Exponential stability of uniform Euler–Bernoulli beams with non-collocated boundary controllers

We study the stability of a robot system composed of two Euler–Bernoulli beams with non-collocated controllers. By the detailed spectral analysis, we prove that the asymptotical spectra of the system are distributed in the complex left-half plane and there is a sequence of the generalized eigenfunctions that forms a Riesz basis in the energy space. Since there exist at most finitely many spectral points of the system in the right half-plane, to obtain the exponential stability, we show that one can choose suitable feedback gains such that all eigenvalues of the system are located in the left half-plane. Hence the Riesz basis property ensures that the system is exponentially stable. Finally we give some simulation for spectra of the system.     

关于整函数超级的进一步结果

运用正规族理论研究了整函数与其高阶导数分担无穷级函数增长级与超级的相关结果.从亚纯函数超级大于零而使球面导数无界的角度出发,然后综合运用Pang-Zaclman引理,数学归纳法和Nevanlinna理论等方法证明了该结果,推广和改进了已有的结果.     

相对n-FP-内射模

给出了n-FP-内射模的定义,M为左R-模,如果对任意的左R-模N有Ext1(N,M)=0,则称M为n-FP-内射模,作为应用,给出了n-FP-内射模的一些等价条件.     

Short,enantioselective, gram-scale synthesis of (−)-zephyranthine

A reasonable synthesis design by strategically integrating functional group manipulation into the ring system construction resulted in a short, enantioselective, gram-scale total synthesis of (−)-zephyranthine. The concise route includes a catalytic Michael/Michael cascade for the asymmetric synthesis of a penta-substituted cyclohexane with three contiguous stereogenic centers, a remarkable 8-step one-pot operation to easily assemble the zephyranthine tetracyclic skeleton, the regioselective construction of a double bond in the C ring and an asymmetric dihydroxylation. This synthesis is also flexible and paves a potential path to a variety of cyclohexylamine-fused tricyclic or polycyclic alkaloids.

A reasonable synthesis design by strategically integrating functional group manipulation into the ring system construction resulted in a short, enantioselective, gram-scale total synthesis of (−)-zephyranthine.     

On the distinctness of modular reductions of primitive sequences over Z/(232−1)

This paper studies the distinctness of modular reductions of primitive sequences over ${\mathbf{Z}/(2^{32}-1)}$ . Let f(x) be a primitive polynomial of degree n over ${\mathbf{Z}/(2^{32}-1)}$ and H a positive integer with a prime factor coprime with 2³²?1. Under the assumption that every element in ${\mathbf{Z}/(2^{32}-1)}$ occurs in a primitive sequence of order n over ${\mathbf{Z}/(2^{32}-1)}$ , it is proved that for two primitive sequences ${\underline{a}=(a(t))_{t\geq 0}}$ and ${\underline{b}=(b(t))_{t\geq 0}}$ generated by f(x) over ${\mathbf{Z}/(2^{32}-1), \underline{a}=\underline{b}}$ if and only if ${a\left( t\right) \equiv b\left( t\right) \bmod{H}}$ for all t ≥ 0. Furthermore, the assumption is known to be valid for n between 7 and 100, 000, the range of which is sufficient for practical applications.     

分布式微能源网系统集成设计优化研究

分布式冷热电联供是一种多能源综合互补、高效利用的有效方式.本文以广州某2000 m2公寓楼为例构建集"源、储、荷"三位一体的分布式微能源网系统,建立了固体氧化物燃料电池、太阳能集热器等系统关键设备数学模型,基于理想点法优化了系统的集热场面积、热水罐体积、基岩储热容量等关键设计参数,使系统具有最佳的综合性能.结果表明,在...     

基于Shannon-Cosine小波精细积分法的壁画降噪修复方法

为修复受破损且噪声点众多的壁画图像,提出了用偏微分方程（partial differential equation,PDE）扩散的方法对图像进行降噪修复。针对PDE法求解精度较低的问题,提出了一种Shannon-Cosine小波精细积分法,运用小波数值方法对偏微分方程进行离散处理,降低其方程组规模,并采用精细积分法求解,有效提高了计算速度。试验结果表明,采用该算法对受损壁画降噪处理后,视觉上,图像边界更清晰,且噪声点得到有效减少,达到了保边降噪的效果,更符合人眼的视觉效果;客观上,与中值滤波、均值滤波和维纳滤波方法相比,采用本算法处理后的图像其PSNR值和SSIM值均最大。因此,运用Shannon-Cosine小波精细积分法求解图像的PDE模型是可行的,取得了较好的图像降噪效果。     

Simulation of quasi-dimensional combustion model for predicting diesel engine performance

In order to improve the precision of quasi-dimensional combustion model for predicting diesel engine performance and promote the real time operating performance of the simulation model, a new phase-divided spray mixing model is proposed and the quasi-dimensional combustion model of diesel engine working process is developed. The software MATLAB/Simulink is utilized to build the quasi-dimensional combustion model of diesel engine working process, and the performance for diesel engine is simulated. The simulation results agree with experimental data quite well. The comparisons between them show that the relative error of power and brake specific fuel consumption is less than 2.8% and the relative error of nitric oxide and soot emissions is less than 9.1%. By utilization of this simulation model with personal computer, the average computational time for one diesel engine working process is 36 s, which presents good real time operating performance of the model. At the same time, the influence of parameters in calculation of air entrainment on prediction precision of diesel engine’s simulation model is analyzed.     

广义Carmichael数

设n是一个合数,Z_n表示模n的剩余类环,r(x)∈Z_n[x]是一个首一的k(>0)次不可约多项式。本文引入n是k阶摸r(x)的Carmichael数的定义,全体这样的数记为集C_(k,r)(x),由此给出k阶Carmichael数集:C_k={∪C_(k,r)(x)|r(x)过全体Z_n上的首一k次不可约多项式}。显然C_1表示通常的Carmichael数集。作者得到了n∈C_(k,r(x))的一个充要条件,进而得到n∈C_k的一个充要条件及n∈C_2的一个更易计算的充要条件,还证明了C_1(?)C_2以及|C_2|=∞。     

UNBOUNDED COMPLEX SYMMETRIC TOEPLITZ OPERATORS

In this paper,we study unbounded complex symmetric Toeplitz operators on the Hardy space H²(D) and the Fock space g².The technique used to investigate the complex symmetry of unbounded Toeplitz operators is different from that used to investigate the complex symmetry of bounded Toeplitz operators.