Higher-order total variation bounds for expectations of periodic functions and simple integer recourse approximations

We derive bounds on the expectation of a class of periodic functions using the total variations of higher-order derivatives of the underlying probability density function. These bounds are a strict improvement over those of Romeijnders et al. (Math Program 157:3–46, 2016b), and we use them to derive error bounds for convex approximations of simple integer recourse models. In fact, we obtain a hierarchy of error bounds that become tighter if the total variations of additional higher-order derivatives are taken into account. Moreover, each error bound decreases if these total variations become smaller. The improved bounds may be used to derive tighter error bounds for convex approximations of more general recourse models involving integer decision variables.     

Convex subrings of partially ordered rings

The relationship between a poring and a convex subring has been studied most successfully for porings with bounded inversion. The best conceivable results are known for real closed rings. The present paper focuses on the connections between the prime spectra and between the real spectra of a poring and a convex subring. Examples show that for arbitrary porings one may not expect a very close relationship. But with the assumption of bounded inversion or spectral compatibility the results are similar to those for real closed rings (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Solving a non-linear stochastic pseudo-differential equation of Burgers type

In this paper, we study the initial value problem for a class of non-linear stochastic equations of Burgers type of the following form

_∂tu+q(x,D)u+_∂xf(t,x,u)=_h1(t,x,u)+_h2(t,x,u)_Ft,x${\partial }_{t}u+q(x,D)u+{\partial }_{x}f(t,x,u)=h_1(t,x,u)+h_2(t,x,u)F_{t,x}$

for u:(t,x)∈(0,∞)×R?u(t,x)∈R$u:(t,x)\in (0,\infty )\times \mathbb{R}?u(t,x)\in \mathbb{R}$, where q(x,D)$q(x,D)$ is a pseudo-differential operator with negative definite symbol of variable order which generates a stable-like process with transition density, f,_h1,_h2:[0,∞)×R×R→R$f,h_1,h_2:[0,\infty )\times \mathbb{R}\times \mathbb{R}\to \mathbb{R}$ are measurable functions, and _Ft,x$F_{t,x}$ stands for a Lévy space-time white noise. We investigate the stochastic equation on the whole space R$\mathbb{R}$ in the mild formulation and show the existence of a unique local mild solution to the initial value problem by utilising a fixed point argument.     

A simple and effective Verlet-type algorithm for simulating Langevin dynamics

We present a revision to the well known Störmer–Verlet algorithm for simulating second order differential equations. The revision addresses the inclusion of linear friction with associated stochastic noise, and we analytically demonstrate that the new algorithm correctly reproduces diffusive behaviour of a particle in a flat potential. For a harmonic oscillator, our algorithm provides the exact Boltzmann distribution for any value of damping, frequency and time step for both underdamped and overdamped behaviour within the usual stability limit of the Verlet algorithm. Given the structure and simplicity of the method, we conclude that this approach can trivially be adapted for contemporary applications, including molecular dynamics with extensions such as molecular constraints.     

Equivalent dose distribution analysis of Holocene eolian and fluvial quartz sands from Central Oklahoma

Holocene quartz sands were collected from fluvial terrace deposits and eolian dune deposits adjacent to the North Canadian and Cimarron Rivers and their tributaries in Central Oklahoma. Single aliquot regenerative dose optically stimulated luminescence techniques were employed to generate equivalent dose (ED) distribution histograms for each sample. We hypothesize that the ED distributions are convolutions of the distribution arising from natural sedimentary processes, influenced primarily by the degree of solar resetting experienced by individual grains, and a distribution due to experimental error. An estimation of the experimental error distribution for each sample was made and this was then deconvolved from the experimentally measured ED distribution to reveal the ‘sedimentary process’ ED distribution. Objective methods for determining EDs, uncertainties, and confidence parameters from the deconvolved distributions are presented.     

Morita Base Change in Hopf-Cyclic (Co)Homology

In this paper, we establish the invariance of cyclic (co)homology of left Hopf algebroids under the change of Morita equivalent base algebras. The classical result on Morita invariance for cyclic homology of associative algebras appears as a special example of this theory. In our main application we consider the Morita equivalence between the algebra of complex-valued smooth functions on the classical 2-torus and the coordinate algebra of the noncommutative 2-torus with rational parameter. We then construct a Morita base change left Hopf algebroid over this noncommutative 2-torus and show that its cyclic (co)homology can be computed by means of the homology of the Lie algebroid of vector fields on the classical 2-torus.     

The Prins Reaction in the Fragrance Industry: 100th Anniversary (1919–2019)

The Prins reaction, an acid‐catalyzed condensation of alkenes with aldehydes, is used extensively in the fragrance industry. This year we celebrate the 100th anniversary of the discovery of this reaction. In honor of this occasion we present an overview of the diverse applications of the Prins reaction in the synthesis of flavor and fragrance ingredients. To pay tribute to the inventor of the Prins reaction, Hendrik Jacobus Prins, we also provide some insight into his life, scientific, and entrepreneurial accomplishments.     

Contact resistance of quantum tubes

We consider the conductance of a quantum tube connected to a metallic contact. The number of angular momentum states that the tube can support depends on the strength of the radial confinement. We calculate the transmission coefficients which yield the conductance via the Landauer formula, and discuss the relation of our results to armchair carbon nanotubes embedded in a metal. For Al and Au contacts and tubes with a realistic radial confinement we find that the transmission can be close to unity corresponding to a contact resistance close to h / 2 e²per band at the Fermi level in the carbon nanotube.