Periodic orbits and unstable manifolds for ordinary differential equations

Consider the unstable manifold of a hyperbolic periodic orbit of an ordinary differential equation under C¹ perturbations of the vector field and under approximation by a one-step numerical method, which is at least first order. Trajectories bounded backwards in time near the periodic orbit perturb Hausdorff continuously. This result as applied to numerical perturbations improves on Alouges-Debussche [1], who give only continuity of the unstable maniford, and on Beyn [3], who gives continuity of trajectories only when the periodic orbit is unstable. As a corollary, we find that attractors perturb Hausdorff continuously when the attractor equals a union of locally continuous unstable manifolds of invariant sets     

Genus Two Curves with Many Elliptic Subcovers

We determine all genus 2 curves, defined over ?, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in ?₂. For each component, we find a rational parametrization and construct the equation of the corresponding genus 2 curve and its elliptic subcovers in terms of the parameterization. Such families of genus 2 curves are determined for the first time. Furthermore, we prove that there are only finitely many genus 2 curves (up to ?-isomorphism) defined over ?, which have degree 2 and 3 elliptic subcovers also defined over ?.     

Facile growth of monolayer MoS<Subscript>2</Subscript> film areas on SiO<Subscript>2</Subscript>

Areas of single-layer MoS₂ film can be prepared in a tube furnace without the need for temperature control. The films were characterized by means of Raman spectroscopy, photoluminescence, low-energy electron diffraction and microscopy, and X-ray photoelectron spectroscopy and mapping. Transport measurements show n-doped material with a mobility of 0.26 cm² V^-1 s^-1.     

Optimal rates of convergence for estimating Toeplitz covariance matrices

Toeplitz covariance matrices are used in the analysis of stationary stochastic processes and a wide range of applications including radar imaging, target detection, speech recognition, and communications systems. In this paper, we consider optimal estimation of large Toeplitz covariance matrices and establish the minimax rate of convergence for two commonly used parameter spaces under the spectral norm. The properties of the tapering and banding estimators are studied in detail and are used to obtain the minimax upper bound. The results also reveal a fundamental difference between the tapering and banding estimators over certain parameter spaces. The minimax lower bound is derived through a novel construction of a more informative experiment for which the minimax lower bound is obtained through an equivalent Gaussian scale model and through a careful selection of a finite collection of least favorable parameters. In addition, optimal rate of convergence for estimating the inverse of a Toeplitz covariance matrix is also established.     

Direct measurement of strain-induced changes in the band structure of carbon nanotubes

The effect of uniaxial strain on the optical transition energies of single-walled carbon nanotubes with known chiral indices was measured by Rayleigh scattering spectroscopy. Existing theory accurately predicts the trends in the measured strain-induced shifts, but overestimates their magnitude. Modification of the analysis to account for internal sublattice relaxation results in quantitative agreement with experiment.     

Soft swimming: exploiting deformable interfaces for low reynolds number locomotion

Reciprocal movement cannot be used for locomotion at low Reynolds number in an infinite fluid or near a rigid surface. Here we show that this limitation is relaxed for a body performing reciprocal motions near a deformable interface. Using physical arguments and scaling relationships, we show that the nonlinearities arising from reciprocal flow-induced interfacial deformation rectify the periodic motion of the swimmer, leading to locomotion. Such a strategy can be used to move toward, away from, and parallel to any deformable interface as long as the length scales involved are smaller than intrinsic scales, which we identify. A macroscale experiment of flapping motion near a free surface illustrates this new result.     

Development and validation of a sensitive liquid‐chromatography tandem mass spectrometry assay for mycophenolic acid and metabolites in HepaRG cell culture: Characterization of metabolism interactions between p‐cresol and mycophenolic acid

Mycophenolic acid (MPA), a frequently used immunosuppressant, exhibits large inter‐patient pharmacokinetic variability. This study (a) developed and validated a sensitive liquid chromatography–tandem mass spectrometry (LC–MS/MS) assay for MPA and metabolites [MPA glucuronide (MPAG) and acyl‐glucuronide (AcMPAG)] in the culture medium of HepaRG cells; and (b) characterized the metabolism interaction between MPA and p‐cresol (a common uremic toxin) in this in vitro model as a potential mechanism of pharmacokinetic variability. Chromatographic separation was achieved with a C₁₈ column (4.6 × 250 mm,5 μm) using a gradient elution with water and methanol (with 0.1% formic acid and 2 mm ammonium acetate). A dual ion source ionization mode with positive multiple reaction monitoring was utilized. Multiple reaction monitoring mass transitions (m/z) were: MPA (320.95 → 207.05), MPAG (514.10 → 303.20) and AcMPAG (514.10 → 207.05). MPA‐d₃ (323.95 → 210.15) and MPAG‐d₃ (517.00 → 306.10) were utilized as internal standards. The calibration curves were linear from 0.00467 to 3.2 μg/mL for MPA/MPAG and from 0.00467 to 0.1 μg/mL for AcMPAG. The assay was validated based on industry standards. p‐Cresol inhibited MPA glucuronidation (IC₅₀ ≈ 55 μm ) and increased MPA concentration (up to >2‐fold) at physiologically relevant substrate‐inhibitor concentrations (n = 3). Our findings suggested that fluctuations in p‐cresol concentrations might be in part responsible for the large pharmacokinetic variability observed for MPA in the clinic.