Price formation model with zero-Neumann boundary condition

ABSTRACT

This paper concerns the mathematical analysis of a mathematical model for price formation. We take a large number of rational buyers and vendors in the market who are trading the same good into consideration. Each buyer or vendor will choose his optimal strategy to buy or sell goods. Since markets seldom stabilize, our model mimics the real market behavior. We introduce three models. All of them are modifications of the original J.-M. Lasry and P. L. Lions evolution model. In the first modified model, a random term is added to mimic the randomness of trading in the real market. This reflects markets with low volatility, where it might be difficulty to buy or sell goods at specific price. In the second model, we use cumulative density function instead of density function. We give numerical simulations on these two models in order to have a general picture on the solution. In the third model, we add a term associated with the parameter R to destabilize the original Larsy–Lions model and study oscillations and wave solutions depending on different values of R. We also study existence and uniqueness of the solution. Moreover, Several plots are given to demonstrate these results corresponding to the theoretical prediction.     

Chen's Reagent: A Versatile Reagent for Trifluoromethylation,Difluoromethylenation, and Difluoroalkylation in Organic Synthesis

Methyl fluorosulfonyldifluoroacetate(FSO2CF2CO2Me or MFSDA),often called"Chen's reagent",is commonly used to synthesize trifluoromethylated and difluoroalkylated compounds.This important reagent was initially developed as an efficient trifluoromethylating agent by Professor Qing-Yun Chen and co-workers at Shanghai Institute of Organic Chemistry,Chinese Academy of Sciences in 1989.     

Catalytic properties of mesoporous materials supported heteropoly acids for Baeyer-Villiger oxidation of cyclic ketones

Three mesoporous molecular sieves loaded silicotungstic acids, named HSiW/SBA-15, HSiW/MCM-41, HSiW/MCM-48, were prepared and characterised by XRD, FT-IR, TEM and SEM. The catalytic performance of the prepared materials for the Baeyer-Villiger oxidation of cyclic ketones was carried out in the presence of 30%H₂O₂ under mild conditions. These loading materials were proved to be efficient and reusable catalysts, they all exhibited excellent catalytic performance for the Baeyer-Villiger oxidation of cyclic ketones with 30% H₂O₂ as oxidant. Many cyclic ketones were efficiently converted to the corresponding lactones with up to 90% conversions and high selectivities under the optimum reaction conditions.

Cyclic ketones were efficiently oxidised by mesoporous materials sopported silicotungstic acid to the corresponding lactones with 30%H₂O₂ as oxidant. All of the catalysts showed promising recyclability in the reactions.     

Modeling and simulation of weld line location and properties during injection molding based on viscoelastic constitutive equation

Rheologica Acta - Weld lines are one of the typical quality issues of injection molded parts. They are unavoidable even for moderate complex products. To explore the formation of weld lines in...     

基于平面度的燃料电池电化学性能模拟

 固体氧化物燃料电池的翘曲会影响电极-盖板界面的接触情况，从而影响电化学性能，对相关制造工艺提出了很大的挑战．为了分析燃料电池平面度对放电过程的影响，揭示其潜在的风险，我们建立了两个基于有限元法的仿真模型，对考虑平面度缺陷的燃料电池封装和放电进行分析．在对固体氧化物燃料电池进行平面度测量的基础上，首先建立了具有真实燃料电池翘曲特性的几何模型，分析封装过程中接触压力的分布情况．然后将接触电阻的仿真结果导入到三维多物理场耦合模型中，模拟具有平面度缺陷的燃料电池电化学性能．计算结果展示了燃料电池两侧封装过程中接触压力的分布情况．通过对比有接触电阻和无接触电阻的燃料电池电流密度，分析了电池与盖板的接触对放电过程的影响．结果表明，燃料电池的凹陷面较难达到满意的接触状态，需要比凸起面更大的封装压力．燃料电池表面接触电阻的变化将引起电流传导路径的变化，产生局部高电流或低电流．这项工作强调了在燃料电池中保持均匀分布的接触电阻的重要性，为今后的优化工作奠定了基础．     

A longitudinal air–water trans-media dynamic model for slender vehicles under low-speed condition

Nonlinear Dynamics - A trans-media aerial underwater vehicle (TMAUV) could break through the single-medium limitation with the abilities to fly in the air, navigate underwater, and cross the...     

FRET-based ratiometric fluorescent detection of arginine in mitochondrion with a hybrid nanoprobe

A ratiometric fluorescent hybrid nanoprobe CDs-1 for arginine(Arg),exhibiting high sensitivity(the limit of detection,LOD,being 6.5×10^-8 mol/L) and excellent selectivity and anti-interference ability,was fabricated through fluorescence resonance energy transfer(FRET) and the electrostatic attraction between positively-charged hemicyanine molecules and negatively-charged carbon dots(CDs).Arg can be quantitatively detected in the concentration range from 6.0×10^-5 mol/L to 2.7×10^-4 mol/L.Further,due to its ability to target mitochondrion and low cytotoxicity,intracellular Arg was succes s fully tracked through ratiometric fluorescence imaging.     

An improved evaluation of the neutron background in the PandaX-Ⅱ experiment

In dark matter direct detection experiments,neutron is a serious source of background,which can mimic the dark matter-nucleus scattering signals.In this paper,we present an improved evaluation of the neutron background in the PandaX-II dark matter experiment by a novel approach.Instead of fully relying on the Monte Carlo simulation,the overall neutron background is determined from the neutron-induced high energy signals in the data.In addition,the probability of producing a dark-matter-like background per neutron is evaluated with a complete Monte Carlo generator,where the correlated emission of neutron(s)andγ(s)in the(α,n)reactions and spontaneous fissions is taken into consideration.With this method,the neutron backgrounds in the Run 9(26-ton-day)and Run 10(28-ton-day)data sets of PandaX-II are estimated to be(0.66±0.24)and(0.47±0.25)events,respectively.     

A Comparison of Two Isoreticular Metal–Organic Frameworks with Cationic and Neutral Skeletons: Stability,Mechanism, and Catalytic Activity

Although many ionic metal–organic frameworks (MOFs) have been reported, little is known about how the charge of the skeleton affects the properties of the MOF materials. Herein we report how the chemical stability of MOFs can be substantially improved through embedding electrostatic interactions in structure. A MOF with a cationic skeleton is impervious to extremely acidic, oxidative, reductive, and high ionic strength conditions, such as 12 m HCl (301 days), aqua regia (86 days), H₂O₂ (30 days), and seawater (30 days), which is unprecedented for MOFs. DFT calculations suggested that steric hinderance and the repulsive interaction of the cationic framework toward positively charged species in microenvironments protects the vulnerable bonds in the structure. Diverse functionalities can be bestowed by substituting the counterions of the charged framework with identically charged functional species, which broadens the horizon in the design of MOFs adaptable to a demanding environment with specific functionalities.     

CsVO2F(IO3): An Excellent SHG Material Featuring an Unprecedented 3D [VO2F(IO3)]− Anionic Framework

The first alkali-metal vanadium iodate fluoride, CsVO₂F(IO₃), with a novel 3D anionic framework, has been rationally designed and hydrothermally synthesized. The 3D [VO₂F(IO₃)]⁻ framework in CsVO₂F(IO₃) is built from 0D Λ-shaped cis-[VO₃F(IO₃)₂]⁴⁻ polyanions via corner-sharing of oxo anions and bridging of the iodate groups. CsVO₂F(IO₃) displays both a strong second-harmonic generation (SHG) 1.1 times as strong as KTiOPO₄ (KTP) under 2.05 μm laser radiation and high laser-induced damage threshold (LIDT) of 107.9 MW cm⁻². This work provides a new route to design SHG crystals with stable 3D anionic structures from low-dimensional structural building units.