Existence of proper semihypergroups of type U on the right

We generalize the classical definition of hypergroups of type U on the right to semihypergroups, and we prove some properties of their subsemihypergroups and subhypergroups. In particular, we obtain that a finite proper semihypergroup of type U on the right can exist only if its order is at least 6. We prove that one such semihypergroup of order 6 actually exists. Moreover, we show that there exists a hypergroup of type U on the right of cardinality 9 containing a proper non-trivial subsemihypergroup. In this way, we solve a problem left open in [D. Freni, Sur les hypergroupes de type U et sous-hypergroupes engendrés par un sous-ensemble, Riv. Mat. Univ. Parma 13 (1987) 29-41].     

Persistence of Eigenvalues and Multiplicity in the Dirichlet Problem for the Laplace Operator on Nonsmooth Domains

We consider the Dirichlet eigenvalue problem for the Laplace operator on a variable nonsmooth domain. We extend a result of Lupo and Micheletti concerning the structure of the set of domain perturbations which leave the multiplicity of an eigenvalue unchanged, and we study the set of perturbations which leave a certain eigenvalue unchanged.     

Method for superposing reconstructed images from digital holograms of the same object recorded at different distance and wavelength

A method for allowing direct perfect superimposition and comparison of Fresnel-transform reconstructions of digital holograms recorded of the same object at different distances and wavelengths is proposed and demonstrated. The method takes into account the dependence of the reconstruction pixel on the distance and the wavelength by the Fresnel-transform algorithm. The method avoids the need for image scaling at the end of the reconstruction process that usually is performed in multi-wavelength digital holography. Demonstration is given by superposing the numerical reconstructions of holograms recorded at different distances and wavelengths. The method can be potentially very useful for real-time monitoring in biological processes or for recognition and ranging by multiple wavelengths of a target with fast movements or finally for very fast investigation and study of very fast processes.     

Chloroform sorption in nanoporous crystalline and amorphous phases of syndiotactic polystyrene

The transport of chloroform in films of atactic polystyrene and of semicrystalline syndiotactic polystyrene in its nanoporous form (δ‐form) has been investigated by gravimetric analysis. Experimental tests have been performed at 35, 49, and 56 °C and at several vapor pressures ranging from 0.5 to 100 Torr. Nonequilibrium lattice fluid prediction of the amorphous sorption behavior was used to enucleate the sorption contribution of the crystalline nanoporous phase from semicrystalline samples. Sorption behavior of the crystalline phase has been interpreted on the basis of Langmuir equation. Moreover, the chloroform sorption at low activities in the crystalline nanoporous phase has been predicted by using Grand Canonical Monte Carlo molecular simulations. Isosteric heats of sorption were also experimentally evaluated for the crystalline phase, and compared with the corresponding prediction of molecular simulation. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 8–15, 2008     

A biogenetically new tetraterpene alcohol from elodea canadensis

On the basis of spectroscopic data structure 1 is proposed for a tetraterpene alcohol isolated from Elodea canadensis. A new biogenetic route is suggested for its formation.     

Intense shake-up satellites in the XPS spectra of planar and sterically hindered N-piperidyl-nitrobenzenes and -nitrothiophens

The shake-up satellites present in the O_1s and N_1s energy regions of the XPS spectra of the planar 4-N-piperidyl-nitrobenzene (1) and 2-N-piperidyl-5-nitrothiophen (3), and of the sterically hindered 2-N-piperidyl-nitrobenzene (2), 2-N-piperidyl-3-nitrothiophen (4) and 3-N-piperidyl-2-nitrothiophen (5) and, for comparison, of 2-bromo-3-nitrothiophen (6) have been analyzed with the help of CNDO/S CI calculations. The spectra of the planar derivatives closely resemble these of the related compounds previously analysed, the main satellites deriving from the transition between the highest occupied molecular orbital (HOMO, localized at the donor-ring moiety) towards the lowest unoccupied one (LUMO, localized at the nitro group). Calculations indicate that in the ortho derivatives new relaxation processes are allowed upon N_1s/NO₂ ionization. In 2, where the angle of rotation θ is closer to 90° than 60°, the NR ₂ lone-pair orbital relaxes through space towards the core-ionized N/NO₂ atom. In 4 and 5, where 45° ? θ ? 60°, both through-ring and through-space relaxations are present. The assignment of the main N_1s/NO₂ line in 1 is discussed.     

The accuracy of ab initio molecular geometries for systems containing second-row atoms

The performance of the standard hierarchy of ab initio models--that is, Hartree-Fock theory, second-order Moller-Plesset theory, coupled-cluster singles-and-doubles theory, and coupled-cluster singles-doubles-approximate-triples theory--in combination with correlation-consistent basis sets is investigated for equilibrium geometries of molecules containing second-row elements. From an analysis on a collection of 31 molecules (yielding statistical samples of 41 bond distances and 13 bond angles), the statistical errors (mean deviation, mean absolute deviation, standard deviation, and maximum absolute deviation) are established at each level of theory. The importance of core correlation is examined by comparing calculations in the frozen-core approximation with calculations where all electrons are correlated.