Boundary value problems and Mayer-Vietoris sequence

Milan Journal of Mathematics - We define formally non characteristic hypersurfaces for a complex of differential operators and we establish a Mayer-Vietoris sequence. We give applications to...     

Discontinuità e ipersuperfici caratteristiche in magnetofluidodinamica relativistica

Sunto L'A., dopo aver mostrato come si riduce il numero delle equazioni della m.f.d. in relatività generale quando la conducibilità elettrica è infinita, esamina le ipersuperfici di discontinuità nelle derivate delle funzioni incognite e ricerca le soluzioni proprie dei sistemi di equazioni lineari omogenee nei parametri di discontinuità. In primo luogo viene esaminato il sistema, indeterminato, che si deduce dalla solenoidalità del tensore energetico e dalle equazioni di Maxwell; successivamente si esaminano i sistemi determinati o associandovi l'ipotesi che il fluido sia barotropico, comprimibile o incomprimibile, o che valga un'equazione termica di stato e il principio di conservazione della densità numerica delle particelle. Si distingue tra ipersuperfici che siano luogo di linee di corrente e di linee di forza per il campo magnetico, e ipersuperfici che siano in vari modi intersecate da linee di corrente e da linee di forza, ottenendone le equazioni differenziali, nonchè i legami tra i parametri di discontinuità.

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Summary The A., after having shown how the number of the equations of magnetofluid-dynamics in general relativity is reduced when the electrical conductivity is infinite, studies the discontinuity manifolds of the derivatives of the unknown functions and looks for the eigensolutions of the linear homogeneous equations in the jumps of the derivatives. Firstly the A. studies the indeterminate system derived from the equations which state that the divergence of the energy-tensor is null and from the Maxwell equations; successively, he studies the systems which are determined by the hypothesis that either the fluid is incompressible, or is compressible and barotropic, or by a caloric state equation and by the conservation law of the numerical density of the particles. A distinction is made form manyfolds locus of path lines and locus of lines of force for the magnetic field and manyfolds which are variously crossed by path lines and by lines of force. The differential equations of the manyfolds and the relations from the jumps are found.

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Lavoro eseguito nell'ambito dell'attività dei Gruppi di ricerca Matematici del C.N.R.     

Ion pairs formed by alkali metals. Complex of caesium with 4-nitropyridine

The ESR spectra of the 4-nitropyridine/caesium system in dimethoxyethane have been measured in the range of temperature between ?100 and +20°C. These spectra are drastically different from those of the ion pairs obtained with the lighter alkali metals, and an interpretation is offered.     

A 3D QSAR approach to the search for geometrical similarity in a series of nonpeptide angiotensin II receptor antagonists

Summary A 3D QSAR methodology based on the combined use of conformational analysis and chemometrics was applied to perform a comparative analysis of the 3D conformational features of 13 nonpeptide angiotensin II receptor antagonists showing different levels of binding affinity. Conformational analysis by using a molecular mechanics MM2 method was carried out for each of these structures to obtain conformational minima. These minima were described by ten interatomic distances which define the relative spatial disposition of five significant atoms belonging to relevant functional groups present in all the 13 molecules. The structure-activity relationship between the interatomic distances and the biological activity was then assessed by using chemometric methods (cluster analysis, principal component analysis, classification methods). With our indirect approach based on the search for geometrical similarity it was possible, even though structural information on the receptor active site was lacking, to identify the 3D geometrical requirements for the binding affinity of nonpeptide angiotensin II receptor inhibitors.     

Modulation of hydrophobic effect by cosolutes

This work concerns a comparison of the hydration properties and self-association behavior in aqueous solution of three biologically relevant simple molecules: tert-butyl alcohol (TBA), trimethylamine-n-oxide (TMAO), and glycine betaine (GB). These molecules were used as a model to study hydrophobic behavior in water solutions. In particular, water perturbation induced by TBA, TMAO, and GB molecules was studied as a function of the solute molar fraction X(2) (0 < X(2) < 0.04) by Raman spectra of water in the fundamental OH-stretching region (3,800-2,800 cm(-1)). Furthermore, possible hydrophobic clustering of these molecules was investigated by studying the behavior of the alkyl CH stretching band in the 3,100-2,900 cm(-1) frequency region as a function of X(2). To establish the existence of a correlation between the effects of these three solutes on the micellization process and changes in the properties of the solvent, the behavior of the critical micelle concentration of sodium dodecyl sulfate was also investigated as a function of the added amount of TBA, TMAO, and GB. On the whole, these data show that there is no direct correlation between a solute's effect on the water structure and its effect on micelle or protein stability. Results indicate that, while TBA starts to self-aggregate at approximately X(2) = 0.025, both TMAO and GB do not exhibit any significant self-aggregation up to the highest concentration considered. In addition, nonadditive perturbations of the H-bonded networks of solvent water are observed in the case of TBA solutions, but are absent in both the TMAO and GB cases. The absence of these nonlinear effects in TMAO and GB water solutions allow for tracing the microscopical mechanism of the neutrality of these osmolytes toward hydrophobic effects. This confers the compatibility to these two osmolytes, which can be accumulated at high concentrations without interfering with biochemical processes in the cell.     

Polar effects and structural variation in 4-substituted 1-phenylbicyclo[2.2.2]octane derivatives: a quantum chemical study

The transmission of polar effects through the bicyclo[2.2.2]octane framework has been investigated by ascertaining how the geometry of a phenyl group at a bridgehead position is affected by a variable substituent at the opposite bridgehead position. We have determined the molecular structure of several Ph-C(CH(2)-CH(2))(3)C-X molecules (where X is a charged or dipolar substituent) from HF/6-31G and B3LYP/6-311++G molecular orbital calculations and have progressively replaced each of the three -CH(2)-CH(2)- bridges by a pair of hydrogen atoms. Thus the bicyclo[2.2.2]octane derivatives were changed first into cyclohexane derivatives in the boat conformation, then into n-butane derivatives in the anti-syn-anti conformation, and eventually into assemblies of two molecules, Ph-CH(3) and CH(3)-X, appropriately oriented and kept at a fixed distance. For each variable substituent the deformation of the benzene ring relative to X = H remains substantially the same even when the substituent and the phenyl group are no longer connected by covalent bonds. This provides unequivocal evidence that long-range polar effects in bicyclo[2.2.2]octane derivatives are actually field effects, being transmitted through space rather than through bonds. Varying the substituent X in a series of Ph-C(CH(2)-CH(2))(3)C-X molecules gives rise to geometrical variation (relative to X = H) not only in the benzene ring but also in the bicyclo[2.2.2]octane cage. The two deformations are poorly correlated. The rather small deformation of the benzene ring correlates well with traditional measures of long-range polar effects in bicyclo[2.2.2]octane derivatives, such as sigma(F) or sigma(I) values. The much larger deformation of the bicyclo[2.2.2]octane cage is controlled primarily by the electronegativity of X, similar to deformation of the benzene ring in Ph-X molecules. Thus the field and electronegativity effects of the substituent are well separated and can be studied simultaneously, as they act on different parts of the molecular skeleton.     

Quantum mechanical study of the correlation of attack and recoil angles for the Cl + H2 reaction using the stereodirected and discrete variable representations on two potential energy surfaces

The zero total angular momentum (J = 0) S matrix elements, calculated using a time-dependent wave packet method for the Cl (2P) + H2 reaction on two different potential energy surfaces, have been matrix transformed to the stereodirected and Gauss-Legendre discrete variable representations. Although the results in the two representations are (as expected) quantitatively different with respect to the angular selectivity and specificity of the reactive process, the qualitative similarity has allowed us to draw for the first time conclusions with respect to some characteristics of the potential energy surface.     

Molecular structure and benzene ring deformation of three ethynylbenzenes from gas-phase electron diffraction and quantum chemical calculations

The molecular structures of ethynylbenzene and s-triethynylbenzene have been accurately determined by gas-phase electron diffraction and ab initio/DFT MO calculations and are compared to that of p-diethynylbenzene from a previous study [Domenicano, A.; Arcadi, A.; Ramondo, F.; Campanelli, A. R.; Portalone, G.; Schultz, G.; Hargittai, I. J. Phys. Chem. 1996, 100, 14625]. Although the equilibrium structures of the three molecules have C2v, D3h, and D2h symmetry, respectively, the corresponding average structures in the gaseous phase are best described by nonplanar models of Cs, C3v, and C2v symmetry, respectively. The lowering of symmetry is due to the large-amplitude motions of the substituents out of the plane of the benzene ring. The use of nonplanar models in the electron diffraction analysis yields ring angles consistent with those from MO calculations. The molecular structure of ethynylbenzene reported from microwave spectroscopy studies is shown to be inaccurate in the ipso region of the benzene ring. The variations of the ring C-C bonds and C-C-C angles in p-diethynylbenzene and s-triethynylbenzene are well interpreted as arising from the superposition of independent effects from each substituent. In particular, experiments and calculations consistently show that the mean length of the ring C-C bonds increases by about 0.002 A per ethynyl group. MO calculations at different levels of theory indicate that though the length of the C[triple bond]C bond of the ethynyl group is unaffected by the pattern of substitution, the C(ipso)-C(ethynyl) bonds in p-diethynylbenzene are 0.001-0.002 A shorter than the corresponding bonds in ethynylbenzene and s-triethynylbenzene. This small effect is attributed to conjugation of the two substituents through the benzene ring. Comparison of experimental and MO results shows that the differences between the lengths of the C(ipso)-C(ethynyl) and C(ipso)-C(ortho) bonds in the three molecules, 0.023-0.027 A, are correctly computed at the MP2 and B3LYP levels of theory but are overestimated by a factor of 2 when calculated at the HF level.     

Ant colony optimization for the arc routing problem with intermediate facilities under capacity and length restrictions

The aim of this paper is to introduce a new ant colony optimization procedure for the Arc Routing Problem with Intermediate Facilities under Capacity and Length Restrictions (CLARPIF), a variant of the Capacitated Arc Routing Problem (CARP) and of the Capacitated Arc Routing Problem with Intermediate Facilities (CARPIF). Computational results show that this algorithm is capable of providing substantial improvements over other known heuristics.