Vinogradov's Theorem with Fouvry-Iwaniec Primes

We show that every sufficiently large $x\equiv 3(4)$ can be written as the sum of three primes, each of which is a sum of a square and a prime square. The main tools are a transference version of the circle method and various sieve related ideas.Comment: 52 page

The Exceptional Set in Goldbach's Problem with Almost Twin Primes

We consider the exceptional set in the binary Goldbach problem for sums of two almost twin primes. Our main result is a power-saving bound for the exceptional set in the problem of representing $m=p_1+p_2$ where $p_1+2$ has at most $2$ prime divisors and $p_2+2$ has at most $3$ prime divisors. There are three main ingredients in the proof: a new transference principle like approach for sieves, a combination of the level of distribution estimates of Bombieri--Friedlander--Iwaniec and Maynard with ideas of Drappeau to produce power savings, and a generalisation of the circle method arguments of Montgomery and Vaughan that incorporates sieve weights

The basidiomycetous yeast Trichosporon may cause severe lung exacerbation in cystic fibrosis patients - clinical analysis of Trichosporon positive patients in a Munich cohort

Background: The relevance of Trichosporon species for cystic fibrosis (CF) patients has not yet been extensively investigated. Methods: The clinical course of CF patients with Trichosporon spp. in their respiratory secretions was analysed between 2003 and 2010 in the Munich CF center. All respiratory samples of 360 CF patients (0 - 52.4 years; mean FEV1 2010 81.4% pred) were investigated. Results: In 8 patients (2.2%, 3 male, mean age 21.8 years) Trichosporon was detected at least once. One patient carried T. asahii. One patient carried T. mycotoxinivorans and one patient T. inkin as determined by DNA sequencing. As potential risk factors for Trichosporon colonization steroid treatment, allergic bronchopulmonary aspergillosis (ABPA) and CF associated diabetes were identified in 6, 5, and 2 patients respectively. For one patient, the observation period was not long enough to determine the clinical course. One patient had only a single positive specimen and exhibited a stable clinical course determined by change in forced expiratory volume in one second (FEV1), body-mass-index (BMI), C-reactive protein (CRP) and immunoglobulin G (IgG). Of 6 patients with repeatedly positive specimen (mean detection period 4.5 years), 4 patients had a greater decline in FEV1 than expected, 2 of these a decline in BMI and 1 an increase in IgG above the reference range. 2 patients received antimycotic treatment: one patient with a tormenting dry cough subjectively improved under Amphotericin B inhalation; one patient with a severe exacerbation due to T. inkin was treated with i.v. Amphotericin B, oral Voriconazole and Posaconazole which stabilized the clinical condition. Conclusions: This study demonstrates the potential association of Trichosporon spp. with severe exacerbations in CF patients

Modern Applications of the Circle Method

In this thesis we use recent versions of the Circle Method to prove three theorems in the area of additive number theory. It is conjectured that every even integer except two is the sum of two primes. We do not know how to prove this yet. However, we can show that the set of exceptions has zero density. Our first result is that this stays true if one considers sums of two primes that lie in some sufficiently dense subset and are well distributed in residue classes. To show this, we use Green's transference Circle Method and some additive combinatorics. If we allow an additional variable, that is consider three primes, we can say much more. Vinogradov proved that every large odd integer is the sum of three primes. The central result of the thesis is to generalize this work to a sparse set of primes, the so-called Fouvry-Iwaniec primes. These are the primes that are sum of a square and a prime square. We use the the transference Circle Method as described by Maynard, Matomäki, and Shao in their work on Vinogradov’s Theorem with almost equal summands. As in the paper of Fouvry and Iwaniec a big role is played by dissections into Type I and II sums and stepping into the Gaussian Integers. We also require different techniques in the area of sieve theory such as the Rosser-Iwaniec beta sieve and Chen's sieve switching. Finally we consider the number of representations of squares by non-singular homogeneous cubic polynomials in six or more variables. For this result we use Heath-Brown's delta Circle Method, Hooley's considerations for counting zeroes of cubic forms, and deep results in the area of algebraic geometry based on Deligne's solution of the Riemann Hypothesis for varieties over finite fields

Venture capital deal structurering in Nederland

Dit artikel analyseert 122 deals door Nederlandse venture capital-partijen. Uit de resultaten blijkt dat de deal-structurering is in te delen in vier functies. De eerste functie is selectiemiddel van ondernemer en ondernemingsplan. De tweede functie is het verkleinen van de agency-problemen tussen ondernemer en investeerder. De derde functie is het beperken van het risico voor de investeerder. De vierde functie die aangetroffen wordt is het indammen van de dreiging van toekomstige heronderhandelingen tussen de investeerder en de ondernemer over de opbrengsten van de onderneming. Ten slotte blijkt uit het onderzoek dat de ondernemer op het gebied van deal-structurering een informatieachterstand heeft op de investeerder