Approximating Clarke’s subgradients of semismooth functions by divided differences

We show that the algorithm presented in an earlier paper by Studniarski (Numer. Math., 55:685–693, 1989) can be applied, after only a small modification, to approximate numerically Clarke’s subgradients of semismooth functions of two variables. Results of computational testing of this modified algorithm are also reported.      

Determination of Emodin and Phenolic Acids in the Petioles of Rheum undulatum and Rheum rhaponticum

JPC – Journal of Planar Chromatography – Modern TLC - Emodin and twelve phenolic acids (ellagic, gallic, protocatechuic, homoprotocatechuic, caffeic, p-hydroxybenzoic, p-coumaric,...     

The Low Energy Limit of String Theory and its Compactifications with Background Fluxes

String theory is consistently defined in ten dimensions. In order to extract any information about four-dimensional physics, we need to understand the properties of the six-dimensional compact manifold orthogonal to our four-dimensional universe. A possibility that is being very much explored lately is to look at manifolds on which background fluxes are turned on. In this article, we present an introduction to string theory, focusing on its massless sector. We then review traditional compactifications to four–dimensions, and finally motivate and describe the so-called flux compactifications. We interpret the allowed six-dimensional manifolds from the point of view of generalized complex geometry.     

Do intramolecular halogen bonds exist? Ab initio calculations and crystal structures’ evidences

Cl···O intramolecular contacts are analysed here. Hence the Cambridge Structural Database (CSD) search was performed to find five-membered Cl–C=C–C=O pseudo-rings closed through Cl···O intramolecular contacts. Such rings were analysed and it was found that some of Cl···O distances are smaller than the corresponding sum of van der Waals radii. Additionally ab initio MP2/6-311++G(d,p) calculations and AIM analyses were carried out here on 3-chloropropenal and its fluoro derivatives to deepen the nature of intramolecular Cl···O interactions, some of findings may indicate that they are attractive and stabilizing ones. This paper is dedicated to Prof. T. M. Krygowski on the occasion of his 70th birthday     

Thiol-ene chemistry as an effective tool for hydrophobization of cotton fabrics

In this paper, several methods of hydrophobization of cotton fabrics using the thio-ene click reaction were compared. Durable, superhydrophobic textiles were obtained in an easy way. Various variants of functionalized silsesquioxanes were used for the hydrophobization of fabrics. The synthesis of bifunctional silsesquioxanes (RSiMe₂O)₄(ViSiMe₂O)₄Si₈O₁₂ and (RSiMe₂O)₄(R’SiMe₂O)₄Si₈O₁₂ were performed via hydrothiolation of silsesquioxane derivative (ViSiMe₂O)₈Si₈O₁₂. Alkoxysilyl, alkyl and fluoroalkyl moieties were introduced as functional groups. Samples were prepared using four methods, differing in the modification method and the number of stages. During the research, fabrics were modified via (a) the dip-coating process, (b) carrying out thiol-ene click reactions directly on the surface of the fabric and (c) using both of these methods. The hydrophobicity of the fabric was evaluated by measuring the Water contact angle (WCA). The obtained samples were also examined using infrared analysis (FT-IR), Scanning electron microscope (SEM), and Elemental analysis (SEM–EDS). All analyses were performed before and after the washing process in order to verify the stability of the performed modifications.

Graphical abstract

     

Structural assignment of organotin hydrides containing the oxazoline ligand

A series of triorganotin hydrides and diorganotin dihydrides containing the optically active 2-(4-isopropyl-2-oxazolinyl)-5-phenyl ligand have been characterized by means of the multinuclear low-temperature NMR investigations, the results of which are discussed. In the corresponding organotin hydrides values of the ¹J(¹H-^117/119Sn) couplings appeared to be temperature dependent, supporting an axial/equatorial position of the hydrogen attached to the tin.     

Theoretical study of the electronic structure of CnS (n=1-6) thiocumulenes

Linear sulfur-carbon chains C(n)S (n=1-6) of astronomical interest were examined by means of several theoretical methods. The three smallest compounds of the series were chosen to evaluate the performance of several computational models, including Hartree-Fock theory, density functional theory with the Becke's three parameter exchange functional and the correlation functional of Lee, Yang, and Parr (B3LYP), and electron-correlated methods (second-order Moller-Plesset perturbation method (MP2), configuration interaction method including single and double excitations (CISD), and quadratic configuration interaction method including single and double excitations (QCISD) in combination with a large variety of basis sets. The systematic comparison between the experiment and theory indicates that the B3LYP/6-311G** method can be considered suitable for the study of the electronic structures of the C(n)S compounds. The electronic ground states of the C(n)S molecules alternate between 1Sigma and 3Sigma for odd and even values of n, respectively. The B3LYP/6-311G** wave functions for these electronic ground states were analyzed by means of the atoms in molecules (AIM) and natural bond orbital (NBO) methods. Both approaches suggest that the electronic structures for the singlet and triplet compounds must be considered separately. According to the NBO method, singlet compounds can be properly represented by acetylenic structures with alternating single and triple bonds (S[triple bond]C-C[triple bond]C...). However, triplet compounds are better described by means of double bond-double bond cumulenic structures (S=C=C=C=C...) as a consequence of the average between different alpha and beta electronic densities. AIM delocalization indexes and NBO interactions between localized orbitals also indicate that these structures are strongly pi delocalized. Finally, the different singlet and triplet structures proposed provide a consistent explanation for the geometries, dipole moments, and spin-density values of the C(n)S compounds studied.