The Spectrum of the Martin-Morales-Nadirashvili Minimal Surfaces Is Discrete

We show that the spectrum of a complete submanifold properly immersed into a ball of a Riemannian manifold is discrete, provided the norm of the mean curvature vector is sufficiently small. In particular, the spectrum of a complete minimal surface properly immersed into a ball of ℝ³ is discrete. This gives a positive answer to a question of Yau (Asian J. Math. 4:235–278, 2000).     

Trivial and simple spectrum for SL(d, ℝ) cocycles with free base and fiber dynamics

Let AC_D(M,SL(d,R)) denote the pairs (f,A) so that f ∈ A ⊂ Diff¹(M) is a C¹-Anosov transitive diffeomorphisms and A is an SL(d,R) cocycle dominated with respect to f. We prove that open and densely in AC_D(M,SL(d,R)), in appropriate topologies, the pair (f,A) has simple spectrum with respect to the unique maximal entropy measure μ_f. Then, we prove prevalence of trivial spectrum near the dynamical cocycle of an area-preserving map and also for generic cocycles in AutLeb(M) × L^p(M,SL(d,R)).     

HERFD XAS/ATR-FTIR batch reactor cell

An autoclave reactor was modified to perform simultaneously high energy resolution fluorescence detected X-ray absorption spectroscopy (HERFD XAS) and attenuated total reflectance Fourier transform infrared (ATR-FTIR) spectroscopy measurements without altering the reactor design. This operando cell allows one to follow changes in the electronic and geometric structure of the catalyst with HERFD XAS and relate them to the simultaneously detected activity and reaction species with ATR-FTIR formed during the reaction in the liquid phase. The capability of the cell is demonstrated by two studies. The first shows the reduction of Au/CeO(2) precursors in different solvents. The second shows that mainly Au(0) is present in the hydrogenation of nitrobenzene over Au/CeO(2).     

Plenty of hyperbolicity on a class of linear homogeneous jerk differential equations

Aequationes mathematicae - We consider $$3times 3$$ partially hyperbolic linear differential systems over an ergodic flow $$X^t$$ and derived from the linear homogeneous differential equation...     

Preparation of PMMA Nanoparticles Loaded with Benzophenone-3 through Miniemulsion Polymerization

Summary: The present paper analyzes the production of poly(methyl methacrylate) – PMMA – nanoparticles loaded with benzophenone-3 through miniemulsion polymerization. The obtained product is homogeneous and stable, allowing for preparation of photo-protective formulations. It is observed in particular that bezophenone-3 interacts with the reacting system, promoting the growth of the PMMA chains produced in miniemulsion.     

Homoclinic tangencies versus uniform hyperbolicity for conservative 3-flows

We prove that a volume-preserving three-dimensional flow can be C¹-approximated by a volume-preserving Anosov flow or else by another volume-preserving flow exhibiting a homoclinic tangency. This proves the conjecture of Palis for conservative 3-flows and with respect to the C¹-topology.     

FTIR Emission Spectra, Molecular Constants, and Potential Curve of Ground State GeO

Extensive new high-temperature, high-resolution FTIR emission spectroscopy measurements for the five common isotopomers of GeO are combined with previous diode laser and microwave measurements in combined isotopomer analyses. New Dunham expansion parameters and an accurate analytical potential energy function are determined for the ground X1Sigma+ state. Copyright 1999 Academic Press.     

Eigenvalue Estimates for Submanifolds with Locally Bounded Mean Curvature

We present a method to obtain lower bounds for firstDirichlet eigenvalue in terms of vector fields with positivedivergence. Applying this to the gradient of a distance functionwe obtain estimates of eigenvalue of balls inside the cut locus and of domains M B _N (p, r) in submanifolds M Nwith locally bounded mean curvature. Forsubmanifolds of Hadamard manifolds with bounded mean curvaturethese lower bounds depend only on the dimension of the submanifold and the bound on its mean curvature.     

Stable weakly shadowable volume-preserving systems are volume-hyperbolic

We prove that any C1-stable weakly shadowable volume-preserving diffeomorphism defined on a compact manifold displays a dominated splitting E ⊕ F. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.     

A Review of Multiple Scale Fibrous and Composite Systems for Heating Applications

Different types of heating systems have been developed lately, representing a growing interest in both the academic and industrial sectors. Based on the Joule effect, fibrous structures can produce heat once an electrical current is passed, whereby different approaches have been followed. For that purpose, materials with electrical and thermal conductivity have been explored, such as carbon-based nanomaterials, metallic nanostructures, intrinsically conducting polymers, fibers or hybrids. We review the usage of these emerging nanomaterials at the nanoscale and processed up to the macroscale to create heaters. In addition to fibrous systems, the creation of composite systems for electrical and thermal conductivity enhancement has also been highly studied. Different techniques can be used to create thin film heaters or heating textiles, as opposed to the conventional textile technologies. The combination of nanoscale and microscale materials gives the best heating performances, and some applications have already been proven, even though some effort is still needed to reach the industry level.