Duality in Function Spaces

In this paper we use Bartle’s technique to study duality between a topological space and a function space. Normally such a duality forms an essential part of Functional Analysis. We introduce several new topologies such as the topology of even convergence T_e, the closed-cocompact topology T_{k ′}, the (strong) local proximal convergence. We explore the topological groups of self-homeomorphisms of a topological space and shed light on the earlier work of Arens, Dieudonné, Di Concilio. We also study the concepts such as evenly equidistant, functionally equicontinuous, due to Bouziad-Troallic and topologically equicontinuous due to Royden. In memory of Professor Enrico Meccariello who made a considerable contribution to this work and who suddenly passed away before his time     

Membrane lipid domains and dynamics as detected by Laurdan fluorescence

2-Dimethylamino-6-lauroylnaphthalene (Laurdan) is a membrane probe of recent characterization, which shows high sensitivity to the polarity of its environment. Steady-state Laurdan excitation and emission spectra have different maxima and shape in the two phospholipid phases, due to differences in the polarity and in the amount of dipolar relaxation. In bilayers composed of a mixture of gel and liquid-crystalline phases, the properties of Laurdan excitation and emission spectra are intermediate between those obtained in the pure phases. These spectral properties are analyzed using the generalized polarization (GP). TheGP value can be used for the quantitation of each phase. The wavelength dependence of theGP value is used to ascertain the coexistence of different phase domains in the bilayer. Moreover, by following the evolution of Laurdan emission vs. time after excitation, the kinetics of phase fluctuation in phospholipid vesicles composed of coexisting gel and liquid-crystalline phases was determined.GP measurements performed in several cell lines did not give indications of coexistence of phase domains in their membranes. In natural membranes, Laurdan parameters indicate a homogeneously fluid environment, with restricted molecular motion in comparison with the phospholipid liquid-crystalline phase. The influence of cholesterol on the phase properties of the two phospholipid phases is proposed to be the cause of the phase behavior observed in natural membranes. In bilayers composed of different phospholipids and various cholesterol concentrations, Laurdan response is very similar to that arising from cell membranes. In the absence of cholesterol, from the steady-state and time-resolved measurements of Laurdan in phospholipid vesicles, the condition for the occurrence of separate coexisting domains in the bilayer has been determined: the molecular ratio between the two phases must be in the range between 30% and 70%. Below and above this range, a single homogeneous phase is observed, with the properties of the more concentrated phase, slightly modified by the presence of the other. Moreover, in this concentration range, the calculated dimension of the domains is very small, between 20 and 50 Å.     

Geometric dependence of casimir energy and scalar green's functions

It is well known that the Casimir Energy depends on the geometry of the conducting cavity. In this note, scalar Green's functions are used to determine the Casimir energy's dependence on terms bilinear in the extrinsic curvatures of the cavity's surface, and thus to resolve the controversy over the Casimir energy's finiteness.     

Zinc(II)cysteine and zinc(II)cystine systems: Selection of species from potentiometric data

Summary The formation constants of species formed in the systems H⁺-Zn²⁺-cysteine and H⁺-Zn²⁺-cystine have been determined in aqueous solution at 37° and I = 0.15 mot dm^–3 (NaClO₄), using the pH-metric method. The existence of the following species [ZnL], [ZnL₂], [ZnL₂H] and [Zn₂L₃] (2.3 pH 7.7) was proved for the Zn²⁺-cysteine system, whereas for the Zn²⁺-cystine [Zn₂L] (5.3 pH 6.4) was the only species found. In the Zn²⁺-cystine system the pH range was severely restricted because of precipitation occurring at pH > 6.4. A new experimental and numerical approach was employed in order to implement the possibility of rigorously selecting the species present in each system. The results have been compared with data previously reported on the same systems, considering in particular the different sets of species found in the various works.     

Poly condensed nitrogen heterocycles. V. Two novel ring systems: Pyrazolo[5,1-c]-1,2,4-thiadiazine and pyrazolo[3,4-c]-1,2-thiazine

The title compounds were obtained by reaction of aminopyrazoles IV and VII with ω-acetophenonesulfonyl chloride (II, R = C₆H₅). In agreement with the general pattern of the distribution of electron density in the pyrazole nucleus, this work confirms that the position 4 of ring is the favoured site of electrophilic attacks.     

The oxime rearrangement cyclization. Alkenyl,styryl and vinyl chloride terminators in the synthesis of Δ1-pyrrolines

Functionalized γ,δ-unsaturated oximes, constructed by regiospecific alkylation of appropriate oximes, may be rearranged and cyclized to Δ¹-pyrrolines in good yield.     

Palladium-catalyzed carbonylation of enol triflates. A novel method for one-carbon homologation of ketones to α,β-unsaturated carboxylic acid derivatives

Ketones can be homologated to α,gb-unsaturated esters or amides via their enol triflates by a palladium-catalyzed reaction with carbon monoxide and alcohols or amines.