An inequality of W. L. Wang and P. F. Wang

In this note we present a proof of the inequality Hn/H′n≤Gn/G′n where Hn and Gn (resp. H′n and G′n) denote the weighted harmonic and geometric means of x1,…,xn (resp. 1−x1,…,1−xn) with xi∈(0,1/2], i=1,…,n

Markierungsverfahren zur Synthese 4-[18F]Fluorprolyl-haltiger Peptide

The requirement of selective radiopharmaceuticals for PET-diagnostics necessitates the development of new labelling methods taking into account the substantial and structural diversity of the compounds to be labelled . Therefore different concepts for $^{18}$F-fluorination of peptides, which are increasingly important as pharmaceuticals, via proline moieties were explored and evaluated in this work. The direct nucleophilic kryptate based $^{18}$F-fluorination of the model peptide Z-Pro-Leu-Gly-4- (4R)-(TsO)Pro-OMe showed, that the peptide is not stable under the basic labelling conditions, and as a result the $^{18}$F-fluorination is not possible. Perfluorbutane-l-sulfonyl[ $^{18}$F]fluoride is a possible reagent for $^{18}$F-fluorination of sensitive hydroxy groups containing biomolecules due to the mild reaction conditions at which aliphatic alcohols are fluorinated by this reagent. By kryptate catalysed, nucleophilic $^{18}$F-fluorination of N,N-bis(perfluorobutane-l-sulfonyl)aniline and evaporation of the active product no-carrier-added perfluorobutane-l-sulfonyl[ $^{18}$F]fluoride can be achieved either dissolved in toluene (RCY: 83 ± 3 %) or adsorbed an a polystyrole-matrix (LiChrolut$^{®}$ EN) with a total yield of 75 ± 6 %. In the presence of an equimolar amount of perfluorobutane-1-sulfonylfluoride as carrier N-Boc-Hyp- OMe can be $^{18}$F-fluorinated with a radiochemical yield of > 90 % and the two model peptides Z-Pro- Leu-Gly-Hyp-OMe and Z-Gly-Leu-Hyp-Gly-Leu-OMe with 40 - 45 % and 30 - 35 %, while in the case of no-carrier-added synthesis only ca. 1 % of the $^{18}$F-fluoroproduct is obtained . The necessary addition of perfluorobutane-l-sulfonylfluoride carrier allows naturally only the synthesis of radiotracers with low molar activity. For performance of the $^{18}$F-fluorination via perfluorobutane-l-sulfonyl[ $^{18}$F]fluoride of the model peptide N-Boc-Hyp-Leu-OH, which is covalently bound to a Wang resin via the C-terminus, the $^{18}$F-fluorination reagent is prepared in absence of a solvent and adsorbed an the Wang resin with a yield of 31 ± 3 %, based on [$^{18}$F]fluoride. The subsequent $^{18}$F-fluorination of the peptide, which was done in the presence of an equimolar amount of perfluorobutane-1-sulfonylfluoride, proceeds with a radiochemical yield of merely 4 ± 1 %. Altematively, the condensation of 4-[$^{18}$F]fluoroproline-methylester via TBTU at the C-terminus of Z-Pro-Leu-Gly-OH could be carried out under no-carrrier-added conditions with a radiochemical yield of 70 - 80 %. The required 4-[$^{18}$F]fluoroproline-methylester could be achieved with a radiochemical yield of 30 - 40 % by $^{18}$F-substitution of N-Boc-trans-4-(ptoluenesulfonyloxy)- proline-methylester, by which the trans-product is also formed in addition to the cis-product, and the cleavage of the Boc group. As a result of these studies another prosthetic group is available for no-carrier-added labelling of peptides

Yinuo Wang, Piano

Sonata in E minor, Op. 90 / Ludwig van Beethoven; Canon in D minor; Prelude in F-sharp minor, Op. 23, No. 1; Daisies, Op. 38, No. 3; Prelude in D minor, Op. 23, No. 3; Prelude in B minor, Op. 32, No. 10; Prelude in G-flat major, Op. 23, No. 10; Etude in D minor, Op. 39, No. 8; Etude in D major, Op. 39, No. 9; Rhapsody on a Theme of Paganini / Sergei Rachmaninof

Uniqueness of asymptotic cones of complete noncompact shrinking gradient Ricci solitons with Ricci curvature decay

We discuss an elementary consequence of the works of (1) Brett Kotschwar and Lu Wang and (2) Ovidiu Munteanu and Jiaping Wang

A note on stability for maximal FF-free graphs

Popielarz, Sahasrabudhe and Snyder in 2018 proved that maximal $K_{r+1}$-free graphs with $(1-\frac{1}{r})\frac{n^2}{2}-o(n^{\frac{r+1}{r}})$ edges contain a complete $r$-partite subgraph on $n-o(n)$ vertices. This was very recently extended to odd cycles in place of $K_3$ by Wang, Wang, Yang and Yuan. We further extend it to some other 3-chromatic graphs, and obtain some other stability results along the way.Comment: 10 page

Preventing Employer Misclassification of Student Interns and Trainees

[Excerpt] The legality of unpaid internships has been recently examined in the media with news of Harper’s Bazaar’s former intern Xuedan “Diana” Wang filing suit against the Hearst Corporation on February 1, 2012. Ms. Wang was “head intern,” responsible for supervising eight interns in her charge. As intern to the magazine Harper’s Bazaar, she worked 40 to 55 hours weekly transporting clothing to public relations firms as an unofficial messenger service. Ms. Wang is part of a class action lawsuit against the Hearst Corporation seeking back pay for compensation of five months of unpaid labor

Optimal regularity of minimal graphs in the hyperbolic space

We discuss the global regularity of solutions $f$ to the Dirichlet problem for minimal graphs in the hyperbolic space when the boundary of the domain $\Omega\subset\mathbb R^n$ has a nonnegative mean curvature and prove an optimal regularity $f\in C^{\frac{1}{n+1}}(\bar{\Omega})$. We can improve the H\"older exponent for $f$ if certain combinations of principal curvatures of the boundary do not vanish, a phenomenon observed by F.-H. Lin.Comment: Accepted by Calc. Var. Partial Differential Equation