Preparation of stereodefined homoallylic amines from the reductive cross-coupling of allylic alcohols with imines

Regio-, diastereo-, and enantioselective coupling reactions between imines and allylic alcohols have been developed. These coupling reactions deliver complex homoallylic amine products through a convergent C-C bond forming process that does not proceed through intermediate allylic organometallic reagents. In general, convergent coupling, by exposure of an allylic alkoxide to a preformed Ti-imine complex, occurs with allylic transposition in a predictable and stereocontrolled manner. While simple diastereoselection in these reactions is high, delivering anti-products with ≥20:1 selectivity, the organometallic transformation described is compatible with a diverse range of functionality and substrates (including aliphatic and aromatic imines, allylic silanes, trisubstituted alkenes, vinyl- and aryl halides, trifluoromethyl groups, thioethers, and aromatic heterocycles). Alkene geometry of the products is a complex function of the allylic alcohol structure and is consistent with a mechanistic proposal based on syn-carbometalation followed by syn-elimination by way of a boat-like transition state geometry. Single asymmetric coupling reactions provide a means to translate the stereochemical information of the allylic alcohol to the homoallylic amine or to control diastereoselection in the coupling reactions of achiral allylic alcohols with chiral imines. Double asymmetric coupling reactions are also described that afford a unique means to control stereoselection in these complex convergent coupling processes. Finally, empirical models are proposed that are consistent with the observed stereochemical course of these coupling reactions en route to chiral homoallylic amines possessing di- or trisubstituted alkenes and anti- or syn- relative stereochemistry at the allylic and homoallylic positions.     

Sulfur-rich CpCo(dithiolene) complexes: Isostructural or non-isostructural couples of CpCo(III) with CpNi(III) dithiolene complexes

Eight new sulfur-rich [CpCo(dithiolene)] complexes were synthesized from [Zn(dmit)₂]²⁻ as a starting material. The structures, electrochemical behavior and electronic absorption spectra of the sulfur-rich [CpCo(S₂C₂S₂Y)] complexes could be compared with the early data of analogous Ni complexes. [CpCo(pddt)] (Y = -(CH₂)₃-), [CpCo(dpdt)] (Y = -CH₂C(CH₂)CH₂-), [CpCo(bddt)] (Y = -(CH₂)₄-), [CpCo(dtdt)] (Y = -CH₂SCH₂-) and [CpCo(poddt)] (Y = -CH₂C(O)CH₂-) crystallized in all isostructural with the corresponding paramagnetic [CpNi(dithiolene)] complexes, but [CpCo(dmid)] (Y = CO), [CpCo(dddt)] (Y = -(CH₂)₂-) and [CpCo(F₂pddt)] (Y = -CH₂CF₂CH₂-) crystallized in non-isostructural with them. These molecules are associated with intermolecular short S?S contacts in the crystals. [CpCo(F₂pddt)] did not show any remarkable S?S contacts but indicated interesting fluorine segregation and Cp?Cp face-to-face interactions. Redox potentials of [CpCo(dithiolene)] complexes were obtained with the cyclic voltammetry measurements and dimerized by electrochemical oxidations. Electronic absorption spectra of [CpCo(dithiolene)] complexes showed visible absorption in the range of 585-701 nm as lowest energy wavelengths (? = 9800-11,800 M⁻¹ cm⁻¹) in solutions, and they were higher energy than those of [CpNi(dithiolene)] complexes (near-IR).     

Low-loss multilayered metamaterial exhibiting a negative index of refraction at visible wavelengths

We experimentally demonstrate a low-loss multilayered metamaterial exhibiting a double-negative refractive index in the visible spectral range. To this end, we exploit a second-order magnetic resonance of the so-called fishnet structure. The low-loss nature of the employed magnetic resonance, together with the effect of the interacting adjacent layers, results in a figure of merit as high as 3.34. A wide spectral range of negative index is achieved, covering the wavelength region between 620 and 806 nm with only two different designs.     

Extending reference scan drift correction to high-magnification high-cone-angle tomography

The reference scan method is a simple yet powerful method for measuring spatial drift of the x-ray spot during a low-cone-angle μ-CT experiment. As long as the drift is smooth, and occurring on a time scale that is long compared to the acquisition time of each projection, this method provides a way to compensate for the drift by applying 2D in-plane translations to the radiographs. Here we show that this compensation may be extended to the regime of high-magnification, high-cone-angle CT experiments where source drift perpendicular to the detector plane can cause significant magnification changes throughout the acquisition.     

Overlap Cycles for Steiner Quadruple Systems

Steiner quadruple systems are set systems in which every triple is contained in a unique quadruple. It is well known that Steiner quadruple systems of order v, or SQS(v), exist if and only if . Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, are a type of cyclic Gray code. Overlap cycles are generalizations of universal cycles that were introduced in 2010 by Godbole, et al. Using Hanani's SQS constructions, we show that for every with there exists an SQS(v) that admits a 1‐overlap cycle.     

Composition Operators on the Lipschitz Space of a Tree

The Lipschitz space ${\mathcal{L}}$ of an infinite tree T rooted at o is defined as the space consisting of the functions ${f : T \rightarrow \mathbb{C}}$ such that $$\beta_f = {\rm sup}\{|f(v) - f(v^-)| : v \in T\backslash\{o\}, \,v^- {\rm parent \, of \,} v\}$$ is finite. Under the norm ${\|f\|_\mathcal{L} = |f(o)|+\beta_f,\mathcal{L}}$ is a Banach space. In this article, the functions φ mapping T into itself whose induced composition operator ${C_{\varphi} : f \mapsto f \circ \varphi}$ on the Lipschitz space is bounded, compact, or an isometry, are characterized. Specifically, it is shown that the symbols of the bounded composition operators are the Lipschitz maps of T into itself viewed as a metric space under the edge-counting distance. The symbols inducing compact operators have finite range while those inducing isometries on ${\mathcal{L}}$ are precisely the onto maps fixing the root and whose images of neighboring vertices coincide or are themselves neighboring vertices. Finally, the spectrum of the operators ${C_\varphi}$ that are isometries is studied in detail.     

Overconvergent modular sheaves and modular forms for GL 2/F

Given a totally real field F and a prime integer p which is unramified in F, we construct p-adic families of overconvergent Hilbert modular forms (of non-necessarily parallel weight) as sections of, so called, overconvergent Hilbert modular sheaves. We prove that the classical Hilbert modular forms of integral weights are overconvergent in our sense. We compare our notion with Katz’s definition of p-adic Hilbert modular forms. For F = ?, we prove that our notion of (families of) overconvergent elliptic modular forms coincides with those of R. Coleman and V. Pilloni.     

1-Overlap cycles for Steiner triple systems

A number of applications of Steiner triple systems (e.g. disk erasure codes) exist that require a special ordering of its blocks. Universal cycles, introduced by Chung, Diaconis, and Graham in 1992, and Gray codes are examples of listing elements of a combinatorial family in a specific manner, and Godbole invented the following generalization of these in 2010. 1-overlap cycles require a set of strings to be ordered so that the last letter of one string is the first letter of the next. In this paper, we prove the existence of 1-overlap cycles for automorphism free Steiner triple systems of each possible order. Since Steiner triple systems have the property that each block can be represented uniquely by a pair of points, these 1-overlap cycles can be compressed by omitting non-overlap points to produce rank two universal cycles on such designs, expanding on the results of Dewar.