain the Hausdorff measure of their escaping set is infinity.     

随机线性互补问题的无约束优化再定式

针对随机线性互补问题,提出等价的无约束优化再定式模型,即由D-间隙函数定义的确定性的无约束期望残差极小化问题.通过拟Monte Carlo方法,将样本进行了推广,得到了相关的离散近似问题.在适当的条件下,提出了最优解存在的充分条件,以及探究了离散近似问题的最优解及稳定点的收敛性.另外,在针对一类带有常系数矩阵的随机互补线性问题,研究了解存在的充要条件.     

刘维尔底频的解析拟周期三维斜对称线性系统的可约性*

文章主要研究一类具有刘维尔底频的解析拟周期三维斜对称线性系统的可约性.作者构造了一类三维刘维尔频率(含超刘维尔频率), 证明了在一定的非退化条件下,当扰动足够小时该类底频系统的正测旋转可约性.     

Some Weak Specification Properties and Strongly Mixing

In this paper,the authors first construct a dynamical system which is strongly mixing but has no weak specification property.Then the authors introduce two new concepts which are called the quasi-weak specification property and the semi-weak specification property in this paper,respectively,and the authors prove the equivalence of quasi-weak specification property,semi-weak specification property and strongly mixing.     

Reflected Quadratic BSDEs Driven by G-Brownian Motions∗

In this paper, the authors consider a reflected backward stochastic differential equation driven by a G-Brownian motion (G-BSDE for short), with the generator growing quadratically in the second unknown. The authors obtain the existence by the penalty method, and some a priori estimates which imply the uniqueness, for solutions of the G-BSDE. Moreover, focusing their discussion at the Markovian setting, the authors give a nonlinear Feynman-Kac formula for solutions of a fully nonlinear partial differential equation.     

关于循环图的曲面嵌入

该文集中探讨循环图的曲面嵌入性质.决定了所有循环图的最小亏格(其中包括可定向亏格与不可定向亏格)和最大亏格.对于固定的整数l(≥3)和充分大的 自然数n,只有一种方式将4 -正则循环图C(n,l)嵌入到环面上使得其每一个面都是4 -边形.特别地,循环图$C(2l+2,l)$在加入若干条新边后可以同时将环面与Klein瓶进行三角剖分.     

Block型代数的量子化

文献[1]研究了一类Block型代数的李双代数结构, 该文对此代数进行了量子化.     

一类非线性方程的Backlund变换以及紧孤立波解的线性稳定性

引进五阶线性色散项方程K(m,n,1),用逆算符方法得到了sin型多重compacton 解(紧孤立波解);利用齐次平衡法得到了K(2,2,1)方程的Backlund变换,并且得到一些新的孤立波解;最后研究了sin型多重compacton解的线性稳定性.     

线性流形上反埃尔米特广义汉密尔顿矩阵的最小二乘问题与最佳逼近问题

利用反埃尔米特广义汉密尔顿矩阵的表示定理,得到了线性流形上反埃尔米特广义汉密尔顿矩阵反问题的最小二乘解的一般表达式,建立了线性矩阵方程在线性流形上可解的充分必要条件．对于任意给定的n阶复矩阵,证明了相关最佳逼近问题解的存在性与惟一性,并推得了最佳逼近解的表达式．     

一类随机算子方程随机解的存在性

研究了一类随机算子方程的随机解，推广了几个重要的定理. 同时，得到了若干新的结果.      

一类椭圆型随机偏微分方程弱解的存在性

设$D$是$R^N$ ($N>1$)中有界开集,$(\Omega, {\cal F}, P)$是一个完备的概率空间.该文研究了下列随机边值问题弱解的存在性问题\[\left\{\begin{array}{ll}-{\rm div} A(x,\omega,u, \nabla u)=f(x,\omega, u),\,\, &;(x,\omega)\in D\times \Omega,\\u=0, &;(x,\omega)\in \partial D\times \Omega,\end{array}\right.\]其中, div与 $\nabla $ 表示仅对 $x$求微分. 首先,作者引入了弱解的概念; 然后,作者转化随机问题为高维确定性问题;最后,作者证明了该问题弱解的存在性.     

On a Dual Risk Model Perturbed by Diffusion with Dividend Threshold

In the dual risk model, the surplus process of a company is a L′evy process with sample paths that are skip-free downwards. In this paper, the authors assume that the surplus process is the sum of a compound Poisson process and an independent Wiener process. The dual of the jump-diffusion risk model under a threshold dividend strategy is discussed. The authors derive a set of two integro-differential equations satisfied by the expected total discounted dividend until ruin. The cases where profits follow an exponential or mixtures of exponential distributions are solved. Applying the key method of the Laplace transform, the authors show how the integro-differential equations are solved. The authors also discuss the conditions for optimality and show how an optimal dividend threshold can be calculated as well.     

Global Existence, Uniqueness and Pathwise Property of Solutions to a Stochastic R¨ossler-Lorentz System

The authors integrate two well-known systems, the R¨ossler and Lorentz systems, to introduce a new chaotic system, called the Lorentz-R¨ossler system. Then, taking into account the effect of environmental noise, the authors incorporate white noise in both R¨ossler and Lorentz systems to have a corresponding stochastic system. By deriving the uniform a priori estimates for an approximate system and then taking them to the limit, the authors prove the global existence, uniqueness and the pathwise property of solutions to the Lorentz-R¨ossler system. Moreover, the authors carried out a number of numerical experiments, and the numerical results demonstrate their theoretic analysis and show some new qualitative properties of solutions which reveal that the Lorentz-R¨ossler system could be used to design more complex and more secure nonlinear hop-frequence time series.     

A sharp bound for the degree of proper monomial mappings between balls

The authors prove that a proper monomial holomorphic mapping from the two-ball to the N-ball has degree at most 2N-3, and that this result is sharp. The authors first show that certain group-invariant polynomials (related to Lucas polynomials) achieve the bound. To establish the bound the authors introduce a graph-theoretic approach that requires determining the number of sinks in a directed graph associated with the quotient polynomial. The proof also relies on a result of the first author that expresses all proper polynomial holomorphic mappings between balls in terms of tensor products.