Substitution reactions of gaseous ions in a three‐dimensional quadrupole ion trap

Substitution reactions between gaseous ions and neutral substrate molecules are of ongoing high interest. To investigate these processes in a qualitative and quantitative manner, we have constructed a device, with which a defined amount of a volatile substrate can be mixed with a defined amount of helium gas and added into a three‐dimensional quadrupole ion trap. From the known inner volume of the device, the known ratio n_substrate:n_He of the mixture, and the determined absolute partial pressure of helium in the ion trap, we can derive the partial pressure of the substrate in the ion trap and, thus, convert the directly observable pseudo–first‐order rate constants of the substitution reactions into absolute bimolecular rate constants. We have tested the device by investigating a series of S_N2 reactions of Br ^? and CF₃CH₂O ^? anions as well as ligand exchange reactions of ligated Na⁺ cations. As the obtained results suggest, the described device makes it possible to determine the bimolecular rate constants of substitution reactions as well as other ion‐molecule reactions with satisfactory accuracy and reliability.     

Loading‐Dependent Structural Model of Polymeric Micelles Encapsulating Curcumin by Solid‐State NMR Spectroscopy

Detailed insight into the internal structure of drug‐loaded polymeric micelles is scarce, but important for developing optimized delivery systems. We observed that an increase in the curcumin loading of triblock copolymers based on poly(2‐oxazolines) and poly(2‐oxazines) results in poorer dissolution properties. Using solid‐state NMR spectroscopy and complementary tools we propose a loading‐dependent structural model on the molecular level that provides an explanation for these pronounced differences. Changes in the chemical shifts and cross‐peaks in 2D NMR experiments give evidence for the involvement of the hydrophobic polymer block in the curcumin coordination at low loadings, while at higher loadings an increase in the interaction with the hydrophilic polymer blocks is observed. The involvement of the hydrophilic compartment may be critical for ultrahigh‐loaded polymer micelles and can help to rationalize specific polymer modifications to improve the performance of similar drug delivery systems.     

Linearization of radiative heating and cooling rates for the case of non-scattering planetary atmospheres

Rates of radiative heating and cooling of the non-scattering planetary atmosphere and scattering underlying surface are analytically linearized with respect to the atmospheric and surface parameters. Resulting expressions for sensitivities of radiative heating and cooling rates are used to formulate the linearized 1D radiative model of atmospheric dynamics which directly incorporates the relevant linearized atmospheric and surface parameters. Applications to more sophisticated models of atmospheric dynamics, as well as extension to the case of presence of atmospheric scattering, are briefly discussed.     

Stability of Viscoelastic Wave Equation with Structural $\delta$-Evolution in $\mathbb{R}^{n}$

The aim of this paper is to study the Cauchy problem for the viscoelastic wave equation for structural $\delta$-evolution models. By using the energy method in the Fourier spaces, we obtain the decay estimates of the solution to considered problem.     

Normal approximation and fourth moment theorems for monochromatic triangles

Given a graph sequence denote by T₃(G_n) the number of monochromatic triangles in a uniformly random coloring of the vertices of G_n with colors. In this paper we prove a central limit theorem (CLT) for T₃(G_n) with explicit error rates, using a quantitative version of the martingale CLT. We then relate this error term to the well-known fourth-moment phenomenon, which, interestingly, holds only when the number of colors satisfies . We also show that the convergence of the fourth moment is necessary to obtain a Gaussian limit for any , which, together with the above result, implies that the fourth-moment condition characterizes the limiting normal distribution of T₃(G_n), whenever . Finally, to illustrate the promise of our approach, we include an alternative proof of the CLT for the number of monochromatic edges, which provides quantitative rates for the results obtained in [7].     

Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings

This paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of $g^{\prime }$ controlled by g.     

Space-time finite element methods stabilized using bubble function spaces

ABSTRACT

In this paper, a stabilized space-time finite element method for solving linear parabolic evolution problems is analyzed. The proposed method is developed on a base of a space-time variational setting, that helps on the simultaneous and unified discretization in space and in time by finite element techniques. Stabilization terms are constructed by means of classical bubble spaces. Stability of the discrete problem with respect to an associated mesh dependent norm is proved, and a priori discretization error estimates are presented. Numerical examples confirm the theoretical estimates.     

Sum rules in multiphoton coincidence rates

We show that sums of carefully chosen coincidence rates in a multiphoton interferometry experiment can be simplified by replacing the original unitary scattering matrix with a coset matrix containing 0s. The number and placement of these 0s reduces the complexity of each term in the sum without affecting the original sum of rates. In particular, the evaluation of sums of modulus squared of permanents is shown to turn in some cases into a sum of modulus squared of determinants. The sums of rates are shown to be equivalent to the removal of some optical elements in the interferometer.