Solid-state molecular organization and solution behavior of methane-1,1-diphosphonic acid derivatives of heterocyclic amines: the role of the topochemical ring modification and the intramolecular hydrogen bonds in monosubstituted piperid-1-ylmethane-1,1-diphosphonic acids

The crystal structures of 3-methylpiperid-1-ylmethane-1,1-diphosphonic (2), 4-methylpiperid-1-ylmethane-1,1-diphosphonic (3), 2-ethylpiperid-1-ylmethane-1,1-diphosphonic (4), and 2-methylpiperid-1-ylmethane-1,1-diphosphonic (5) acids have been determined and are discussed with respect to their molecular organization and crystal-packing preferences. The chair conformation, predominant also in solution, favors equatorial positioning of the bulky substituents of the heterocyclic N and C atoms. The molecular geometry also provides access to intramolecular hydrogen-bond formation between the axial protons located on the nitrogen atoms, as well as the carbon atoms closest to it, and phosphonic/phosphonate oxygen atoms. The molecules preferably arrange in monolayers, observed in all crystals with an exception of 3. The layers are held in place in the third direction through van der Waals interactions. The analysis of two-dimensional hydrogen-bonded networks is concentrated on revealing how the substituent's topology of the molecule affects the solid-state organization in well-defined structures and is aimed at unraveling the consequences and the possible conformational changes by stepwise network disruption upon crystal dissolution in water. The solution NMR studies are focused on revealing the role that the topochemistry of the substituent plays for the stereodynamics in 2-5. It is demonstrated that in contrast to piperid-1-ylmethane-1,1-diphosphonic acid (1), in which the ring inversion/rotation around the C-N bond concerted with the N-H...O hydrogen-bond breaking/formation process leads to a mixture of two interconverting conformers, the concerted N-H...O breaking/rotation/N-H...O formation process in 2 and 3 allows for a predominance of one conformer in solution. However, placement of a substituent at 2-position in the ring hampers the rotation around the C-N bond; this makes 4 and 5 significantly less flexible relative to compounds 1-3. In addition, both compounds 4 and 5 are proved to exist as a mixture of two conformers, the equilibrium of which in acidic solution is shifted towards the conformer found in solid state. In alkaline solutions of 4 and 5, the equilibrium is shifted towards the conformer that is forced by the flipping of the heterocyclic ring. These results correlate well with recently documented differences in the biological potency of this group of compounds.     

Silver Zeolite as Promoter in Glycoside Synthesis. The Synthesis of 2-Deoxy-β-D-Glycopyranosides

The use of silver zeolite as a promoter for the preparation of β-linked 2-deoxygtycosides and disaccharides of biological relevance has been explored. Starting from benzoylated glycosyl bromides, the total yield of glycosides varies from 54 to 84% and the α:β ratio from 0.25 to 1.18.     

Application of inverse linear parametric models in the identification of rail track irregularities

Requirements for current trains to be increasingly available have created the need to develop systems that can predict the quality of both trains and infrastructure components. The paper presents a new approach to the detection of rail truck irregularities, based on the measurements of bearing box acceleration during the operation of rail vehicles. The proposed procedure is based on an inverse problem solution, estimating track irregularities from measured acceleration of the applied model of vehicle dynamics. The simulation study of the proposed method, as well as its implementation, is presented. The method has been successfully applied for the identification of rail irregularities on a typical Polish railroad and vehicle.     

Boundary Value Problems with a Parameter of Differential Equations with Deviated Arguments

The aim of the present paper is to study boundary value problems with a parameter of differential equations with deviated arguments. The existence, uniqueness and continuous dependence of the solution on the right-hand side of our problem are considered.     

A class of B-(p,r)-invex functions and mathematical programming

Invexity of a function is generalized. The new class of nonconvex functions, called B-(p,r)-invex functions with respect to η and b, being introduced, includes many well-known classes of generalized invex functions as its subclasses. Some properties of the introduced class of B-(p,r)-invex functions with respect to η and b are studied. Further, mathematical programming problems involving B-(p,r)-invex functions with respect to η and b are considered. The equivalence between saddle points and optima, and different type duality theorems are established for this type of optimization problems.     

Molecular dynamics simulation of phase transition in AgNO3

Structural phase transition in AgNO₃ at high temperature is simulated by molecular dynamics. The simulations are based on the potentials calculated from the Gordon-Kim modified electron-gas formalism extended to molecular ionic crystals. AgNO₃ transforms into rhombohedral structure at high temperature and the phase transition is associated with the rotations of the NO₃ ions and displacements of the NO₃ and Ag ions.