Search results for " function"
showing 10 items of 9395 documents
Global Non-monotonicity of Solutions to Nonlinear Second-Order Differential Equations
2018
We study behavior of solutions to two classes of nonlinear second-order differential equations with a damping term. Sufficient conditions for the first derivative of a solution x(t) to change sign at least once in a given interval (in a given infinite sequence of intervals) are provided. These conditions imply global non-monotone behavior of solutions.
A Unifying Framework for Perturbative Exponential Factorizations
2021
We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of theWilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.
Stochastic dynamics of nonlinear systems with a fractional power-law nonlinear term: The fractional calculus approach
2011
Fractional power-law nonlinear drift arises in many applications of engineering interest, as in structures with nonlinear fluid viscous–elastic dampers. The probabilistic characterization of such structures under external Gaussian white noise excitation is still an open problem. This paper addresses the solution of such a nonlinear system providing the equation governing the evolution of the characteristic function, which involves the Riesz fractional operator. An efficient numerical procedure to handle the problem is also proposed.
An Application of the Fixed Point Theory to the Study of Monotonic Solutions for Systems of Differential Equations
2020
In this paper, we establish some conditions for the existence and uniqueness of the monotonic solutions for nonhomogeneous systems of first-order linear differential equations, by using a result of the fixed points theory for sequentially complete gauge spaces.
Approximating the solutions of differential inclusions driven by measures
2019
The matter of approximating the solutions of a differential problem driven by a rough measure by solutions of similar problems driven by “smoother” measures is considered under very general assumptions on the multifunction on the right-hand side. The key tool in our investigation is the notion of uniformly bounded $$\varepsilon $$-variations, which mixes the supremum norm with the uniformly bounded variation condition. Several examples to motivate the generality of our outcomes are included.
Precise Characterization of the Rich Structural Landscape Induced by Pressure in Multifunctional FeVO4
2020
We have studied the high-pressure behavior of FeVO4 by means of single-crystal X-ray diffraction (XRD) and density functional theory (DFT) calculations. We have found that the structural sequence o...
Defect interaction and local structural distortions in Mg-doped LaGaO3: A combined experimental and theoretical study
2017
A combined experimental and theoretical study of Mg-doped LaGaO3 electrolyte was carried out, with the aim to unveil the interaction between oxygen vacancy (Vo) and perovskite B site cations. LaGaO3 (LG) and LaGa0.875Mg0.125O2.938 (LGM0125) samples were comprehensively characterized by X-ray absorption spectroscopy (XAS) and X-ray diffraction, in order to investigate short- and long-range structures of both undoped and Mg-doped materials. XAS analysis evidenced a preferential Ga-Vo interaction in LGM0125, confirmed by periodic hybrid density functional theory calculations, which were combined with a symmetry-independent classes (SICs) approach in order to (a) obtain a detailed picture of th…
Proposal of a new diffractive corneal inlay to improve near vision in a presbyopic eye
2020
[EN] A new class of diffraction-based corneal inlays for treatment of presbyopia is described. The inlay is intended to achieve an improvement of the near focus quality over previous designs. Our proposal is a two-zone hybrid device with separated amplitude and phase areas having a central aperture and no refractive power. An array of micro-holes is distributed on the surface of the inlay conforming a binary photon sieve. In this way, the central hole of the disk contributes to the zero order of diffraction, and the light diffracted by the micro-holes in the peripheral photon sieve produces a real focus for near vision. We employed ray-tracing software to study the performance of the new in…
Crystal structure of BaCa(CO3)2 alstonite carbonate and its phase stability upon compression
2021
Authors thank the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades (MICINN) and the Agencia Estatal de Investigación under projects MALTA Consolider Ingenio 2010 network (MAT2015-71070- REDC) and PGC2018-097520-A-I00 (cofinanced by EU FEDER funds) and from the Generalitat Valenciana under project PROMETEO/2018/123. D.S.-P. and A.O.R. acknowledge the financial support of the Spanish MINECO for RyC-2014-15643 and RyC-2016-20301 Ramón y Cajal grants, respectively. C.P. acknowledges the financial support from the Spanish Ministerio de Economia y Competitividad (MINECO project FIS2017-83295-P). Authors also thank Dr. Nicolescu and the Mineralogy and Meteoritic…
Substituent Effect in 2-Benzoylmethylenequinoline Difluoroborates Exhibiting Through-Space Couplings. Multinuclear Magnetic Resonance, X-ray Diffract…
2012
The series of nine 2-benzoylmethylenequinoline difluoroborates have been synthesized and characterized by multinuclear magnetic resonance, X-ray diffraction (XRD), and computational methods. The through-space spin-spin couplings between (19)F and (1)H/(13)C nuclei have been observed in solution. The NMR chemical shifts have been correlated to the Hammett substituent constants. The crystal structures of six compounds have been solved by XRD. For two derivatives the X-ray wave function refinement was performed to evaluate the character of bonds in the NBF(2)O moiety by topological and integrated bond descriptors.