Über die lokale Zetafunktion von Shimuravarietäten. Monodromiefiltration und verschwindende Zyklen in ungleicher Charakteristik

Ohne Zusammenfassung

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On the local zeta function of Shimura varieties. Monodromy filtration and vanishing cycles in unequal characteristic

     

Preparation of functionalized, conformationally constrained DTPA analogues from L- or D-serine and trans-4-hydroxy-L-proline. Hydroxymethyl substituents on the central acetic acid and on the backbone

The enantio- and diastereospecific syntheses of conformationally constrained diethylenetriaminepentaacetic acid (DTPA) analogues that are functionalized with a hydroxymethyl linker substituent on the central acetic acid or on the backbone are described. Key synthetic steps include (i) displacement of the 4-hydroxyl group of N-BOC-trans-4-hydroxy-L-proline benzyl ester, via activation as the triflate, with suitable amines derived from L- or D-serine, (ii) the low-temperature alkylation of diethylenetriamines with the triflate of benzyl glycolate, thereby minimizing competitive lactamization, to give DTPA pentabenzyl esters, and (iii) deprotection to afford the corresponding DTPA analogues under very mild hydrogenolysis conditions.     

Optimization of Fabry-Perot ring resonator embedding a grating based mirror

We study a triangular arrangement of two flat mirrors and a grating mirror for coupling a \(-1{\mathrm{st}}\) diffracted order light beam into a traveling-wave intra-cavity light recirculation and out-of-cavity output, combining the \(0\,{\mathrm{th}}\) and the repeatedly diffracted secondary \(+1{\mathrm{st}}\) order beams. The thus designed and then optimized grating Fabry-Perot ring cavity demonstrates high output contrast and detection resolution for wavelength, cavity length and incidence angle.     

Co-Assembly between Fmoc Diphenylalanine and Diphenylalanine within a 3D Fibrous Viscous Network Confers Atypical Curvature and Branching

Supramolecular polymer co-assembly is a useful approach to modulate peptide nanostructures. However, the co-assembly scenario where one of the peptide building blocks simultaneously forms a hydrogel is yet to be studied. Herein, we investigate the co-assembly formation of diphenylalanine (FF), and Fmoc-diphenylalanine (FmocFF) within the 3D network of FmocFF hydrogel. The overlapping peptide sequence between the two building blocks leads to their co-assembly within the gel state modulating the nature of the FF crystals. We observe the formation of branched microcrystalline aggregates with an atypical curvature, in contrast to the FF assemblies obtained from aqueous solution. Optical microscopy reveal the sigmoidal kinetic growth profile of these aggregates. Microfluidics and ToF-SIMS experiments exhibit the presence of co-assembled structures of FF and FmocFF in the crystalline aggregates. Molecular dynamics simulation was used to decipher the mechanism of co-assembly formation.     

Solid Phase Synthesis. Evidence for and Quantification of Intra res in Reactions

Abstract

Intrareaction occurs between moieties attached to copolystyrene-2% divinylbenzene resin as used in solid phase synthesis even when only 0.5% of the phenyl residues are functionalized. Evidence for this interaction has been obtained from the dimeric products resulting from Dieckmann cyclization of resin bound sebacates and ω-cyanopelargonyl thiol resin esters, from kinetic and product data on radioactivity scrambling during the Dieckmann cyclization of uniquely singly labeled tertiary alkyl pimeloyl resin esters, and from anhydride formation with carboxymethyl resin. The extent to which site-site interactions can occur as a function of the percentage functionalization has been measured quantitatively by radiotracer studies on intraresin anhydride formation from carboxymethyl substituted resin. The synthesis and characterization of the resin bound re-actants is described, and the significance of these observations is discussed.     

Analytic solution for the nondegenerate quantum control problem

We present an analytic solution for the nondegenerate quantum control problem, i.e., the transfer of a deliberate amount of population, 0%-100%, between arbitrary initial Psi(t)> and final Psi'(t)> states, which can be expanded in terms of nondegenerate energy eigenstates k>. The solution constitutes a robust two-photon multicomponent adiabatic passage, via an intermediate eigenstate 0>, which relies on three types of "null states."