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1.
Journal of Dynamics and Differential Equations - We start to discuss some aspects of the scattering theory for the Sturm–Liouville operator $$L:\dfrac{1}{y}\left[ -D^2+q\right] $$ . In...  相似文献   
2.
The identification of emergent structures in complex dynamical systems is a formidable challenge. We propose a computationally efficient methodology to address such a challenge, based on modeling the state of the system as a set of random variables. Specifically, we present a sieving algorithm to navigate the huge space of all subsets of variables and compare them in terms of a simple index that can be computed without resorting to simulations. We obtain such a simple index by studying the asymptotic distribution of an information-theoretic measure of coordination among variables, when there is no coordination at all, which allows us to fairly compare subsets of variables having different cardinalities. We show that increasing the number of observations allows the identification of larger and larger subsets. As an example of relevant application, we make use of a paradigmatic case regarding the identification of groups in autocatalytic sets of reactions, a chemical situation related to the origin of life problem.  相似文献   
3.

In this study, the N-dimensional radial Schrodinger equation with an anharmonic sextic potential is solved by the extended Nikirov-Uranov method. We prove that the radial function can be factorised as the product between an exponential function and a polynomial function solution of the biconfluent Heun equation. The approach investigated in this article aims to be an alternative to other known methods of solving, as it has the advantage of dealing with simple, first-order differential and algebraic equations and avoiding numerous and laborious coordinate transformations and series expansions.

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Many researches have been devoted to rechargeable power generators that can store (but also release) energy. This availability is ensured through (e. g.) the oxygen evolution reaction (OER). However, (i) large values of the overpotentials and (ii) a progressive detriment of the anode (graphite) electrode limit the ultimate device. In view of enhancing the electrode performances, graphite was protected by following different strategies, which oblige to follow precise preparation protocols. Here, we prove that a thin layer of free-base porphyrin molecules is able to protect the underneath graphite electrode from detriment even if many (about 100) electrochemical cycles are performed.  相似文献   
6.
Using a direct approach, we prove a two-dimensional epiperimetric inequality for the one-phase problem in the scalar and vectorial cases and for the double-phase problem. From this we deduce, in dimension 2, the C1,α regularity of the free boundary in the scalar one-phase and double-phase problems, and of the reduced free boundary in the vectorial case, without any restriction on the sign of the component functions. Furthermore, we show that in the vectorial case each connected component of might have cusps, but they must be a finite number. © 2018 Wiley Periodicals, Inc.  相似文献   
7.
Rembrandt's painting Old Woman Praying, 1629/30, is the most valuable and exceptional work of art of the Residenzgalerie Salzburg (RGS). It is painted on a gilded copper plate with dimensions of only approximately 15 × 12 cm. The painting probably belongs to a series of three small-scale tronies, all executed on gilded copper plates. This particular picture preparation, which represents a special feature in Rembrandt's work, is quite unusual in the history of art. Previous investigations on the comparable paintings The Laughing Man, 1629/30, in the Mauritshuis, The Hague and the Self Portrait, 1630, in the National Museum, Stockholm showed that the gilding of the copper plate was applied over a lead white ground. To characterize the painting in the RGS, X-ray fluorescence (XRF) mapping was performed in a collaboration between the Research Office Residenzgalerie, Land Salzburg, the XGLab S.R.L, Milan, and the Conservation Science Department of the Kunsthistorische Museum Vienna (KHM). The results indicate a different structure for this painting than that used for The Laughing Man and the Self Portrait. The gilding was applied directly onto the copper plate, but with three areas with the gilding missing. It seems likely that in these sections, the gold was purposely removed to provide a different darker effect. XRF mapping yielded valuable insights into the structure of the painting and its technique as well as the principal pigments used for its composition.  相似文献   
8.
The rotational spectra of three C‐deuterated isotopologues of the dimer of formic acid have been measured, thanks to the small dipole moment induced by asymmetric H→D substitution(s). For the DCOOH–HCOOH species, the concerted double proton transfer of the two hydroxy hydrogen atoms takes place between two equivalent minima and generates a tunneling splitting of 331.2(6) MHz. This splitting can be reproduced by a 3D model with a barrier of 2559 cm?1 (30.6 kJ mol?1) as obtained from theoretical calculations.  相似文献   
9.
Dense gas effects, encountered in many engineering applications, lead to unconventional variations of the thermodynamic and transport properties in the supersonic flow regime, which in turn are responsible for considerable modifications of turbulent flow behavior with respect to perfect gases. The most striking differences for wall-bounded turbulence are the decoupling of dynamic and thermal effects for gases with high specific heats, the liquid-like behavior of the viscosity and thermal conductivity, which tend to decrease away from the wall, and the increase of density fluctuations in the near wall region. The present work represents a first attempt of quantifying the influence of such dense gas effects on modeling assumptions employed for the closure of the Reynolds-averaged Navier–Stokes equations, with focus on the eddy viscosity and turbulent Prandtl number models. For that purpose, we use recent direct numerical simulation results for supersonic turbulent channel flows of PP11 (a heavy fluorocarbon representative of dense gases) at various bulk Mach and Reynolds numbers to carry out a priori tests of the validity of some currently-used models for the turbulent stresses and heat flux. More specifically, we examine the behavior of the modeled eddy viscosity for some low-Reynolds variants of the \(k-\varepsilon \) model and compare the results with those found for a perfect gas at similar conditions. We also investigate the behavior of the turbulent Prandtl number in dense gas flow and compare the results with the predictions of two well-established turbulent Prandtl number models.  相似文献   
10.
In this paper, the structure of locally finite groups of infinite rank whose subgroups of infinite rank are permutable in a subgroup of finite index is investigated.  相似文献   
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