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We consider the diffusion process X on ℝ with radial diffusion and drift coefficients. We prove that once the one-dimensional diffusion | X| has algebraic L-convergence, so does X. And some classical examples are discussed. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the family of harmonic measures (indexed by with ) on the unit sphere in , for . We study the corresponding optimal constants of logarithmic Sobolev and Poincaré inequalities, denoted respectively by and . We show that the Poincaré constant essentially depends on the dimension only, as . The behavior of is more intricate and depends on the interplay between position and dimension. [Copyright &y& Elsevier]

Constructing some proper functional spaces, we obtain the corresponding norm for the operator (−ℒ), and then, via spectral theory, we revisit two variational formulas of the spectral gap, given by M. F. Chen [Front. Math. China, 2010, 5(3): 379-515], for transient birth-death processes. [ABSTRACT FROM AUTHOR]

Using forward-backward stochastic calculus, we prove convex concentration inequalities for some additive functionals of the solution of stochastic differential equations with jumps admitting an invariant probability measure. As a consequence, transportation-information inequalities are obtained and bounds on option prices for interest rate derivatives are given as an application. [ABSTRACT FROM AUTHOR]

The structures of two one-dimensional coordination complexes, [MII(3-Bzpy)2(N(CN)2)2] (M = Mn ( 1) and Co ( 2) and 3-Bzpy = 3-benzoylpyridine), have been determined in this work. The two structures are isomorphous, crystallize in a monoclinic P21/ c space group, and show almost the same crystal structure. The magnetic measurements of the two compounds (2-300 K) indicate that antiferromagnetic exchanges exist between the metal ions of the two compounds. [ABSTRACT FROM AUTHOR]

The bug triaging process, an essential process of assigning bug reports to the most appropriate developers, is related closely to the quality and costs of software development. Since manual bug assignment is a labor-intensive task, especially for large-scale software projects, many machine learning-based approaches have been proposed to triage bug reports automatically. Although developer collaboration networks (DCNs) are dynamic and evolving in the real world, most automated bug triaging approaches focus on static tossing graphs at a single time slice. Also, none of the previous studies consider periodic interactions among developers. To address the problems mentioned above, in this article, we propose a novel spatial–temporal dynamic graph neural network (ST-DGNN) framework, including a joint random walk (JRWalk) mechanism and a graph recurrent convolutional neural network (GRCNN) model. In particular, JRWalk aims to sample topological structures in a developer collaboration network with two sampling strategies by considering both developer reputation and interaction preference. GRCNN has three components with the same structure, i.e., hourly-periodic, daily-periodic, and weekly-periodic components, to learn the spatial–temporal features of nodes on dynamic DCNs. We evaluated our approach's effectiveness by comparing it with several state-of-the-art graph representation learning methods in three domain-specific tasks (i.e., the bug fixer prediction task and two downstream tasks of graph representation learning: node classification and link prediction). In the three tasks, experiments on two real-world, large-scale developer collaboration networks collected from the Eclipse and Mozilla projects indicate that the proposed approach outperforms all the baseline methods on three different time scales (i.e., long-term, medium-term, and short-term predictions) in terms of F 1 − score. [ABSTRACT FROM AUTHOR]

TiO2 nanotubes with diameters of 10 nm and lengths up to 600 nm were fabricated by directly using commercial TiO2 powders P25 as the precursors via sonication-hydrothermal combination approach. TiO2 nanotubes were characterized by means of X-ray powder diffractometer (XRD), scanning electron microscope (SEM), selected area electron diffraction pattern (SAED) and transmission electron microscope (TEM). The light scattering property of film electrodes modified with TiO2 nanotubes was studied and revealed that TiO2 nanotubes can be used as the light scattering centers to increase the light absorption in dye-sensitized solar cells. The TiO2 nanotubes film electrodes mixed with 10% small nanoparticles TiO2 had both strong light scattering property and fine mechanical characteristics, and this kind of electrodes can be used as electrodes in improving the conversion efficiencies of dye-sensitized solar cells. [ABSTRACT FROM AUTHOR]