形式三角矩阵环上的有限表示模

形式三角矩阵环,又称广义三角矩阵环,这类环及其上的模在环模理论中扮演着重要的角色.本文对形式三角矩阵环上的有限表示模进行了一些探讨.     

基于抛光基材的热蒸镀铜箔生长高平整单层石墨烯薄膜

在石墨烯的化学气相沉积工艺中,铜箔是决定石墨烯薄膜质量的重要因素。传统铜箔由于制备工艺的限制,存在大量的缺陷,导致石墨烯薄膜的成核密度较高。本工作选用抛光铝板、抛光不锈钢板、微晶玻璃和SiO₂/Si作为基材,用热蒸镀法制备了不同粗糙度的铜箔,并详细讨论了以该系列铜箔生长高平整度石墨烯薄膜的条件及铜箔对石墨烯薄膜品质的影响。实验结果表明,铜箔以(111)取向为主,与基材分离后,表面具有纳米级平整度。在生长石墨烯后,从SiO₂/Si剥离的铜箔成核密度是4种基材中最小的。同时,从SiO₂/Si剥离的铜箔晶体结构变化最不明显,具有良好的结晶性,表面几乎不存在铜晶界缺陷。当压强为3 000 Pa,氢气和甲烷流速分别为300 mL/min和0.5 mL/min时,可以获得约1 mm横向尺寸的石墨烯单晶晶畴。     

光刻机硅片表面不平度原位检测技术

随着光刻特征尺寸的不断减小,硅片表面不平度对光刻性能的影响越来越显著.该文提出了一种新的硅片表面不平度的原位检测技术本文在分析特殊测试标记成像规律的基础上,讨论了测试标记的对准位置偏移量与硅片表面起伏高度的变化规律,提出了一种新的硅片表面不平度原位检测技术.实验表明,该技术可实现硅片表面不平度及硅片表面形貌的高准确度原位测量.该技术考虑了光刻机承片台吸附力的非均匀性对硅片表面不平度的影响,更真实反映曝光工作状态下的硅片表面不平度大小.与现有的原位检测方法相比,硅片表面不平度的测量空间分辨率提高了1.67%倍,可实现硅片表面形貌的原位检测.     

Properties of mono-weakly hyponormal 2-variable weighted shifts

In this paper, we study several properties for mono-weakly hyponormal 2-variable weighted shifts. First, we consider propagation phenomena for mono-weakly hyponormal (resp. mono-polynomially hyponormal) 2-variable weighted shifts. Next, we contemplate the mono-weak hyponormality under the Schur product. Finally, we study whether the mono-weak hyponormality is invariant under powers.     

Study of gain flatness for multi-channel amplification in single stage EDFA for WDM applications

In this paper, gain flatness is studied for simultaneous 16-ITU-T channel amplifications at C-band (1,532–1,558 nm) in a single stage EDFA for WDM application at different average inversion levels. The inversion levels are varied due to the change of the input signal levels from the targeted operating point and also for dropping few numbers of channels. Specially designed gain flattening filter (GFF) is used in order to get the flat gain with gain variation ±0.5 dB for −20 dBm/ch input signal power (total input signal power is −8.0 dBm) at a fixed average inversion level which is maintained by proper selection of optimum fibre length and pump power. A specific loss spectrum of GFF is obtained by writing a chirped fibre Bragg grating of length 20 mm. Gain variations are studied by changing the total input signal levels from −8.0 dBm to −20.0 dBm and maintained within 20.0 ± 0.5 dB by using automatic gain control (AGC) circuit. About 15 out of 16 channels are dropped and observed ± 0.5 dB gain-variation which is an important parameter in optical network system.     

Atomically flat single terminated oxide substrate surfaces

Scientific interest in atomically controlled layer-by-layer fabrication of transition metal oxide thin films and heterostructures has increased intensely in recent decades for basic physics reasons as well as for technological applications. This trend has to do, in part, with the coming post-Moore era, and functional oxide electronics could be regarded as a viable alternative for the current semiconductor electronics. Furthermore, the interface of transition metal oxides is exposing many new emergent phenomena and is increasingly becoming a playground for testing new ideas in condensed matter physics. To achieve high quality epitaxial thin films and heterostructures of transition metal oxides with atomically controlled interfaces, one critical requirement is the use of atomically flat single terminated oxide substrates since the atomic arrangements and the reaction chemistry of the topmost surface layer of substrates determine the growth and consequent properties of the overlying films. Achieving the atomically flat and chemically single terminated surface state of commercially available substrates, however, requires judicious efforts because the surface of as-received substrates is of chemically mixed nature and also often polar. In this review, we summarize the surface treatment procedures to accomplish atomically flat surfaces with single terminating layer for various metal oxide substrates. We particularly focus on the substrates with lattice constant ranging from 4.00 Å to 3.70 Å, as the lattice constant of most perovskite materials falls into this range. For materials outside the range, one can utilize the substrates to induce compressive or tensile strain on the films and explore new states not available in bulk. The substrates covered in this review, which have been chosen with commercial availability and, most importantly, experimental practicality as a criterion, are KTaO₃, REScO₃ (RE = Rare-earth elements), SrTiO₃, La_0.18Sr_0.82Al_0.59Ta_0.41O₃ (LSAT), NdGaO₃, LaAlO₃, SrLaAlO₄, and YAlO₃. Analyzing all the established procedures, we conclude that atomically flat surfaces with selective A- or B-site single termination would be obtained for most commercially available oxide substrates. We further note that this topmost surface layer selectivity would provide an additional degree of freedom in searching for unforeseen emergent phenomena and functional applications in epitaxial oxide thin films and heterostructures with atomically controlled interfaces.     

宽带FRA中同时实现信号增益与噪声平坦的快速算法

首先优化了多波抽运拉曼光纤放大器的功率耦合方程,并利用小信号方法解决反向抽运的边值问题,其次采用遗传算法同时实现了信号增益谱和噪声谱的平坦.计算表明:双向抽运方式下系统噪声谱在C L波段(1.53~1.61μm)比反向抽运更为平坦;抽运光数目与增益平坦度呈非线性关系并存在下限值.通过多次测试,对于10波抽运,100信道的DWDM系统(带宽为80 nm),增益波动小于1 dB的优化时间可控制在400 s以内.     

Stability for a random evolution equation with Gaussian perturbation

In this paper we consider a random evolution equation which is perturbed by Gaussian type noise, and show how to construct its coupled solutions. On the basis of the coupling results, we discuss the asymptotic flatness and the stability in total variation norm for the solutions of the equation. In addition, we also prove the Feller continuity, and the existence and uniqueness of invariant measures of the solutions.     

Does the flatness of the velocity derivative blow up at a finite Reynolds number?

A tentative suggestion is made that the flatness of the velocity derivative could reach an infinite value at finite (though very large) Reynolds number, with possible implications for the singularities of the Navier—Stokes equations. A direct test of this suggestion requires measurements at Reynolds numbers presently outside the experimental capacity, so an alternative suggestion that can be tested at accessible Reynolds numbers is also made.     

Codimension one spheres in Rn with double tangent balls

In contrast to the situation in $\text{R}$³, where a 2-sphere with double tangent balls at each point must be tamely embedded in $\text{R}$³, there exist wild (n?1)-spheres in $\text{R}$ⁿ for n>3 with this same geometric property. However, if the sphere Σ is tame moduio a subset X that lies in a polyhedron P that is tame in Σ, the dimension of P is less than n?2, n>4, and Σ has double tangent balls over X, then Σ must be tame in $\text{R}$ⁿ. Also if the tangent balls extend over P and are pairwise congruent, the dimensional restriction on P can be dropped. Examples are given to support the necessity of the hypotheses of the included theorems.