Cahn–Hilliard and thin film equations with nonlinear mobility as gradient flows in weighted-Wasserstein metrics

In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and certain thin film equations. The considered evolution equations are in the form of a gradient flow for a perturbed Dirichlet energy with respect to a Wasserstein-like transport metric, and weak solutions are obtained as curves of maximal slope. Our main assumption is that the mobility of the particles is a concave function of their spatial density. A qualitative difference of our approach to previous ones is that essential properties of the solution – non-negativity, conservation of the total mass and dissipation of the energy – are automatically guaranteed by the construction from minimizing movements in the energy landscape.     

Variation on a theme by Bobylëv and Villani

It is shown that the collisional gain operator for a Maxwell gas does not increase the Fisher information. Our proof is a variant of the one given by Villani in 1998 [2], but it is shorter and based on Fourier techniques rather than direct estimates. The method we use also applies to general (non-symmetric) Wild convolutions.     

Transannular cyclizations of zerumbone epoxide

Formic acid catalyzed rearrangement of zerumbone epoxide 3 gives three major bicyclic products, 4–6. The most important rearrangement is conrotatory electrocyclic Nazarow reaction. The structures were deduced from spectral and chemical evidence. ¹³C NMR are presented. An X-ray study has independently confirmed the proposed structures.     

A Comprehensive Review on the Techniques for Extraction of Bioactive Compounds from Medicinal Cannabis

Cannabis is well-known for its numerous therapeutic activities, as demonstrated in pre-clinical and clinical studies primarily due to its bioactive compounds. The Cannabis industry is rapidly growing; therefore, product development and extraction methods have become crucial aspects of Cannabis research. The evaluation of the current extraction methods implemented in the Cannabis industry and scientific literature to produce consistent, reliable, and potent medicinal Cannabis extracts is prudent. Furthermore, these processes must be subjected to higher levels of scientific stringency, as Cannabis has been increasingly used for various ailments, and the Cannabis industry is receiving acceptance in different countries. We comprehensively analysed the current literature and drew a critical summary of the extraction methods implemented thus far to recover bioactive compounds from medicinal Cannabis. Moreover, this review outlines the major bioactive compounds in Cannabis, discusses critical factors affecting extraction yields, and proposes future considerations for the effective extraction of bioactive compounds from Cannabis. Overall, research on medicinal marijuana is limited, with most reports on the industrial hemp variety of Cannabis or pure isolates. We also propose the development of sustainable Cannabis extraction methods through the implementation of mathematical prediction models in future studies.     

Short proofs of normalization for the simply- typed λ-calculus,permutative conversions and Gödel's T

 Inductive characterizations of the sets of terms, the subset of strongly normalizing terms and normal forms are studied in order to reprove weak and strong normalization for the simply-typed λ-calculus and for an extension by sum types with permutative conversions. The analogous treatment of a new system with generalized applications inspired by generalized elimination rules in natural deduction, advocated by von Plato, shows the flexibility of the approach which does not use the strong computability/candidate style à la Tait and Girard. It is also shown that the extension of the system with permutative conversions by η-rules is still strongly normalizing, and likewise for an extension of the system of generalized applications by a rule of ``immediate simplification'. By introducing an infinitely branching inductive rule the method even extends to G?del's T. Received 12 October 1998 Published online: 19 December 2002 Mathematics Subject Classification (2000): 03B40 Keywords or phrases: λ-calculus – Permutative/commuting conversions – Sum types – Generalized application – G?del's T_q-ω-rule – Inductive characterization     

A multidimensional nonlinear sixth-order quantum diffusion equation

This paper is concerned with the analysis of a sixth-order nonlinear parabolic equation whose solutions describe the evolution of the particle density in a quantum fluid. We prove the global-in-time existence of weak nonnegative solutions in two and three space dimensions under periodic boundary conditions. Moreover, we show that these solutions are smooth and classical whenever the particle density is strictly positive, and we prove the long-time convergence to the spatial homogeneous equilibrium at a universal exponential rate. Our analysis strongly uses the Lyapunov property of the entropy functional.     

Multi-dimensional smoothing transformations: Existence,regularity and stability of fixed points

We analyze a class of smoothing transformations on probability measures in multiple space dimensions. Applying a synthesis of probabilistic methods and Fourier analysis, we prove existence and uniqueness of a fixed point inside the class of probability measures of finite second moment, characterize it as a scale mixture of Gaussians, and discuss its regularity. We also classify its tail, which might be of Pareto type. As an application, we study the stability of stationary solutions in a Kac-type kinetic model. In particular, we prove that the domain of attraction is precisely the probability measures of finite second moment.     

Langzeitversuche zur Reproduzierbarkeit von Jodbestimmungen in Bewuchsproben nach der Sandell-Kolthoff-Reaktion

Ohne ZusammenfassungWir danken Herrn Prof. Dr. H. W. Nürnberg, Direktor des Instituts für Angewandte Physikalische Chemie für sein stetes Interesse am Fortgang der Arbeiten, Herrn R. Flucht für zuverlässige Mitarbeit.