Minimal kernels of Dirac operators along maps

Let M be a closed spin manifold and let N be a closed manifold. For maps and Riemannian metrics g on M and h on N, we consider the Dirac operator of the twisted Dirac bundle . To this Dirac operator one can associate an index in . If M is 2‐dimensional, one gets a lower bound for the dimension of the kernel of out of this index. We investigate the question whether this lower bound is obtained for generic tupels .     

Enhancing the Water Stability of Al‐MIL‐101‐NH2 via Postsynthetic Modification

The resistance of metal–organic frameworks towards water is a very critical issue concerning their practical use. Recently, it was shown for microporous MOFs that the water stability could be increased by introducing hydrophobic pendant groups. Here, we demonstrate a remarkable stabilisation of the mesoporous MOF Al‐MIL‐101‐NH₂ by postsynthetic modification with phenyl isocyanate. In this process 86 % of the amino groups were converted into phenylurea units. As a consequence, the long‐term stability of Al‐MIL‐101‐URPh in liquid water could be extended beyond a week. In water saturated atmospheres Al‐MIL‐101‐URPh decomposed at least 12‐times slower than the unfunctionalised analogue. To study the underlying processes both materials were characterised by Ar, N₂ and H₂O sorption measurements, powder X‐ray diffraction, thermogravimetric and chemical analysis as well as solid‐state NMR and IR spectroscopy. Postsynthetic modification decreased the BET equivalent surface area from 3363 to 1555 m² g^?1 for Al‐MIL‐101‐URPh and reduced the mean diameters of the mesopores by 0.6 nm without degrading the structure significantly and reducing thermal stability. In spite of similar water uptake capacities, the relative humidity‐dependent uptake of Al‐MIL‐101‐URPh is slowed and occurs at higher relative humidity values. In combination with ¹H‐²⁷Al D ‐HMQC NMR spectroscopy experiments this favours a shielding mechanism of the Al clusters by the pendant phenyl groups and rules out pore blocking.     

Structural impact of GTP binding on downstream KRAS signaling

Oncogenic RAS proteins, involved in ∼30% of human tumors, are molecular switches of various signal transduction pathways. Here we apply a new protocol for the NMR study of KRAS in its (inactive) GDP- and (activated) GTP-bound form, allowing a comprehensive analysis of the backbone dynamics of its WT-, G12C- and G12D variants. We found that Tyr32 shows opposite mobility with respect to the backbone of its surroundings: it is more flexible in the GDP-bound form while more rigid in GTP-complexes (especially in WT- and G12D-GTP). Using the G12C/Y32F double mutant, we showed that the presence of the hydroxyl group of Tyr32 has a marked effect on the G12C-KRAS-GTP system as well. Molecular dynamics simulations indicate that Tyr32 is linked to the γ-phosphate of GTP in the activated states – an arrangement shown, using QM/MM calculations, to support catalysis. Anchoring Tyr32 to the γ-phosphate contributes to the capture of the catalytic waters participating in the intrinsic hydrolysis of GTP and supports a simultaneous triple proton transfer step (catalytic water → assisting water → Tyr32 → O1G of the γ-phosphate) leading to straightforward product formation. The coupled flip of negatively charged residues of switch I toward the inside of the effector binding pocket potentiates ligand recognition, while positioning of Thr35 to enter the coordination sphere of the Mg²⁺ widens the pocket. Position 12 mutations do not disturb the capture of Tyr32 by the γ-phosphate, but (partially) displace Gln61, which opens up the catalytic pocket and destabilizes catalytic water molecules thus impairing intrinsic hydrolysis.

Nucleotide exchange to the physiological, activated, GTP-bound form of KRAS results in the anchoring of Tyr32 within the active site.     

Expanding the Ligand Classes Used for Mn(II) Complexation: Oxa-aza Macrocycles Make the Difference

We report two macrocyclic ligands based on a 1,7-diaza-12-crown-4 platform functionalized with acetate (tO2DO2A²⁻) or piperidineacetamide (tO2DO2AM^Pip) pendant arms and a detailed characterization of the corresponding Mn(II) complexes. The X−ray structure of [Mn(tO2DO2A)(H₂O)]·2H₂O shows that the metal ion is coordinated by six donor atoms of the macrocyclic ligand and one water molecule, to result in seven-coordination. The Cu(II) analogue presents a distorted octahedral coordination environment. The protonation constants of the ligands and the stability constants of the complexes formed with Mn(II) and other biologically relevant metal ions (Mg(II), Ca(II), Cu(II) and Zn(II)) were determined using potentiometric titrations (I = 0.15 M NaCl, T = 25 °C). The conditional stabilities of Mn(II) complexes at pH 7.4 are comparable to those reported for the cyclen-based tDO2A²⁻ ligand. The dissociation of the Mn(II) chelates were investigated by evaluating the rate constants of metal exchange reactions with Cu(II) under acidic conditions (I = 0.15 M NaCl, T = 25 °C). Dissociation of the [Mn(tO2DO2A)(H₂O)] complex occurs through both proton− and metal−assisted pathways, while the [Mn(tO2DO2AM^Pip)(H₂O)] analogue dissociates through spontaneous and proton-assisted mechanisms. The Mn(II) complex of tO2DO2A²⁻ is remarkably inert with respect to its dissociation, while the amide analogue is significantly more labile. The presence of a water molecule coordinated to Mn(II) imparts relatively high relaxivities to the complexes. The parameters determining this key property were investigated using ¹⁷O NMR (Nuclear Magnetic Resonance) transverse relaxation rates and ¹H nuclear magnetic relaxation dispersion (NMRD) profiles.     

Well Ordering Groups with no Monotone Arithmetic Progressions

Károlyi–Kós and Ardal–Brown–Jungic proved that every vector space over \(\mathbb {Q}\) has an ordering with no monotone three term arithmetic progression (3-AP). We show that every solvable group has a well ordering with no monotone 6-AP, and each hypoabelian group has an ordering omitting monotone 5-APs. Finally, we prove that every group has a well ordering with no infinite monotone AP.     

Zum zeitlichen Verlauf des Kriechens von Zementstein und Beton

Zusammenfassung Es wird eine Kriechfunktion abgeleitet, die die bekannten, empirisch bestimmten Kriechfunktionen als Spezialfälle enthält. Für die relative Endkriechverformung ergibt sich sowohl aus der exakten Lösung als auch aus den Näherungen der Wert 2/E. Für die Halbwertszeit, nach der die Hälfte des Endkriechmaßes erreicht wird, bekommt mann = 2l RZ , E. R ist eine Größe, die der inneren Reibung proportional ist. Es wird eine Beziehung angegeben, dieR mit der AktivierungsenergieQ verknüpft. Mit den aus Kriechkurven zu entnehmenden Werten fürR ist damit auchQ bekannt.

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Summary A formula for creep deformation as a function of time has been derived. It has been shown, that the empirical functions previously used by several authors are special cases of this more general function. The final creep deformation is found to be 2/E. Half of the final creep deformation is reached after a time ofn=21RZ/qE. R is a value, which is proportional to internal friction. There exists a relation betweenR and the activation energy. The activation energy can be calculated ifR is evaluated from creep data.

     

Synthesis of 4-unsubstituted 2H-1,2,3-benzothiadiazine 1,1-dioxides via ortho lithiation of protected benzaldehyde derivatives

Variously substituted 2-phenyl-1,3-dioxolanes and 2-(2-bromophenyl)-1,3-dioxolanes, prepared from the corresponding benzaldehydes, were lithiated ortho to the acetal group. Reaction of the lithio derivatives with sulfur dioxide led to the lithium sulfinate salts, which gave, upon oxidative chlorination with sulfuryl chloride, the corresponding benzenesulfonyl chlorides. Then, depending on the aromatic substitution pattern of the molecule, several protocols were elaborated for the functional group transformations leading to the target compounds. Ring closure was performed with hydrazine hydrate or acetylhydrazine, in the latter case with one-pot removal of the acetyl group. The 4-unsubstituted 2H-1,2,3-benzothiadiazine 1,1-dioxides thus obtained are potential drug candidates based on their structural similarity to biologically active phthalazinones.