Three-dimensional (3D) assemblies based on carbon nanomaterials still lag behind their individual one-dimensional building blocks in terms of mechanical and electrical properties. Here we demonstrate a simple strategy for the fabrication of an open porous 3D self-organized double-hierarchical carbon nanotube tube structure with properties advantageous to those existing so far. Even though no additional crosslinking exists between the individual nanotubes, a high reinforcement effect in compression and tensile characteristics is achieved by the formation of self-entangled carbon nanotube (CNT) networks in all three dimensions, employing the CNTs in their high tensile properties. Additionally, the tubular structure causes a self-enhancing effect in conductivity when employed in a 3D stretchable conductor, together with a high conductivity at low CNT concentrations. This strategy allows for an easy combination of different kinds of low-dimensional nanomaterials in a tube-shaped 3D structure, enabling the fabrication of multifunctional inorganic-carbon-polymer hybrid 3D materials.

The purpose of this article is to give a streamlined and selfcontained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent.

We present a streamlined approach to relative oscillation criteria based on effective Prüfer angles adapted to the use at the edges of the essential spectrum.Based on this we provided a new scale of oscillation criteria for general Sturm-Liouville operators which answer the question whether a perturbation inserts a finite or an infinite number of eigenvalues into an essential spectral gap. As a special case we recover and generalize the Gesztesy-Ünal criterion (which works below the spectrum and contains classical criteria by Kneser, Hartman, Hille, and Weber) and the well-known results by Rofe-Beketov including the extensions by Schmidt.

We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Toda lattice for decaying initial data in the soliton region. In addition, we point out how to reduce the problem in the remaining region to the known case without solitons.

Abstract. We develop an analog of classical oscillation theory for SturmLiouville operators which, rather than measuring the spectrum of one single operator, measures the difference between the spectra of two different operators. This is done by replacing zeros of solutions of one operator by weighted zeros of Wronskians of solutions of two different operators. In particular, we show that a Sturm-type comparison theorem still holds in this situation and demonstrate how this can be used to investigate the number of eigenvalues in essential spectral gaps. Furthermore, the connection with Krein's spectral shift function is established.

Laser diodes are efficient light sources. However, state-of-the-art laser diode-based lighting systems rely on light-converting inorganic phosphor materials, which strongly limit the efficiency and lifetime, as well as achievable light output due to energy losses, saturation, thermal degradation, and low irradiance levels. Here, we demonstrate a macroscopically expanded, three-dimensional diffuser composed of interconnected hollow hexagonal boron nitride microtubes with nanoscopic wall-thickness, acting as an artificial solid fog, capable of withstanding~10 times the irradiance level of remote phosphors. In contrast to phosphors, no light conversion is required as the diffuser relies solely on strong broadband (full visible range) lossless multiple light scattering events, enabled by a highly porous (>99.99%) nonabsorbing nanoarchitecture, resulting in efficiencies of~98%. This can unleash the potential of lasers for high-brightness lighting applications, such as automotive headlights, projection technology or lighting for large spaces.

We extend relative oscillation theory to the case of Sturm-Liouville operators H u = r −1 (−(pu ) + qu) with different p's. We show that the weighted number of zeros of Wronskians of certain solutions equals the value of Krein's spectral shift function inside essential spectral gaps.

In this study, a strategy to prepare CuO/Cu2O/Cu microwires that are fully covered by a nanowire (NW) network using a simple thermal-oxidation process is developed. The CuO/Cu2O/Cu microwires are fixed on Au/Cr pads with Cu microparticles. After thermal annealing at 425 °C, these CuO/Cu2O/Cu microwires are used as room-temperature 2-propanol sensors. These sensors show different dominating gas responses with operating temperatures, e.g., higher sensitivity to ethanol at 175 °C, higher sensitivity to 2-propanol at room temperature and 225 °C, and higher sensitivity to hydrogen gas at ∼300 °C. In this context, we propose the sensing mechanism of this three-in-one sensor based on CuO/Cu2O/Cu. X-ray diffraction (XRD) studies reveal that the annealing time during oxidation affects the chemical appearance of the sensor, while the intensity of reflections proves that for samples oxidized at 425 °C for 1 h the dominating phase is Cu2O, whereas upon further increasing the annealing duration up to 5 h, the CuO phase becomes dominant. The crystal structures of the Cu2O–shell/Cu–core and the CuO NW networks on the surface were confirmed with a transmission electron microscope (TEM), high-resolution TEM (HRTEM), and selected area electron diffraction (SAED), where (HR)­TEM micrographs reveal the monoclinic CuO phase. Density functional theory (DFT) calculations bring valuable inputs to the interactions of the different gas molecules with the most stable top surface of CuO, revealing strong binding, electronic band-gap changes, and charge transfer due to the gas molecule interactions with the top surface. This research shows the importance of the nonplanar CuO/Cu2O layered heterostructure as a bright nanomaterial for the detection of various gases, controlled by the working temperature, and the insight presented here will be of significant value in the fabrication of new p-type sensing devices through simple nanotechnology.