The universal central extension of the three-point loop algebra

We consider the three-point loop algebra,

where denotes a field of characteristic 0 and is an indeterminate. The universal central extension of was determined by Bremner. In this note, we give a presentation for via generators and relations, which highlights a certain symmetry over the alternating group . To obtain our presentation of , we use the realization of as the tetrahedron Lie algebra.

     

BCK一代数的扩张(1)

本文给出BCK一代数三种新的扩张方法,并用扩张方法,给出s阶BCK一代数的完全分类.     

BCK-代数的几个计数定理

本文推广了文献中的有限BCK-代数子代数个数估计定理,给出了任意BCK-代数的子代数个数下界的一个估计。对于n阶BCK-代数和n阶半直接既约交换BCK-代数,本文分别给出了其子代数个数下界的较具体的表达公式。另处我们还讨论了互不同构的n阶BCK-代数的个数的下界值的估计问题。     

比较逻辑的研究

本文引入几种比较运算,并讨论了它们的表示、有关性质及其在处理逻辑函数中的应用。此外,还提出了使用晶体管的比较逻辑门及通用比较逻辑门的设计。作者认为,由于比较运算揭示了电路中开关元件的作用实质,因此,充分利用晶体管功能的比较逻辑单元,可在数字集成电路的设计中得到应用。     

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.