Heavy tails for an alternative stochastic perpetuity model

In this paper we consider a stochastic model of perpetuity-type. In contrast to the classical affine perpetuity model of Kesten (1973) and Goldie (1991) all discount factors in the model are mutually independent. We prove that the tails of the distribution of this model are regularly varying both in the univariate and multivariate cases. Due to the additional randomness in the model the tails are not pure power laws as in the Kesten–Goldie setting but involve a logarithmic term.     

Bounded stationary reflection II

Bounded stationary reflection at a cardinal λ is the assertion that every stationary subset of λ reflects but there is a stationary subset of λ that does not reflect at arbitrarily high cofinalities. We produce a variety of models in which bounded stationary reflection holds. These include models in which bounded stationary reflection holds at the successor of every singular cardinal $\mu >{\mathrm{?}}_{\omega }$ and models in which bounded stationary reflection holds at ${\mu }^{+}$ but the approachability property fails at μ.     

Coupling of CFD Simulations and Population Balance Modeling to Predict Brownian Coagulation in an Emulsion Polymerization Reactor

In this study a framework consisting of a computational fluid dynamics simulation coupled to a population balance model for the modeling of emulsion polymerizations is proposed. The combined approach is used to understand the impact of changing length and time scales, as well as mixing conditions on the particle size distribution (PSD) of a polymer latex under different conditions. It is shown that the effect of agitation rate can have a profound impact on the distribution of ionic species in the reactor, and thus on the evolution of the PSD.

     

应用图论分析与最优化理论来数据挖掘大规模水牛普里昂蛋白结构数据

图论、最优化理论显然在蛋白质结构的研究中大有用场. 首先, 调查/回顾了研究蛋白质结构的所有图论模型. 其后, 建立了一个图论模型: 让蛋白质的侧链来作为图的顶点, 应用图论的诸如团、 $k$-团、 社群、 枢纽、聚类等概念来建立图的边. 然后, 应用数学最优化的现代摩登数据挖掘算法/方法来分析水牛普里昂蛋白结构的大数据. 成功与令人耳目一新的数值结果将展示给朋友们.     

考虑损伤的修正梯度弹性理论

梯度弹性理论在描述材料微结构起主导作用的力学行为时具有显著优势,将其与损伤理论相结合,可在材料破坏研究中考虑微结构的影响.基于修正梯度弹性理论,将应变张量、应变梯度张量和损伤变量作为Helmholtz自由能函数的状态变量,并在自然状态附近对自由能函数作Taylor展开,进而由热力学基本定律,推导出修正梯度弹性损伤理论本构方程的一般形式.编制有限元程序,模拟土样损伤局部化带的发展演化过程.结果表明,修正梯度弹性损伤理论消除了网格依赖性;损伤局部化带不是与损伤同时发生,而是在损伤发展到一定程度后再逐渐显现出来.     

Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions

In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd.     

Mapping the Complete Photocycle that Powers a Large Stokes Shift Red Fluorescent Protein

Large Stokes shift (LSS) red fluorescent proteins (RFPs) are highly desirable for bioimaging advances. The RFP mKeima, with coexisting cis- and trans-isomers, holds significance as an archetypal system for LSS emission due to excited-state proton transfer (ESPT), yet the mechanisms remain elusive. We implemented femtosecond stimulated Raman spectroscopy (FSRS) and various time-resolved electronic spectroscopies, aided by quantum calculations, to dissect the cis- and trans-mKeima photocycle from ESPT, isomerization, to ground-state proton transfer in solution. This work manifests the power of FSRS with global analysis to resolve Raman fingerprints of intermediate states. Importantly, the deprotonated trans-isomer governs LSS emission at 620 nm, while the deprotonated cis-isomer's 520 nm emission is weak due to an ultrafast cis-to-trans isomerization. Complementary spectroscopic techniques as a table-top toolset are thus essential to study photochemistry in physiological environments.     

Two-Dimensional Conjugated Metal-Organic Frameworks with Large Pore Apertures and High Surface Areas for NO2 Selective Chemiresistive Sensing

The emergence of two-dimensional conjugated metal–organic frameworks (2D c-MOFs) with pronounced electrical properties (e.g., high conductivity) has provided a novel platform for efficient energy storage, sensing, and electrocatalysis. Nevertheless, the limited availability of suitable ligands restricts the number of available types of 2D c-MOFs, especially those with large pore apertures and high surface areas are rare. Herein, we develop two new 2D c-MOFs (HIOTP-M, M=Ni, Cu) employing a large p-π conjugated ligand of hexaamino-triphenyleno[2,3-b:6,7-b′:10,11-b′′]tris[1,4]benzodioxin (HAOTP). Among the reported 2D c-MOFs, HIOTP-Ni exhibits the largest pore size of 3.3 nm and one of the highest surface areas (up to 1300 m² g⁻¹). As an exemplary application, HIOTP-Ni has been used as a chemiresistive sensing material and displays high selective response (405 %) and a rapid response (1.69 min) towards 10 ppm NO₂ gas. This work demonstrates significant correlation linking the pore aperture of 2D c-MOFs to their sensing performance.     

Large scale synthesis of red emissive carbon dots powder by solid state reaction for fingerprint identification

Red emissive carbon dots(CDs) powder was synthesized on a large scale from phloroglucinol and boric acid by a novel solid state reaction with yield up to 75%. This method is safe and convenient, for it needs neither high pressure reactors nor complicated post-treatment procedures. The as-prepared carbon dots powder exhibited strong red fluorescence with excitation-independent behavior. XPS measurement and PL spectra suggest that such red fluorescence arise from boron-doped structures in CDs, which increases along with the boron concentration on CDs surface but decreases when the concentration quenching effect takes place. To overcome the aggregation induced fluorescence quenching of the solid CDs powder,the conventional methods are dispersing CDs into a large amount of inert substrates. But our present work provides a new strategy to realize strong red fluorescence of CDs in solid state. As a result, such carbon dots powder works well for latent fingerprint identification on various material surfaces.