Finite valued feedback laws and piecewise classical solutions

Often, in engineering literature, we find control systems in which the open loop inputs are piecewise constant and take values in a finite set. Such open loop inputs cause the system to have fairly regular solutions. On the other hand, when acting in closed loop, feedback laws taking values in a finite set may not be reinterpreted as open loop inputs of the considered type. In fact, pathological behaviours such as the accumulation of discontinuities may appear (Zeno phenomenon). We give some conditions which can be used as tools for building finite valued feedback laws not causing such pathological behaviours.     

On the complexity of suboptimal decoding for list and decision feedback schemes

We consider bounded distance list decoding, such that the decoder calculates the list of all codewords within a sphere around the received vector. We analyze the performance and the complexity of this suboptimum list decoding scheme for the binary symmetric channel. The reliability function of the list decoding scheme is equivalent to the sphere-packing bound, where the decoding complexity is asymptotically bounded by 2^nR(1-R). Furthermore, we investigate a decision feedback strategy that is based on bounded distance list decoding. Here, any output with zero or many codewords will call for a repeated transmission. In this case the decoding complexity will be of the order 2^nR(1-C), where C denotes the channel capacity. The reliability function is close to Forney's feedback exponent.     

Towards Strong Duality in Integer Programming

We consider in this paper the Lagrangian dual method for solving general integer programming. New properties of Lagrangian duality are derived by a means of perturbation analysis. In particular, a necessary and sufficient condition for a primal optimal solution to be generated by the Lagrangian relaxation is obtained. The solution properties of Lagrangian relaxation problem are studied systematically. To overcome the difficulties caused by duality gap between the primal problem and the dual problem, we introduce an equivalent reformulation for the primal problem via applying a pth power to the constraints. We prove that this reformulation possesses an asymptotic strong duality property. Primal feasibility and primal optimality of the Lagrangian relaxation problems can be achieved in this reformulation when the parameter p is larger than a threshold value, thus ensuring the existence of an optimal primal-dual pair. We further show that duality gap for this partial pth power reformulation is a strictly decreasing function of p in the case of a single constraint. Dedicated to Professor Alex Rubinov on the occasion of his 65th birthday. Research supported by the Research Grants Council of Hong Kong under Grant CUHK 4214/01E, and the National Natural Science Foundation of China under Grants 79970107 and 10571116.     

A 24-GHz Patch Array with a Power Amplifier/Low-Noise Amplifier MMIC

This paper presents an active patch array designed at 24 GHz. It can be used as a front-end component for a phased array. A series resonant array structure is chosen which is compact and easy excite. With 5 elements, the array proved a 12-dB antenna gain. A power amplifier and a low noise amplifier are designed on a single GaAs chip (PALNA). Bias switch is used in the PALNA, which greatly reduces the switch loss in a transceiver and increases the efficiency. 20-dB small signal gain is achieved in both power amplifier and low noise amplifier. The active patch array is built by the combination of the patch array and PALNA. The measured active gain of this antenna is 35-dB for the PA mode and 31-dB for the LNA mode. This active patch array can obtain an EIRP of 34 dBm with a total radiated power of 22dBm and a maximum PAE of 32%. To check the noise performance, we applied sources at both normal temperature and 77K (liquid nitrogen) and extracted the noise figure (3.5 dB) of the active antenna by the Y factor method. The results proved that the active antenna is working efficiently as both a transmitting and receiving antenna.     

Sums of Two Exact Powers

An asymptotic formula is obtained for the number of representations of an element of a finite field as a weighted sum of two prescribed powers of primitive elements. This generalises previous work on sums of primitive elements, including that relating to some conjectures of Golomb.     

溅射功率对多层膜质量的影响

用磁控溅射技术制备薄膜，用X射线衍射研究在基片和靶间距离固定的情况下不同的溅射功率对薄膜结构的影响。结果表明：过低的溅射功率下淀积的薄膜有畸变的X射线衍射特征峰，特征峰强度小，半峰全宽大。而比较高溅射功率得到的薄膜有比较尖锐的X射线衍射特征峰，强度高和半峰全宽非常窄。研究表明，X射线衍射特征峰强度小和半峰全宽大的薄膜结构疏松，而强度高和半峰全宽非常窄的薄膜结构致密。     

受激喇曼散射在掺铒光纤放大器中的影响

本文在分析了均匀掺杂分布式光纤放大器（d－EDFA）的基础上，提出了沿传输方向掺杂浓度单调下降（单变），和降升结合（两变）的两种渐变型分布式光纤放大器，并用传输方程研究了透明传输和最佳掺杂浓度下，受激喇曼散射对均匀、单变和两变型三种d－EDFA的各种特性的影响．     

一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算

利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.     

Collective mechanism for nuclear stopping and transverse flow in heavy-ion collisions

The role of filamentation instability of quark-gluon plasma, in explaining collective phenomena in relativistic heavy-ion collisions, has been analyzed. Using equations of SU(2) two fluid color hydrodynamics it is shown that this instability can significantly enhance nuclear stopping and might contribute to collective sideward flows.     

X波段五腔渡越管振荡器的理论与实验研究

 提出了一种新结构的X波段五腔渡越管振荡器，进行了理论和实验研究。根据场分布进行了一维非线性分析，结果表明该结构可以产生高功率微波，并判断了工作模式，为TM₀₁模的3π/5模。采用粒子模拟验证了一维非线性分析的结论，并优化设计出五腔渡越管振荡器,优化结果为：输出功率约1 GW， 工作频率9.3 GHz，束波转换效率约22%。实验中，通过参数调节，得到频率约9.25 GHz，峰值功率约780 MW，脉宽（半高宽）21 ns的输出微波，束波转换效率约为16%。实验结果与模拟结果基本符合。