Existence of Optimal Controls for Semilinear Parabolic Equations without Cesari-Type Conditions

   Abstract. Optimal control problems governed by semilinear parabolic partial differential equations are considered. No Cesari-type conditions are assumed. By proving the existence theorem and the Pontryagin maximum principle of optimal ``state-control" pairs for the corresponding relaxed problems, an existence theorem of optimal pairs for the original problem is established.     

改善高功率激光二极管阵列光束质量的一种新方法

根据波导模理论，推导了高功率激光二极管阵列的远场分布，根据其分布特点，设计了一种离轴外腔.运用这种外腔，在工作电流为17A时，光束的束宽积从自由运转时的1100mm·mrad减小到128mm·mrad，二极管阵列的光束质量提高了8.5倍左右，输出功率约为自由运转时的75%.     

有机电致发光器件的动态电学特性

利用交流阻抗谱技术，研究了有机发光二极管ITO/Alq₃(90 nm)/Al的载流子传导机理.根据器件对不同频率的响应曲线及其等效电路模型，该器件可看作是由并联的电阻R_p和电容C_p再与电阻R_s串联而成，并根据实验数据求出了R_p，C_p和R_s的数值.实验结果表明器件的载流子传输机理属于指数分布式的陷阱电荷限制电流，其介电弛豫时间随偏压的增加而逐渐减小. 关键词： 3')" href="#">Alq₃ 陷阱电荷限制电流 交流阻抗谱 有机发光二极管     

Transverse-mode controlling of a large-mode-area multimode fiber laser

Coiling technique is used to control the transverse mode of a large-mode-area (LMA) multimode fiber laser. By winding the fiber to a coil with different radius, high-order modes of a multimode fiber laser are suppressed one by one and finally 15.4-W single-transverse-mode output is achieved when the coil radius is 20 mm. It is found that as the coil radius decreases, the beam quality of a multimode fiber laser gets better but the slope efficiency drops for higher-order modes are discriminated. During the experiment, as the coil radius of multimode fiber changes, output characteristic of the laser has been measured. Meanwhile,the mode loss of different modes is calculated theoretically. It is proved that the experimental measured results fit well with the theoretically calculated results.     

Joint Distribution of Rises and Falls

The marginal distributions of the number of rises and the number of falls have been used successfully in various areas of statistics, especially in non-parametric statistical inference. Carlitz (1972, Duke Math. J. 39, 268–269) showed that the generating function of the joint distribution for the numbers of rises and falls satisfies certain complex combinatorial equations, and pointed out that he had been unable to derive the explicit formula for the joint distribution from these equations. After more than two decades, this latter problem remains unsolved. In this article, the joint distribution is obtained via the probabilistic method of finite Markov chain imbedding for random permutations. A numerical example is provided to illustrate the theoretical results and the corresponding computational procedures.     

Characterization of graphs with infinite cyclic edge connectivity

In this paper, we characterize the graphs with infinite cyclic edge connectivity. Then we design an efficient algorithm to determine whether a graph has finite cyclic edge connectivity or infinite cyclic edge connectivity.     

Synchronization of neural networks based on parameter identification and via output or state coupling

For neural networks with all the parameters unknown, we focus on the global robust synchronization between two coupled neural networks with time-varying delay that are linearly and unidirectionally coupled. First, we use Lyapunov functionals to establish general theoretical conditions for designing the coupling matrix. Neither symmetry nor negative (positive) definiteness of the coupling matrix are required; under less restrictive conditions, the two coupled chaotic neural networks can achieve global robust synchronization regardless of their initial states. Second, by employing the invariance principle of functional differential equations, a simple, analytical, and rigorous adaptive feedback scheme is proposed for the robust synchronization of almost all kinds of coupled neural networks with time-varying delay based on the parameter identification of uncertain delayed neural networks. Finally, numerical simulations validate the effectiveness and feasibility of the proposed technique.     

Structures and Absolute Configurations of Three 7,8‐Secolabdane Diterpenes from the Chinese Liverwort Pallavicinia ambigua

The known 7,8‐secolabdane type diterpenoids neopallavicinin ( 1 ), pallavicinin ( 2 ), and 18‐hydroxypallavicinin ( 3 ) were isolated from Pallavicinia ambigua, and their structures were determined. The X‐ray crystal structure of 1 was solved, and, in combination with CD and NMR studies, the absolute configurations of 1 – 3 were established. A possible biogenetic pathway for 1 and 2 from a single labdane precursor is proposed.     

On the elementary theory of rings of Witt vectors with a multiplicative set of representatives for the residue field

We indicate a complete set of elementary invariants for the ring of Witt vectors over a perfect field of prime characteristic, where this ring is equipped with its unique multiplicative set of representatives for the residue field. Received: 31 March 1998