Rate of convergence in the law of large numbers for supercritical general multi-type branching processes

We provide sufficient conditions for polynomial rate of convergence in the weak law of large numbers for supercritical general indecomposable multi-type branching processes. The main result is derived by investigating the embedded single-type process composed of all individuals having the same type as the ancestor. As an important intermediate step, we determine the (exact) polynomial rate of convergence of Nerman’s martingale in continuous time to its limit. The techniques used also allow us to give streamlined proofs of the weak and strong laws of large numbers and ratio convergence for the processes in focus.     

Span 80 effect on the solvent extraction for heavy oil recovery

In this study, we used the Span 80 to enhance solvent extraction process, and we explored the mechanism. The results indicated different solvents would obtain different oil recovery, and toluene showed the optimal oil recovery, and the n-heptane showed the lowest oil recovery. The complex solvents could improve oil recovery. Toluene could make the heavy oil show the lowest viscosity (89.6 Pa.S), and n-heptane make the heavy oil show the highest viscosity (176.3 Pa.S). Complex solvents could decrease the heavy oil viscosities. The higher C/H was, the higher heavy oil recovery was, and when the asphaltene and resins content increase, the C/H would increase. The C/H showed the highest value (9.09, by toluene) and the lowest value (8.15). In this study, Span 80 could increase heavy oil C/H ratio, decrease heavy oil viscosity. Span 80 could make the sands surface more hydrophilic, and then the solvent loss would decrease. The oil recovery was high after 10 times recycle use.     

Multifractal detrended fluctuation analysis of derivative and spot markets

We investigate the multifractal properties of price increments in the cases of derivative and spot markets. Through the multifractal detrended fluctuation analysis, we estimate the generalized Hurst and the Renyi exponents for price fluctuations. By deriving the singularity spectrum from the above exponents, we quantify the multifractality of a financial time series and compare the multifractal properties of two different markets. The different behavior of each agent-group in transactions is also discussed. In order to identify the nature of the underlying multifractality, we apply the method of surrogate data to both sets of financial data. It is shown that multifractality due to a fat-tailed distribution is significant.     

The Sixth Painlevé Equation as Similarity Reduction of $${\widehat{\mathfrak{gl}}_3}$$ Generalized Drinfel’d–Sokolov Hierarchy

Scaling symmetry of -type Drinfel’d–Sokolov hierarchy is investigated. Applying similarity reduction to the hierarchy, one can obtain the Schlesinger equation with (n + 1) regular singularities. Especially in the case of n = 3, the hierarchy contains the three-wave resonant system and the similarity reduction gives the generic case of the Painlevé VI equation. We also discuss Weyl group symmetry of the hierarchy.      

Spherically Averaged Endpoint Strichartz Estimates For The Two­Dimensional Schrödinger Equation

The endpoint Strichartz estimates for the Schrödinger equation is known to be false in two dimensions[7]. However, if one averages the solution in L2 in the angular variable, we show that the homogeneous endpoint and the retarded half­endoint estimates hold, but the full retarded endpoint fails. In particular, the original verisions of these estimates hold for radial data     

Structure and Photoelectric Characteristics of Functional Polymers and of Compositions Based on Them

The electronic processes in disordered organic solids were analyzed, classified, and summarized. They include the photogeneration of charge pairs, electron transport, geminal and bimolecular recombination, and the capture of charge carriers in local electronic states. General criteria were formulated for the targeted search for and the creation of new prospective polymers and their compositions with organic pigments and related compounds having specific photoelectric characteristics for electrographic and holographic media, photoelectric converters, and electroluminescent and photorefractive devices.     

The Trace Conjecture – A Counterexample

In the paper Geometric K-Theory for Lie Groups and Foliations, Baum and Connes conjecture in a remark following Corollary 2 of their famous Isomorphism conjecture that for a finitely generated group with torsion, the trace map tr: K₀(C^*)R maps K₀(C^*) onto the additive subgroup of Q generated by all rational numbers of the form 1/n where n is the order of a finite subgroup of . We construct a counterexample to this conjecture.