Finite-gap Solutions of the Fuchsian Equations

We find a new class of Fuchsian equations, with algebro-geometric solutions associated to a hyperelliptic curve. A method for calculating its arithmetic genus and branching points is suggested. Numerous examples are given.     

Spin-glass behavior and magnetocaloric effect in melt-spun TbCuAl alloys

Magnetic properties and magnetocaloric effects of amorphous and crystalline TbCuAl ribbons are investigated by measuring their ac susceptibilities including a nonlinear term and dc magnetizations. The in-phase third harmonic ac susceptibility is found to be negative. It can be well fitted by the expression at high temperatures, indicating a spin-glass behavior in amorphous TbCuAl alloy. ΔT_f(ω)/[T_f(ω)Δlog₁₀ω], a possible distinguishing criterion to judge the presence of a spin-glass behavior is ∼0.011. The frequency-dependent data can be well fitted by the conventional critical slowing down law and the spin-glass transition temperature is obtained to be 20.1 K. The maximum of magnetic entropy change reaches 4.5 J kg⁻¹ K⁻¹ for a field change of 0-50 000 Oe, while the crystalline TbCuAl compound experiences a simple ferromagnetic-to-paramagnetic phase transition. The peak value of magnetic entropy change is obtained at the Curie temperature and reaches 14.4 J kg⁻¹ K⁻¹ for the same field change, which is much larger than that of amorphous TbCuAl alloy.     

Fractal localized structures related to Jacobian elliptic functions in the higher-order Broer－Kaup system

This work reveals a novel phenomenon—that the localized coherent structures of a (2﹢1)﹣dimensional physical model possesses fractal behaviours. To clarify the interesting phenomenon, we take the (2﹢1)﹣dimensional higher-order Broer－Kaup system as a concrete example. Starting from a B?cklund transformation, we obtain a linear equation, and then a general solution of the system is derived. From this some special localized excitations with fractal behaviours are obtained by introducing some types of lower-dimensional fractal patterns that related to Jacobian elliptic functions.     

Spectrophonic humidity-trace detection in hydrogen and air

A spectrophone with low resonant frequency compatible with the repetition frequency of a pulsed discharge CO laser is described. The spectrophone is used for humidity detection in hydrogen and air. The simple and inexpensive system provides a detection capacity of 10–100ppb/ . The responsivity of the resonant spectrophone is interpreted taking the dependence of the acoustical quality factor on the geometry into account.     

Application of a CW chemical laser for remote pollution monitoring and process control

The measurement of the concentration of gaseous hydrogen fluoride in the exhaust of an aluminum plant by resonance absorption of the radiation of a cw chemical HF laser is reported. The HF concentration has been evaluated taking into account the simultaneous absorption of water vapor and carbon dioxide at the HF laser frequencies. The absorption cross sections for H₂O and CO₂ at the HF laser lines have been determined in laboratory experiments.     

猪瘟病毒HCLV株E_2核苷酸序列与结构分析

用 Ｒ Ｔ Ｐ Ｃ Ｒ技术从 Ｃ Ｓ Ｆ Ｖ Ｈ Ｃ Ｌ Ｖ 株 Ｆ４８２ 代感染兔脾的细胞总 Ｒ Ｎ Ａ 中分段扩增出了 Ｃ Ｓ Ｆ Ｖ Ｅ２ 基因特异的３ 个部分重叠的 Ｄ Ｎ Ａ 片段（大小分别为 ４９９ ｂｐ、５７２ ｂｐ 和 ２４５ ｂｐ）,并将之分别克隆到ｐ Ｇ Ｅ Ｍ Ｔ 载体上 经核苷酸序列测定和片段重叠完成了包含 Ｅ２ 全长基因的 １ １４４ ｂｐ 序列的测定,其 Ｇ Ｃ含量为４９．０％ ：核苷酸序列与国外报道的各株病毒的 Ｅ２ 基因同源性分别为８３．５％ ～９７．５％ ;其推导的氨基酸序列的同源性也分别为８９．３％～９６．２％ ,变异主要分布在 Ｅ２ 蛋白的 Ｎ 半部分     

A new quantum group associated with a ‘nonstandard’ braid group representation

A new quantum group is derived from a nonstandard braid group representation by employing the Faddeev-Reshetikhin-Takhtajan constructive method. The classical limit is not a Lie superalgebra, despite relations like x ²–y ²=0. We classify all finite-dimensional irreducible representations of the new Hopf algebra and find only one- and two-dimensional ones.     

Dirichlet norms,capacities and generalized isoperimetric inequalities for Markov operators

We define the notion of p-capacity for a reversible Markov operator on a general measure space and prove that uniform estimates for the ratio of capacity and measure are equivalent to certain imbedding theorems for the Orlicz and Dirichlet norms. As a corollary we get results on connections between embedding theorems and isoperimetric properties for general Markov operators and, particularly, a generalization of the Kesten theorem on the spectral radius of random walks on amenable groups for the case of arbitrary graphs with non-finitely supported transition probabilities.     

On a problem of Erdős and Lovász: Random lines in a projective plane

Letn(k) be the least size of an intersecting family ofk-sets with cover numberk, and let _k denote any projective plane of orderk–1.Theorem There is a constant A such that ifH is a random set ofm Aklogk lines from _k then P_r(H<)0(k).Corollary If there exists a _k thenn(k)=O(klogk). These statements were conjectured by P. Erds and L. Lovász in 1973.Supported in part by NSF-DMS87-83558 and AFOSR grants 89-0066, 89-0512 and 90-0008