Influence of the comatic aberration of an apertured lens on the focused polychromatic Gaussian beams

The focusing of polychromatic Gaussian beams by an apertured lens with comatic aberration is investigated in this paper. We study the influence of the comatic aberration and truncation parameter on the intensity distribution at the focal plane, and singularities and spectral behavior near the focal plane in detail. The simulation results show that the maximum intensity at the focal plane will shift and split with the gradual increment of comatic aberration. We also find that the decrease of truncation parameter will counteract the influence of comatic aberration, which leads to the intensity variation. Furthermore, the singularity transformation and spectral anomalies are discussed. It is found that with the increment of comatic aberration, some singularities are split into several new singularities, and by combining some of these new singularities with other singularities near the focal plane, they vanish or form new singularities with the continuing increase of comatic aberration. The decreasing value of truncation parameter will cause similar phenomena.     

红外用CVD ZnS多晶材料的研制

论述了制备红外用CVD ZnS多晶材料的化学气相沉积工艺和热等静压处理工艺。针对CVD ZnS多晶材料具备优良的光学和力学性能,采用化学气相沉积工艺和热等静压处理技术成功研制出大尺寸多晶材料,其最大尺寸达到250mm×15mm。测试了CVD ZnS样品的各项光学、力学性能指标。样品的全波段透过率均接近ZnS材料的本征水平,折射指数均匀性优于2×10^-5,在1.06μm的吸收系数为2×10^-3cm^-1,抗弯强度达到104MPa。     

Peripheral Modifications of meso-Hydroxyporphyrins: Formation of π-Electronic Anions and Ion-Pairing Assemblies

Phenyl groups were introduced at the β-positions proximal to the meso-hydroxy moiety in hydroxyporphyrin Ni^II complexes by oxidized BINAP Pd^II complexes. Ion-pairing assemblies of deprotonated π-electronic anions, anionic site of which was stabilized by the introduced phenyl moieties with a bulky cation, were formed. They showed charge-by-charge assemblies, assembly modes of which were modulated by the anionic building units.     

计算代数方程组孤立奇异解的符号数值方法

求解代数方程组是计算代数几何的最基本问题之一,孤立奇异解的计算则是其中最具挑战性的课题之一,在科学与工程计算中有着广泛的应用,如机器人、计算机视觉、机器学习、人工智能、运筹学、密码学和控制论等.本文结合作者的研究成果,综述了符号数值方法在计算代数系统孤立奇异解、特别是近似奇异解精化与验证方面的研究进展,并对未来的研究方向提出了展望.     

Visible-Light-Induced Heptacene Generation under Ambient Conditions: Utilization of Single-crystal Interior as an Isolated Reaction Site

The photo-induced generation of unstable molecules generally requires stringent conditions to prevent oxidation and the concomitant decomposition of the products. The visible-light-induced conversion of two heptacene precursors to heptacene was studied. Single crystals of bis- and mono-α-diketone-type heptacene precursors ( 7-DK2 and 7-DK1 , respectively), were prepared to investigate the effect of precursor structure on reactivity. The photoirradiation of a 7-DK2 single crystal cleaved only one α-diketone group, forming an intermediate bearing a pentacene subunit, while that of a 7-DK1 single crystal gave rise to characteristic absorption peaks of heptacene and their increase in intensity with photoirradiation time, indicating the generation of heptacene without decomposition. Heptacene production was not observed when the precursors were photoirradiated in solution, implying that the single crystal interior provided isolation from the external environment, thus preventing heptacene oxidation.     

第二类端点奇异Fredholm积分方程的分数阶退化核方法

本文针对第二类端点奇异Fredholm积分方程构造基于分数阶Taylor展开的退化核方法，设计了两种计算格式，一是在全区间上使用分数阶Taylor展开式近似核函数，二是在包含奇点的小区间上采用分数阶插值，在剩余区间上采用分段二次多项式插值逼近核函数.讨论了两种退化核方法收敛的条件，并给出了混合插值法的收敛阶估计.数值算例表明对于非光滑核函数分数阶退化核方法有着良好的计算效果，且混合二次插值法比全区间上的分数阶退化核方法有着更广泛的适用范围.     

Sobolev type theorems for an operator with singularity

Spaces of Sobolev type are discussed, which are defined by the operator with singularity: , where and . This operator appears in a one-dimensional harmonic oscillator governed by Wigner's commutation relations. Smoothness of and continuity of () are studied where is in each space of Sobolev type, and results similar to Sobolev's lemma are obtained. The proofs are carried out based on a generalization of the Fourier transform. The results are applied to the Schrödinger equation.

     

Zeta Function on a Generalised Cone

The analytic properties of the -function for a Laplace operator on a generalised cone are studied in some detail using Cheeger's approach and explicit expressions are given. In the compact case, the -function of the Laplace operator turns out to be singular at the origin. As a result, strictly speaking, the -function regularisation does not regularise and a further subtraction is required for the related one-loop effective potential.     

Removable singularities of plurisubharmonic functions of restricted growth

LetG be a domain in ⁿ ,n2, letA be a connected complex (n–1)-dimensional submanifold ofG, and let be a plurisubharmonic function inGA. We obtain conditions on the growth of that guarantee the local boundedness of at a point a A G and the existence of a plurisubharmonic extension of toG.Translated fromMatematicheskie Zametki, Vol. 64, No. 1, pp. 64–72, July, 1998.The author wishes to express her gratitude to Professor E. M. Chirka for numerous useful discussions and for his assistance in writing the present text.     

Direction-Dependent Free Energy Singularity of the Antiferroelectric Asymmetric Six-Vertex Model

The transition from the ordered commensurate phase to the incommensurate Gaussian phase of the antiferroelectric asymmetric six-vertex model is investigated by keeping the temperature constant below the roughening point and varying the external fields (h, v). In the (h, v) plane, the phase boundary is approached along straight lines v = k h, where (h, v) measures the displacement from the phase boundary. It is found that the free energy singularity displays the exponent 3/2 typical of the Pokrovski–Talapov transition f const(h)^3/2 for any direction other than the tangential one. In the latter case f shows a discontinuity in the third derivative.