Elastic waves in quasiperiodic structures

We study the transverse and sagittal elastic waves in different quasiperiodic structures by means of the full transfer-matrix technique and surface Green-function matching method. The quasiperiodic structures follow Fibonacci, Thue-Morse and Rudin-Shapiro sequences, respectively. We consider finite structures having stress-free bounding surfaces and different generation orders, including up to more than 1000 interfaces. We obtain the dispersion relations for elastic waves and spatial localization of the different modes. The fragmentation of the spectrum for different sequences is evident for intermediate generation orders, in the case of transverse elastic waves, whereas, for sagittal elastic waves, higher generation orders are needed to show clearly the spectrum fragmentation. The results of Fibonacci and Thue-Morse sequences exhibit similarities not present in the results of Rudin-Shapiro sequences.     

A dynamic boundary value problem arising in the ecology of mangroves

We consider an evolution model describing the vertical movement of water and salt in a domain splitted in two parts: a water reservoir and a saturated porous medium below it, in which a continuous extraction of fresh water takes place (by the roots of mangroves). The problem is formulated in terms of a coupled system of partial differential equations for the salt concentration and the water flow in the porous medium, with a dynamic boundary condition which connects both subdomains.We study the existence and uniqueness of solutions, the stability of the trivial steady state solution, and the conditions for the root zone to reach, in finite time, the threshold value of salt concentration under which mangroves may live.     

A predictive vapor-pressure equation

A simple equation is presented for predicting the temperature dependence of the vapor-pressure of a pure substance along the entire (liquid + vapor) coexistence curve, from the triple point to the critical point. The proposed equation is based on the use of a dimensionless temperature reduced by using critical and triple point values, and of the Clausius–Clapeyron equation as a zeroth-order approximation. The pressure and temperature at the triple point, the normal boiling temperature, and the pressure and temperature at the critical point are required as input data. The proposed equation is verified for 53 fluids by using NIST data. These data are reproduced with an overall average deviation of 0.55%.     

Similarities in the Intensities of Analogous Rydberg–Rydberg Transitions in the Molecular Series CF x Cl y (x=3, 2, 1; y=1, 2, 3)

In this work, the photoabsorption behaviour of the molecular series CF₃Cl, CF₂Cl₂ and CFCl₃, involving their ground state and two different Rydberg series, has been studied. The discrepancies or similarities in the intensities of homologous transitions in the three CF _x Cl _y molecules have been analysed on account of their electronic structure. Absorption oscillator strengths have been calculated with the Molecular quantum defect orbital (MQDO) approach. Electronic transitions between states belonging to two different unperturbed Rydberg series of the same molecule have been calculated by us for the first time. The quality of the achieved oscillator strengths has been assessed by comparison with, to our knowledge, scarce experimental data available in the literature, through analysis of the discrepancies or similarities in the intensities of homologous transitions in the molecular series CF _x Cl _y when states of different type are involved, and by testing the compliance of regularities by the Rydberg series object of our study.Article for the special issue dedicated to J.-P. Malrieu     

Electron impact mass spectra of phosphine sulphides and selenides

An electron impact mass spectral study of phosphine sulphides and selenides established the effect of the heteroatom and the role of the ortho substituent in the fragmentation pattern.     

Minimal free resolutions that are not supported by a CW-complex

We provide the first examples of minimal free resolutions of monomial ideals which cannot be supported by any CW-complex. Their existence answers negatively the fundamental question of whether every monomial ideal admits a minimal cellular resolution.     

Brønsted acid−catalyzed synthesis of tetrasubstituted allenes and polysubstituted 2H-chromenes from tertiary propargylic alcohols

A practical and environmentally benign Brønsted acid?catalyzed protocol for the preparation of all-carbon tetrasubstituted allenes, consisting in the direct S_N? addition of tri- or dimethoxy arenes or allyltrimethylsilane to tertiary propargylic alcohols, has been developed. In addition, a straightforward synthesis of densely substituted 2H-chromenes by metal-free tandem allenylation/heterocyclization reaction of methoxyphenols and tertiary alkynols is presented.     

Electron ionization mass spectra of indolenines obtained using sector and ion trap mass spectrometers

The electron impact (EI)-induced fragmentations of 18 indolenines were studied using both double-focusing and ion trap mass spectrometers. The compounds used in this study were synthesized to provide correlations of characteristic fragment ions with specific structural differences. In 2-hydroxyindolenines the hydroxy group was involved in a major fragmentation process by interacting with the ester side chain to generate an alpha,beta-unsaturated gamma-lactone structure, with concomitant loss of the corresponding alcohol. In contrast, loss of an alkyl radical, derived solely from the 2-alkoxy group, is a major primary decomposition process for 2-alkoxyindolenines. EI-MS analyses using sector and ion trap spectrometers resulted in similar fragmentation patterns.     

Fine-tuning furan toxicity: fast and quantitative DNA interchain cross-link formation upon selective oxidation of a furan containing oligonucleotide

Oligonucleotides containing a furan modified internal nucleoside have been synthesized; selective in situ oxidation of the furan moiety to a reactive enal species in the presence of a complementary DNA strand gives rise to fast and efficient formation of an interstrand cross-link.     

A Random Multivalued Uniform Boundedness Principle

We present a generalization of the Uniform Boundedness Principle valid for random multivalued linear operators, i.e., multivalued linear operators taking values in the space L₀(,Y) of random variables defined on a probability space with values in the Banach space Y. Namely, for a family of such operators that are continuous with positive probability, if the family is pointwise bounded with probability at least >0, then the operators are uniformly bounded with a probability that in each case can be estimated in terms of and the index of continuity of the operator. To achieve this result, we develop the fundamental theory of multivalued linear operators on general topological vector spaces. In particular, we exhibit versions of the Closed Graph Theorem, the Open Mapping Theorem, and the Uniform Boundedness Principle for multivalued operators between F-spaces.Mathematics Subject Classifications (2000) 46A16, 46A30, 47A06, 47B80, 60H25.