高温高压下SrB4O7：Eu2+玻璃的晶化

 利用X射线衍射和Eu²⁺发射光谱方法研究了非晶玻璃SrB₄O₇在高温高压下的晶化。结果表明：在5.0 GPa压力下，200 ℃仍为玻璃态，只有几个强度极低的小峰，表明有晶化的迹象；600 ℃时已基本晶化，但为SrB₄O₇正交相与SrB₄O₇高压立方相二相共存；当温度提高到1 000 ℃时，晶化成了近单相的与常压SrB₄O₇粉末晶体相同的正交结构。伴随晶化度的加强，Eu²⁺发射强度增强，与Ｘ射线衍射结果相一致。     

A shape-optimization technique for the capillary surface problem

Summary The problem of the construction of an equilibrium surface taking the surface tension into account leads to Laplace-Young equation which is a nonlinear elliptic free-boundary problem. In contrast to Orr et al. where an iterative technique is used for direct solution of the equation for problems with simple geometry, we propose here an alternative approach based on shape optimization techniques. The shape of the domain of the liquid is varied to attain the optimality condition. Using optimal control theory to derive expressions for the gradient, a numerical scheme is proposed and simple model problems are solved to validate the scheme.     

Lower Bounds for the Height and Size of the Ideal Class Group in CM-Fields

 We prove that, under the assumption of the Generalized Riemann Hypothesis, the exponent of the ideal class group of a CM-field goes to infinity with its absolute discriminant. This gives a positive answer to a question raised by Louboutin and Okazaki [4]. Received September 10, 2001; in revised form April 5, 2002     

A $\Gamma$-convergence result for doubling metric measures and associated perimeters

Abstract. In this paper we study the notion of perimeter associated with doubling metric measures or strongly weights. We prove that the metric perimeter in the sense of L. Ambrosio and M. Miranda jr. coincides with the metric Minkowski content and can be obtained also as a -limit of Modica-Mortola type degenerate integral functionals. Received: 27 August 2001 / Accepted: 29 November 2001 / Published online: 10 June 2002 Investigation supported by University of Bologna, funds for selected research topics and by GNAMPA of INdAM, Italy. The authors are very grateful to Luigi Ambrosio and Francesco Serra Cassano for making their preprints available to them, for listening with patience and for many unvaluable suggestions.     

A remark on the moduli field of a curve

We give a purely algebro-geometric proof of the fact that every nonsingular projective curve can be defined over a finite extension of its moduli field. This extends a result byWolfart [7] to curves over fields of arbitrary characteristic. Received: 30 November 2001     

Symmetric Groups and Lattices

This paper deals with various problems in lattice theory involving local extrema. In particular, we construct infinite series of highly symmetric spherical 3-designs which include some of the examples constructed in [9] in dimensions 5 and 7. We also construct new types of dual-extreme lattices.Received June 29, 2002; in final form January 14, 2003 Published online May 16, 2003     

On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

 We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond–J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Perron algorithm. Received September 30, 2001; in revised form January 8, 2002     

Computational complexity of stable partitions with B-preferences

Consider a special stable partition problem in which the player's preferences over sets to which she could belong are identical with her preferences over the most attractive member of a set and in case of indifference the set of smaller cardinality is preferred. If the preferences of all players over other (individual) players are strict, a strongly stable and a stable partition always exists. However, if ties are present, we show that both the existence problems are NP-complete. These results are very similar to what is known for the stable roommates problem. Received: July 2000/Revised: October 2002 RID="*" ID="*"  This work was supported by the Slovak Agency for Science, contract #1/7465/20 “Combinatorial Structures and Complexity of Algorithms”.     

The Yamabe problem for almost Hermitian manifolds

The conformal class of a Hermitian metric g on a compact almost complex manifold (M^2m, J) consists entirely of metrics that are Hermitian with respect to J. For each one of these metrics, we may define a J-twisted version of the Ricci curvature, the J-Ricci curvature, and its corresponding trace, the J-scalar curvature s^J. We ask if the conformal class of g carries a metric with constant s^J, an almost Hermitian version of the usual Yamabe problem posed for the scalar curvature s. We answer our question in the affirmative. In fact, we show that (2m−1)s^J−s=2(2m−1)W(ω, ω), where W is the Weyl tensor and ω is the fundamental form of g. Using techniques developed for the solution of the problem for s, we construct an almost Hermitian Yamabe functional and its corresponding conformal invariant. This invariant is bounded from above by a constant that only depends on the dimension of M, and when it is strictly less than the universal bound, the problem has a solution that minimizes the almost complex Yamabe functional. By the relation above, we see that when W (ω, ω) is negative at least one point, or identically zero, our problem has a solution that minimizes the almost Hermitian Yamabe functional, and the universal bound is reached only in the case of the standard 6-sphere equipped with a suitable almost complex structure. When W(ω, ω) is non-negative and not identically zero, we prove that the conformal invariant is strictly less than the universal bound, thus solving the problem for this type of manifolds as well. We discuss some applications.