Stability of the preservation of the equality of distance

We study the stability problem for mappings satisfying the equation

‖f(x−y)‖=‖f(x)−f(y)‖.     

Influence of others on one's decision: A model of group choice

The paper suggests a model of decision of group members in supporting or opposing a given social issue. The central assumption states that the probability of a positive decision of nth person depends on the number of positive choices among the n-1 persons who preceded him in making the decision. Formulas are given for the expectation and variance of the total group support. It is also shown how these results may be applied to optimally allocating the resources among various propaganda tasks.     

On mappings preserving equilateral triangles

Let E be a Euclidean space, dim E 2. We say that f : E E preserves equilateral triangles if for all triples of points x, y, z E we have We show that if E is a finite-dimensional Euclidean space, dim E 2, f:E E is measurable and preserves equilateral triangles, then it is a similarity transformation (an isometry multiplied by a positive constant). Moreover, in spaces at least three-dimensional we get a similarity transformation without any regularity assumption. Some generalizations as well as some interesting examples are also presented in the paper.     

Inhibiting effect of beta-cyclodextrin on thymine dimerization photosensitized by para-aminobenzoic acid

Beta-cyclodextrin can act as an efficient inhibitor of the photosensitized dimerization of thymine by para-aminobenzoic acid (PABA) in aqueous solution. This can be explained by considering the formation of an inclusion complex between PABA and beta-cyclodextrin.     

Ipertrofan Revisited—The Proposal of the Complete Stereochemistry of Mepartricin A and B

Being a methyl ester of partricin, the mepartricin complex is the active substance of a drug called Ipertrofan (Tricandil), which was proven to be useful in treatment of benign prostatic hyperplasia and chronic nonbacterial prostatitis/chronic pelvic pain syndrome. Nevertheless, no direct structural evidence on the stereochemistry of its components has been presented to date. In this contribution, we have conducted detailed, NMR-driven stereochemical studies on mepartricins A and B, aided by molecular dynamics simulations. The absolute configuration of all the stereogenic centers of mepartricin A and B was defined as 3R, 7R, 9R, 11S, 13S, 15R, 17S, 18R, 19S, 21R, 36S, 37R, and 38S, and proposed as 41R. The geometry of the heptaenic chromophore of both compounds has been established as 22E, 24E, 26E, 28Z, 30Z, 32E, and 34E. Our studies on mepartricin ultimately proved that partricins A and B are structurally identical to the previously described main components of the aureofacin complex: gedamycin and vacidin, respectively. The knowledge of the stereochemistry of this drug is a fundamental matter not only in terms of studies on its molecular mode of action, but also for potential derivatization, aiming at improvement of its pharmacological properties.     

Green analytical chemistry as an integral part of sustainable education development

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Cocrystals “Divorce and Marriage”: When a Binary System Meets an Active Multifunctional Synthon in a Ball Mill

A well-defined and stable “AB” binary system in the presence of “C” a crystalline synthon ground in a ball mill undergoes selective transformation in the solid state according to the equation AB+C→AC+B. When the amount of C is increased two times then the equation AB+2C→AC+BC is valid. The other variants are more complex. The pathway BC+A is allowed and leads to the AC and B products. The pathway AC+B is not preferred, and no transformation is observed. These non-obvious correlations were observed for cocrystal of barbituric acid (BA):thiobarbituric acid (TBA) recently reported by Shemchuk et al. (Chem. Commun. 2016 , 52, 11815–11818) in the presence of 1-hydroxy-4,5-dimethyl-imidazole 3-oxide (HIMO). This synthon shows high affinity for the BA_0.5TBA_0.5 cocrystal as well for its individual components, BA and TBA. Single-quantum, double-quantum (SQ-DQ) 2D ¹H very fast MAS NMR with a spinning rate of 60 kHz was employed as a basic and most diagnostic tool for the study of cocrystals transformations. Analysis of the experimental data was supported by theoretical calculations, including computation of the stabilization energy, E^stab, defined as the energy difference between the energy of a co-crystal and the sum of the energies of particular components in the respective stoichiometric ratios. Two mechanisms of synthon replacement have been proposed. Pathway 1 assumes a concerted mechanism of substitution. In this approach, synthon attack is synchronized in time with the departure of one of the components of the binary system. Pathway 2 implies a non-concerted process, with an intermediate stage in which three separate components are present. Evidence suggesting a preference for Pathway 2 is shown.