Regional, Single Point, and Global Blow-Up for the Fourth-Order Porous Medium Type Equation with Source

Blow-up behaviour for the fourth-order quasilinear porous medium equation with source,ut=-（｜u｜^nu）xxxx＋｜u｜^p-1u in R×R＋,where n 〉 0, p 〉 1, is studied. Countable and finite families of similarity blow-up patterns of the form us（x,t）=（T-t）^-1/p-1f（y）,where y=x/（T-t）^β＇ β=p-（n＋1）/4（p-1）,which blow-up as t → T^- 〈∞ are described. These solutions explain key features of regional （for p = n＋1）, single point （for p 〉 n＋1）, and global （for p ∈ （1,n＋1））blowup. The concepts and various variational, bifurcation, and numerical approaches for revealing the structure and multiplicities of such blow-up patterns are presented.     

带移民的碰撞分枝过程的唯一性

本文提出了一种带移民的碰撞分枝过程,它由三部分组成:马氏分枝过程、碰撞分枝过程和状态独立的移民过程,给出了该过程正则性和唯一性判别准则。     

Computer‐Aided Optimization of Conditions for Fast and Controlled ICAR ATRP of n‐Butyl Acrylate

The potential of initiators for continuous activator regeneration atom transfer radical polymerization (ICAR ATRP) for the synthesis of well‐defined poly(n‐butyl acrylate) is analyzed by means of simulations. The kinetic model accounts for reactivity differences between secondary and tertiary macrospecies and considers the possible influence of diffusional limitations. CuBr₂ is used as transition metal salt and the commercially available N,N,N′,N″,N″‐pentamethyldiethylenetriamine as ligand. For targeted chain lengths (TCLs) up to 1000, the ICAR ATRP can be performed relatively quickly, and with ppm levels of ATRP catalyst. For moderate TCLs, slightly higher ppm levels are required if excellent control over chain length is also desired. In all cases, limited loss of end‐group functionality (EGF) results.

     

Bisexual Galton‐Watson Branching Process in Varying Environments

Abstract

In this paper we introduce a bisexual Galton‐Watson branching process (BGWP) in which the offspring probability distribution is different in each generation. We obtain some relations among the probability generating functions (pgf) involved in the model and, making use of mean growth rates and fractional linear functions (flf), we provide sufficient and necessary conditions for its almost sure extinction.     

Asymptotic Behavior of Critical Primitive Multi-Type Branching Processes with Immigration

Under natural assumptions a Feller-type diffusion approximation is derived for critical multi-type branching processes with immigration when the offspring mean matrix is primitive (in other words, positively regular). Namely, it is proved that a sequence of appropriately scaled random step functions formed from a sequence of critical primitive multi-type branching processes with immigration converges weakly toward a squared Bessel process supported by a ray determined by the Perron vector of the offspring mean matrix.     

Limiting Distributions for Multitype Branching Processes

In this article, the asymptotic behavior of multitype Markov branching processes with discrete or continuous time is investigated in the positive regular and nonsingular case when both the initial number of ancestors and the time tend to infinity. Some limiting distributions are obtained as well as multivariate asymptotic normality is proved. The article also considers the relative frequencies of distinct types of individuals motivated by applications in the field of cell biology. We obtained non-random limits for the frequencies and multivariate asymptotic normality when the initial number of ancestors is large and the time of observation increases to infinity. In fact this paper continues the investigations of Yakovlev and Yanev [32 Yakovlev , A.Y. , and Yanev , N.M. 2009 . Relative frequencies in multitype branching processes . Annals of Applied Probability 19 ( 1 ): 1 – 14 . [Google Scholar]] where the time was fixed. The new obtained limiting results are of special interest for cell kinetics studies where the relative frequencies but not the absolute cell counts are accessible to measurement.     

Rate Coeffcients and Branching Ratio for Multi-Channel Hydrogen Abstractions from CH3OH by F

The hydrogen abstraction reaction F+CH₃OH has two possible reaction pathways: HF+CH₃O and HF+CH₂OH. Despite the absence of intrinsic barriers for both channels, the former has a branching ratio comparable to the latter, which is far from the statistical limit of 0.25 (one out of four available H atoms). Furthermore, the measured branching ratio of the two abstraction channels spans a large range and is not quantitatively reproduced by previous theoretical predictions based on the transition-state theory with the stationary point information calculated at the levels of M?ller-Plesset perturbation theory and G2. This work reports a theoretical investigation on the kinetics and the associated branching ratio of the two competing channels of the title reaction using a quasi-classical trajectory approach on an accurate full-dimensional potential energy surface (PES) fitted by the permutation invariant polynomial-neural network approach to ca. 1.21x10⁵ points calculated at the explicitly correlated (F12a) version of coupled cluster singles doubles and perturbative triples (CCSD(T)) level with the aug-cc-pVDZ basis set. The calculated room temperature rate coeffcient and branching ratio of the HF+CH₃O channel are in good agreement with the available experimental data. Furthermore, our theory predicts that rate coeffcients have a slightly negative temperature dependence, consistent with barrierless nature of the reaction.     

钯原子谱线的分支比测量

运用钯元素空心阴极灯和高分辨率光栅单色仪测量了钯原子4d⁹6s和4d⁹5d组态的7个偶宇称能级的发射光谱,确定了这些能级向4d⁹5p组态能级跃迁产生的15条谱线的跃迁分支比.本文大部分结果是对文献中钯元素原子相关光谱参数的重要修正. 关键词： 原子光谱 钯原子 分支比 空心阴极灯     

Moderate Deviation for the Rightmost Position in a Branching Brownian Motion

We study the moderate deviation probability of the position of the rightmost particle in a branching Brownian motion and obtain its moderate deviation function. Firstly, Chauvin and Rouault studied the large deviation probability for the rightmost position in a branching Brownian motion. Recently, Derrida and Shiconsidered lower deviation for the same model. By contrast, Our main result is more extensive.     

Ignition of hydrogen–oxygen and stoichiometric hydrogen–methane–oxygen mixtures on hot wires at low pressures

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