Simultaneous determination of solubility, dissolution and dilution enthalpies of a substance from a single calorimetric experiment

The thermodynamics of dissolution in water of a set of substances has been studied calorimetrically. The examined substances were: potassium chloride, (glycyl-glycyl)diketopiperazine, (alanyl-alanyl)diketopiperazine, (leucyl-glycyl)diketopiperazine. They were chosen on the basis of their solubilities, going from a highly soluble electrolyte to the sparingly soluble diketopiperazines. It is shown that, using a commercially available calorimeter, it is possible to perform in a single calorimetric experiment the simultaneous determination of all thermodynamic parameters characterizing dissolution of a substance in a given solvent, i.e. solubility, dissolution enthalpy and dilution enthalpy. The solubility values in water obtained through the proposed method are in good agreement with those reported in the literature and obtained by other techniques.     

Crystalline protein domains and lipid bilayer vesicle shape transformations

Cellular membranes can take on a variety of shapes to assist biological processes including endocytosis. Membrane-associated protein domains provide a possible mechanism for determining membrane curvature. We study the effect of tethered streptavidin protein crystals on the curvature of giant unilamellar vesicles (GUVs) using confocal, fluorescence, and differential interference contrast microscopy. Above a critical protein concentration, streptavidin domains align and percolate as they form, deforming GUVs into prolate spheroidal shapes in a size-dependent fashion. We propose a mechanism for this shape transformation based on domain growth and jamming. Osmotic deflation of streptavidin-coated GUVs reveals that the relatively rigid streptavidin protein domains resist membrane bending. Moreover, in contrast to highly curved protein domains that facilitate membrane budding, the relatively flat streptavidin domains prevent membrane budding under high osmotic stress. Thus, crystalline streptavidin domains are shown to have a stabilizing effect on lipid membranes. Our study gives insight into the mechanism for protein-mediated stabilization of cellular membranes.     

Excess enthalpies of aqueous ternary solutions of urea and polyols at 25°C

The heats of dilution of nine ternary solutions of urea and polyols have been determined at 25°C. Excess enthalpies and their virial coefficients h _xy have been evaluated and compared with the data reported in the literature for mono- and polyfunctional alcohols and other oxygenated nonelectrolytes. The group additivity approach of Savage and Wood was applied and the contributions to the enthalpy coefficients, due to the water mediated interactions between urea and the functional groups –CH₂–, –OH, and –O– were determined. On the other hand, by using empirical combination rules among the cross- and self-enthalpic interaction coefficients it is possible to emphasize the large differences in the behavior (even in the presence of urea) of the polyols (and in particular of cyclitols) and of saccharides.     

A Characterization of Nilpotent Leibniz Algebras

W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits an invertible Leibniz-derivation. In this paper, using the definition of a Leibniz-derivation from Moens (2010), we show that a similar result for non-Lie Leibniz algebras is not true. Namely, we give an example of non-nilpotent Leibniz algebra that admits an invertible Leibniz-derivation. In order to extend the results of the paper by Moens (2010) for Leibniz algebras, we introduce a definition of a Leibniz-derivation of Leibniz algebras that agrees with Leibniz-derivation of the Lie algebra case. Further, we prove that a Leibniz algebra is nilpotent if and only if it admits an invertible Leibniz-derivation of Definition 3.4. Moreover, the result that a solvable radical of a Lie algebra is invariant with respect to a Leibniz-derivation was extended to the case of Leibniz algebras.     

A reliable approach to the solution of Navier–Stokes equations

In this paper we will demonstrate an affective approach of solving Navier–Stokes equations by using a very reliable transformation method known as the Cole–Hopf transformation, which reduces the problem from nonlinear into a linear differential equation which, in turn, can be solved effectively.     

Corrigendum to “Maximal linear groups induced on the Frattini quotient of a p-group” [J. Pure Appl. Algebra 222 (10) (2018) 2931–2951]

We give a correction to Fig. 1 and supporting text published in the paper: ‘Maximal linear groups induced on the Frattini quotient of a p-group’, J. Pure Appl. Algebra 222 (10) (2018) 2931–2951.     

Large Cliques in -Free Graphs

Dedicated to the memory of Paul Erdős A graph is called -free if it contains no cycle of length four as an induced subgraph. We prove that if a -free graph has n vertices and at least edges then it has a complete subgraph of vertices, where depends only on . We also give estimates on and show that a similar result does not hold for H-free graphs––unless H is an induced subgraph of . The best value of is determined for chordal graphs. Received October 25, 1999 RID="*" ID="*" Supported by OTKA grant T029074. RID="**" ID="**" Supported by TKI grant stochastics@TUB and by OTKA grant T026203.