Characterization of the absence of a spectral gapfor a class of periodic Jacobi operators

Let q ∈ {2, 3} and let 0 = s₀ < s₁ < … < s_q = T be integers. For m, n ∈ Z, we put ¯m,n = {j ∈ Z| m? j ? n}. We set l_j = s_j − s_j−1 for j ∈ 1, q. Given (p₁,, p_q) ∈ R^q, let b: Z → R be a periodic function of period T such that b(·) = p_j on s_j−1 + 1, s_j for each j ∈ 1, q. We study the spectral gaps of the Jacobi operator (Ju)(n) = u(n + 1) + u(n − 1) + b(n)u(n) acting on l²(Z). By [λ_2j , λ_2j−1] we denote the jth band of the spectrum of J counted from above for j ∈ 1, T. Suppose that p_m ≠ p_n for m ≠ n. We prove that the statements (i) and (ii) below are equivalent for λ ∈ R and i ∈ 1, T − 1.     

Statistical simulation based on right skewed distributions

Statistical simulations in medical and biological research are usually conducted with normal random numbers. However, in many cases, the distributions of real data in medical fields are usually right skewed. The conclusions led by simulations with the misspecified model might be misleading because of a gap between real data’s distribution and theoretical one. In this paper, we provide the simulation procedure for right skewed data based on reparameterized, easily interpretable parameters of the Box–Cox transformation model which includes multivariate distributions and regression models. We also show that the provided procedure is widely applicable to real world based on laboratory data, and then we provide parameter vector sets obtained by reparameterized parameter estimates that would cover almost all situations in which the distributions of data were right skewed and unimodal.     

Facile synthesis of Gramicidin S via cyclication of a linear pentapeptide

Azide and N-hydroxysuccinimide ester of five pentapeptides related to gramicidin S (cyclic decapeptide) were cyclized to determine the ratio of dimer to monomer in the cyclization product, the pentapeptide derivative with D-Phe as C-terminus giving the dimer in good yield.     

Homological mirror symmetry for singularities of type D

We prove homological mirror symmetry for Lefschetz fibrations obtained as Sebastiani–Thom sums of polynomials of types A or D. The proof is based on the behavior of the Fukaya category under Sebastiani–Thom summation of a polynomial of type D.     

Simple cubic self-assembly of PbS quantum dots by finely controlled ligand removal through gel permeation chromatography

The geometry in self-assembled superlattices of colloidal quantum dots (QDs) strongly affects their optoelectronic properties and is thus of critical importance for applications in optoelectronic devices. Here, we achieve the selective control of the geometry of colloidal quasi-spherical PbS QDs in highly-ordered two and three dimensional superlattices: Disordered, simple cubic (sc), and face-centered cubic (fcc). Gel permeation chromatography (GPC), not based on size-exclusion effects, is developed to quantitatively and continuously control the ligand coverage of PbS QDs. The obtained QDs can retain their high stability and photoluminescence on account of the chemically soft removal of the ligands by GPC. With increasing ligand coverage, the geometry of the self-assembled superlattices by solution-casting of the GPC-processed PbS QDs changed from disordered, sc to fcc because of the finely controlled ligand coverage and anisotropy on QD surfaces. Importantly, the highly-ordered sc supercrystal usually displays unique superfluorescence and is expected to show high charge transporting properties, but it has not yet been achieved for colloidal quasi-spherical QDs. It is firstly accessible by fine-tuning the QD ligand density using the GPC method here. This selective formation of different geometric superlattices based on GPC promises applications of such colloidal quasi-spherical QDs in high-performance optoelectronic devices.

Gel permeation chromatography can finely control ligand coverage of PbS quantum dots. Self-assembly of these QDs with different ligand density leads to the formation of 2D square, hexagonal and 3D simple cubic and face-centered cubic superlattices.     

Nickel-catalyzed regio- and stereoselective hydrophosphinylation of internal ynamides with H-phosphinates

A method for the catalytic hydrophosphinylation of internal ynamides with H-phosphinates has been developed for the first time. The protocol employing the catalyst generated from NiBr₂ and PPh₃ could be applied to several types of ynamides and H-phosphinates, affording (E)-β-aminovinylphosphinates in a highly regio- and stereoselective manner.     

Comparison of luminescent properties of helicene-like bibenzothiophenes with <Emphasis Type="Italic">o</Emphasis>-carborane and 5,6-dicarba-<Emphasis Type="Italic">nido</Emphasis>-decaborane

This article describes comparison of the anchoring effect on electronic properties of the helicene-like bibenzothiophene between o-carborane and 5,6-dicarba-nido-decaborane. The o-carborane and nido-decaborane-fused bibenzothiophenes were simultaneously obtained in the same reaction and successfully isolated. Initially, the X-ray single crystal analysis revealed that the helicene-like distorted structure was realized in the nido-decaborane-fused bibenzothiophene. From optical measurements in the solution state, distinct different characteristics depending on the type of anchors were observed. It was summarized that the absorption and luminescent properties originated from weak π-conjugation at the bibenzothiophene moiety in the o-carborane-fused compound were obtained, whereas robust π-conjugation and significant emission from the intramolecular charge transfer state were detected from the nido-decaborane-fused compound. These data can be explained by the theoretical results that π-conjugation was restrictedly developed within the bibenzothiophene moiety in frontier orbitals of the o-carborane-fused compound. In contrast, π-conjugation can be constructed even through the distorted bibenzothiophene because of the nido-decaborane unit. Moreover, the intramolecular charge transfer state should be realized because of electronic interaction involving the nido-decaborane unit in the excited state. Furthermore, it was demonstrated that the nido-decaborane-fused compound possessed solid-state emission and mechanochromic luminescent properties. The π-conjugation on the distorted structure supported by the nido-decaborane anchor should play a significant role in suppressing aggregation-caused quenching followed by presenting solid-state emission with stimuli responsiveness.