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The stochastic inverse eigenvalue problem aims to reconstruct a stochastic matrix from its spectrum. Recently, Zhao et al. [A geometric nonlinear conjugate gradient method for stochastic inverse eigenvalue problems. SIAM J Numer Anal. 2016;54(4):2015–2035] proposed a constrained optimization model on the manifold of so-called isospectral matrices and adapted a modified. Polak-Ribière-Polyak conjugate gradient method to the geometry of this manifold. However, not every stochastic matrix is an isospectral one and the model in Zhao et al. is based on the assumption that for each stochastic matrix there exists a (possibly different) isospectral, stochastic matrix with the same spectrum. We are not aware of such a result in the literature, but prove the claim at least for 3 × 3 matrices. In this paper, we suggest to extend the above model by considering matrices which differ from isospectral ones only by multiplication with a block diagonal matrix with 2 × 2 blocks from the special linear group. First, we show that each stochastic matrix can be written in such a form. We prove that our model has a minimizer and show how the Polak–Ribiére–Polyak conjugate gradient method works on the corresponding more general manifold. We demonstrate by numerical examples that the new, more general method performs similarly as those in Zhao et al. [ABSTRACT FROM AUTHOR]

Geometrical frustration among interacting spins combined with strong quantum fluctuations destabilize long-range magnetic order in favor of more exotic states such as spin liquids. By following this guiding principle, a number of spin liquid candidate systems were identified in quasi-two-dimensional (quasi-2D) systems. For 3D, however, the situation is less favorable as quantum fluctuations are reduced and competing states become more relevant. Here we report a comprehensive study of thermodynamic, magnetic and dielectric properties on single crystalline and pressed-powder samples of PbCuTe2O6, a candidate material for a 3D frustrated quantum spin liquid featuring a hyperkagome lattice. Whereas the low-temperature properties of the powder samples are consistent with the recently proposed quantum spin liquid state, an even more exotic behavior is revealed for the single crystals. These crystals show ferroelectric order at TFE ≈ 1 K, accompanied by strong lattice distortions, and a modified magnetic response—still consistent with a quantum spin liquid—but with clear indications for quantum critical behavior. [ABSTRACT FROM AUTHOR]

We present the fabrication and characterization of selective CNT-based gas sensor, which is capable of discriminating between four test gases (NH 3 , ethanol, CO and CO 2 ). Different metals are utilized in order to alter the response of each sensing element towards the different test gases. We discuss as well the different possibilities for metal combinations in the sensor arrays. The optimum combination between the metallic nanoparticles is obtained through an efficient and quick framework. We study the effect of the thickness of the CNT thin-film on the reproducibility and the response of the sensor array. Furthermore, we investigate the response of the fabricated CNT sensor array towards a mixture of two gases. Such kind of characterization was performed by exposing the CNT sensor array to a mixture of (NH 3 , ethanol) and (NH 3 , CO) at different ratios for each mixture. We show that the response towards a mixture of two gases lies in the plane between the data points of each gas separately. [ABSTRACT FROM AUTHOR]

Eine Vielzahl an Studien belegt die negativen Auswirkungen des Verkehrs auf die Umwelt. Schwermetalle und Mikroplastik setzen sich durch den Brems‐ und Reifenabrieb ab. Allein ein Reifen verliert 1,5 kg an Gewicht innerhalb der ersten vier Gebrauchsjahre. Daher haben wir uns folgende Frage gestellt: Welchen Einfluss hat der Straßenverkehr auf umliegende Bodenflächen? [ABSTRACT FROM AUTHOR]