Lack of anomalous diffusion in linear translationally-invariant systems determined by only one initial condition

It is shown that as far as the linear diffusion equation meets both time- and space-translational invariance, the time dependence of a moment of degree α is a polynomial of degree at most equal to α, while all connected moments are at most linear functions of time. As a special case, the variance is an at most linear function of time.     

Numerical analysis of the initial conditions in fractional systems

Fractional dynamics is a growing topic in theoretical and experimental scientific research. A classical problem is the initialization required by fractional operators. While the problem is clear from the mathematical point of view, it constitutes a challenge in applied sciences. This paper addresses the problem of initialization and its effect upon dynamical system simulation when adopting numerical approximations. The results are compatible with system dynamics and clarify the formulation of adequate values for the initial conditions in numerical simulations.     

Hierarchical assemblies of Si3N4 nanostructures

In the present work, for the first time, we report the growth of hierarchical assemblies of Si₃N₄ nanostructures via catalyst-assisted pyrolysis of a polymeric precursor on the Si substrates. The synthesized products were characterized by using field emission scanning electron microscopy, X-ray diffraction, and transmission electron microscopy. It is found that the size of the catalytic droplet plays a critical role on the formation of hierarchical assemblies of Si₃N₄ nanostructures rather than common single nanowire. A mechanism based on the Vapor–Liquid–Solid (VLS) process was proposed for the assembly of hierarchical Si₃N₄ nanostructures.     

Boundary problems for fractional differential equations

In this paper, the existence of solutions of fractional differential equations with nonlinear boundary conditions is investigated. The monotone iterative method combined with lower and upper solutions is applied. Fractional differential inequalities are also discussed. Two examples are added to illustrate the results.     

Ni/TPC催化剂的制备、表征及在秸秆热解燃气重整中的应用

以废弃汽车外轮胎热解后的副产物轮胎热解焦（Tyre pyrolysis char，TPC）为原料，利用均匀沉淀法制备以轮胎焦为载体的负载型Ni/TPC催化剂，采用EDX、SEM、XRD、TG、BET手段对催化剂进行了表征与分析，同时使用管式炉测试了Ni/TPC催化剂在秸秆热解燃气重整中的催化性能，并考察了热解温度、保温时间、镍负载量及催化时间对秸秆热解燃气重整效果的影响。研究结果表明，TPC富含焦和金属，Ni/TPC催化剂分散均匀，热稳定性好，比表面积为62 m²/g。催化剂活性测试显示，Ni/TPC催化剂用于作物秸秆热解燃气重整具有很强的催化活性，可显著提高燃气中可燃气体含量；热解温度在750℃、保温时间10 min、30%的Ni负载量时Ni/TPC催化剂的催化效率最高，连续使用850 min后，燃气中的H₂含量仍相对提高到50%以上，长时间使用后活性结构由Ni₃ZnC_0.7转变成FeNi₃，催化活性依然较强且趋于稳定，TPC可以作为良好的新型镍基催化剂载体。     

Entire large solutions of semilinear equations involving the fractional Laplacian

We investigate the existence and nonexistence of positive entire large solutions of a class of semilinear equations involving the fractional Laplacian. Sharp lower and upper bounds of the minimal solution, if it exists, are also given.     

Fractional Bilinear Stochastic Equations with the Drift in the First Fractional Chaos

Abstract

In the paper we compute the explicit form of the fractional chaos decomposition of the solution of a fractional stochastic bilinear equation with the drift in the fractional chaos of order one and initial condition in a finite fractional chaos. The large deviations principle is also obtained for the one-dimensional distributions of the solution of the equation perturbed by a small noise.     

On Weak Solutions of Stochastic Differential Equations II

In the first part of this article a new method of proving existence of weak solutions to stochastic differential equations with continuous coefficients having at most linear growth was developed. In this second part, we show that the same method may be used even if the linear growth hypothesis is replaced with a suitable Lyapunov condition.     

Flash Vacuum Pyrolysis: Techniques and Reactions

Flash vacuum pyrolysis (FVP) had its beginnings in the 1940s and 1950s, mainly through mass spectrometric detection of pyrolytically formed free radicals. In the 1960s many organic chemists started performing FVP experiments with the purpose of isolating new and interesting compounds and understanding pyrolysis processes. Meanwhile, many different types of apparatus and techniques have been developed, and it is the purpose of this review to present the most important methods as well as a survey of typical reactions and observations that can be achieved with the various techniques. This includes preparative FVP, chemical trapping reactions, matrix isolation, and low temperature spectroscopy of reactive intermediates and unstable molecules, the use of online mass, photoelectron, microwave, and millimeterwave spectroscopies, gas‐phase laser pyrolysis, pulsed pyrolysis with supersonic jet expansion, very low pressure pyrolysis for kinetic investigations, solution‐spray and falling‐solid FVP for involatile compounds, and pyrolysis over solid supports and reagents. Moreover, the combination of FVP with matrix isolation and photochemistry is a powerful tool for investigations of reaction mechanism.     

Statistical inference for Vasicek-type model driven by Hermite processes

Let $Z$ denote a Hermite process of order $q\ge 1$ and self-similarity parameter $H\in (\frac{1}{2},1)$. This process is $H$-self-similar, has stationary increments and exhibits long-range dependence. When $q=1$, it corresponds to the fractional Brownian motion, whereas it is not Gaussian as soon as $q?2$. In this paper, we deal with a Vasicek-type model driven by $Z$, of the form $d{X}_t=a(b?X_t)dt+d{Z}_t$. Here, $a>0$ and $b\in \mathbb{R}$ are considered as unknown drift parameters. We provide estimators for $a$ and $b$ based on continuous-time observations. For all possible values of $H$ and $q$, we prove strong consistency and we analyze the asymptotic fluctuations.