Consistent Lyapunov exponent Estimation for one-dimensional dynamical systems

Summary  The author proves the consistency of a nearest neighbor estimator of the Lyapunov exponent for a general class of one-dimensional ergodic dynamical systems. The author shows that this estimator has good practical properties on a set of simulations.     

Hamiltonian Formulation of FRW Equations of Cosmology

We give a general Hamiltonian formulation of the Friedmann-Robertson-Walker (FRW) fundamental equations of a homogeneous and isotropic universe in the Standard Cosmological model. It gives some interesting insight on the 3-curvature of the universe, which is found to be obtained in terms of the scale factor (also termed radius of the universe) and its first derivative. It also leads to an easy determination of the Schrödinger equation for the (R) wave function of the universe, in the radiative era.     

Impact of potassium on the heats of adsorption of adsorbed CO species on supported Pt particles by using the AEIR method

The heats of adsorption at several coverages of the linear and bridged CO species (denoted L and B, respectively) adsorbed on the Pt⁰ sites of the 2.9 wt% Pt/10% K/Al₂O₃ catalyst are determined using the Adsorption Equilibrium Infrared spectroscopy method. The addition of K on 2.9% Pt/Al₂O₃ modifies significantly the adsorption of CO on the Pt particles: (a) the ratio L/B is decreased from 8.4 to 1, (b) a new adsorbed CO species is detected with an IR band at 1763 cm⁻¹, (c) the heats of adsorption of L and B CO species are significantly altered and the positions of their IR bands are shifted. The heats of adsorption of L CO species are decreased: i.e. 206 and 105 kJ/mol at low coverages on Pt/Al₂O₃ and Pt/K/Al₂O₃ respectively. Two B CO species denoted B1 and B2, with different heats of adsorption are observed on Pt/K/Al₂O₃. The heats of adsorption of B2 CO species (major B CO species) are significantly larger than those measured in the absence of K: i.e. 94 and 160 kJ/mol at low coverages on Pt/Al₂O₃ and Pt/K/Al₂O₃ respectively, whereas those of B1 CO species (minor species) are similar: 90 kJ/mol at low coverages. These values are consistent with the qualitative High Resolution Electron Energy Loss Spectrometry literature data on Pt(1 1 1) modified by potassium.     

A study on densities of sets of points and lines

In this paper, firstly, our purpose is to give the relationship among the densities of the sets of collinear points, the relationship among the densities of the sets of noncollinear points, and the relationship among the densities of the sets of the intersecting lines in Euclidean plane, respectively. In addition to that, we define the density formulas for the sets of points and lines under the two‐parameter planar Euclidean motion. By means of these results, we obtain essential properties that explain the connection among the densities of the sets of points and among the densities of the sets of intersecting lines under the two‐parameter planar Euclidean motion.     

A review on recent advances in hierarchically porous metal and metal oxide nanostructures as electrode materials for supercapacitors and non-enzymatic glucose sensors

The remarkable significance of electrode materials in industrial processes, energy, sustainability and diabetes monitoring has captivated scientists to develop advance nanomaterials for the benefit of life across the globe. Here in, the recent developments in nanostructured porous metal and metal oxide composite materials for supercapacitor applications and non-enzymatic glucose sensors (NEGS) has been extensively discussed. The essential and active electrode materials from the research and application perspective has been emphasized in detail. We have also evaluated the worthiness, taxonomical classification, efficiency, specific capacitance and sensitivity of these materials for the aforementioned potential applications. Eventually, we concluded the review by providing the aspect ratio, surface morphology, particle size and specific surface area of these materials that plays an indispensable role for their promising potential applications.     

REACTION DES O,O-DIETHYL OXO-1 ALKANEPHOSPHONATES AVEC LES DERIVES DE L'HYDRAZINE: UNE VOIE DE SYNTHESE DES HYDRAZONES α-PHOSPHONATEES ET DES HYDRAZIDES

Abstract

Under the normal conditions, the reaction of hydrazine and methylhydrazine with OO-diethyl 1 oxoalkane phosphonates 1 proceeds by cleavage of the phosphorus-carbon bond and leads to the formation of diethylphosphite 2 and N-acylhydrazide 3 . A procedure has been developed for the synthesis of new primary hydrazone of OO-diethyl 1-oxoalkane phosphonates 4 . A mechanism is proposed. The structure of those compounds 4 was confirmed by NMR and IR spectroscopy.     

An oxo‐bridged centrosymmetric tetranuclear titanium compound

The title compound, octa‐tert‐butoxybis­[μ₃‐2,2′‐(N‐methyl­imino)­diethanolato]­di‐μ‐oxo‐tetratitanium(IV), [Ti₂O{(OCH₂CH₂)₂(NCH₃)}{(CH₃)₃CO}₄]₂ or [Ti₄(C₅H₁₁NO₂)₂(C₄H₉O)₈O₂], lies about an inversion centre, and displays the less usual zigzag configuration. One O atom of the N‐methyl­diethoxo­amine ligand bridges the symmetry‐related Ti atoms, while the other bridges the two independent Ti atoms, with the N atom binding to give a facial configuration. Four ^tBuO⁻ ligands and a bridging oxide complete the respective five‐ and sixfold coordination of the two Ti atoms. The Ti—O bond lengths range in a self‐consistent fashion from 1.7624 (17) to 2.0878 (18) Å, while the Ti—N bond length is 2.374 (2) Å.     

A blow-up result in a Cauchy viscoelastic problem

In this work we consider a Cauchy problem for a nonlinear viscoelastic equation. Under suitable conditions on the initial data and the relaxation function, we prove a finite-time blow-up result.     

A Blow-Up Result in a Nonlinear Wave Equation with Delay

In this paper, we consider a nonlinear wave equation with delay. We show that under suitable conditions on the initial data, the weights of the damping, the delay term and the nonlinear source, the energy of solutions blows up in a finite time.