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31.
For any self-adjoint realization S of a singular Sturm-Liouville equation on an interval (a,b) with limit-circle endpoints, we construct a family of self-adjoint realizations S r ,r ∈ (0,∞), of this equation on subintervals (a r ,b r ) of (a,b) such that every eigenvalue of S is the limit of a continuous eigenvalue branch of this family. Of particular interest are the cases when at least one endpoint is oscillatory or the leading coefficient function changes sign. In these cases, we show that the index determining each continuous eigenvalue branch has an infinite number of jump discontinuities and give an explicit characterization of these discontinuities. 相似文献
32.
33.
Liang Kong 《Advances in Mathematics》2007,213(1):271-340
We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R×R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over VL⊗VR, where VL and VR are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over VL⊗VR equipped with a nondegenerate invariant bilinear form. By assuming slightly stronger conditions on VL and VR, we show that a conformal full field algebra over VL⊗VR equipped with a nondegenerate invariant bilinear form exactly corresponds to a commutative Frobenius algebra with a trivial twist in the category of VL⊗VR-modules. The so-called diagonal constructions [Y.-Z. Huang, L. Kong, Full field algebras, arXiv: math.QA/0511328] of conformal full field algebras are given in tensor-categorical language. 相似文献
34.
采用均相沉积法制备了不同Er3+离子浓度掺杂的Y2O3纳米晶, 应用XRD,SEM和PL光谱对该体系材料进行了表征.在Y2O3:Er3+纳米材料体系中, 观察和研究了Stokes及anti-Stokes PL谱强度与Er3+离子摩尔浓度变化的关系, 当Er3+离子浓度为2.0mol%时, anti-Stokes PL强度最强.粉末X
关键词:
氧化钇纳米晶
anti-Stokes PL
双光子吸收 相似文献
35.
K. Kong Wan 《Foundations of Physics》1991,21(9):1107-1116
Traditionally spatial transformations such as translations and rotations are formulated in terms of transformations of the entire spatial space. In other words, transformations are taken automatically to be of a global nature. This paper investigates a local approach to spatial transformations; local transformations lead naturally to local observables in quantum mechanics. 相似文献
36.
CH3S CH2SH异化反应的理论研究 总被引:2,自引:1,他引:1
利用密度泛函理论(DFT)和从头算(ab initio)研究了CH3S←→CH2SH互异化的反应机理.采用HF、B3LYP、MP2理论水平和中等基组6-31(d),计算了CH3S、CH2SH及其过渡态的结构参数、谐振频率、零点能(ZPF)、总能量和相对能量,并利用B3LYP/6-31(d)的方法计算了反应的内禀反应坐标(IRC),给出了分子构型和自旋污染沿反应坐标的变化曲线,以及最小能量曲线(MEP)、绝热能量曲线.此外,利用传统过渡态理论(CTST)研究了该互异化反应的速率常数和平衡常数在200~1000K的变化. 相似文献
37.
After the laser was invented in 1960, a phase conjugation mirror has been respected to be the most fantastic one for the laser
resonator composition because it can compensate any distortions of the laser beams occurred by the many inhomogenuities of
the laser media and optical components. Among the many phase conjugation configurations, the stimulated Brillouin scattering
phase conjugation mirror is the most simple one and many researchers have tried to utilize it to develop high power/energy
laser systems. For realizing a high energy/power laser system the thermal problem is the most difficult to solve, and some
researchers suggested a beam combination technique to reduce the thermal load of the big laser media to many small sized ones.
To accomplish the beam combination using stimulated Brillouin scattering phase conjugation mirrors (SBS-PCMs), it is necessary
to lock/control the phases of the SBS-PCMs. And some researchers have developed several ways for it, but they can lock the
phases of a limited number of beams overlapped at the foci less than 5, or lock the phases by back-seeding technique but it
loses the phase conjugation characteristics. For realization of the laser fusion driver, it is necessary to combine more than
10 or 100 beams. And the authors have developed recently a new phase controlling/locking technique which is isolated and independent
totally from other beams and it can be applied to an unlimited number of beams in principle. 相似文献
38.
T.W. Lim S.H. Park D.Y. Yang H.J. Kong K.S. Lee 《Applied Physics A: Materials Science & Processing》2006,84(4):379-383
A nano-surfacing process (NSP) is proposed to directly fabricate three-dimensional (3D) concavo–convex-shaped microstructures such as micro-lens arrays using two-photon polymerization (TPP), a promising technique for fabricating arbitrary 3D highly functional micro-devices. In TPP, commonly utilized methods for fabricating complex 3D microstructures to date are based on a layer-by-layer accumulating technique employing two-dimensional sliced data derived from 3D computer-aided design data. As such, this approach requires much time and effort for precise fabrication. In this work, a novel single-layer exposure method is proposed in order to improve the fabricating efficiency for 3D concavo–convex-shaped microstructures. In the NSP, 3D microstructures are divided into 13 sub-regions horizontally with consideration of the heights. Those sub-regions are then expressed as 13 characteristic colors, after which a multi-voxel matrix (MVM) is composed with the characteristic colors. Voxels with various heights and diameters are generated to construct 3D structures using a MVM scanning method. Some 3D concavo–convex-shaped microstructures were fabricated to estimate the usefulness of the NSP, and the results show that it readily enables the fabrication of single-layered 3D microstructures. PACS 85.40.Hp; 81.16.Nd; 42.82.Cr 相似文献
39.
本文用Fuzzy数学的观点探讨了Fuzzy聚类分析,并通过对脊髓灰质炎病毒抗体水平的Fuzzy聚类分析,获得了良好的聚类效果,为该项问题的研究提供了科学依据。 相似文献
40.
The correlation times (τc) and cross relaxation rates of toluene, dimethylformamide, tetrahydrofuran, water-acetone and water-dioxane adsorbed on silica gel, alumina and charcoal were obtained by measurements of the integrated intensities of cross and diagonal peaks in their NOESY spectra. The (τc) of the above mentioned systems is in the range of 10?6?10?9 s, much longer than that in the liquid (10?12?10?14 s). It was found that intramolecular rotation of toluene adsorbed on charcoal is slower than that on SiO2, Al2O3 and the inversion of α and β protons in tetrahydrofuran is very fast (τc = 1.76×10?9 s). The cross relaxation plays an important role in the relaxation of molecules adsorbed on solid surfaces with low electron densities. 相似文献