(P,Q)(P,Q) complex hypercontractivity

Let $\xi$ be the standard normal random vector in $\mathbb{R}^{k}$. Under some mild growth and smoothness assumptions on any increasing $P, Q : [0, \infty) \mapsto [0, \infty)$ we show $(P,Q)$ complex hypercontractivity $$Q^{-1}(\mathbb{E} Q(|T_{z}f(\xi)|))\leq P^{-1}(\mathbb{E}P(|f(\xi)|))$$ holds for all polynomials $f:\mathbb{R}^{k} \mapsto \mathbb{C}$, where $T_{z}$ is the hermite semigroup at complex parameter $z, |z|\leq 1$, if and only if \begin{align*} \left|\frac{tP''(t)}{P'(t)}-z^{2}\frac{tQ''(t)}{Q'(t)}+z^{2}-1\right|\leq \frac{tP''(t)}{P'(t)}-|z|^{2}\frac{tQ''(t)}{Q'(t)}+1-|z|^{2} \end{align*} holds for all $t>0$ provided that $F''>0$, and $F'/F''$ is concave, where $F = Q\circ P^{-1}$. This extends Hariya's result from real to complex parameter $z$. Several old and new applications are presented for different choices of $P$ and $Q$. The proof uses heat semigroup arguments, where we find a certain map $C(s)$, which interpolates the inequality at the endpoints. The map $C(s)$ itself is composed of four heat flows running together at different times

Novel foods and food ingredients: what is the mission of scientists and technologists?

The situation concerning world food production is changing dramatically. On the one hand, the world population is expected to grow still further, reaching about 8 billion peo- ple in the middle of the 21st century. Novel phenomena, such as ageing of the human population and excess weight in developing countries pose new nutrition problems. Food scares, which were enhanced by recent BSE and tox- icological outbreaks, hinder the applicability of some solu- tions. Under these conditions, scientists and technologists should participate actively in the tasks of informing the population as well as finding new ways to provide people with the optimal amount of nutritious food.(undefined

Greek Accounting Standards and Debt Covenants. Changes in Contracting

Businesses, organizations, and even more governments are strongly related with information provided by accounting in order for CEO’s or managers and even more members of parliament to make decisions. Financial statements which contain multiple criteria, and how managers or shareholders treat them influence the decisionmaking of organizations and all types of businesses, public and private. Auditing financial statements ensures their reliability and validity. Both lenders and borrowers must choose the right set of debt covenants to minimize risk from their respective perspectives. It is critical to use and select debt covenants in relation to the side of interest. For instance, in past decades, financial covenants based on balance sheet variables are more likely in debt contracting. Nowadays, the trend of choosing a batch of covenants in contracting changed. In this paper, we investigate the relationship between changing the Greek direction and accounting standard setting. Greek accounting standards are moving away from “old-fashioned” book- and record-keeping standards. This was a great change that took place in 2015, and since then, new notions of accounting practice have been introduced. Fair value, net realizable value, present value, cash equivalents, and useful economic life are some concepts that were first used in accounting the process in Greek economy. Changes were massive and everyone involved with accounting, financial statements, and the way they were introduced should change the way they are analyzed. We hypothesized that this significant shift in accounting standard setting reduces the value of analyzing balance sheets in debt contracting. Since 2015, balance sheet-based covenants started to vanish, especially from private debt contracting. We tried to correlate borrowers and their likelihood in using balance sheet-based covenants. The correlation between the change in accounting standard setting and the concurrent change in trend of choosing accounting-based covenants in debt contracting is being investigated. The results are consistent with our hypothesis. A mechanism that separates multiple covenants and correlates them with significant debt characteristics will be an innovative tool for managers and credit institutions, as well as a more definite way of auditing, for instance, by digitalizing it, which will be a great tool for everyone involved in businesses. Keywords: accounting-based covenants, debt contracting, Greek accounting standard

ITG 14

International audienceAn intracellular esterase from Propionibacterium freudenreichii ssp. freudenreichii ITG 14 was purified by anion exchange and gel filtration chromatography. The enzyme had a molecular weight of 47 400 g$\cdot$mol$^{-1}$ as determined by gel filtration chromatography, with an optimum activity on $\alpha$-naphthyl-acetate at pH 6.0 and at 65 °C, with $K_{\rm M}$ = 1.2 mmol$\cdot$L$^{-1}$. The esterase hydrolyzed synthetic substrates of low molecular weight (C2-C4), and among triglycerides only triacetin. Sulfhydryl group reagents and metal chelators had limited or no effect on enzyme activity; highest inhibition was observed with phenylmethyl sulfonyl fluoride (PMSF).Purification et caractérisation d'une estérase intracellulaire de Propionibacterium freudenreichii ssp. freudenreichii ITG 14. Une estérase intracellulaire extraite de Propionibacterium freudenreichii ssp. freudenreichii ITG 14 a été purifiée par chromatographie échangeuse d'anions et chromatographie d'exclusion de taille. L'enzyme avait une masse moléculaire de 47 400 g$\cdot$mol$^{-1}$, comme déterminé par chromatographie d'exclusion de taille, et elle avait une activité maximale sur le substrat $\alpha$-naphthyl-acétate à pH 6,0 et 65 °C, avec $K_{\rm M}$ = 1,2 mmol$\cdot$L$^{-1}$. L'estérase dégradait des substrats synthétiques de faible poids moléculaire (C2-C4), et parmi les triglycérides seulement la triacétine. Des groupements sulfydryles et des chélateurs de métaux n'avaient aucun effet ou un effet limité sur l'activité enzymatique ; la plus forte inhibition a été observée lors de l'utilisation du PMSF

Λογαριθμική ανισότητα Brunn-Minkowski και το λογαριθμικό πρόβλημα Minkowski

Η θεωρία Brunn-Minkowski βασίζεται στη σύνδεση του αθροίσματος Minkowski κυρτών σωμάτων με τον όγκο. Κεντρικό ρόλο σε αυτή τη θεωρία έχουν η ανισότητα Brunn-Minkowski και οι μεικτοί όγκοι του Minkowski. Η αντικατάσταση του αθροίσματος Minkowski από άλλου τύπου αθροίσματα δημιουργεί σε όλη τη θεωρία νέα ερωτήματα όπως: νέου τύπου ανισότητες, προβλήματα ύπαρξης, μοναδικότητας και χαρακτηρισμού μέτρων με γεωμετρική σημασία. Στο πρώτο μέρος της εργασίας μελετάμε το ερώτημα αν για την κλάση των συμμετρικών κυρτών σωμάτων ισχύει μια ισχυρότερη ανισότητα τύπου Brunn-Minkowski, γνωστή ως λογαριθμική ανισότητα Brunn-Minkowski. Περιγράφουμε τις αποδείξεις των μέχρι τώρα γνωστών αποτελεσμάτων γι’ αυτό το πρόβλημα. Στο δεύτερο μέρος της εργασίας μελετάμε ένα «πρόβλημα Minkowski». Με τον όρο αυτό αναφέρεται κανείς γενικά σε προβλήματα χαρακτηρισμού μέτρων πάνω στην σφαίρα τα οποία προέρχονται από κυρτά σώματα. Το πρόβλημα που μελετάμε είναι να βρεθούν ικανές και αναγκαίες συνθήκες για ένα πεπερασμένο μέτρο Borel πάνω στη σφαίρα του n-διάστατου Ευκλείδειου χώρου έτσι ώστε να είναι το cone-volume μέτρο ενός κυρτού σώματος. Στην περίπτωση που το μέτρο είναι άρτιο, οι Boroczky, Lutwak, Yang και Ζhang απέδειξαν ότι η κρίσιμη συνθήκη σχετίζεται με τη συγκέντρωση του μέτρου στις σφαίρες υποχώρων μικρότερης διάστασης.n this Thesis we study two open problems from the Brunn-Minkowski theory. The main theme is the interplay between vector addition and volume of convex bodies in Euclidean space. In the first part of the Thesis, we study the question whether the logarithmic Brunn-Minkowski inequality, a stronger inequality than the classical Brunn-Minkowski inequality, holds true for the class of the symmetric convex bodies. We present the known, up to now, results and partial answers to this question. In the second part of the Thesis, we study the Minkowski problem for the cone-volume measure. The question is to give necessary and sufficient conditions for a Borel measure on the sphere so that it is the cone-volume measure of a convex body. We present the answer to this question in the symmetric case. The crucial condition is related to the concentration of measure on spheres of subspaces of lower dimension