An Extension of the Admissibility-Type Conditions for the Exponential Dichotomy of C 0-Semigroups

In the present paper we obtain a sufficient condition for the exponential dichotomy of a strongly continuous, one-parameter semigroup , in terms of the admissibility of the pair . It is already known the equivalence between the -admissibility condition and and the hyperbolicity of a C ₀-semigroup , when we assume a priori that the kernel of the dichotomic projector (denoted here by X ₂) is T(t)-invariant and is an invertible operator. We succeed to prove in this paper that the admissibility of the pair still implies the existence of an exponential dichotomy for a C ₀-semigroup even in the general case where the kernel of the dichotomic projector, X ₂, is not assumed to be T(t)-invariant.      

Parity nonconservation contribution to the nuclear magnetic resonance shielding constants of chiral molecules: a four-component relativistic study

A systematic four-component relativistic study of the parity nonconservation (PNC) contribution to the (isotropic) NMR shielding constants of chiral molecules is presented for the P enantiomers of the series H(2)X(2) (X=(17)O,(33)S,(77)Se,(125)Te,(209)Po). The PNC contributions are obtained within a linear response approach at the Hartree-Fock level. A careful design of the basis sets is necessary. The four-component relativistic results based on the Dirac-Coulomb Hamiltonian are compared with the nonrelativistic Levy-Leblond results and those obtained by the spin-free modified Dirac Hamiltonian. The calculations confirm the nonrelativistic scaling law Z(2.4) of the PNC contribution with respect to nuclear charge Z. However, the calculations also show that the overall scaling is significantly modified by relativistic effects. The scalar relativistic effect scales as Z(4.7) for the selected set of molecules, whereas the spin-orbit effect, of opposite sign, scales better than Z(6) and completely dominates the PNC contribution for the heaviest elements. This opens up the intriguing possibility of the experimental observation of PNC effects on NMR parameters of molecules containing heavy atoms. The presented formalism is expected to be valuable in assisting the search for suitable candidate molecules.     

Mathieu and Heun Solutions to the Wheeler–De Witt Equation for Hyperbolic Universes

For the spatially open Friedmann–Robertson–Walker (FRW) Universe with stiff matter and radiation as non-interacting matter sources, the scale function coming from the integration of the Friedmann equation is expressed in terms of elliptic integrals. For a negative cosmological constant, we identify the allowed ranges for the model’s parameters. Within the quantum analysis, the Wheeler–De Witt (WDW) equation turns into a modified Morse equation whose solutions are Mathieu and Heun functions.     

Chemical analysis of Gothic mortar from a bridge pier in Roudnice nad Labem (Czech Republic)

In this paper, a Gothic mortar originating from the remains of a bridge pier in Roudnice nad Labem (Czech Republic) was analyzed. The inorganic composition of the mortar showing special mechanical properties was studied using polarizing light microscopy, scanning electron microscopy coupled with energy dispersive X-ray spectrometry, and X-ray diffraction, while the protein content was analyzed by peptide mass mapping using matrix-assisted laser desorption/ionization—time of flight mass spectrometry and nanoliquid chromatography coupled to tandem mass spectrometry. Two types of inorganic binders having a composition similar to mineral wollastonite and hydraulic lime and milk protein additive were detected. We believe that organic and inorganic binders added together to the mortar increase its hardness and firmness in the aquatic environment.     

The precision of DCE-MRI using the tissue homogeneity model with continuous formulation of the perfusion parameters

The present trend in dynamic contrast-enhanced MRI is to increase the number of estimated perfusion parameters using complex pharmacokinetic models. However, less attention is given to the precision analysis of the parameter estimates. In this paper, the distributed capillary adiabatic tissue homogeneity pharmacokinetic model is extended by the bolus arrival time formulated as a free continuous parameter. With the continuous formulation of all perfusion parameters, it is possible to use standard gradient-based optimization algorithms in the approximation of the tissue concentration time sequences. This new six-parameter model is investigated by comparing Monte-Carlo simulations with theoretically derived covariance matrices. The covariance-matrix approach is extended from the usual analysis of the primary perfusion parameters of the pharmacokinetic model to the analysis of the perfusion parameters derived from the primary ones. The results indicate that the precision of the estimated perfusion parameters can be described by the covariance matrix for signal-to-noise ratio higher than ~ 20 dB. The application of the new analysis model on a real DCE-MRI data set is also presented.     

Influence of temperature and UV intensity on photo-polymerization reaction studied by photo-DSC

Photo-DSC was used to investigate the cure kinetics of a photo-initiated resin. The exothermal photo-polymerization reactions were performed in isothermal mode. The irradiation of photo-initiated resin was studied under different conditions of temperature, UV lamp intensity, and reaction atmosphere (nitrogen and air). The results obtained by photo-DSC allowed us to determine kinetic data of the photo-polymerized reactions: the global activation energy and reaction enthalpy, and the conversion as a function of time and temperature. Modulated temperature DSC measurements were carried out to verify whether vitrification occurs during polymerization. The conversion at the top and bottom of irradiated samples was obtained by FT-IR spectroscopy before and after photo-polymerization. A non-homogenous photo-polymerization into the material was observed, probably because of the light absorptions effects within the uppermost layers.     

Iron-iron oxide core-shell nanoparticles are active and magnetically recyclable olefin and alkyne hydrogenation catalysts in protic and aqueous media

We report for the first time the use of iron-iron oxide core-shell nanoparticles for the hydrogenation of olefins and alkynes under mild conditions in ethanol and in an aqueous medium. This catalyst proves robust towards the presence of oxidants, such as oxygen and water, is magnetically recoverable and shows selectivity towards the less activated double bonds.     

Bilinear Fourier Restriction Theorems

We provide a general scheme for proving L ^p estimates for certain bilinear Fourier restrictions outside the local L ² setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood?CPaley inequality.     

Synthesis and Reactivity of [PdCl(terpy)]Cl

 [PdCl(terpy)]Clċ3H₂O has been synthesized both by interaction of [PdCl₄]²⁻ and cis-[Pd(DMSO)₂Cl₂] with terpy (2,2^′:6^′,2^′′-terpyridine). Complex formation of [PdCl(terpy)]⁺ with L-cysteine, S-methyl-L-cysteine, and L-methionine was studied as a function of temperature (298–308 K) using of stopped-flow spectrophotometry in methanol-water (95:5 (v/v)). The ionic strength and acidity of the solutions were adjusted to 0.10 molċdm⁻³ with CH₃SO₃H. The second-order rate constant for the reaction of [PdCl (terpy)]⁺ with L-cysteine amounts to 9.60±0.5 M ⁻¹s⁻¹. L-Methionine and S-methyl-L-cysteine are unreactive under the same experimental conditions. The entropy of activation is strongly negative, which is compatible with an associative mechanism.