Synthesis,characterization, and biological activity of some complex combinations of nickel with α-ketoglutaric acid and 1-(o-tolyl)biguanide

The four divalent nickel complexes having α-ketoglutaric acid (H₂A) and 1-(o-tolyl)biguanide (TB) ligands have been synthesized, characterized, and tested for antibacterial and antitumor activity.The proposed formulas for these complexes are [Ni(TB)(HA)(H₂O)₂]Cl (C1), [Ni(TB)(HA)(H₂O)₂]Br (C2), [Ni(TB)(HA)]NO₃·H₂O (C3), and [Ni(TB)(HA)]CH₃COO (C4), where HA represents deprotonated H₂A.For the four complexes and for the ligands used in the synthesis, the antibacterial activity against Staphylococcus aureus ATCC 25923 and Pseudomonas aeruginosa ATCC 27853 and antitumor activity in HeLa tumor cells were tested. A moderate cytotoxic effect of C3 and C4 complexes has been observed on the development and metabolic activity of HeLa cells, whereas C1 and C2 ligands have a very low effect on them.The synthesized complexes (obtained) inhibit adherence to the inert substrate of bacterial strains S. aureus and P. aeruginosa; therefore, they may be candidates for (potential) therapeutic applications.     

Characterization of the photochromism of dihydropyrenes with photophysical techniques

Dihydropyrenes are negative photochromes and their photophysical characterization, achieved in the past decade, is reviewed. Special emphasis is given to the theoretical background and to the experimental details which are relevant for the characterization of bi-stable systems, such as photochromic ones. In contrast to most photochromic compounds, dihydropyrenes have long lifetimes for their photoreactive excited states making it possible to tune their reactivity with the introduction of substituents. This knowledge is applicable for the design of more efficient photochromic molecules and for multichromophoric systems.     

Maor,Eli: Music by the Numbers. From Pythagoras to Schoenberg

Mathematische Semesterberichte -     

Chain regularity of isotactic polypropylene determined by different thermal fractionation methods

The chain regularity of isotactic polypropylene (iPP) homopolymer and random copolymers was characterized by different thermal fractionation methods in this study. Different stepwise temperature programs were applied in a calorimeter (DSC), in order to develop a method which is significantly faster than stepwise isothermal segregation technique (SIST) and provides reliable information about the chain regularity of iPP. Our studies prove that self-seeding accelerates the crystallization process during annealing in SSA–DSC experiments (successive self-nucleation and annealing). Consequently, the time of isothermal steps can be shortened significantly in the SSA–DSC method. On the other hand, we found that step time should not be too short if the goal of the measurement is the determination of average chain regularity. Our results clearly indicate that both the experimental conditions and the evaluation technique influence the obtained results. A standard experimental procedure is proposed for reliably determining the average chain regularity of iPP. The length of the SSA–DSC temperature program developed in this study is much shorter compared to that of the conventional SIST measurements used recently for such experiments. The proposed SSA–DSC program makes the reliable characterization of a large number of samples on an acceptable timescale possible.     

Cubic irrationals and periodicity via a family of multi-dimensional continued fraction algorithms

We construct a countable family of multi-dimensional continued fraction algorithms, built out of five specific multidimensional continued fractions, and find a wide class of cubic irrational real numbers \(\alpha \) so that either \((\alpha , \alpha ^2)\) or \((\alpha , \alpha -\alpha ^2)\) is purely periodic with respect to an element in the family. These cubic irrationals seem to be quite natural, as we show that, for every cubic number field, there exists a pair \((u, u')\) with \(u\) a unit in the cubic number field (or possibly the quadratic extension of the cubic number field by the square root of the discriminant) such that \((u, u')\) has a periodic multidimensional continued fraction expansion under one of the maps in the family generated by the initial five maps. These results are built on a careful technical analysis of certain units in cubic number fields and our family of multi-dimensional continued fractions. We then recast the linking of cubic irrationals with periodicity to the linking of cubic irrationals with the construction of a matrix with nonnegative integer entries for which at least one row is eventually periodic.     

The S1/S2 exciton interaction in 2-pyridone·6-methyl-2-pyridone: Davydov splitting, vibronic coupling, and vibronic quenching

The excitonic splitting between the S(1) and S(2) electronic states of the doubly hydrogen-bonded dimer 2-pyridone[middle dot]6-methyl-2-pyridone (2PY·6M2PY) is studied in a supersonic jet, applying two-color resonant two-photon ionization (2C-R2PI), UV-UV depletion, and dispersed fluorescence spectroscopies. In contrast to the C(2h) symmetric (2-pyridone)(2) homodimer, in which the S(1) ← S(0) transition is symmetry-forbidden but the S(2) ← S(0) transition is allowed, the symmetry-breaking by the additional methyl group in 2PY·6M2PY leads to the appearance of both the S(1) and S(2) origins, which are separated by Δ(exp) = 154 cm(-1). When combined with the separation of the S(1) ← S(0) excitations of 6M2PY and 2PY, which is δ = 102 cm(-1), one obtains an S(1)/S(2) exciton coupling matrix element of V(AB, el) = 57 cm(-1) in a Frenkel-Davydov exciton model. The vibronic couplings in the S(1)/S(2) ← S(0) spectrum of 2PY·6M2PY are treated by the Fulton-Gouterman single-mode model. We consider independent couplings to the intramolecular 6a(') vibration and to the intermolecular σ(') stretch, and obtain a semi-quantitative fit to the observed spectrum. The dimensionless excitonic couplings are C(6a(')) = 0.15 and C(σ(')) = 0.05, which places this dimer in the weak-coupling limit. However, the S(1)/S(2) state exciton splittings Δ(calc) calculated by the configuration interaction singles method (CIS), time-dependent Hartree-Fock (TD-HF), and approximate second-order coupled-cluster method (CC2) are between 1100 and 1450 cm(-1), or seven to nine times larger than observed. These huge errors result from the neglect of the coupling to the optically active intra- and intermolecular vibrations of the dimer, which lead to vibronic quenching of the purely electronic excitonic splitting. For 2PY·6M2PY the electronic splitting is quenched by a factor of ~30 (i.e., the vibronic quenching factor is Γ(exp) = 0.035), which brings the calculated splittings into close agreement with the experimentally observed value. The 2C-R2PI and fluorescence spectra of the tautomeric species 2-hydroxypyridine·6-methyl-2-pyridone (2HP·6M2PY) are also observed and assigned.     

Synthesis of new 10,11-dihydrodibenzo[a,d]cycloheptene S-thiocarbamate derivatives via a benzylic Newman–Kwart rearrangement

New S-thiocarbamates possessing a 10,11-dihydro-5H-dibenzo[a,d]cycloheptene moiety were obtained unexpectedly in the process of preparing new O-thiocarbamates starting from 5-dibenzosuberol (10,11-dihydro-5H-dibenzo[a,d]cyclohepten-5-ol) and aroyl-isothiocyanates. These compounds were obtained via a benzylic Newman–Kwart rearrangement mechanism. The structures of the new thiocarbamates were confirmed by elemental analysis, IR, and NMR spectroscopy and by X-ray crystallography.     

Railway delay management with passenger rerouting considering train capacity constraints

Delay management for railways is concerned with the question of whether a train should wait for a delayed feeder train or depart on time. The answer should not only depend on the length of the delay but also consider other factors, such as capacity restrictions. We present an optimization model for delay management in railway networks that accounts for capacity constraints on the number of passengers that a train can effectively carry. While limited capacities of tracks and stations have been considered in delay management models, passenger train capacity has been neglected in the literature so far, implicitly assuming an infinite train capacity. However, even in open systems where no seat reservation is required and passengers may stand during the journey if all seats are occupied, physical space is naturally limited, and the number of standing seats is constrained for passenger safety reasons. We present a mixed-integer nonlinear programming formulation for the delay management problem with passenger rerouting and capacities of trains. Our model allows the rerouting of passengers missing their connection due to delays or capacity constraints. We linearize the model in exact and approximate ways and experimentally compare the different approaches with the solution of a reference model from the literature that neglects capacity constraints. The results demonstrate that there is a significant impact of considering train capacity restrictions in decisions to manage delays.