Non-coercive Lyapunov functions for infinite-dimensional systems

We show that the existence of a non-coercive Lyapunov function is sufficient for uniform global asymptotic stability (UGAS) of infinite-dimensional systems with external disturbances provided the speed of decay is measured in terms of the norm of the state and an additional mild assumption is satisfied. For evolution equations in Banach spaces with Lipschitz continuous nonlinearities these additional assumptions become especially simple. The results encompass some recent results on linear switched systems on Banach spaces. Finally, we derive new non-coercive converse Lyapunov theorems and give some examples showing the necessity of our assumptions.     

Multidimensional thermoelasticity for nonsimple materials – well-posedness and long-time behavior

An initial-boundary value problem for the multidimensional type III thermoelaticity for a nonsimple material with a center of symmetry is considered. In the linear case, the well-posedness with and without a (second-order in space) Kelvin–Voigt and/or frictional damping in the elastic part as well as the lack of exponential stability in the elastically undamped case are proved. Further, a frictional damping for the elastic component is shown to lead to exponential stability. A Cattaneo-type hyperbolic relaxation for the thermal part is introduced and the well-posedness and uniform stability under a nonlinear frictional damping are obtained using a compactness-uniqueness-type argument. Additionally, a connection between exponential stability and exact observability of unitary strongly continuous groups is established.     

Numerical distribution functions for seasonal unit root tests with OLS and GLS detrending

This paper implements the approach introduced by MacKinnon (J Bus Econ Stat 12:167–176, 1994, J Appl Econom 11:601–618, 1996) to estimate the response surface of the test statistics of seasonal unit root tests with OLS and GLS detrending for quarterly and monthly time series. The Gauss code that is available in the supplementary material of the paper produces p values for five test statistics depending on the sample size, deterministic terms and frequency of the data. A comparison with previous studies is undertaken, and an empirical example using airport passenger arrivals to a tourist destination is carried out. Quantile function coefficients are reported for simple computation of critical values for tests at 1, 5 and 10 % significance levels.     

Arylidene Pyruvic Acids Motif in the Synthesis of New 2H,5H-Chromeno[4′,3′:4,5]thiopyrano[2,3-d]thiazoles via Tandem Hetero-Diels–Alder-Hemiacetal Reaction

We have developed a tandem hetero-Diels–Alder-hemiacetal reaction using arylidene pyruvic acids with 5-(ortho-hydroxybenzylidene)-substituted 4-thioxo-2-thiazolidinones, leading to 6-hydroxy-2-oxo-5-phenyl-3,5a,6,11b-tetrahydro-2H,5H-chromeno[4′,3′:4,5]thiopyrano[2,3-d][1,3]thiazole-6-carboxylic acids. The stereochemistry of cycloaddition was confirmed by NMR spectra and a single-crystal x-ray diffraction analysis.     

Synthesis,Modification, and Anticonvulsant Activity of 3′‐R1‐Spiro[indoline‐3,6′‐[1,2,4]triazino[2,3‐c]quinazolin]‐2,2′(7′H)‐diones Derivatives

Previously unknown 3′‐R¹‐5‐R²‐spiro[indoline‐3,6′‐[1,2,4]triazino[2,3‐c]quinazoline]‐2,2′‐(7′H)‐diones and their N‐substituted analogues were obtained via reaction of 6‐R¹‐3‐(2‐aminophenyl)‐1,2,4‐triazin‐5‐ones with isatin and its substituted derivatives. It was shown that alkylation of 3′‐R¹‐5‐R²‐spiro[indoline‐3,6′‐[1,2,4]triazino[2,3‐c]quinazolin]‐2,2′‐(7′H)‐diones by N‐R³‐chloroacetamides or chloroacetonitrile in the presence of а base proceeds by N‐1 atom of isatin fragment. The spectral properties (¹H and ¹³C NMR spectra) of synthesized compounds were studied, and features of spectral patterns were discussed. The high‐effective anticonvulsant and radical scavenging agents among 3′‐R¹‐5‐R²‐spiro[indoline‐3,6′‐[1,2,4]triazino[2,3‐c]quinazolin]‐2,2′(7′H)‐diones and their N‐substituted derivatives were detected. It was shown that compounds 2.2 , 2.8 , and 3.1 exceed or compete the activity of the most widely used in modern neurology drug—lamotrigine on the pentylenetetrazole‐induced seizures model. The aforementioned fact may be considered as a reason for further profound study of synthesized compounds using other pathology models.     

Merocyanines based on 1,3‐indanedione: electronic structure and solvatochromism

A series of merocyanines derived from 1,3‐indanedione and heterocycles of various electron‐donating properties was studied in detail. Their solvatochromic properties were explored in a wide range of solvent polarities to reveal the dependences of their chromacity and electronic structure on the key structural parameters – the properties of a donor heterocycle and the polymethine chain length. Also the dyes were studied by NMR spectroscopy and by quantum chemical calculations, both with the semiempirical AM1 and the non‐empirical density functional theory/B3LYP method. The solvatochromic properties of the explored dyes are rather close to those of merocyanines derived from malononitrile as acceptor group. Appreciable distinctions were observed only in protic ethanol; obviously, they are connected with the formation of solvent–solute H‐bonds in the case of 1,3‐indanedione derivatives. The electron‐acceptor properties of 1,3‐indanedione were found to be somewhat stronger in comparison with those of malononitrile even in aprotic solvents, contrary to the known literature data. Analysis of the merocyanines' molecular orbitals and simulation of their electronic spectra were carried out both in vacuum and in the solvent matrix, and the absorption electronic transitions were analyzed. Static nonlinear optical properties were calculated for both the new merocyanines and the corresponding cationic and anionic cyanine dyes. Copyright © 2010 John Wiley & Sons, Ltd.     

Establishing plasmon contribution to chemical reactions: alkoxyamines as a thermal probe

The nature of plasmon interaction with organic molecules is a subject of fierce discussion about thermal and non-thermal effects. Despite the abundance of physical methods for evaluating the plasmonic effects, chemical insight has not been reported yet. In this contribution, we propose a chemical insight into the plasmon effect on reaction kinetics using alkoxyamines as an organic probe through their homolysis, leading to the generation of nitroxide radicals. Alkoxyamines (TEMPO- and SG₁-substituted) with well-studied homolysis behavior are covalently attached to spherical Au nanoparticles. We evaluate the kinetic parameters of homolysis of alkoxyamines attached on a plasmon-active surface under heating and irradiation at a wavelength of plasmon resonance. The estimation of kinetic parameters from experiments with different probes (Au–TEMPO, Au–SG1, Au–SG1–TEMPO) allows revealing the apparent differences associated with the non-thermal contribution of plasmon activation. Moreover, our findings underline the dependency of kinetic parameters on the structure of organic molecules, which highlights the necessity to consider the nature of organic transformations and molecular structure in plasmon catalysis.

Kinetic study of alkoxyamine homolysis revealed the impact of non-thermal effects in plasmon-assisted reactions.