Hyperbolic spaces are of strictly negative type

We study finite metric spaces with elements picked from, and distances consistent with, ambient Riemannian manifolds. The concepts of negative type and strictly negative type are reviewed, and the conjecture that hyperbolic spaces are of strictly negative type is settled, in the affirmative. The technique of the proof is subsequently applied to show that every compact manifold of negative type must have trivial fundamental group, and to obtain a necessary criterion for product manifolds to be of negative type.

     

Randomized algorithms for the separation of point sets and for solving quadratic programs

A randomized algorithm for finding a hyperplane separating two finite point sets in the Euclidean space ^d and a randomized algorithm for solving linearly constrained general convex quadratic problems are proposed. The expected running time of the separating algorithm isO(dd! (m + n)), wherem andn are cardinalities of sets to be separated. The expected running time of the algorithm for solving quadratic problems isO(dd! s) wheres is the number of inequality constraints. These algorithms are based on the ideas of Seidel's linear programming algorithm [6]. They are closely related to algorithms of [8], [2], and [9] and belong to an abstract class of algorithms investigated in [1]. The algorithm for solving quadratic problems has some features of the one proposed in [7].This research was done when the author was supported by the Alexander von Humboldt Foundation, Germany.On leave from the Institute of Mathematics and Mechanics, Ural Department of the Russian Academy of Sciences, 620219 Ekaterinburg, S. Kovalevskaya str. 16, Russia.     

On k-Strictly Convex and k-Very Smooth Banach Spaces

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Curing of liquid epoxy resin in plasma discharge

Epoxy resins in the solid state, liquid state and during polymerisation were treated by microwave oxygen plasma and analysed by FTIR spectra. Curing, etching and oxidation kinetics of epoxy resin were observed. In the liquid resin and polymerising mixture the effect of structure modification was observed more intensively than in the case of solid sample due to a mixing process. A modification of bulk layers of liquid epoxy resin was observed under plasma action. The polymerisation reaction of epoxy resin with amine hardening agent can be released in plasma discharge at low pressure.     

Conduction mechanism of metal-TiO2–Si structures

The conduction model has been proposed for the metal-TiO₂–Si (MIS) structures. Rutile films have been prepared on Si substrates by magnetron sputtering of TiO₂ target and annealing in the air at temperatures T?=?800 and 1050 K. The current-voltage (CVC) and capacitance-voltage characteristics of the structures have been measured over the range of T?=?283–363 K. At positive potentials on the gate, the conductivity of the MIS structures is determined by the space charge-limited current in the dielectric layer.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

Goniopolarimetry: Space-borne radio astronomy with imaging capabilities

The principles of space-based low-frequency radio astronomy (below 50 MHz) are briefly introduced. As the wavelength range considered does not allow the use of focusing systems, goniopolarimetric (or direction-finding) techniques have been developed. These inversion techniques provide the direction of the wave vector, the polarization state and the flux of the observed electromagnetic wave. In case of spatially extended sources, we can also infer an order of magnitude of the apparent source size. These techniques are presented, and their limitations are discussed. An example from a recent study illustrates the techniques and capabilities.     

直觉I-Fuzzy拓扑空间的杨忠道定理

以L~*-格值上Lukasiewicz蕴含算子为工具引入了直觉I-Fuzzy拓扑空间中导集概念,接着给出它的一些性质,最后证明了直觉I-Fuzzy拓扑空间中导集的杨忠道定理.