Conical Kakeya and Nikodym sets in finite fields

A Kakeya set contains a line in each direction. Dvir proved a lower bound on the size of any Kakeya set in a finite field using the polynomial method. We prove analogues of Dvir's result for non-degenerate conics, that is, parabolae and hyperbolae (but not ellipses which do not have a direction). We also study so-called conical Nikodym sets where a small variation of the proof provides a lower bound on their sizes. (Here ellipses are included.)Note that the bound on conical Kakeya sets has been known before, however, without an explicitly given constant which is included in our result and close to being best possible.     

Synthesis and crosslinking reaction of a novel polymer containing benzoxazine and phenyleneethynylene moieties in the main chain

A novel polymer, poly( 1 ) containing benzoxazine and phenyleneethynylene moieties in the main chain with number‐average molecular weights ranging from 1400 to 9800 was obtained quantitatively by the Sonogashira–Hagihara coupling polymerization of the corresponding iodophenyl‐ and ethynylphenyl‐substituted monomer 1 . Poly( 1 ) was heated at 200 °C under N₂ for 2 h to obtain the cured polymer, poly( 1 )′ via the ring‐opening polymerization of the benzoxazine moieties. The structures of the polymer before and after curing were confirmed by ¹H‐NMR, IR, and UV–vis absorption and reflectance spectroscopies. Poly( 1 )′ was thermally more stable than monomer 1 and poly( 1 ). A specimen was prepared from a mixture of poly( 1 ) and phenol‐diaminodiphenylmethane type benzoxazine 2 by heating at 200 °C for 2 h under N₂. The poly( 1 )/ 2 resin was thermally stable than bisphenol‐A type benzoxazine resin 3 . Poly( 1 ) exhibited XRD peaks corresponding to the d‐spacings of 1.26–0.98 and 0.40 nm, assignable to the repeating monomer unit and alignment of polymer molecules, respectively. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 2581–2589     

Automorphism groups of designs with λ=1

If $G$ is a finite group and $k=q>2$ or $k=q+1$ for a prime power $q$ then, for infinitely many integers $v$, there is a 2-$(v,k,1)$-design $\mathbf{D}$ for which $\mathrm{Aut}\mathbf{D}?G$.     

Molecular dynamics of the intramolecular 1, 3-dipolar ene reaction of a nitrile oxide and an alkene: non-statistical behavior of a reaction involving a diradical intermediate*

ABSTRACT

Potential energy surfaces and molecular dynamics of the intramolecular 1, 3-dipolar cycloaddition and ene reaction of a nitrile oxide with an alkene were performed in the gas phase and in dichloromethane with density functional theory. One hundred trajectories were propagated in the gas phase and in dichloromethane, respectively. Twenty percent of the trajectories in the gas phase involve bicyclic intermediate and the mean time gap is 472fs. A dynamically stepwise reaction is observed. In dichloromethane, more reactive trajectories were obtained and the time gap is larger than that in the gas phase.     

LiB6Si: An indirect band gap semiconductor

Using first-principle calculations, mechanical properties, electronic structure, and Raman spectra of LiB₆Si structure were investigated. The band structures calculated by GGA-PBE and HSE06 methods reveal that LiB₆Si is an indirect band gap semiconductor. The band gap estimated by HSE06 method is about 2.24 eV, which is in good agreement with that of experimental value 2.27 eV. The calculated tensile stress-strain curves of LiB₆Si reveal that [010] direction is the cleavage direction under tensile strains. The calculated Raman spectra of LiB₆Si are also in good agreement with that of measured. The position of the band gap may provide a basis for further photocatalysis research on LiB₆Si.     

Metamorphic InAs(Sb)/InGaAs/InAlAs nanoheterostructures grown on GaAs for efficient mid-IR emitters

High-efficiency semiconductor lasers and light-emitting diodes operating in the 3–5?μm mid-infrared (mid-IR) spectral range are currently of great demand for a wide variety of applications, in particular, gas sensing, noninvasive medical tests, IR spectroscopy etc. III-V compounds with a lattice constant of about 6.1?Å are traditionally used for this spectral range. The attractive idea to fabricate such emitters on GaAs substrates by using In(Ga,Al)As compounds is restricted by either the minimum operating wavelength of ～8?μm in case of pseudomorphic AlGaAs-based quantum cascade lasers or requires utilization of thick metamorphic In_xAl_1-xAs buffer layers (MBLs) playing a key role in reducing the density of threading dislocations (TDs) in an active region, which otherwise result in a strong decay of the quantum efficiency of such mid-IR emitters. In this review we present the results of careful investigations of employing the convex-graded In_xAl_1-xAs MBLs for fabrication by molecular beam epitaxy on GaAs (001) substrates of In(Ga,Al)As heterostructures with a combined type-II/type-I InSb/InAs/InGaAs quantum well (QW) for efficient mid-IR emitters (3–3.6?μm). The issues of strain relaxation, elastic stress balance, efficiency of radiative and non-radiative recombination at T?=?10–300?K are discussed in relation to molecular beam epitaxy (MBE) growth conditions and designs of the structures. A wide complex of techniques including in-situ reflection high-energy electron diffraction, atomic force microscopy (AFM), scanning and transmission electron microscopies, X-ray diffractometry, reciprocal space mapping, selective area electron diffraction, as well as photoluminescence (PL) and Fourier-transformed infrared spectroscopy was used to study in detail structural and optical properties of the metamorphic QW structures. Optimization of the growth conditions (the substrate temperature, the As₄/III ratio) and elastic strain profiles governed by variation of an inverse step in the In content profile between the MBL and the InAlAs virtual substrate results in decrease in the TD density (down to 3?×?10⁷ cm^?2), increase of the thickness of the low-TD-density near-surface MBL region to 250–300?nm, the extremely low surface roughness with the RMS value of 1.6–2.4?nm, measured by AFM, as well as rather high 3.5?μm-PL intensity at temperatures up to 300?K in such structures. The obtained results indicate that the metamorphic InSb/In(Ga,Al)As QW heterostructures of proper design, grown under the optimum MBE conditions, are very promising for fabricating the efficient mid-IR emitters on a GaAs platform.     

Improving waterproof/breathable performance of electrospun poly(vinylidene fluoride) fibrous membranes by thermo‐pressing

Facing the ever‐increasing demand for waterproof/breathable materials, a rapid and efficient fabrication method of these functional materials with excellent performance as well as robust mechanical properties remains challenging. Herein, a simple and scalable strategy referred to as thermo‐pressing is introduced to improve the waterproof/breathable performance and mechanical properties of electrospun PVDF fibrous membranes. The synergistic effect of temperature and pressure acted on the electrospun PVDF membranes on the fiber morphology and crystal structure was investigated, which can be able to effectively enhance waterproof performance and mechanical properties, endowing the as‐prepared membranes with a modest breathability. The membranes thermo‐pressed at 150 °C with a pressure of 8.27 MPa exhibit robust tensile strength of 40.65 MPa, which is superior to those of the previous reports (below 32.8 MPa). Notably, the optimized membranes enable to show a high hydrostatic pressure of 102 kPa, good WVTR of 10.87 kg m⁻² d⁻¹ and excellent abrasion resistance, which implies that the thermo‐pressing is an efficient and facile way to steer the fiber morphology and crystal structure of electrospun membranes to improve their application performance. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 36–45     

Synthesis of phenanthroimidazole-based four coordinate organoboron compounds

The synthesis of N,C-coordinated organoboron compounds (B1-B4) based on phenanthroimidazole described. All the compounds were characterized by various spectroscopic techniques. Single crystal X-ray diffraction analysis of the compounds B1 and B3 revealed that the vicinity around the boron atom adopts tetrahedral geometry. Except compound B4, other organoboron compounds (B1-B3) does not show solvatochromism. All our newly synthesized organoboron compounds exhibited moderate to good solution state quantum yields (0.07–0.88) and moderate solid state quantum yields.     

石墨毡载纳米δ-MnO2高性能除铵净水材料研究

首先制备了α-MnO₂纳米花簇、β-MnO₂纳米针和δ-MnO₂微米颗粒三种不同晶型的MnO₂粉末材料，对其结构、形貌及吸附除铵能力进行了表征和测试.结果表明，层间距（7.2Å）大于NH₄⁺直径（2.96Å）和水合NH₄⁺直径（6.62Å）的δ-MnO₂相比其他两种晶型的MnO₂有更高的NH₄⁺吸附量；接着研究采用KMnO₄原位氧化还原法在石墨毡（GF）上直接生长超薄δ-MnO₂纳米片（MnO₂NPs）阵列构筑了石墨毡载纳米MnO₂（MnO₂NPs/GF）多级结构材料，制备简单，无须成型造粒就可直接用作除铵净水材料，研究结果表明，MnO₂NPs/GF不仅具有较高的吸附量（15 mg·g^－1）与良好的选择性，同时还展现了优异的快速吸附和稳定的循环使用性能.MnO₂NPs/GF对水中NH₄⁺的吸附符合准二级动力学模型，其吸附等温线符合Langmuir吸附等温式，是吸附-离子交换法除铵的理想材料.