Synthesis and transformation of novel cyclic β-amino acid derivatives from (+)-3-carene

The regio- and stereoselective addition of chlorosulfonyl isocyanate to (+)-3-carene 1 resulted in β-lactam 2, which was converted to N-Boc-β-amino acid 4, β-amino ester 7, and carboxamide derivatives 18 and 20 via N-Boc activation and mild ring opening. The corresponding β-amino ester 7 was transformed to 2-thioxopyrimidin-4-one 11 and 2,4-pyrimidinedione 13. LAH reduction of 5 and 7 resulted in amino alcohols 6 and 8. The reaction of 8 with phenyl isothiocyanate, followed by cyclisation, furnished 1,3-oxazine 15.     

Chemoenzymatic synthesis of highly enantiomerically enriched secondary alcohols with a thiazolic core

Stereoselective preparative enzymatic acylation and hydrolysis/methanolysis of various C-substituted rac-thiazol-2-yl-methanols were achieved for the preparation of enantiopure or enantiomerically enriched, naturally occurring 2-hydroxymethylthiazoles. The absolute configurations of the resulting secondary alcohols were determined by a detailed ¹H NMR study of Mosher’s derivatives.     

On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays

In this paper, we consider a class of nonlinear neutral differential equations with state-dependent delays in both the neutral and the retarded terms. We study well-posedness and continuous dependence issues and differentiability of the parameter map with respect to the initial function and other possibly infinite dimensional parameters in a pointwise sense and also in the C-norm.     

Efficient syntheses of zoledronic acid as an active ingredient of a drug against osteoporosis

The reaction of 1H-imidazol-1-ylacetic acid and two equivalents of phosphorus trichloride/phosphorous acid at 75?°C in sulfolane, or in the presence of catalytic amounts of [bmim][BF₄] afforded zoledronic acid in yields up to 75%. The joint use of the ionic liquid additive and sulfolane as the solvent was synergetic affording highly valuable zoledronic acid in a record yield of 93%.     

Degeneracy induced scaling of the correlation length for periodic models

The broken symmetric phase of scalar models exhibits an infrared fixed point which is induced by the degenerate effective potential. The definition of the correlation length in the infrared regime enables us to determine the type of the phase transition in the model. It is shown that the massive sine-Gordon model exhibits a continuous, while the layered sine-Gordon model has an infinite order Kosterlitz–Thouless type phase transition.     

Microscopic reversibility or detailed balance in ion channel models

Mass action type deterministic kinetic models of ion channels are usually constructed in such a way as to obey the principle of detailed balance (or, microscopic reversibility) for two reasons: first, the authors aspire to have models harmonizing with thermodynamics, second, the conditions to ensure detailed balance reduce the number of reaction rate coefficients to be measured. We investigate a series of ion channel models which are asserted to obey detailed balance, however, these models violate mass conservation and in their case only the necessary conditions (the so-called circuit conditions) are taken into account. We show that ion channel models have a very specific structure which makes the consequences true in spite of the imprecise arguments. First, we transform the models into mass conserving ones, second, we show that the full set of conditions ensuring detailed balance (formulated by Feinberg) leads to the same relations for the reaction rate constants in these special cases, both for the original models and the transformed ones.     

Statistical convergence of sequences and series of complex numbers with applications in Fourier Analysis and Summability

This is a survey paper on recent results indicated in the title. In contrast to the famous examples of Kolmogorov and Fejér on the pointwise divergence of Fourier series, the statistical convergence of the Fourier series of any integrable function takes place at almost every point; and the statistical convergencr of the Fourier series of any continuous function is uniform. Furthermore, Tauberian conditions are also presented, under which ordinary convergence of any sequence of real or complex numbers follows from its statistical summability.