Schnitt- und überdeckungszahlen kombinatorischer Sphären

Ohne Zusammenfassung     

Zur Relativgeometrie: Symmetrische Zusammenhänge auf Hyperflächen

Ohne Zusammenfassung     

Characterizability of Free Motion in Special Relativity

The concept of forcefree motion is primitive, i.e., unexplained, in special relativity. The paper demonstrates a way to characterize it by more primitive, directly operationally interpreted notions. These are the worldlines of (more or less) pointlike, but non-quantum bodies and of light signals, clock parametrizations of the former kind of worldlines and the direction, in which an observer sees a light signal go out. Already at this general level one can define the radar distance and the radar (initial) velocity of one body with respect to another, and can define in a reasonable manner that two bodies move in opposite directions with respect to an observer. These concepts are then used to formulate a certain criterion for path structures which can experimentally be tested without presupposing inertial frames, atomic clocks, etc. It is demonstrated that the path structure of free motion in gravity-free regions of space-time, i.e., in the domain of validity of special relativity, satisfies that criterion.     

Diastereoselective carbenes: Stereoelectronic control of bent singlet trans-2′-substituted cyclobutylcarbenes

The UM06-2X/aug-cc-pVTZ//UM06-2X/6-311G(d) theoretical models of representative singlet trans-2′-substituted cyclobutylcarbenes were computed. The :CH-group of carbenes with an ERG is bent toward the c-C₄H₇-ring’s proximal C1′–C2′ single bond. The :CH-group of carbenes with an EWG is bent toward the c-C₄H₇-ring’s distal C1′–C4′ single bond. The contrasting stereoelectronic effect was computationally tested using trimethylsilyl vs. bromo substituents to determine if exo-1- and exo-2-substituted bicyclo[2.1.0]pentanes would be produced in diastereomeric excess.     

Host-Guest Complexation of Oxaliplatin and Para-Sulfonatocalix[n]Arenes for Potential Use in Cancer Therapy

P-sulfonatocalix[n]arenes have demonstrated a great potential for encapsulation of therapeutic drugs via host-guest complexation to improve solubility, stability, and bioavailability of encapsulated drugs. In this work, guest-host complexes of a third-generation anticancer drug (oxaliplatin) and p-4-sulfocalix[n]arenes (n = 4 and 6; p-SC4 and p-SC6, respectively) were prepared and investigated, using ¹H NMR, UV, Job’s plot analysis, and DFT calculations, for use as cancer therapeutics. The peak amplitude of the prepared host-guest complexes was linearly proportional to the concentration of oxaliplatin in the range of 1.0 × 10⁻⁵ M⁻¹ to 2.1 × 10⁻⁴ M⁻¹. The reaction stoichiometry between either p-SC4 or p-SC6 and oxaliplatin in the formed complexes was 1:1. The stability constants for the complexes were 5.07 × 10⁴ M⁻¹ and 6.3 × 10⁴ M⁻¹. These correspond to complexation free energy of −6.39 and −6.52 kcal/mol for p-SC4 and p-SC6, respectively. Complexation between oxaliplatin and p-SC4 or p-SC6 was found to involve hydrogen bonds. Both complexes exhibited enhanced biological and high cytotoxic activities against HT-29 colorectal cells and MCF-7 breast adenocarcinoma compared to free oxaliplatin, which warrants further investigation for cancer therapy.     

Copper-Catalyzed Oxidative Cross-Coupling of Electron-Deficient Polyfluorophenylboronate Esters with Terminal Alkynes

We report herein a mild procedure for the copper-catalyzed oxidative cross-coupling of electron-deficient polyfluorophenylboronate esters with terminal alkynes. This method displays good functional group tolerance and broad substrate scope, generating cross-coupled alkynyl(fluoro)arene products in moderate to excellent yields. Thus, it represents a simple alternative to the conventional Sonogashira reaction.     

Foiled carbenes revisited: When sigma-stabilization surpasses pi-stabilization

The bicyclic alkenylidenes 9 (bicyclo[3.2.1]oct-2-en-8-ylidene) and 17 (bicyclo[3.3.1]non-2-en-9-ylidene) were claimed to be stabilized foiled carbenes. Our B3LYP and MP2 computations confirm previous experimental data. Moreover, they show that these carbenes are very reactive and rearrange rapidly, mainly through a 1,2-vinyl shift by overcoming a low barrier (1.2 to 5.4 kcal/mol). This is in contrast to the high barriers (up to 30 kcal/mol) predicted for the same type of rearrangements in norborn-2-en-7-ylidene derivatives. In 17 and bicyclo[4.1.1]oct-2-en-7-ylidene (23), the divalent carbon atom is even bent away from the double bond!     

Toward selective reactions with C-H bonds: a rationale for the regio- and stereochemistry of dichlorocarbene insertions into cyclic hydrocarbons

DFT calculations have been performed to study the course of dichlorocarbene insertion reactions into alkanes and to better understand the regio- and stereoselectivities observed. At the B3LYP/6-31G(d) level of theory, the selectivity of dichlorocarbene insertions into a number of hydrocarbons agrees well with the obtained experimental results. The reactivity of a specific C-H bond is determined by the capacity of the remaining alkyl fragment to effectively delocalize the partial positive charge buildup during the reaction. This activity can readily be estimated by calculation of the hydride transfer potential (HTP). A comparison with the structure and the stability of the corresponding cation is useful to emphasize the origins of the selectivity. Dichlorocarbene is also predicted to react efficiently with acidic C-H bonds through a nucleophilic-electrophilic mechanism. In principle, an attack of a carbene on an appropriately substituted three-membered ring may lead to fragmentation of the molecule.     

Krylov Subspace Reduced-Order Modeling Methods for Structural Dynamic Finite Element Systems

Computational resources can be used more efficiently by introducing reduced-order models, instead of solving large systems of equations of the original model. In this contribution, the Krylov subspace method, a reduced-order modeling method, is studied and compared to the modal decomposition for a rubber wheel model. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)