Photofragment translational spectroscopy of iodobenzene at 266 nm

The photofragmentation of C_6 H_5I at 266 nm is investigated on the nuiversal crossed molecular beam machine, and the translational spectroseopy as well as the angular distribution of I atom is measured. The results reveal that under the laser intensity of 10~8 W/cm~2 the single-phuton dissociation competes with multi-photon processes. In singlephoton dissociation the anisotropy parameter β is 0.4 and the average translational energy is only 1.04 keal/mol, which indicates that this process is a slow predissociation. In two-photon phutofragmentation the average translational energy is 51.64 kcal/mol, which accounts for about 35% of the available energy. Another photofragmentation channel is even more faster, whose peak in time-of-flight spectra corresponds to four or five photon absorptions. The branching ratio of these three channels is determined to be about 3: 3: 4.     

Complementarity of universal calibration SEC and 13C NMR in determining the branching state of polyethylene

The quantitation of long‐chain branching (LCB) and short‐chain branching (SCB) in polyethylene (PE) was accomplished with a combination of carbon nuclear magnetic resonance (¹³C NMR) spectroscopy and size exclusion chromatography (SEC) with universal calibration. We demonstrate how the spectroscopic and chromatographic techniques can supplement each other, as neither is capable individually of completely describing the molecular architecture imparted by the various types of branching. The essential lack of impact of SCB on the hydrodynamic volume imposes a limit on SEC for determining this type of branching, whereas highly effective LCB in the PE molecule may not offer a statistically large enough amount of long chains for accurate determination by NMR. A variety of examples are given for PE, showcasing the advantages and shortcomings of each analytical method and their complementarity. Additionally, the importance of choosing an appropriate linear standard and viscosity shielding ratio (ϵ) for the Zimm–Stockmayer branching calculations employed for analyzing SEC data is emphasized with an examination of the effect on the results of using a branched standard and various ϵ values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 3120–3135, 2000     

Tiny families of functions with random properties: A quality-size trade-off for hashing

We present three explicit constructions of hash functions, which exhibit a trade-off between the size of the family (and hence the number of random bits needed to generate a member of the family), and the quality (or error parameter) of the pseudorandom property it achieves. Unlike previous constructions, most notably universal hashing, the size of our families is essentially independent of the size of the domain on which the functions operate. The first construction is for the mixing property—mapping a proportional part of any subset of the domain to any other subset. The other two are for the extraction property—mapping any subset of the domain almost uniformly into a range smaller than it. The second and third constructions handle, respectively, the extreme situations when the range is very large or very small. We provide lower bounds showing that our constructions are nearly optimal, and mention some applications of the new constructions. © 1997 John Wiley & Sons, Inc. Random Struct. Alg., 11 , 315–343 (1997)     

Universal Expression of Efficiency at Maximum Power: A Quantum-Mechanical Brayton Engine Working with a Single Particle Confined in a Power-Law Trap

We propose a quantum-mechanical Brayton engine model that works between two superposed states, employing a single particle confined in an arbitrary power-law trap as the working substance. Applying the superposition principle, we obtain the explicit expressions of the power and efficiency, and find that the efficiency at maximum power is bounded from above by the function:η+ =θ/(θ+ 1), with being a potential-dependent exponent.     

Universal function for the brilliance of undulator radiation considering the energy spread effect

Angular and spatial profiles of undulator radiation have been investigated to derive a universal function that evaluates the brilliance of undulator radiation and takes into account the effects of electron beam emittance and energy spread. It has been found that the effects of energy spread on the angular divergence and source size can be expressed by simple analytic expressions, and a universal brilliance function has been derived by convolution with the electron beam distribution functions. Comparisons with numerical results have been carried out to show the validity and applicability of the universal function.     

Commutativity of the centralizer of a subalgebra in a universal enveloping algebra

Let G be a reductive algebraic group over an algebraically closed field of characteristic zero, and let \(\mathfrak{h}\) be an algebraic subalgebra of the tangent Lie algebra \(\mathfrak{g}\) of G. We find all subalgebras \(\mathfrak{h}\) that have no nontrivial characters and whose centralizers \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} \) and \(P(\mathfrak{g})^\mathfrak{h} \) in the universal enveloping algebra \(\mathfrak{U}(\mathfrak{g})\) and in the associated graded algebra \(P(\mathfrak{g})\), respectively, are commutative. For all these subalgebras, we prove that \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} = \mathfrak{U}(\mathfrak{h})^\mathfrak{h} \otimes \mathfrak{U}(\mathfrak{g})^\mathfrak{g} \) and \(P(\mathfrak{g})^\mathfrak{h} = P(\mathfrak{h})^\mathfrak{h} \otimes P(\mathfrak{g})^\mathfrak{g} \). Furthermore, we obtain a criterion for the commutativity of \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} \) in terms of representation theory.     

万有Teichmüller空间不同模型中的测地线唯一性

研究万有Teichmülle空间不同模型中的测地线的唯一性问题。证明了在万有Teichmülle空间中存在两个点,它们之间的测地线唯一,但在万有Teichmülle空间的Schwarz导数与Pre-Schwarz导数模型中,这两个点所对应的点之间的测地线不唯一。     

Coefficient of Performance at Maximum χ-Criterion for Feynman Ratchet as a Refrigerator

The χ-criterion is defined as the product of the energy conversion efficiency and the heat absorbed per unit time by the working substance [de Tomás et al., Phys. Rev. E 85 (2012) 010104(R)]. The χ-criterion for Feynman ratchet as a refrigerator operating between two heat baths is optimized. Asymptotic solutions of the coefficient of performance at maximum χ-criterion for Feynman ratchet are investigated at both large and small temperature difference. An interpolation formula, which fits the numerical solution very well, is proposed. Besides, the sufficient condition for the universality of the coefficient of performance at maximum χ is investigated.     

热机载荷作用下三维界面裂纹问题的权函数法分析

热机载荷共同作用下双材料和复合材料中的裂纹扩展往往发生在界面处,并且工程中实际遇到的裂纹大多数是三维裂纹.由于通用权函数仅仅与裂纹体的几何形状有关,与载荷、时间无关,因此在求解复杂冲击载荷下界面裂纹应力强度因子随时间的变化过程时,避免了反复的应力分析,计算效率得到提高.根据Betti互易原理,论文推导出三维界面裂纹问题通用权函数法的普遍表达式,并给出了热机载荷共同作用下三维界面Ⅰ型、Ⅱ型和Ⅲ型裂纹问题通用权函数法的有限元格式.通过与实例计算比较,表明此方法得到的结果可以达到满意的工程应用精度.