An Edgeworth expansion for functionals of Gaussian fields and its applications

This paper is concerned with the rate of convergence in the normal approximation of the sequence $\left\{F_n\right\}$, where each $F_n$ is a functional of an infinite-dimensional Gaussian field. We develop new and powerful techniques for computing the exact rate of convergence in distribution with respect to the Kolmogorov distance. As a tool for our works, the Edgeworth expansion of general orders, with an explicitly expressed remainder, will be obtained, and this remainder term will be controlled to find upper and lower bounds of the Kolmogorov distance in the case of an arbitrary sequence $\left\{F_n\right\}$. As applications, we provide the optimal fourth moment theorem of the sequence $\left\{F_n\right\}$ in the case when $\left\{F_n\right\}$ is a sequence of random variables living in a fixed Wiener chaos or a finite sum of Wiener chaoses. In the former case, our results show that the conditions given in this paper seem more natural and minimal than ones appeared in the previous works.     

A study on the degradation of polylactic acid in the presence of phosphonium ionic liquids

In this overview study, two ionic liquids (IL) with different anions (decanoate, tetrafluoroborate) but with the same phosphonium-based cation that showed promising plasticizing/lubricating behavior in polylactic acid (PLA) were screened for their effects on the polymer degradation under thermomechanical, thermo-oxidative (at 160 °C), hydrolytic (100% humidity, 60 °C), conditions, and during soil immersion. Depending on the particular medium and conditions used, degradation was followed by changes in molecular weight, melt viscosity, sample weight and appearance, morphology, crystallinity, acid number, and pH. The effects of the IL containing a decanoate anion were more pronounced on lubrication and also on degradation as evidenced by reduced melt viscosities and accelerated thermomechanical, isothermal, hydrolytic, and soil degradation. The IL containing the tetrafluoroborate anion showed higher thermal stability compared with the IL containing decanoate anion as also confirmed from thermal degradation rate constants which were calculated from random chain scission statistics. Accelerated hydrolytic degradation was observed in PLA containing the tetrafluoroborate based IL but to a lesser extent than the decanoate based IL. The catalytic role of the decanoate anion in hydrolytic degradation was confirmed through experiments with model compounds. X-ray diffraction (XRD) data on the materials exposed to soil degradation provided evidence that the initially amorphous polymer attained a certain degree of crystallinity as a result of the significant MW reduction.     

Higher Order Terms of the Spectral Heat Content for Killed Subordinate and Subordinate Killed Brownian Motions Related to Symmetric α-Stable Processes in ℝ ${mathbb {R}}$

Potential Analysis - We investigate the 3rd term of the spectral heat content for killed subordinate and subordinate killed Brownian motions on a bounded open interval D = (a,b) in a real line when...     

A formal construction of a divergence-free basis in the nonconforming virtual element method for the Stokes problem

Numerical Algorithms - We develop a formal construction of a pointwise divergence-free basis in the nonconforming virtual element method of arbitrary order for the Stokes problem introduced in Zhao...     

Non-linear transport by solitons in nanofibers of polymers in high magnetic field

Nonlinear local excitations like solitons, polarons, and bipolarons are known to be responsible for physical properties of conducting polymers. Recent experiments on nano-fibers in high electric and magnetic fields provide a further insight by demonstrating an effect of vanishing magnetoconductance (MC) in the polyacetylene (PA)—in contrast to other polymers. Here we present new experimental data and describe the theoretical model based on notion of solitons—dimerization kinks which can carry either the spin or the charge; they are allowed only in the PA with its degenerate ground state. The solitons experience a confinement force due to the interchange coupling which is erased by the electric field and disappears above critical field strength. The unbinding by tunneling allows for the transport of individual solitons, which sweeps off the spins residing at electronic intragap states associated with polarons, hence the vanishing MC.     

Wave-front phase measurements of high-order harmonic beams by use of point-diffraction interferometry

We report the wave-front phase measurement of high-order harmonics employing point-diffraction interferometry. The high-order harmonics generated in a gas-filled hollow tube showed excellent spatial coherence over nearly the whole cross section of the harmonic beams. Using this coherent harmonic source in the extreme-ultraviolet-soft-x-ray region, we have demonstrated the operation of a point-diffraction interferometer and measured the wave-front phase of high-order harmonics.     

A generalization of a 4-dimensional Einstein manifold

A weakly Einstein manifold is a natural generalization of a 4-dimensional Einstein manifold. In this paper, we shall give a characterization of a weakly Einstein manifold in terms of so-called generalized Singer-Thorpe bases. As an application, we prove a generalization of the Hitchin inequality for compact weakly Einstein 4-manifolds. Examples are provided to illustrate the theorems.     

Preparation of ethyl 2-aryl 2,3-alkadienoates via palladium-catalyzed selective cross-coupling reactions

Pd-catalyzed cross-coupling reactions of aryl iodides containing not only an electron-donating group but also an electron-withdrawing group on the aryl ring with organoindium reagents generated in situ from indium and ethyl 4-bromo-2-alkynoates produced selectively ethyl 2-aryl-2,3-alkadienoates in good yield.     

Stereocontrolled enantioselective addition of diethylzinc to aldehydes using new chiral aminoalcohols

The new chiral β-aminoalcohols of indolinylmethanols ( 1 ) and their reduced derivatives ( 2 ) were synthesized from (S)-indoline-2-carboxylic acid. Both (R) and (S) enantiomers of the optically active secondary alcohols have been successfully obtained in high enantiomeric excess from the stereoselective addition of diethylzinc to the aldehydes catalyzed by the chiral aminoalcohols ( 1 and 2 ). The sense of the asymmetric induction and the degrees of enantioselectivities turned out to be highly dependent on the structure of the catalysts: The presence of the catalyst 1 afforded the (S)-configuration of the corresponding alcohols; on the other hand, the presence of 2 afforded the (R)-configuration of the alcohols in high enantiomeric selectivity.