Intermolecular hydrogen bonding as an aid to the preferential exhibition of the smectic C phase in troponoid liquid crystals

Abstract

2-(4-Alkoxybenzoyloxy)-5-alkylaminotropone and 5-alkoxy-2-(4-alkylaminobenzoyloxy)tropone liquid crystals showed the smectic C phase exclusively. Variable temperature FT-IR spectra indicated that intermolecular hydrogen bonding between the NH and tropone C=O groups assisted the appearance of the mesophase. 4-Alkoxyphenyl 4-alkylaminobenzoates were non-mesogenic.     

A New Approach to The Synthesis of Enantiomerically Pure 4-Deoxy Sugars

In a recent paper² we have reported the design and synthesis of 3-C-lithiated 5,6-dihydro-1,4-dithiin-2-yl[(4-methoxybenzyl)oxy]methane (1) which can be utilized as an allylic alcohol anion equivalent and leads to three-carbon elongations of various electrophiles by introduction of a fully protected hydroxypropenyl moiety. The latter contains a double bond, which can be unravelled to the cis configuration by diastereoselective removal³ of the dimethylene-disulfur bridge, as well as a protected primary hydroxyl group that, depending on the deprotection conditions used (DDQ/NaBH₄ or DDQ), may either lead to the free allylic alcohol or to an α,β-unsaturated aldehyde.     

A corresponding states principle-based equation for the surface tension of Alkenes

This study presents a new formula for the surface tension prediction of alkenes. As a first step, an analysis of the available data of the experimental surface tension data for alkenes was performed. The experimental data were collected, after a careful literature survey, for the following pure fluids: propene, 1-hexene, 1-heptene, 1-octene, 1-decene, 1-tetradecene, and 1-pentadecene. Then, the experimental data were regressed with the most reliable semi-empirical correlating methods based on the corresponding state theory existing in the literature. As a final step, an analysis of the available data of the experimental surface tension data for alkenes was performed starting from the two recently proposed equations for the prediction of the surface tension of refrigerants based on the corresponding states principle. To minimize the deviation between the predicted data and the experimental data and to find the optimal equation coefficients for experimental data regression, a (μ + λ)-evolution strategy was adopted. The analysis showed that the equation that gave the best results for the prediction of the surface tension of alkenes was the one with a very limited number of parameters. The finally proposed equation is very simple and gives a noticeable improvement with respect to the existing equations. It is based on the corresponding state principle, containing the acentric factor, the critical temperature, and pressure.     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

The Solow model improved through the logistic manpower growth law

In this paper the neo-classical economic Solow-Swan model (1956) has been improved replacing its Malthusian manpower law with the Verhulst (logistic) one. The relevant ordinary differential equation for the ratio capital/work has been then integrated in closed form via the Hypergeometric function₂ F ₁. The logistic growth injection for the manpower is detected to induce a more slow dynamics onto the Solow-Swan system, which keeps its stability. Increasing developments are displayed as the technologic progress rises. Further sceneries are tested and the congruence of the new solution with the classical one is shown switching to zero the selflimitation coefficent in the logistic law. Research supported by MURST grant:Metodi matematici in economia     

Groups in which every non-abelian subgroup is permutable

A subgroupH of a groupG is said to bepermutable ifHX=XH for every subgroupX ofG. In this paper the structure of groups in which every subgroup either is abelian or permutable is investigated. This work was done while the last author was visiting the University of Napoli Federico II. He thanks the “Dipartimento di Matematica e Applicazioni” for its financial support.     

Positive\partial \bar \partial - closed currents and non-Kähler geometrycurrents and non-Kähler geometry

In this paper some new results on positive \(\partial \bar \partial - closed\) currents are applied to modifications \(f:\bar M \to M\) . The main result in this topic is that every smooth proper modification of a compact Kähler manifoldM is balanced. Moreover, under suitable hypotheses on the map, the Kähler degrees of \(\bar M\) corresponds to homological properties of the exceptional set of the modification. More examples ofp-Kähler manifolds are discussed in the last section of the paper.