Palladium‐Catalyzed Construction of Quaternary Stereocenters by Enantioselective Arylation of γ‐Lactams with Aryl Chlorides and Bromides

Herein, we report the first Pd‐catalyzed enantioselective arylation of α‐substituted γ‐lactams. Two sets of conditions were developed for this transformation, allowing for the use of either aryl chlorides or bromides as electrophiles. Utilizing a highly electron‐rich dialkylphosphine ligand we have been able to construct α‐quaternary centers in good yields (up to 91 % yield) and high enantioselectivities (up to 97 % ee).     

Lewis Base/Brønsted Acid Co‐catalyzed Enantioselective Sulfenylation/Semipinacol Rearrangement of Di‐ and Trisubstituted Allylic Alcohols

An enantioselective sulfenylation/semipinacol rearrangement of 1,1‐disubstituted and trisubstituted allylic alcohols was accomplished with a chiral Lewis base and a chiral Brønsted acid as cocatalysts, generating various β‐arylthio ketones bearing an all‐carbon quaternary center in moderate to excellent yields and excellent enantioselectivities. These chiral arylthio ketone products are common intermediates with many applications, for example, in the design of new chiral catalysts/ligands and the total synthesis of natural products. Computational studies (DFT calculations) were carried out to explain the enantioselectivity and the role of the chiral Brønsted acid. Additionally, the synthetic utility of this method was exemplified by an enantioselective total synthesis of (?)‐herbertene and a one‐pot synthesis of a chiral sulfoxide and sulfone.     

Asymmetric Grignard Synthesis of Tertiary Alcohols through Rational Ligand Design

A simple, general and practical method is reported for highly enantioselective construction of tertiary alcohols through the direct addition of organomagnesium reagents to ketones. Discovered by rational ligand design based on a mechanistic hypothesis, it has an unprecedented broad scope. It utilizes a new type of chiral tridentate diamine/phenol ligand that is easily removed from the reaction mixture. It is exemplified by application to a formal asymmetric synthesis (>95:5 d.r.) of vitamin E.     

Copper‐Catalyzed Enantioselective Construction of Tertiary Propargylic Sulfones

Tertiary propargylic sulfones are of significant importance in organic synthesis and medicinal chemistry, but to date no general asymmetric synthesis approach has been developed. We disclose a versatile copper‐catalyzed sulfonylation of propargylic cyclic carbonates using sodium sulfinates that allows the construction of propargylic sulfones featuring elusive quaternary stereocenters. This method provides the first successful example of such an enantioselective propargylic sulfonylation, features high asymmetric induction, wide functional group tolerance, and scalability, and enables attractive product diversification.     

Nonlinear Optical Switching in Regioregular Porphyrin Covalent Organic Frameworks

Covalent organic frameworks (COFs) have garnered immense scientific interest among porous materials because of their structural tunability and diverse properties. However, the response of such materials toward laser‐induced nonlinear optical (NLO) applications is hardly understood and demands prompt attention. Three novel regioregular porphyrin (Por)‐based porous COFs—Por‐COF‐HH and its dual metalated congeners Por‐COF‐ZnCu and Por‐COF‐ZnNi—have been prepared and present excellent NLO properties. Notably, intensity‐dependent NLO switching behavior was observed for these Por‐COFs, which is highly desirable for optical switching and optical limiting devices. Moreover, the efficient π‐conjugation and charge‐transfer transition in ZnCu‐Por‐COF enabled a high nonlinear absorption coefficient (β=4470 cm/GW) and figure of merit (FOM=σ₁/σ_o, 3565) value compared to other state‐of‐the‐art materials, including molecular porphyrins (β≈100–400 cm/GW), metal–organic frameworks (MOFs; β≈0.3–0.5 cm/GW), and graphene (β=900 cm/GW).     

Caractère de Chern bivariant

We construct a bivariant Chern character with values in Jones-Kassel's bivariant cyclic cohomology. This is done forK-theoretic objects such as idempotents, bimodules, quasi-homomorphisms à la Cuntz and extensions of algebras.

     

The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang ref="#br0240" class="workspace-trigger">[24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang ref="#br0240" class="workspace-trigger">[24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Curvature Estimates for the Level Sets of Solutions to the Monge-Amp`ere Equation detD2u = 1

For the Monge-Ampere equation det D2u = 1, the authors find new auxiliary curvature functions which attain their respective maxima on the boundary. Moreover, the upper bounded estimates for the Gauss curvature and the mean curvature of the level sets for the solution to this equation are obtained.     

On a time-depending Monge–Ampère type equation

In this paper, we prove a comparison result between a solution u(x,t)$u(x,t)$, x∈Ω⊂R²$x\in \Omega \subset {\mathbb{R}}^2$, t∈(0,T)$t\in (0,T)$, of a time depending equation involving the Monge–Ampère operator in the plane and the solution of a conveniently symmetrized parabolic equation. To this aim, we prove a derivation formula for the integral of a smooth function g(x,t)$g(x,t)$ over sublevel sets of u$u$, {x∈Ω:u(x,t)<?}$\{x\in \Omega :u(x,t)<?\}$, ?∈R$?\in \mathbb{R}$, having the same perimeter in R²${\mathbb{R}}^2$.