Effects of catch crops on the content of sulfur (S) and selenium (Se) in vegetables

Selenium is an essential nutrient for animals, humans and microorganisms. Se deficiency in humans has been linked to a plethora of physiological disorders. Increasing evidences point to an anticarcinogenic potential of Se-compounds. To address Se deficiency in the human diet, agronomists and plant breeders are pursuing complementary strategies to produce crops with greater Se concentrations. Catch crops have been used successfully in agriculture, increasing nitrogen and sulfur content in the soil and avoiding nutrient leaching. In this experiment we study whether catch crops can have similar beneficial effects regarding Se

The dynamics of a class of quasi-periodic Schr\"odinger cocycles

Let $f:\mathbb{T}\to\mathbb{R}$ be a Morse function of class $C^2$ with exactly two critical points, let $\omega\in\mathbb{T}$ be Diophantine, and let $\lambda>0$ be sufficiently large (depending on $f$ and $\omega$). For any value of the parameter $E\in \mathbb{R}$ we make a careful analysis of the dynamics of the skew-product map $$\Phi_E(\theta,r)=\left(\theta+\omega,\lambda f(\theta)-E-1/r\right),$$ acting on the "torus" $\mathbb{T}\times\widehat{\mathbb{R}}$. The map $\Phi_E$ is intimately related to the quasi-periodic Schr\"odinger cocycle $(\omega,A_E): \mathbb{T}\times \mathbb{R}^2 \to \mathbb{T}\times \mathbb{R}^2$, $(\theta,x)\mapsto (\theta+\omega, A_E(\theta)\cdot x)$, where $A_E:\mathbb{T}\to \text{SL}(2,\mathbb{R})$ is given by $A_{E}(\theta)=\left(\begin{matrix}0 & 1 \\ -1 & \lambda f(\theta)-E \end{matrix} \right), \quad E\in \mathbb{R}.$ More precisely, $(\omega,A_E)$ naturally acts on the space $\mathbb{T}\times\widehat{\mathbb{R}}$, and $\Phi_E$ is the map thus obtained. The analysis of $\Phi_E$ allows us to derive three main results: (1) The (maximal) Lyapunov exponent of the Schr\"odinger cocycle $(\omega,A_E)$ is $\gtrsim \log \lambda$, uniformly in $E\in \mathbb{R}$. This implies that the map $\Phi_E$ has exactly two ergodic probability measures for all $E\in \mathbb{R}$; (2) If $E$ is on the edge of an open gap in the spectrum $\sigma(H)$ of the associated Schr\"odinger operator $H_\theta$, then there exist a phase $\theta\in\mathbb{T}$ and a vector $u\in l^2(\mathbb{Z})$, exponentially decaying at $\pm\infty$, such that $H_\theta u=Eu$; (3) The map $\Phi_E$ is minimal iff $E\in \sigma(H)\setminus\{\text{edges of open gaps}\}$. In particular, $\Phi_E$ is minimal for all $E$ for which the fibered rotation number $\alpha(E)$ associated to $(\omega,A_E)$ is irrational with respect to $\omega$

Universality and distribution of zeros and poles of some zeta functions

This paper studies zeta functions of the form $\sum_{n=1}^{\infty} \chi(n) n^{-s}$, with $\chi$ a completely multiplicative function taking only unimodular values. We denote by $\sigma(\chi)$ the infimum of those $\alpha$ such that the Dirichlet series $\sum_{n=1}^{\infty} \chi(n) n^{-s}$ can be continued meromorphically to the half-plane $\operatorname{Re} s>\alpha$, and denote by $\zeta_{\chi}(s)$ the corresponding meromorphic function in $\operatorname{Re} s>\sigma(\chi)$. We construct $\zeta_{\chi}(s)$ that have $\sigma(\chi)\le 1/2$ and are universal for zero-free analytic functions on the half-critical strip $1/2<\operatorname{Re} s <1$, with zeros and poles at any discrete multisets lying in a strip to the right of $\operatorname{Re} s =1/2$ and satisfying a density condition that is somewhat stricter than the density hypothesis for the zeros of the Riemann zeta function. On a conceivable version of Cram\'{e}r's conjecture for gaps between primes, the density condition can be relaxed, and zeros and poles can also be placed at $\beta+i \gamma$ with $\beta\le 1-\lambda \log\log |\gamma|/\log |\gamma|$ when $\lambda>1$. Finally, we show that there exists $\zeta_{\chi}(s)$ with $\sigma(\chi) \le 1/2$ and zeros at any discrete multiset in the strip $1/2<\operatorname{Re} s \le 39/40$ with no accumulation point in $\operatorname{Re} s >1/2$; on the Riemann hypothesis, this strip may be replaced by the half-critical strip $1/2 < \operatorname{Re} s < 1$.Comment: This is the final version of the paper which has been accepted for publication in Journal d'Analyse Math\'{e}matiqu

On the Marginally Relevant Operator in z=2 Lifshitz Holography

We study holographic renormalization and RG flow in a strongly-coupled Lifshitz-type theory in 2+1 dimensions with dynamical exponent z=2. The bottom-up gravity dual we use is 3+1 dimensional Einstein gravity coupled to a massive vector field. This model contains a marginally relevant operator around the Lifshitz fixed point. We show how holographic renormalization works in the presence of this marginally relevant operator without the need to introduce explicitly cutoff-dependent counterterms. A simple closed-form expression is found for the renormalized on-shell action. We also discuss how asymptotically Lifshitz geometries flow to AdS in the interior due to the marginally relevant operator. We study the behavior of the renormalized entanglement entropy and confirm that it decreases monotonically along the Lifshitz-to-AdS RG flow.Comment: 28 pages, 5 figures, v2: updated sec. 4.4, references added, typos correcte

Excited B and D Mesons at OPAL

Two recent OPAL publications dealing with spectroscopy of heavy-light mesons will be discussed. In the charm sector, a search for a narrow radial excitation of the D*+- is performed. No signal is seen, and an upper limit of the production rate of narrow radial excitations close to the predicted mass of 2.629 GeV is derived. Orbitally excited B** mesons are investigated in another analysis, where for the first time a measurement of their branching ratio into final states involving a B* is performed. Attempts are made to separate the B** signal into the four contributing resonances.Comment: Talk given at EPSHEP 2001, Budapest. To appear in the proceeding

Interpolation and sampling in small Bergman spaces

Carleson measures and interpolating and sampling sequences for weighted Bergman spaces on the unit disk are described for weights that are radial and grow faster than the standard weights $(1-|z|)^{-\alpha}$, $0<\alpha<1$. These results make the Hardy space $H^2$ appear naturally as a "degenerate" endpoint case for the class of Bergman spaces under study