Variation in essential oil content and composition of Ridolfia segetum Moris based on 30-hour prolonged fractionated extraction procedure

Abstract

A comprehensive study on essential oil samples extracted from Ridolfia segetum Moris (Apiaceae) collected in Tarquinia (Italy) is reported. In this study, a 30-hour, fractionated, steam distillation procedure for essential oil preparation was applied. The gas chromatographic-mass spectrometry analysis showed monoterpene o-cymene and phenylpropanoid dill-apiol as the major essential oil’s constituents revealing a new chemotype dependent on extraction duration. Great impact of the duration of the distillation process on chemical profile of essential oil was observed; prolonged distillation gives chemically more diverse essential oil samples. Preliminary microbiological evaluations of the essential oils samples revealed some activity, although not high, against Candida albicans.     

Analysis of a Cahn–Hilliard–Brinkman model for tumour growth with chemotaxis

Phase field models recently gained a lot of interest in the context of tumour growth models. Typically Darcy-type flow models are coupled to Cahn–Hilliard equations. However, often Stokes or Brinkman flows are more appropriate flow models. We introduce and mathematically analyse a new Cahn–Hilliard–Brinkman model for tumour growth allowing for chemotaxis. Outflow boundary conditions are considered in order not to influence tumour growth by artificial boundary conditions. Existence of global-in-time weak solutions is shown in a very general setting.     

New lower bounds on the radius of spatial analyticity for the KdV equation

The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than $t^{?1/4}$ as time t goes to infinity. This improves the works of Selberg and da Silva (2017) [30] and Tesfahun (2017) [34]. Our strategy mainly relies on a higher order almost conservation law in Gevrey spaces, which is inspired by the I-method.     

The character and the wave front set correspondence in the stable range

We relate the distribution characters and the wave front sets of unitary representation for real reductive dual pairs of type I in the stable range.     

Deformation of Gabor systems

We introduce a new notion for the deformation of Gabor systems. Such deformations are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space. With this new notion we prove a strong deformation result for Gabor frames and Gabor Riesz sequences that covers the known perturbation and deformation results. Our proof of the deformation theorem requires a new characterization of Gabor frames and Gabor Riesz sequences. It is in the style of Beurling's characterization of sets of sampling for bandlimited functions and extends significantly the known characterization of Gabor frames “without inequalities” from lattices to non-uniform sets.     

Homogeneous variable exponent Besov and Triebel–Lizorkin spaces

We introduce homogeneous Besov and Triebel–Lizorkin spaces with variable indexes. We show that their study reduces to the study of inhomogeneous variable exponent spaces and homogeneous constant exponent spaces. Corollaries include trace space characterizations and Sobolev embeddings.