Infrared spectra of two isomers of OCS-C2H2 and OCS-C2D2 in the region of OCS ν1 fundamental

Infrared spectra of OCS-C₂H₂ and OCS-C₂D₂ complexes in the region of the C-O stretching fundamental of OCS (∼2060 cm⁻¹) are studied in a pulsed supersonic slit-jet expansion using a tunable diode laser. For each complex, two bands are observed and assigned to distinct near-parallel and the T-shaped isomers. Ground state parameters were previously determined from microwave studies, so analysis of the infrared spectra gives information on the vibrational shifts upon complex formation as well as rotational and centrifugal distortion parameters for the excited states. All four bands show a red shift with respect to the monomer band origin, with the T-shaped isomer having a much larger shift than the near-parallel isomer. Disappearance of the T-shaped isomer when argon is used as a carrier gas supports the notion that the near-parallel isomer is the lowest energy form of the complex.     

A descent principle for the Dirac-dual-Dirac method

Let G be a torsion-free discrete group with a finite-dimensional classifying space BG. We show that G has a dual-Dirac morphism if and only if a certain coarse (co-)assembly map is an isomorphism. Hence the existence of a dual-Dirac morphism for such groups is a metric, that is, coarse, invariant. We get results for groups with torsion as well.     

在可交换四元数空间中的双曲方程的特征边值问题

讨论了一阶和二阶双曲复方程的特征边值问题.对其中两种线性方程,分别在不同的情况下获得通解和可解条件.而对于拟线性的二阶双曲复方程,证明了解的存在性和唯一性.     

无衍射特殊光束的产生与三维表征

无衍射光束(如贝塞尔光束、艾里光束)因具有无衍射、自愈合的特性, 在很多领域都有广泛的应用. 本文提出使用纯相位型空间光调制器对光场的复振幅进行调控, 从而可以产生多种复杂模式的无衍射光束, 如强度可独立调控的多个零阶贝塞尔光束, 两个高阶贝塞尔光束干涉生成的花瓣状无衍射光束, 具有多个主瓣的加速光束等特殊的无衍射光束. 通过在待测焦场附近放置一个平面反射镜, 使其沿光轴快速扫描光场, 并由数字相机同步拍摄反射回来的一系列二维光场强度分布信息, 可实现对无衍射光束三维光场强度分布的快速测量和表征. 本实验方法和技术可以快速产生各种复杂的特殊光场并获得其精确的三维可视化重建效果, 在光学显微、光学俘获、光学微加工等领域有潜在的应用价值.     

多复变数的二阶微分从属

在文[1－2]的基础上讨论了多复变数中的二阶微分从属，取得了一些结果。这些结果是文[1-5]中的一些结果的推广。     

Fusion,fission, and annihilation of complex waves for the(2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff system

With the help of the symbolic computation system, Maple and Riccati equation( ξ= a0+ a1ξ+ a22ξ), expansion method, and a linear variable separation approach, a new family of exact solutions with q = lx + my + nt + Γ(x, y,t) for the(2+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff system(GCBS) are derived. Based on the derived solitary wave solution, some novel localized excitations such as fusion, fission, and annihilation of complex waves are investigated.     

A generalized Schrödinger equation via a complex Lagrangian of electrodynamics

In this paper we give a generalized form of the Schrödinger equation in the relativistic case, which contains a generalization of the Klein-Gordon equation. By complex Legendre transformation, the complex Lagrangian of electrodynamics produces a complex relativistic Hamiltonian H of electrodynamics, on the holomorphic cotangent bundle T′* M. By a special quantization process, a relativistic time dependent Schrödinger equation, in the adapted frames of (T′* M, H) is obtained. This generalized Schrödinger equation can be expressed with respect to the Laplace operator of the complex Hamilton space (T′*M, H). Finally, under some additional conditions on the proper time s of the complex space-time M and the time parameter t along the quantum state, by the method of separation of variables, we obtain two classes of solutions for the Schrödinger equation, one for the weakly gravitational complex curved space M, and the second in the complex space-time with Schwarzschild metric.     

Ionic conductivity in three crystalline phases of LiBH4 under pressure

The AC electrical conductivity of LiBH₄ was investigated below 2 GPa between 1 Hz and 1.6 MHz. The high-temperature phase has an ionic conductivity of up to 0.01 S cm^?1, while the low-temperature phases have conductivities two orders of magnitude lower. All phases show an Arrhenius behaviour with activation energies E _a between 0.5 and 0.7 eV, in good agreement with earlier data except for phase III, which is found to have the highest activation energy of the phases studied. The high-temperature phase has a minimum in E _a near 1 GPa, close to the triple point, correlated with a sudden change in activation volume. These features may indicate an isostructural phase transition. The conductivities of the ambient temperature phases increase temporarily by an order of magnitude after transitions between these phases, probably due to new diffusion channels via structural defects. The phase diagram agrees well with earlier results.     

2—Harmonic Totally Real Submanifolds in a Complex Projective Space

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Trees, parking functions, syzygies, and deformations of monomial ideals

For a graph , we construct two algebras whose dimensions are both equal to the number of spanning trees of . One of these algebras is the quotient of the polynomial ring modulo certain monomial ideal, while the other is the quotient of the polynomial ring modulo certain powers of linear forms. We describe the set of monomials that forms a linear basis in each of these two algebras. The basis elements correspond to -parking functions that naturally came up in the abelian sandpile model. These ideals are instances of the general class of monotone monomial ideals and their deformations. We show that the Hilbert series of a monotone monomial ideal is always bounded by the Hilbert series of its deformation. Then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals. In some cases these resolutions coincide with Scarf resolutions. We prove several formulas for Hilbert series of monotone monomial ideals and investigate when they are equal to Hilbert series of deformations. In the appendix we discuss the abelian sandpile model.