Beiträge zur Dispersoidchemie des Torfes. IV

Ohne Zusammenfassung     

Beiträge zur allgemeinen Kolloidchemie. VIII

Ohne Zusammenfassung     

New properties of a certain method of summation of generalized hypergeometric series

In a recent paper (Appl. Math. Comput. 215:1622–1645, 2009), the authors proposed a method of summation of some slowly convergent series. The purpose of this note is to give more theoretical analysis for this transformation, including the convergence acceleration theorem in the case of summation of generalized hypergeometric series. Some new theoretical results and illustrative numerical examples are given.     

Boundary and initial fluctuation effect on dynamic behaviour of a laminated solid

Two problems will be studied in this contribution. First, we analyse some phenomena which take place in a laminated solid and are caused by a fluctuation of time-dependent boundary tractions. Second, we investigate the transient effect of initial displacement fluctuations on the behaviour of a laminate. To solve the above problems we propose a new macroscopic 3D model for investigations of initial-boundary value problems in elastodynamics of a laminated medium.     

On the modelling of dynamic problems for plates with a periodic structure

Summary The subject of analysis is the bending of elastic plates exhibiting a nonhomogeneous periodic structure and/or a periodically variable thickness in a certain direction parallel to the plate's midplane. The fundamental modelling problem is how to obtain an effective 2D-model of a plate under consideration, i.e., a 2D-model represented by PDEs with constant coefficients. This problem for periodic plates has been solved independently in [5] and [10], using asymptotic homogenization. However, homogenization neglects dynamic phenomena related to the plate's rotational inertia and cannot be applied to the analysis of higher-order vibration frequences. The main aim of this contribution is to formulate a new non-asymptotic effective 2D-model of a periodic plate which is free from the mentioned drawbacks and describes the dynamic behaviour of plates having the thickness of the order of the period length. The proposed model is applied to the analysis of some vibration problems.     

Synthesis of unsymmetrical alkyl acetals via addition of primary alcohols to allyl ethers mediated by ruthenium complexes

Abstract  

Ru-catalyzed synthesis of mixed alkyl–alkyl acetals via addition of primary alcohols to allyl ethers has been extended to include long-chain and/or functionalized substrates. The catalytic systems for these reactions were generated from RuCl₂(PPh₃)₃ and [RuCl₂(1,5-COD)]_x and phosphines [PPh₃ or P(p-chlorophenyl)₃] or SbPh₃. Of particular importance is the almost quantitative elimination of transacetalization. The addition proceeds through allyl complexes, not via isomerization of allyl ethers––subsequent addition of ROH to vinyl ethers.     

Multi-degree reduction of tensor product Bézier surfaces with general boundary constraints

We propose an efficient approach to the problem of multi-degree reduction of rectangular Bézier patches, with prescribed boundary control points. We observe that the solution can be given in terms of constrained bivariate dual Bernstein polynomials. The complexity of the method is O(mn₁n₂) with m ? min(m₁, m₂), where (n₁, n₂) and (m₁, m₂) is the degree of the input and output Bézier surface, respectively. If the approximation—with appropriate boundary constraints—is performed for each patch of several smoothly joined rectangular Bézier surfaces, the result is a composite surface of global C^r continuity with a prescribed r ? 0. In the detailed discussion, we restrict ourselves to r ∈ {0, 1}, which is the most important case in practical application. Some illustrative examples are given.     

Ring-expanded bicyclic β-lactams: a structure-chiroptical properties relationship investigation by experiment and calculations

In the present work, the validity of the helicity rule relating the absolute configuration of the bridgehead carbon atom in bicyclic β-lactams to the sign of the 220 nm band observed in their electronic circular dichroism (ECD) spectra is examined for ring-expanded cephalosporin analogues. To this end, a series of model compounds with a seven-membered ring condensed with the β-lactam unit was synthesized. A key step of their synthesis was either the ring-closing metathesis (RCM) or the free radical cyclization leading to the seven-membered ring with an S, O, or C atom at the 6 position in the bicyclic skeleton. To investigate the scope and limitations of the simple, empirically established helicity rule, a combination of ECD spectroscopy, variable-temperature ECD measurements, X-ray analysis, and time-dependent density functional theory (TD-DFT) calculations was used. A comparison of the experimental ECD spectra with the spectra simulated by TD-DFT calculations gives a reasonable interpretation of the Cotton effects observed in the 240-215 nm spectral range. The results suggest that the helicity rule does not apply to the investigated compounds because of the planarity of their amide chromophore. Thus, these compounds do not constitute an exception to the rule that was established for bi- and polycyclic β-lactams with the nonplanar amide chromophore only.     

Investigation of the low-frequency vibrations of crystalline tartaric acid using terahertz spectroscopy and solid-state density functional theory

The room temperature and cryogenic terahertz (THz) spectra (10-95 cm(-1)) of l-tartaric acid and dl-tartaric acid were investigated. At 293 K, the l-tartaric acid spectrum showed four absorption features at 36.4, 61.6, 78.7, and 87.3 cm(-1) in the experimental spectrum. Once cooled to 78 K, these features narrowed and shifted to 35.9, 63.4, 81.1, and 90.1 cm(-1). The THz spectrum of dl-tartaric acid is significantly different, containing only a single absorption at 79.9 cm(-1) at room temperature, which shifts to 82.9 cm(-1) at 78 K. Solid-state density functional theory calculations [B3LYP/6-311G(2d,2p)] were performed to simulate the crystalline structure of both molecular solids and to assign the observed spectral features to specific atomic motions. The THz spectrum of l-tartaric acid is particularly interesting in that it contains a theoretically unaccounted for spectral feature that may arise from second-order phonon processes and also exhibits an anomalous red-shifting absorption feature with cooling that is shown to originate from negative thermal expansion of the crystal.