Rado Numbers fora(x+y)=bz

In the case of existence the smallest numberN=Ra_kis called a Rado number if it is guaranteed that anyk-coloring of the numbers 1, 2, …, Ncontains a monochromatic solution of a given system of linear equations. We will determine Ra_k(a, b) for the equationa(x+y)=bzifb=2 andb=a+1. Also, the case of monochromatic sequences {x_n} generated bya(x_n+x_n+1)=bx_n+2 is discussed.     

A splitting theorem for equifocal submanifolds in simply connected compact symmetric spaces

A submanifold in a symmetric space is called equifocal if it has a globally flat abelian normal bundle and its focal data is invariant under normal parallel transportation. This is a generalization of the notion of isoparametric submanifolds in Euclidean spaces. To each equifocal submanifold, we can associate a Coxeter group, which is determined by the focal data at one point. In this paper we prove that an equifocal submanifold in a simply connected compact symmetric space is a non-trivial product of two such submanifolds if and only if its associated Coxeter group is decomposable. As a consequence, we get a similar splitting result for hyperpolar group actions on compact symmetric spaces. These results are an application of a splitting theorem for isoparametric submanifolds in Hilbert spaces by Heintze and Liu.

     

Capturing the Genesis of an Active Fischer–Tropsch Synthesis Catalyst with Operando X‐ray Nanospectroscopy

A state‐of‐the‐art operando spectroscopic technique is applied to Co/TiO₂ catalysts, which account for nearly half of the world's transportation fuels produced by Fischer–Tropsch catalysis. This allows determination of, at a spatial resolution of approximately 50 nm, the interdependence of formed hydrocarbon species in the inorganic catalyst. Observed trends show intra‐ and interparticular heterogeneities previously believed not to occur in particles under 200 μm. These heterogeneities are strongly dependent on changes in H₂/CO ratio, but also on changes thereby induced on the Co and Ti valence states. We have captured the genesis of an active FTS particle over its propagation to steady‐state operation, in which microgradients lead to the gradual saturation of the Co/TiO₂ catalyst surface with long chain hydrocarbons (i.e., organic film formation).     

On empty convex polytopes

Letn andd be integers,n>d 2. We examine the smallest integerg(n,d) such that any setS of at leastg(n,d) points, in general position in E^d, containsn points which are the vertices of an empty convexd-polytopeP, that is, SintP = 0. In particular we show thatg(d+k, d) = d+2k–1 for 1 k iLd/2rL+1.     

An access to 3,4-(aminomethano)proline in racemic and enantiomerically pure form

Protected racemic and enantiomerically pure 3,4-(aminomethano)prolines rac-9 and (2S,2'R,3R,4R)-9 have been prepared applying a titanium-mediated reductive cyclopropanation as a key step. Thus, cyclopropanations of N,N-dibenzylformamide with titanacyclopropanes generated in situ from racemic or enantiomerically pure tert-butyl N-Boc-3,4-dehydroprolinates rac-8 or (S)-8 proceed diastereoselectively, and furnish the protected racemic and enantiomerically pure diamino acid 9. The latter was incorporated into three tripeptides containing glycyl, alanyl and phenylalanyl moieties.     

Base pairing and replicative processing of the formamidopyrimidine-dG DNA lesion

The 2,6-diamino-4-hydroxy-5-formamidopyrimidine of 2'-deoxyguanosine (FaPydG) is one of the major DNA lesions found after oxidative stress in cells. To clarify the base pairing and coding potential of this major DNA lesion with the aim to estimate its mutagenic effect, we prepared oligonucleotides containing a cyclopentane based analogue of the DNA lesion (cFaPydG). In addition, oligonucleotides containing the cyclopentane analogue of 2'-deoxyguanosine (cdG), and oligonucleotides containing 8-oxo-7,8-dihydro-2'-deoxyguanosine (8-oxodG) were synthesized. The thermodynamic stability of duplexes containing these building blocks and all canonical counterbases were determined by concentration dependent melting-point measurements (van't Hoff plots). The data reveal that cFaPydG greatly destabilizes a DNA duplex (DeltaDeltaG degrees (298K) approximately 2-4 kcal mol(-1)). The optimal base pairing partner for the cFaPydG lesion is dC. Investigation of duplexes containing dG and cdG shows that the effect of substituting the deoxyribose by a cyclopentane moiety is marginal. The data also provide strong evidence that the FaPydG lesion is unable to form a base pair with dA. Our computational studies indicate that the syn-conformation required for base pairing with dA is energetically unfavorable. This is in contrast to 8-oxodG for which the syn-conformation represents the energetic minimum. Kinetic primer extension studies using S. cerevisiae Pol eta reveal that cFaPydG is replicated in an error-free fashion. dC is inserted 2-3 orders of magnitude more efficiently than dT or dA, showing that FaPydG is a lesion which retains the coding potential of dG. This is also in contrast to 8-oxodG, for which base pairing with dC and dA was established.     

Synthetic applications in radical/radical cationic cascade reactions

Oxidative photoinduced electron transfer (PET) reactions have been performed with various cyclic cyclopropyl(vinyl) silyl ethers bearing an olefinic or acetylenic side chain. The reactions result in bi- to tetracyclic ring systems via a fragmentation-radical/radical cationic addition reaction pathway with well defined ring juncture. The mode of cyclisation (endo/exo) can be partially controlled by addition of nucleophiles due to the suppression of radical cationic reaction pathways. Quantum chemical calculation of the cyclisation transition states underline the experimentally found selectivities. Additional mechanistic studies concerning the saturation step reveal that the final radical is saturated mostly by the solvent and traces of water in the solvent.     

Studies on the mechanism of the photo-induced DNA damage in the presence of acridizinium salts-involvement of singlet oxygen and an unusual source for hydroxyl radicals

Mechanistic investigations of the photoinduced DNA damage by acridizinium salts (4a-azonia-anthracene derivatives) are presented. Irradiation of 9-bromoacridizinium in the presence of defined double- and single-stranded DNA oligomers under aerobic conditions leads to both frank strand breaks and alkali-labile sites as determined by polyacrylamide gel electrophoresis (PAGE). The extent of the DNA damage increases significantly in D(2)O and occurs selectively at guanosine residues. These observations reveal the formation of singlet oxygen ((1)O(2)) as reactive species, which oxidizes the DNA bases, above all the guanine bases. Further evidence for (1)O(2) formation was obtained from laser-flash spectroscopic investigations, which show intersystem crossing (S(1) to T(1)) of the excited states of the parent acridizinium and of the 9-bromo- and 9-amino-substituted derivatives. The resulting triplet state is efficiently quenched by oxygen (k(q) > 10(9) s(-)(1)M(-)(1)) to yield (1)O(2). Under anaerobic conditions, no significant alkali-labile lesions are observed, but frank strand breaks are induced; however, to lesser extent than under aerobic conditions. The DNA damage is suppressed in the presence of a radical scavenger, namely t-BuOH, and hydroxyl radicals are shown to be the reactive intermediates by trapping experiments with terephthalic acid. Moreover, the intercalated acridizinium molecules are not involved in the DNA damage reactions. The intercalated acridizinium salt leads to a primary PET reaction with the DNA bases; however, a fast BET transfer is proposed that regains the dye and the DNA, so that the excited intercalated dye does not contribute significantly to the overall DNA damage.     

Structural, volumetric, and thermodynamic characterization of a micellar sphere-to-rod transition

The thermotropic sphere-to-rod transition of nonionic surfactants was characterized in terms of a large set of parameters: the transition temperature and width, the partial volume, coefficient of thermal volume expansion, enthalpy, isobaric heat capacity, and structural parameters, such as radius of gyration and hydrodynamic radius. Data were recorded as a function of concentration of surfactants in H2O and in D2O. To this end, pressure perturbation calorimetry (PPC), small angle neutron scattering (SANS), dynamic light scattering (DLS), differential scanning calorimetry (DSC), and isothermal titration calorimetry (ITC) were applied in a study of aqueous solutions containing myristyl, tridecyl, and lauryl maltoside and heptaethyleneglycoltetradecyl ether (C14EO7). Small changes in the thermodynamic and volumetric parameters (e.g., the partial volume change is approximately +2 per thousand) are discussed in detail as the result of three effects governing the transition. (i) Reduction of the water accessible hydrophobic surface area (ASA(ap)) drives the transition. (ii) Shrinking in headgroup size by thermal dehydration triggers the transition. (iii) Hypothesized gradual ordering of the chains may control the effect of chain length on the transition.