On a conjecture of Cox and Katz

This note shows that a certain toric quotient of the quintic Calabi-Yau threefold in provides a counterexample to a recent conjecture of Cox and Katz concerning nef cones of toric hypersurfaces. Received: 8 February 2001; in final form: 17 September 2001 / Published online: 1 February 2002     

On the density of the space of continuous and uniformly continuous functions

For X a metrizable space and (Y,ρ) a metric space, with Y pathwise connected, we compute the density of (C(X,(Y,ρ)),σ)—the space of all continuous functions from X to (Y,ρ), endowed with the supremum metric σ. Also, for (X,d) a metric space and (Y,‖⋅‖) a normed space, we compute the density of (UC((X,d),(Y,ρ)),σ) (the space of all uniformly continuous functions from (X,d) to (Y,ρ), where ρ is the metric induced on Y by ‖⋅‖). We also prove that the latter result extends only partially to the case where (Y,ρ) is an arbitrary pathwise connected metric space.To carry such an investigation out, the notions of generalized compact and generalized totally bounded metric space, introduced by the author and A. Barbati in a former paper, turn out to play a crucial rôle. Moreover, we show that the first-mentioned concept provides a precise characterization of those metrizable spaces which attain their extent.     

IFS attractors and Cantor sets

We build a metric space which is homeomorphic to a Cantor set but cannot be realized as the attractor of an iterated function system. We give also an example of a Cantor set K in R³ such that every homeomorphism f of R³ which preserves K coincides with the identity on K.     

Electron spin resonance of diluted solid solutions of MnO2 in Y2O3

Electron spin resonance spectra of Mn²⁺ in diluted solid solutions of MnO₂ in Y₂O₃ have been studied at room temperature for Mn concentrations between 0.20 and 2.00 mol%. Isolated Mn²⁺ ions in sites with two different symmetries were observed, as well as Mn²⁺ ions coupled by the exchange interaction. The relative concentration of isolated to coupled Mn²⁺ ions decreases with increasing manganese concentration. The results are consistent with the assumption that the manganese ions occupy preferentially the C₂ symmetry sites. A theoretical calculation based on this model yields an effective range of the exchange interaction between Mn²⁺ ions of 0.53 nm, of the same order as that of Mn²⁺ ions in CaO.     

Study of thermal currents in powder β-spodumene ceramics doped with Cuo, FeO and TiO2

Ternary-phase ceramic system of Li₂O Al₂O₃ 4SiO₂ doped with CuO, FeO and TiO₂ has been prepared and subjected to dc electrical conductivity and thermally stimulated depolarization current (TSDC) measurements as a function of temperature (30-250 °C) and field strength. The electrical conductivity results are explained by assuming both ionic and electronic conduction mechanisms coexist with different contributions over the whole temperature range of experiments. TSDC spectra have been found to be characterized by a broad intense relaxation peak, which can be attributed to an ionic charge polarization. The broad relaxation transitions are apparently a result of the nonuniform nature of this process. Activation energies are calculated for both dc electrical conductivity and TSDC according to Arrhenius equation and initial rise method, respectively.     

Syntactic characterization of closure under connected limits

Summary We give a syntactic characterization of (finitary) theories whose categories of models are closed under the formation of connected limits (respectively the formation of pullbacks and substructures) in the category of all structures. They are also those theories whose consistent extensions by new atomic facts admit in each component an initial structure (respectively an initial term structure), and also thoseT for whichM(T) is locally finitely multi-presentable in a canonical way. We also show that these two properties of theories are nonuniform.     

High pressure X-ray diffraction study of CdAl2Se4 and Raman study of AAl2Se4 (A=Hg, Zn) and CdAl2X4 (X=Se, S)

We report the results of an X-ray diffraction study of CdAl₂Se₄ and of Raman studies of HgAl₂Se₄ and ZnAl₂Se₄ at room temperature, and of CdAl₂S₄ and CdAl₂Se₄ at 80 K at high pressure. The ambient pressure phase of CdAl₂Se₄ is stable up to a pressure of 9.1 GPa above which a phase transition to a disordered rock salt phase is observed. A fit of the volume pressure data to a Birch-Murnaghan type equation of state yields a bulk modulus of 52.1 GPa. The relative volume change at the phase transition at ∼9 GPa is about 10%. The analysis of the Raman data of HgAl₂Se₄ and ZnAl₂Se₄ reveals a general trend observed for different defect chalcopyrite materials. The line widths of the Raman peaks change at intermediate pressures between 4 and 6 GPa as an indication of the pressure induced two stage order-disorder transition observed in these materials. In addition, we include results of a low temperature Raman study of CdAl₂S₄ and CdAl₂Se₄, which shows a very weak temperature dependence of the Raman-active phonon modes.     

Synthesis and characterisation of cadmium titanium oxide thin films by sol-gel technique

Crack free, dense and transparent CdTiO₃ thin films have been prepared by sol-gel technique using titanium butoxide and cadmium acetate. The formation of the CdTiO₃ phase started from 500°C annealing temperature onwards. The complete orthorhombic structure of CdTiO₃ was formed on Silicon (100) substrate at an annealing temperature of 600°C for 5 h. As the annealing temperature increased from 600 to 700°C, we have observed the cadmium silicate phase at the interface of Si and CdTiO₃ phase. Structural, morphological and elemental evolution of these CdTiO₃ thin films produced by sol-gel synthesis were characterised by grazing incidence X-ray diffraction (GIXRD), tapping mode atomic force microscopy (TMAFM), scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS) respectively.     

Au-Au2S复合纳米球壳微粒的空腔谐振及参量讨论

Au-Au2S复合纳米球壳微粒（金纳米球壳），是一种新型复合结构的纳米微粒，其结构为纳米级的Au2S介质球外包裹了一层几个纳米厚的黄金球壳。这种复合纳米球壳微粒可以被抽象为球型谐振腔。报道了它的空腔谐振吸收的实验结果，并且运用经典理论结合介观结构特征，讨论了有关Au-Au2S复合纳米球壳微粒空腔谐振吸收的一些重要参量，其中包括谐振吸收波长、品质因数、谐振能量等。另外，还讨论了金球壳的厚度对这些重要参量的影响。