Cosmic inflation and model comparison

We analyze the implications for inflation of the recently released Planck Cosmic Microwave Background data and explain why the single-field slow-roll scenarios with minimal kinetic terms are favored. Within this class of models, we show how Bayesian model comparison can be used to further exclude about one third of the inflationary scenarios. We also study the end of inflation and show that Planck can already constrain the reheating phase. Finally, we conclude by discussing how future missions will be able to improve our knowledge of the inflationary mechanism.     

LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

Tutorial review on validation of liquid chromatography–mass spectrometry methods: Part I

This is the part I of a tutorial review intending to give an overview of the state of the art of method validation in liquid chromatography mass spectrometry (LC–MS) and discuss specific issues that arise with MS (and MS/MS) detection in LC (as opposed to the “conventional” detectors). The Part I briefly introduces the principles of operation of LC–MS (emphasizing the aspects important from the validation point of view, in particular the ionization process and ionization suppression/enhancement); reviews the main validation guideline documents and discusses in detail the following performance parameters: selectivity/specificity/identity, ruggedness/robustness, limit of detection, limit of quantification, decision limit and detection capability. With every method performance characteristic its essence and terminology are addressed, the current status of treating it is reviewed and recommendations are given, how to determine it, specifically in the case of LC–MS methods.     

Full Bayesian analysis of claims reserving uncertainty

We revisit the gamma–gamma Bayesian chain-ladder (BCL) model for claims reserving in non-life insurance. This claims reserving model is usually used in an empirical Bayesian way using plug-in estimates for the variance parameters. The advantage of this empirical Bayesian framework is that allows us for closed form solutions. The main purpose of this paper is to develop the full Bayesian case also considering prior distributions for the variance parameters and to study the resulting sensitivities.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.     

达布定理和比较定理思想在中值定理类问题中的运用

微分达布定理表明区间内的导函数具有介值性,这使得我们在考虑一些数学分析问题时,往往可以不需要最高阶导函数的连续性.而在微分方程理论中,比较定理的思想对于解的估计非常重要.本文利用比较定理的思想将中值定理类问题转化为微分方程解的估计问题,对于在数学分析的学习中提高学生的认识和兴趣很有意义.     

A De Giorgi Type Result to Divergence Degenerate Elliptic Equation with Bounded Coefficients Related To Hörmander's Vector Fields

In this paper, we consider the divergence degenerate elliptic equation with bounded coefficients constructed by Hörmander's vector fields. We prove a De Giorgi type result, i.e., the local Hölder continuity for the weak solutions to the equation by providing a De Giorgi type lemma and extending the Moser iteration to the setting here. As a consequence, the Harnack inequality of weak solutions is also given.     

位移时空综合分析法及其在边坡工程中的应用

以往对监测位移数据分析方法主要是位移-时间关系分析。但监测数据包含了大量对工程设计和施工都很有用的信息，其中不乏位移-空间方面的信息；另一方面，从工程设计和施工角度看，除需要位移-时间信息外，还需要位移-空间信息。位移时空综合分析法的提出旨在综合位移-时间和位移-空间等两方面的信息，为工程设计和施工服务。该方法依表现形式不同又分为竖线法和曲面法两种。本文将通过五强溪船闸边坡工程实例，来进一步说明位移时空综合分析法的原理及其应用。