On the domain of fractional Laplacians and related generators of Feller processes

In this paper we study the domain of the generator of stable processes, stable-like processes and more general pseudo- and integro-differential operators which naturally arise both in analysis and as infinitesimal generators of Lévy- and Lévy-type (Feller) processes. In particular we obtain conditions on the symbol of the operator ensuring that certain (variable order) Hölder and Hölder–Zygmund spaces are in the domain. We use tools from probability theory to investigate the small-time asymptotics of the generalized moments of a Lévy or Lévy-type process ${(X_t)}_{t\ge 0}$,

$\underset{t\to 0}{\lim }?\frac{1}{t}({\mathbb{E}}^{x}f(X_t)?f(x)),x\in {\mathbb{R}}^d,$

for functions f which are not necessarily bounded or differentiable. The pointwise limit exists for fixed $x\in {\mathbb{R}}^d$ if f satisfies a Hölder condition at x. Moreover, we give sufficient conditions which ensure that the limit exists uniformly in the space of continuous functions vanishing at infinity. As an application we prove that the domain of the generator of ${(X_t)}_{t\ge 0}$ contains certain Hölder spaces of variable order. Our results apply, in particular, to stable-like processes, relativistic stable-like processes, solutions of Lévy-driven SDEs and Lévy processes.     

Vapoluminescent Behavior and the Single-Crystal-to-Single-Crystal Transformations of Chloroform Solvates of [Au2(μ-1,2-bis(diphenylarsino)ethane)2](AsF6)2

The mono- and di-chloroform solvates of [Au₂(μ-1,2-bis(diphenylarsino)ethane)₂](AsF₆)₂ undergo single-crystal-to-single-crystal transformations that result in gain (over 12 hours) or slow loss (over five years) of only one chloroform molecule. The change in solvation results in changes in the structure and luminescence of the digold cation. The cation consists of a pair of slightly bent As-Au-As units that are connected through the two bridging dpae ligands and by aurophilic interactions with Au⋅⋅⋅Au contacts of 3.05152(15) Å in the disolvate or 2.9570(5) Å in the monosolvate.     

Abnormal Nucleophilic Substitution on Methoxytropone Derivatives: Steric Strategy to Synthesize 5-Substituted Azulenes

Azulene is a non-alternant non-benzenoid aromatic system, and in turn, it possesses unusual photophysical properties. Azulene-based conjugated systems have received increasing interest in recent years as optoelectronic materials. Despite the routes available for the preparation of substituted azulene derivatives, there remain few methods that allow regioselective substitution on the seven-membered ring of azulenes due to the subtle reactivity difference among the various positions. This report explores the reactivity of substituted tropolones as the azulene precursors and also provides a new method to create 5-substituted azulenes. The reaction of cyanoacetate enolate with unsubstituted 2-methoxytropone affords azulene through the attack of the nucleophile on the C-2 center (normal pathway). We have observed that 3-substituted 2-methoxytropones undergo steric-guided nucleophilic addition at the C-7 center (abnormal pathway) to afford 5-substituted azulene derivatives. Based on this observation and DFT calculation, a new synthetic strategy is devised for the regioselective synthesis of 5-substituted multifunctional azulenes, which cannot be accessed by any other method.     

On the Change in the Form and Parameters of Silicon Compression Curves under Temperature and Electric Current Impacts

Crystallography Reports - Uniaxial compression of n-type silicon under joint impact of temperature and constant electric current revealed a significant increase in its plasticity in comparison with...     

Copper(II) complexes with pyridoxal dithiocarbazate and thiosemicarbazone ligands: crystal structure,spectroscopic analysis and cytotoxic activity

Transition Metal Chemistry - The present study reports the synthesis and crystal structures of Cu(II) complexes with pyridoxal S-allyldithiocarbazate (H2L1) and pyridoxal thiosemicarbazones...     

Magnetic properties of a polyfluorene derivative containing complexed neodymium ions

Poly[9,9′‐dihexylfluorene‐2,7‐diyl)‐6,6″‐(2,2′:6′,2″‐terpyridine)] (LaPPS75) and its complexes with neodymium were synthesized and characterized. Magnetic measurements showed that the noncomplexed polymer presented a ferromagnetic contribution due to the formation of π stacking, and that in absence of those, the ferromagnetic behavior is suppressed. The pristine polymer, the complexed one and a low‐molecular‐weight model compound with the same structure of the complexed site in the parent polymer were studied. The observed behavior found is presented and discussed, the most important finding was that when a conjugated chain is used as a host for the metallic ion, an amplification of four times for the magnetization is achieved, using the same metallic content for complexed polymer and model compound for comparison. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 304–311     

A New Approach for the Synthesis of Miktoarm Star Polymers Through a Combination of Thiol–Epoxy “Click” Chemistry and ATRP/Ring‐Opening Polymerization Techniques

A new approach was developed for synthesis of certain A₃B₃‐type of double hydrophilic or amphiphilic miktoarm star polymers using a combination of “grafting onto” and “grafting from” methods. To achieve the synthesis of desired miktoarm star polymers, acetyl protected poly(ethylene glycol) (PEG) thiols (M_n = 550 and 2000 g mol^?1) were utilized to generate A₃‐type of homoarm star polymers through an in situ protective group removal and a subsequent thiol–epoxy “click” reaction with a tris‐epoxide core viz. 1,1,1‐tris(4‐hydroxyphenyl)ethane triglycidyl ether. The secondary hydroxyl groups generated adjacent to the core upon the thiol–epoxy reaction were esterified with α‐bromoisobutyryl bromide to install atom transfer radical polymerization (ATRP) initiating sites. ATRP of N‐isopropylacrylamide (NIPAM) using the three‐arm star PEG polymer fitted with ATRP initiating sites adjacent to the core afforded A₃B₃‐type of double hydrophilic (PEG)₃[poly(N‐isopropylacrylamide)] (PNIPAM)₃ miktoarm star polymers. Furthermore, the generated hydroxyl groups were directly used as initiator for ring‐opening polymerization of ε‐caprolactone to prepare A₃B₃‐type of amphiphilic (PEG)₃[poly(ε‐caprolactone)]₃ miktoarm star polymers. The double hydrophilic (PEG)₃(PNIPAM)₃ miktoarm star polymers showed lower critical solution temperature around 34 °C. The preliminary transmission electron microscopy analysis indicated formation of self‐assembly of (PEG)₃(PNIPAM)₃ miktoarm star polymer in aqueous solution. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 146–156     

Validation of quartz crystal rheometry in the megahertz frequency regime

The utility of the quartz crystal microbalance (QCM) as a high‐frequency rheometer operating at 15 MHz was demonstrated. High‐frequency data obtained from a series of rubbery materials were compared with results obtained from traditional dynamic mechanical analysis (DMA) at much lower frequencies. The high‐frequency data enable meaningful shift factors to be obtained at temperatures much further above glass‐transition temperature (T _g) than would otherwise be possible, giving a more complete picture of the temperature dependence of the viscoelastic properties. The QCM can also be used to quantify mass uptake and changes in viscoelastic properties during sample oxidation. The viscoelastic response spanning the full range of behaviors from the rubber to glassy regimes was found to fit well with a six‐element model consisting of three power‐law springpot elements. One of these elements is particularly sensitive to the behavior in the transition regime where the phase angle is maximized. The value of this quantity is obtained from the maximum phase angle, which can be obtained from a temperature sweep at fixed frequency, proving a means for more detailed frequency‐dependent rheometric information to be obtained from a fixed‐frequency measurement at a range of temperatures. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1246–1254     

Singular Hamiltonian elliptic systems with critical exponential growth in dimension two

We will focus on the existence of nontrivial solutions to the following Hamiltonian elliptic system where are numbers belonging to the interval [0, 2), V is a continuous potential bounded below on by a positive constant and the functions f and g possess exponential growth range established by Trudinger–Moser inequalities in Lorentz–Sobolev spaces. The proof involves linking theorem and a finite‐dimensional approximation.     

Importance sampling for non-Markovian tandem queues using subsolutions

Queueing Systems - In this paper, we use importance sampling simulation to estimate the probability that the number of customers in a d-node GI|GI|1 tandem queue reaches some high level N in a busy...