永恆的旋轉木馬
本研究作品主要在探討「平面上各種曲線內關於相鄰等角割線段的新的不變量」與「空間中特殊圓錐曲面的特殊等角割線段的新的不變量」。 若圓錐曲線、蚶線等曲線中有相鄰等角的 條割線段，則這n條割線段之m次方和為定值。在圓錐曲線中這些割線段的交點可以是焦點、曲線內任意點，在蚶線中則為基點。甚至經由反演，還能將此性質推廣至直線上。 研究最後擴及至空間，先考慮特殊橢圓、拋物、雙曲球面，其一焦點為F，將正N面體VN之重心G與F重合，使得VN以F為旋轉中心任意旋轉，此時由F對VN之各頂點做射線交圓錐曲面於 PN，則FPN之倒數m次方和為定值，其中u=1,...,n，N=4, 6, 8, 12, 20 。
The change in NaCl crystals from cubic to octahedral～Sodium polyacrylate stabilizes the {111} face of Miller indices～
When adding 2% or 4% sodium polyacrylate as habit modifier, standard milky-white octahedral NaCl crystals grew gradually in saturated NaCl solution on the bottom of the container. [1] [2] Sodium polyacrylate is well known as a highly water-absorbable polymer with many carboxylate anions. In the case of low concentration (0.01%, 0.02%, 0.05%, 0.1% and 0.5%) sodium polyacrylate many small or microscopic crystals whose shapes were nearly octahedrons and had {111} faces were observed with an optical microscope on the bottoms of the solution containers. In low concentration sodium polyacrylate, octahedral NaCl crystals made up of electrostatically unstable {111} faces grew similarly to crystals in high concentrations of 2% or 4% NaCl. Therefore, by adding sodium polyacrylate to saturated NaCl solution, cleaved rock salt crystals in this sol were observed to find out whether or not a change in crystal morphology from cuboids of {100} faces to octahedrons of {111} faces would occur. Regardless of the sodium polyacrylate concentrations of 0.01%, 0.02%, 0.05%, 0.1%, 0.5% and 2%, all cuboid crystals changed into a pyramidal shape in which four of the side surfaces formed an equilateral triangle. When one side of each equilateral triangle face was rotated so the square face of the crystal was soaked in the NaCl sol, all crystals grew into octahedrons of high transparency. Sodium polyacrylate, even under a low concentration, caused morphological change in the NaCl crystals. Many carboxylate anions in the sodium polyacrylate attracted sodium ions and the repulsive force between the carboxylate anions became weak, excluding the water in the internal space of the polymer. We considered that the stabilizing {111} faces of gathered sodium ions attached to carboxylate anions. Chloride and sodium ions coordinated continuously to minimize the NaCl surface area, growing into an octahedral and lowering the surface energy of the NaCl crystal. [3]
Direct reductive amination of camphor
Terpenoids are an irreplaceable class of natural products. The camphoryl group is an important moiety in the structure of chiral ligands for asymmetric synthesis catalysis or it can be used as an auxiliary group in asymmetric synthesis.[1] The usage of fenchone based molecules for asymmetric catalysis and synthesis is less common because of the difficulty of fenchone modifications due to steric hindrance. Camphor is a readily available starting molecule for the preparation of different compounds with biological activity. For example, camphor diimines demonstrate antiviral activity.[2] Fenchonyl amine-based molecules are potential therapeutic agents for the treatment of Alzheimer’s disease. Amines are a crucial class of organic compounds with multiple academic and industrial applications. There are a plethora of synthetic approaches towards amines synthesis and modifications, reductive amination being one of the most powerful and useful methods. However, the reductive amination of camphor and fenchone remains a challenge. A standard approach to reductive amination with amines other than ammonia and methylamine includes two steps: preparation of azomethines or Schiff bases in the presence of strong Lewis acids and their reduction with more or less conventional reducing agents. The synthesis of fenchonyl amines is even more challenging. There is no universal approach, and almost every manuscript reports some particular protocol different from others. In most cases, the first stage of this process requires quite harsh conditions. For example, the preparation of a Schiff base from camphor and 1-phenylethylamine requires 5-10 days of heating at 150°C.[3] Schiff bases of other primary amines could be prepared under similarly harsh conditions. Preparation of enamines is possible using titanium tetrachloride as a catalyst. The reduction also might be challenging. Sodium borohydride or sodium cyanoborohydride was described as suitable for this goal in several reports.[4] To the best of our knowledge, no papers describe any general approach for the direct reductive amination of camphor or fenchone. There is only one example of camphor direct reductive amination without an external hydrogen source using carbon monoxide as a reducing agent. This protocol is very efficient but its application is limited by the necessity of carbon monoxide and high-pressure equipment for the reaction setup.