M\"untz spaces and Remez inequalities

Two relatively long-standing conjectures concerning M\"untz polynomials are resolved. The central tool is a bounded Remez type inequality for non-dense M\"untz spaces.Comment: 5 page

Optimal randomness certification from one entangled bit

By performing local projective measurements on a two-qubit entangled state one can certify in a device-independent way up to one bit of randomness. We show here that general measurements, defined by positive-operator-valued measures, can certify up to two bits of randomness, which is the optimal amount of randomness that can be certified from an entangled bit. General measurements thus provide an advantage over projective ones for device-independent randomness certification.Comment: 7 pages, 1 figure, computational details at http://nbviewer.ipython.org/github/peterwittek/ipython-notebooks/blob/master/Optimal%20randomness%20generation%20from%20entangled%20quantum%20states.ipyn

On glyphosate

This Editorial briefly discusses the current issues surrounding glyphosate -the most controversial pesticide active ingredient of our time. The paper pays special attention to the effects of glyphosate on plant-pathogen interactions

Importance of Competences in Communication, as Perceived by Business Leaders

From the perspective of a hierarchically ordered company, the expectations of company leaders concerning their employees' necessary competencies play a greater role than vice versa. This paper light on the expectations of leaders and sub-leaders of micro-, small and medium-sized enterprises concerning the competencies of employees in neighbouring parts of Hungary and Slovakia.The authors' collected 28 scientific papers on the issue of communication competencies in order to map out 21 "common denominators" derived from the combined competence lists. A survey was conducted with 222 respondents to measure the subjective importance assigned to these traits and to observe the respondents' attitudes towards the effectiveness of communication training programmes they had participated in. On the Hungarian side, speech competence proved to be the most crucial competence for business leaders, followed by attention/reflection and interpersonal communication skills. In Slovakia, persuasion was reported to be the most crucial trait, the second most important is the application of confirmation and feedback, and the third is speech competence. In terms of the participants' past communication training experiences, the competences of group communication, assertiveness and leadership skills were reported to have been the main areas of focus. The findings indicate that overall satisfaction with communication training programmes depends on neither the amount of participants' leadership experience nor the companies' field(s) of activity, nor the nationality (i.e. the venue) of the companies. The overall satisfaction rate is 2.53 on a four-grade scale among those who ever attended communication training programmes

HIPERTENZIVNE BOLESTI TRUDNOĆE Teorija hipoperfuzionog i hiperperfuzionog oblika preeklampsije

Preeclampsia is one of the most serious complications of pregnancy. Although the etiology of preeclampsia remains obscure, examinations of central hemodynamics and recent epidemiologic data have challenged its homogenous origin. Hypertension could theoretically be secondary to elevated resistance or elevated cardiac output. Accumulating data suggest that both, organ hypoperfusion due to increased resistance of vasculature, the vascular content and also hyperperfusion due to augmented fluid retention may lead to hypertension with proteinuria in pregnancy. »Functio laesa« secondary to hypoperfusion of kidneys manifests in proteinuria in hypoperfusion type but the hypertension itself may also lead to moderate but significant proteinuria during pregnancy. Examination of central hemodynamics seems to be a useful tool for early differentiation of hypo- and hyper-perfusion types for evaluating the outcome, appropriate management and also accurate patients’ recruitment for studies.Preeklampsija je jedna od najozbiljnijih komplikacija trudnoće. Premda etiologija preeklampsije ostaje nepoznata, istraživanja centralne hemodinamike i svježi epidemiološki podaci su doveli u pitanje jedinstvenost njezina postanka. Hipertenzija teoretski može nastati sekundarno zbog povišenog otpora ili zbog povećanog srčanog minutnog volumena. Podatci upućuju da oboje, hipoperfuzija organa zbog povećanog krvožilnog otpora i volumena te isto tako hiperperfuzija zbog povećanog zadržavanja tekućine, mogu u trudnoći uzrokovati hipertenziju s proteinurijom. »Functio laesa« zbog hipoperfuzije bubrega očituje se kao proteinurija u hipoperfuzijskom tipu, a i sama hipertenzija može proizvesti umjerenu do značajnu proteinuriju trudnoće. Istraživanje centralne hemodinamike čini se da je koristan način za rano razlikovanje hipo- i hiper-perfuzijskog tipa da bi se prosudio ishod, odgovarajuće liječenje te pacijentice prikladne u izboru istraživanja

Chaotic mixing induced transitions in reaction-diffusion systems

We study the evolution of a localized perturbation in a chemical system with multiple homogeneous steady states, in the presence of stirring by a fluid flow. Two distinct regimes are found as the rate of stirring is varied relative to the rate of the chemical reaction. When the stirring is fast localized perturbations decay towards a spatially homogeneous state. When the stirring is slow (or fast reaction) localized perturbations propagate by advection in form of a filament with a roughly constant width and exponentially increasing length. The width of the filament depends on the stirring rate and reaction rate but is independent of the initial perturbation. We investigate this problem numerically in both closed and open flow systems and explain the results using a one-dimensional "mean-strain" model for the transverse profile of the filament that captures the interplay between the propagation of the reaction-diffusion front and the stretching due to chaotic advection.Comment: to appear in Chaos, special issue on Chaotic Flo