ChemInform Abstract: YCa3(CrO)3(BO3)4: A Cr3+ Kagome Lattice Compound Showing No Magnetic Order Down to 2 K.

Polycrystalline gaudefroyite‐type YCa₃(CrO)₃(BO₃)₄ with Cr³⁺ ions (3d³, S = 3/2) forming an undistorted Kagome lattice is prepared by reaction of a stoichiometric mixture of Y₂O₃, CaCO₃, Cr₂O₃, H₃BO₃ in a KCl flux (Al₂O₃ crucible, 1000 °C, 1 d) followed by re‐grinding and further annealing (1000 °C, 2 d, 95% yield).     

Numerical study of an ion-exchanged glass waveguide using both two-dimensional and three-dimensional models

A numerical study is carried out to compare the two-dimensional (2-D) case and three-dimensional (3-D) case for the modelling of an ion-exchanged glass waveguide. It is shown that different waveguide widths on the photomask correspond to different ion concentration distributions after an annealing process. A numerical example is presented of two waveguide sections with different widths indicates that due to the abrupt change of the waveguide width, a 3-D theoretical model is required for an accurate prediction of the parameters of ion-exchanged glass waveguides. The good agreement between the modelled and measured results proves that the developed 3-D numerical model can be beneficially utilized in the generalized design of optical devices based on ion-exchange waveguides.     

Humidity sensor based on a single-mode hetero-core fiber structure

Using a small-core single-mode fiber (SCSMF), a novel relative humidity (RH) sensor based on an SMF28-SCSMF-SMF28 fiber structure was proposed in this paper. By depositing a humidity sensitive material, such as poly (ethylene oxide) (PEO) on the bare SCSMF fiber, the proposed structure can act as an RH sensor with high sensitivity. Experiments demonstrated that the proposed RH sensor with PEO coating can achieve a sensitivity of 430 nm per relative humidity unit (RHU) in the RH range from 80% to 83% RH and a sensitivity of 50 nm per RHU in the RH range from 83% to 95% RH.     

Embedding pointed curves in K3 surfaces

Mathematische Zeitschrift - We analyze morphisms from pointed curves to K3 surfaces with a distinguished rational curve, such that the marked points are taken to the rational curve, perhaps with...     

On the local structure of optimal measures in the multi-marginal optimal transportation problem

We consider an optimal transportation problem with more than two marginals. We use a family of semi-Riemannian metrics derived from the mixed, second order partial derivatives of the cost function to provide upper bounds for the dimension of the support of the solution.     

On graphical partitions and planarity

Chvátal gave a necessary condition for a partition to have a planar realization. It is of interest to find: (i) partitions which satisfy the condition of the theorem but have no planar realization, and also (ii) partitions which satisfy the condition and have only planar realizations. We give a list of all such partitions with 6, 7, 8 and 9 elements. We also give an algorithm for generating all graphs with a given partition, an algorithm for generating all subcompositions of a given composition and some general classes of partitions which have planar realizations only and some which have non-planar realizations only.     

The first 1-alkyl-3-perfluoroalkyl-4,5- dimethyl-1,2,4-triazolium salts

Syntheses of quaternary 1-alkyl-3-perfluoroalkyl-4,5-dimethyl-1,2,4-triazolium iodides have led to a variety of new quaternary salts via metathesis reactions. 1,4,5-Trimethyl-3-trifluoro-methyl-1,2,4-triazolium iodide (6) with LiN(SO(2)CF(3))(2), KSO(3)CF(3), AgClO(4), AgBF(4); 1-(3-fluoropropyl)-3-trifluoromethyl-4,5-dimethyl-1,2,4-triazolium iodide (7) with LiN(SO(2)CF(3))(2); and 1,4,5-trimethyl-3-perfluorooctyl-1,2,4-triazolium iodide (8) with LiN(SO(2)CF(3))(2), AgClO(4), AgBF(4) gave excellent yields of new thermally stable and relatively low melting quaternary salts. The structure of 1,4,5-trimethyl-3-perfluorooctyl-1,2,4-triazolium tetrafluoroborate (11c) was confirmed by single-crystal X-ray analysis. Although the molecular weight of 11c (cation) is 3-fold greater than that of the 3-trifluoromethyl derivative 9d, its melting point is 32 degrees C lower.     

Asymptotic enumeration of tournaments with a given score sequence containing a specified digraph

This paper studies the probability that a random tournament with specified score sequence contains a specified subgraph. The exact asymptotic value is found in the case that the scores are not too far from regular and the subgraph is not too large. An n‐dimensional saddle‐point method is used. As a sample application, we prove that almost all tournaments with a given score sequence (not too far from regular) have a trivial automorphism group. ©2000 John Wiley & Sons, Inc. Random Struct. Alg., 16: 47–57, 2000