Long-time behavior of an angiogenesis model with flux at the tumor boundary

This paper deals with a nonlinear system of partial differential equations modeling a simplified tumor-induced angiogenesis taking into account only the interplay between tumor angiogenic factors and endothelial cells. Considered model assumes a nonlinear flux at the tumor boundary and a nonlinear chemotactic response. It is proved that the choice of some key parameters influences the long-time behavior of the system. More precisely, we show the convergence of solutions to different semi-trivial stationary states for different range of parameters.     

Radial solutions of Neumann problems involving mean extrinsic curvature and periodic nonlinearities

We show that if ${{\mathcal A} \subset \mathbb{R}^N}$ is an annulus or a ball centered at zero, the homogeneous Neumann problem on ${{\mathcal A}}$ for the equation with continuous data $$\nabla \cdot \left(\frac{\nabla v}{\sqrt{1 - |\nabla v|^2}} \right) = g(|x|,v) + h(|x|)$$ has at least one radial solution when g(|x|,·) has a periodic indefinite integral and ${\int_{\mathcal A} h(|x|)\,{\rm{d}}x = 0.}$ The proof is based upon the direct method of the calculus of variations, variational inequalities and degree theory.     

Sister Beiter and Kloosterman: A tale of cyclotomic coefficients and modular inverses

For a fixed prime p$p$, the maximum coefficient (in absolute value) M(p)$M\left(p\right)$ of the cyclotomic polynomial _Φpqr(x)${\Phi }_{pqr}\left(x\right)$, where r$r$ and q$q$ are free primes satisfying r>q>p$r>q>p$ exists. Sister Beiter conjectured in 1968 that M(p)≤(p+1)/2$M\left(p\right)\le (p+1)/2$. In 2009 Gallot and Moree showed that M(p)≥2p(1−?)/3$M\left(p\right)\ge 2p(1-?)/3$ for every p$p$ sufficiently large. In this article Kloosterman sums (‘cloister man sums’) and other tools from the distribution of modular inverses are applied to quantify the abundancy of counter-examples to Sister Beiter’s conjecture and sharpen the above lower bound for M(p)$M\left(p\right)$.     

Far-field emission profiles from L3 photonic crystal cavity modes

We experimentally characterize the spatial far-field emission profiles for the two lowest confined modes of a photonic crystal cavity of the L3 type, finding a good agreement with FDTD simulations. We then link the far-field profiles to relevant features of the cavity mode near-fields, using a simple Fabry–Perot resonator model. The effect of disorder on far-field cavity profiles is clarified through comparison between experiments and simulations. These results can be useful for emission engineering from active centers embedded in the cavity.     

300 microJ noncollinear optical parametric amplifier in the visible at 1 kHz repetition rate

We demonstrate an order-of-magnitude energy scaling of a white-light seeded noncollinear optical parametric amplifier in the visible. The generated pulses, tunable between 520 and 650 nm with sub-25-fs duration, had energies up to 310 microJ with 20% blue-pump-to-signal energy conversion efficiency at 540 nm. This new ultrafast source will make possible numerous extreme nonlinear optics applications. As a first application, we demonstrate the generation of tunable vacuum ultraviolet pulses.     

Analysis of oxysterols by electrospray tandem mass spectrometry

Oxysterols are oxygenated derivatives of cholesterol. They are intermediates in cholesterol excretion pathways and may also be regarded as transport forms of cholesterol. The introduction of additional hydroxyl groups to the cholesterol skeleton facilitates the flux of oxysterols across the blood brain barrier, and oxysterols have been implicated in mediating a number of cholesterol-induced metabolic effects. Oxysterols are difficult to analyze by atmospheric pressure ionization mass spectrometry on account of the absence of basic or acidic functional groups in their structures. In this communication, we report a method for the derivatization and analysis of oxysterols by electrospray mass spectrometry. Oxysterols with a 3beta-hydroxy-Delta5 structure were converted by cholesterol oxidase to 3-oxo-Delta4 steroids and then derivatized with the Girard P reagent to give Girard P hydrazones, which were subsequently analyzed by tandem mass spectrometry. The improvement in sensitivity for the analysis of 25-hydroxycholesterol upon oxidation and derivatization was over 1000.     

Structure and dynamics of Br- ion in liquid methanol

A Car-Parrinello molecular dynamics simulation has been performed on a solution of Br- in liquid methanol analyzing with particular attention charge transfer and polarization effects. The first solvation shell has been characterized in terms of H-bonds, and it has been found that the high polarization of the bromide gives rise to a stable solvent cage. The differences in the coordination number with the chloride can be ascribed to the ionic radius and to the stronger perturbations brought by the solvent to the bromide ion.     

Highly optimized fourth-order short-time approximation for path integrals

We derive a fourth-order short-time approximation for use in imaginary-time path-integral simulations. The short-time approximation converges for all continuous and bounded-from-below potentials, attains quartic order of convergence for sufficiently smooth potentials, and utilizes statistically independent random variables for its construction. These properties recommend the approximation as a natural replacement of the trapezoidal Trotter-Suzuki approximation for physical systems with continuous distributions.