Conditional independence models for seemingly unrelated regressions with incomplete data

We consider normal ≡ Gaussian seemingly unrelated regressions (SUR) with incomplete data (ID). Imposing a natural minimal set of conditional independence constraints, we find a restricted SUR/ID model whose likelihood function and parameter space factor into the product of the likelihood functions and the parameter spaces of standard complete data multivariate analysis of variance models. Hence, the restricted model has a unimodal likelihood and permits explicit likelihood inference. In the development of our methodology, we review and extend existing results for complete data SUR models and the multivariate ID problem.     

Fundamental groups of the complements of certain plane non-tame torus sextics

The moduli space of torus sextics with the configuration of singularities {A₂+A₅+2E₆} has two connected components. We compute the fundamental groups π₁(CP²−C) for sextics C in both components and study their differences.     

New examples of Osserman metrics with nondiagonalizable Jacobi operators

Explicit examples of Osserman 4-manifolds with exactly two distinct eigenvalues of the Jacobi operators, α and β=4α≠0, are given. The former has multiplicity two and is a double root of the minimal polynomial of the Jacobi operators.     

The AB2-XA1 electronic transition of NO2: A rovibronic survey covering 14 300-18 000 cm

More than 250 rotationally resolved vibrational bands of the A²B₂-X²A₁ electronic transition of ¹⁵NO₂ have been observed in the 14 300-18 000 cm⁻¹ range. The bands have been recorded in a recently constructed setup designed for high resolution spectroscopy of jet cooled molecules by combining time gated fluorescence spectroscopy and molecular beam techniques. The majority of the observed bands has been rotationally assigned and can be identified as transitions starting from the vibrational ground state or from vibrationally excited (hot band) states. An exceptionally strong band is located at 14 851 cm⁻¹ and studied in more detail as a typical benchmark transition to monitor ¹⁵NO₂ in atmospheric remote sensing experiments. Standard rotational fit routines provide band origins, rotational and spin rotation constants. A subset of 177 vibronic levels of ²B₂ vibronic symmetry has been analyzed in the energy range between 14 300 and 17 250 cm⁻¹, in terms of integrated density and using Next Neighbor Distribution. It is found that the overall statistical properties and polyad structure of ¹⁵NO₂ are comparable to those of ¹⁴NO₂ but that the internal structures of the polyads are completely different. This is a direct consequence of the X²A₁-A²B₂ vibronic mixing.     

Solid-phase epitaxy of CaSi2 on Si(1 1 1) and the Schottky-barrier height of CaSi2/Si(1 1 1)

Thin Ca films were evaporated on Si(1 1 1) under UHV conditions and subsequently annealed in the temperature range 200–650 °C. The interdiffusion of Ca and Si was examined by ex situ Auger depth profiling. In situ monitoring of the Si 2p core-level shift by X-ray photoemission spectroscopy (XPS) was employed to study the silicide formation process. The formation temperature of CaSi₂ films on Si(1 1 1) was found to be about 350 °C. Epitaxial growth takes place at T≥400 °C. The morphology of the films, measured by atomic force microscopy (AFM), was correlated with their crystallinity as analyzed by X-ray diffraction (XRD). According to measurements of temperature-dependent I–V characteristics and internal photoemission the Schottky-barrier height of CaSi₂ on Si(1 1 1) amounts to qΦ_Bn=0.25 eV on n-type and to qΦ_Bp=0.82 eV on p-type silicon.     

HgCl2/I2复合催化剂协同催化合成异丙醇钇的研究

以金属钇和异丙醇为原料，以HgCl2/I2为复合催化剂，通过对金属钇的机械加工以增加其比表面，并将异丙醇脱水使其含水量降低至0．05％，体系在82℃回流5h，经过滤、减压蒸馏，得到了白色海绵状异丙醇钇，其产率高达83％，合成时间比文献报道的缩短了19h，产率提高了8％。文章确定了催化剂的最佳用量为20gY加入60mg HgCl2/I2，研究了合成产率与HgCl2/I2催化剂和HgCl2催化剂的依赖关系及异丙醇中含水量对合成产率的影响，并对HgCl2/I2的催化作用机理进行了初步探讨。     

Inclusion of carbon nanotubes in a TiO2 sol-gel matrix

We report here the successful inclusion of carbon nanotubes (CNs) into a TiO₂ matrix prepared by a sol-gel method. The presence of CNs in the sol-gel matrix and the structure of the film were analyzed principally by transmission electron microscopy. Complementary information about the behavior of embedded carbon nanotubes versus heat treatment and ion irradiation were obtained by X-ray photoelectron spectroscopy. The elaboration of an inorganic matrix containing embedded carbon nanotubes leads to a new nanocomposite. The possible applications of this nanocomposite are discussed.     

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     

Symmetries and conservation laws of partial differential equations: Basic notions and results

The main notions and results which are necessary for finding higher symmetries and conservation laws for general systems of partial differential equations are given. These constitute the starting point for the subsequent papers of this volume. Some problems are also discussed.     

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.