Supramolecularly Regulated Ligands for Asymmetric Hydroformylations and Hydrogenations

Herein we report the use of polyether binders as regulation agents (RAs) to enhance the enantioselectivity of rhodium‐catalyzed transformations. For reactions of diverse substrates mediated by rhodium complexes of the α,ω‐bisphosphite‐polyether ligands 1 – 5 , a – d , the enantiomeric excess (ee) of hydroformylations was increased by up to 82 % (substrate: vinyl benzoate, 96 % ee), and the ee value of hydrogenations was increased by up to 5 % (substrate: N‐(1‐(naphthalene‐1‐yl)vinyl)acetamide, 78 % ee). The ligand design enabled the regulation of enantioselectivity by generation of an array of catalysts that simultaneously preserve the advantages of a privileged structure in asymmetric catalysis and offer geometrically close catalytic sites. The highest enantioselectivities in the hydroformylation of vinyl acetate with ligand 4 b were achieved by using the Rb[B(3,5‐(CF₃)₂C₆H₃)₄] (RbBArF) as the RA. The enantioselective hydrogenation of the substrates 10 required the rhodium catalysts derived from bisphosphites 3 a or 4 a , either alone or in combination with different RAs (sodium, cesium, or (R,R)‐bis(1‐phenylethyl)ammonium salts). This design approach was supported by results from computational studies.     

Enantioselective synthesis of trans-4-methylpipecolic acid

An asymmetric synthesis for the preparation of both enantiomers of trans-methylpipecolic acids is described. It is based on Sharpless epoxidation as a chirality source, regioselective ring opening with allylamine, and ring-closing metathesis to construct the piperidine ring. The stereogenic center at C-4 is set by stereoselective hydrogenation that is directed by the alcohol functionality of an intermediate and proceeds with good diastereomeric control (trans/cis 16/1). Crystallization of the Boc-protected amino acid afforded the target products with excellent chemical (98% de) and enantiomeric purity (99% ee).     

Braces and symmetric groups with special conditions

We study left braces satisfying special conditions, or identities. We are particularly interested in the impact of conditions like Raut and lri on the properties of the left brace and its associated solution of the Yang–Baxter equation (YBE). We show that the solution $(G,r_G)$ of the YBE associated to the structure group $G=G(X,r)$ (with the natural structure of a left brace) of a nontrivial solution $(X,r)$ of the YBE has multipermutation level 2 if and only if G satisfies lri. It is known that every (left) brace with lri satisfies condition Raut. We prove that for a graded Jacobson radical ring with no elements of additive order two the conditions lri and Raut are equivalent. We construct a finite two-sided brace with condition Raut which does not satisfy lri. We show that a finitely generated two-sided brace which satisfies lri has a finite multipermutation level which is bounded by the number of its generators.     

Selective mode suppression in coplanar waveguides using metamaterial resonators

In this paper, it is shown that split-ring resonators (SRRs) and complementary split-ring resonators (CSRRs) can be used to selectively suppress the odd (slot) mode or the even (fundamental) mode, respectively, in coplanar waveguides. To this end, it is necessary to symmetrically etch the SRRs and the CSRRs in the line. An interpretation of this behavior is reported. The paper is also supported by experimental results, and some applications are highlighted.     

The Gelfand-Kirillov dimension of quadratic algebras satisfying the cyclic condition

We consider algebras over a field presented by generators and subject to square-free relations of the form with every monomial , appearing in one of the relations. It is shown that for 1$"> the Gelfand-Kirillov dimension of such an algebra is at least two if the algebra satisfies the so-called cyclic condition. It is known that this dimension is an integer not exceeding . For , we construct a family of examples of Gelfand-Kirillov dimension two. We prove that an algebra with the cyclic condition with generators has Gelfand-Kirillov dimension if and only if it is of -type, and this occurs if and only if the multiplicative submonoid generated by is cancellative.