Probabilism,entropies and strictly proper scoring rules

Accuracy arguments are the en vogue route in epistemic justifications of probabilism and further norms governing rational belief. These arguments often depend on the fact that the employed inaccuracy measure is strictly proper. I argue controversially that it is ill-advised to assume that the employed inaccuracy measures are strictly proper and that strictly proper statistical scoring rules are a more natural class of measures of inaccuracy. Building on work in belief elicitation I show how strictly proper statistical scoring rules can be used to give an epistemic justification of probabilism.An agent's evidence does not play any role in these justifications of probabilism. Principles demanding the maximisation of a generalised entropy depend on the agent's evidence. In the second part of the paper I show how to simultaneously justify probabilism and such a principle. I also investigate scoring rules which have traditionally been linked with entropies.     

Sobolev Stability of Plane Wave Solutions to the Nonlinear Schrödinger Equation

This article explores the questions of long time orbital stability in high order Sobolev norms of plane wave solutions to the NLSE in the defocusing case.     

Semilinear wave models with friction and viscoelastic damping

In this paper, we study the global (in time) existence of small data solutions to the Cauchy problem for the semilinear wave equation with friction, viscoelastic damping, and a power nonlinearity. We are interested in the connection between regularity assumptions for the data and the admissible range of exponents p in the power nonlinearity.     

基于学生群体心理测试系统的设计

心理测试的根本目的是为了让人们在测试过程中，产生某些特定行为，即个体对测试题目的反应，并根据这些行为反应来推论其相应的心理特性。在一定程度上帮助我们了解人类的心理活动，并从中得到帮助。因此，本文对基于学生群体心理测试系统的设计进行深入研究。     

Recent Progress in the $L_p$ Theory for Elliptic and Parabolic Equations with Discontinuous Coefficients

In this paper, we review some results over the last 10-15 years on elliptic and parabolic equations with discontinuous coefficients. We begin with an approach given by N. V. Krylov to parabolic equations in the whole space with $\rm{VMO}_x$ coefficients. We then discuss some subsequent development including elliptic and parabolic equations with coefficients which are allowed to be merely measurable in one or two space directions, weighted $L_p$estimates with Muckenhoupt ($A_p$) weights, non-local elliptic and parabolic equations, as well as fully nonlinear elliptic and parabolic equations.     

基于化学学科认知障碍突破的中考复习教学实践* ——以“二氧化碳的性质”为例

分析学生对二氧化碳的3个典型学科认知障碍,以“二氧化碳的捕捉”为情境,通过“尝试捕捉二氧化碳”“谁在捕捉二氧化碳”“捕捉背后的原理”等3个主要环节,实现对学科认知障碍的突破,展示了一种新的中考复习教学思路。     

Convergence of solutions for the fractional Cahn–Hilliard system

This paper deals with the Cauchy–Dirichlet problem for the fractional Cahn–Hilliard equation. The main results consist of global (in time) existence of weak solutions, characterization of parabolic smoothing effects (implying under proper condition eventual boundedness of trajectories), and convergence of each solution to a (single) equilibrium. In particular, to prove the convergence result, a variant of the so-called ?ojasiewicz–Simon inequality is provided for the fractional Dirichlet Laplacian and (possibly) non-analytic (but $C^1$) nonlinearities.     

Cycloparaphenylene (CPP) series are molecular models for graphene armchair edges: trends in their aromaticity and cyclic conjugation are evaluated

Cycloparaphenylene ([r]CPP) and cyclacene ([r]CA) series are models for short carbon nanotubes. It is shown that armchair edges in model cycloparaphenylenes possess greater aromaticity and cyclic conjugation than do zigzag edges in model cyclacenes. According to Aihara’s bond resonance energy (BRE) and Bosanac and Gutman energy effect (ef) measurements, cycloparaphenylenes are twice as aromatic as cyclacenes. The general solution of all eigenvalues of all members of the cycloparaphenylene series is given. The origin of the recurrence of some eigenvalues are determined.     

Using d-limonene as the non-aromatic and non-chlorinated solvent for the fabrications of high performance polymer light-emitting diodes and field-effect transistors

Aiming to environment protection, green solvents are crucial for commercialization of solution-processed optoelectronic devices. In this work, d-limonene, a natural product, was introduced as the non-aromatic and non-chlorinated solvent for processing of polymer light-emitting diodes (PLEDs) and organic field effect transistors (OFETs). It was found that d-limonene could be a good solvent for a blue-emitting polyfluorene-based random copolymer for PLEDs and an alternating copolymer FBT-Th₄(1,4) with high hole mobility (μ_h) for OFETs. In comparisons to routine solvent-casted films of the two conjugated polymers, the resulting d-limonene-deposited films could show comparable film qualities, based on UV–vis absorption spectra and observations by atomic force microscopy (AFM). With d-limonene as the processing solvent, efficient blue PLEDs with CIE coordinates of (0.16, 0.16), maximum external quantum efficiency of 3.57%, and luminous efficiency of 3.66 cd/A, and OFETs with outstanding μ_h of 1.06 cm² (V s)⁻¹ were demonstrated. Our results suggest that d-limonene would be a promising non-aromatic and non-chlorinated solvent for solution processing of conjugated polymers and molecules for optoelectronic device applications.