Small generators of number fields

If K is a number field of degree n over Q with discriminant D _K and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d ² such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real number field of prime degree n then one can find an integral generator α with . Received: 10 January 1997 / Revised version: 13 January 1998     

Growth and long-run stability

This paper analyses the implications of persistent growth upon the stability properties of dynamic models. Besides the traditional concept of asymptotic stability, new stability criteria-strong/weak absolute, strong/weak relative, strong/weak logarithmic stability-are introduced, and global stability conditions for satisfying these criteria are stated for general first-order autonomous differential equations. The conflict between rapidity of growth and the degree of stability is demonstrated. Economic applications of the stability theorems are illustrated within the growth models of Harrod and Solow.     

W_(18)Cr_4V钢真空油淬白亮层、熔化层形成原因的试验研究

W_(18)Cr_4V钢真空加热油淬后,表面出现白亮层和熔化层等异常现象。本文利用金相显微镜,显微硬度计、扫描电子显微镜和电子探针等手段对白亮层和熔化层进行了分析研究。试验表明,白亮层、熔化层均是真空油淬增碳的结果。本文对白亮层、溶化层形成原因进行了比较深入的分析探讨提出了产生白亮层必须同时具备的三个条件。     

Optimal Domains for <Emphasis Type="Italic">L</Emphasis><Superscript>0</Superscript>-valued Operators Via Stochastic Measures

We study extension of operators T: E→ L⁰([0, 1]), where E is an F–function space and L⁰([0, 1]) the space of measurable functions with the topology of convergence in measure, to domains larger than E, and we study the properties of such domains. The main tool is the integration of scalar functions with respect to stochastic measures and the corresponding spaces of integrable functions. Partially supported by D.G.I. #MTM2006-13000-C03-01 (Spain).     

Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system

We construct a local interacting quantum dimer model on the square lattice, whose zero-temperature phase diagram is characterized by a line of critical points separating two ordered phases of the valence bond crystal type. On one side, the line of critical points terminates in a quantum transition inherited from a Kosterlitz-Thouless transition in an associated classical model. We also discuss the effect of a longer-range dimer interaction that can be used to suppress the line of critical points by gradually shrinking it to a single point. Finally, we propose a way to generalize the quantum Hamiltonian to a dilute dimer model in presence of monomers and we qualitatively discuss the phase diagram.     

LaMgAl11O19∶R(R＝Tb,Mn)的真空紫外光谱特性

采用高温固相反应法合成了LaMgAl11O19∶R (R=Mn, Tb)荧光体, 测量了荧光体的真空紫外激发光谱和相应的发射光谱, 观察到基质吸收带位于170 nm附近, Mn2+离子的吸收位于170～510 nm范围, Tb3+ 离子的4f-5d吸收位于170～250 nm范围. 在147 nm激发下, 它们发射绿光. 真空紫外光谱特性的研究表明, 基质与激活离子之间存在较好的能量传递.     

Spectroscopy on very neutron-rich nuclei beyond N = 20

Recent studies on nuclear structure by using radioactive isotope beams available at the RIKEN projectile-fragment separator (RIPS) are introduced. Special emphasis is given to two selected experiments from recent programs that highlight studies on the magicity loss observed for very neutron-rich nuclei beyond N = 20 in the “island-of-inversion” region; the particle stability of ³¹F, and the low-lying excited states of ³⁴Mg. Received: 1 May 2001 / Accepted: 4 December 2001     

纤维双相钢的组织形成及对性能的影响

研究了纤维双相15Mn2Nb钢组织的形成及对性能的影响.结果表明,纤维双相钢具有优异的强塑性匹配,是一种天然的复合材料.其纤维组织的获取主要取决于合金化和热处理工艺规程,而合金元素Nb阻碍铁素体再结晶是形成纤维组织的关键.     

Effect of Mn substitution on the delicate balance between structure and properties of Gd1.4Ce0.6Sr2RuCu2O10

Some new members of a ruthenocuprate(2212) series have been synthesized by Mn substitution for Ru in Gd_1.4Ce_0.6Sr₂RuCu₂O₁₀. Characterization by x-ray diffraction (XRD) phase analysis has been carried out. Changes in structural features on substitution, including a significant change in lattice parameter for a very low substitution level, have been observed. Four-probe resistivity studies indicate the coexistence of superconductivity and magnetism for the pristine compound and a semiconductor-like upturn in resistivity and the absence of superconductivity even for very low levels of Mn substitution. AC susceptibility measurements show a progressive suppression of the magnetic transition temperature as well as a smearing of the magnetic transition as a function of Mn substitution. Possible reasons for the absence of superconductivity have been discussed.     

Rebuilding of metal components with laser cladding forming

Laser cladding forming (LCF) is a novel powerful tool for the repairing of metal components. Rebuilding of V-grooves on medium carbon steel substrates has been carried out with laser cladding forming technique using stainless steel powder as the cladding material. Microstructure of the deposited layers has been characterized using optical microscopy (OM), scanning electron microscopy (SEM), energy dispersive X-ray microanalysis (EDAX), electron probe microanalysis (EPMA) and X-ray diffraction (XRD). Mechanical properties of the rebuilt V-groove samples have been evaluated by tensile and impacting tests and microhardness measurement. Experimental results show that good fusion bonding between the rebuilt layers and the substrate has been formed, and the microstructure of the cladding layers is mainly composed of fine, dense and defect-free epitaxial columnar dendrites. Due to the effect of grain size refinement, the tensile strength, impacting toughness, elongation and microhardness of the rebuilt samples have been greatly enhanced compared to those of the substrate. Microhardness is also very uniform throughout the rebuilt regions. With the growth of the deposited layers, the microhardness increases gradually. The good ductility of the deposited regions is verified by the SEM fracture analysis.