Partial differential equations with differential constraints

A geometric setting for constrained exterior differential systems on fibered manifolds with n-dimensional bases is proposed. Constraints given as submanifolds of jet bundles (locally defined by systems of first-order partial differential equations) are shown to carry a natural geometric structure, called the canonical distribution. Systems of second-order partial differential equations subjected to differential constraints are modeled as exterior differential systems defined on constraint submanifolds. As an important particular case, Lagrangian systems subjected to first-order differential constraints are considered. Different kinds of constraints are introduced and investigated (Lagrangian constraints, constraints adapted to the fibered structure, constraints arising from a (co)distribution, semi-holonomic constraints, holonomic constraints).     

ChemInform Abstract: A New n = 4 Layered Ruddlesden—Popper Phase K2.5Bi2.5Ti4O13 Showing Stoichiometric Hydration.

Polycrystalline K_2.5Bi_2.5Ti₄O₁₃ (I) is prepared by solid state reaction of KNO₃, Bi₂O₃, and TiO₂ (Al₂O₃ crucible, 750 °C, 16 h).     

Biomimetic total synthesis and structure confirmation of myrtucommulone K

A confirmed structure of meroterpenoid myrtucommulone K, which is vastly different from the originally reported one, is conducted. The first biomimetic total synthesis towards the assignment of its absolute configuration has been efficiently accessed in 5 steps, and key to the success was a heteroatom Diels-Alder cycloaddition. The structure of myrtucommulone K was re-elucidated and confirmed by extensive spectroscopic interpretation of 1D and 2D NMR.     

Enantioselective Synthesis of (+)-Mitomycin K by a Palladium-Catalyzed Oxidative Tandem Cyclization

The mitomycins, a family of bioactive natural products, feature a compact 6/5/5-fused polycyclic ring structure densely decorated with highly reactive and/or fragile quinone, amino ketal, and aziridine as well as carbamate moieties. It is this striking feature that has defeated numerous synthetic attempts towards these apparently small molecules, rendering them one of the most formidable targets for total synthesis. We herein report the first enantioselective synthesis of (+)-mitomycin K, a representative of G series mitomycins. The key step of this synthesis is an enantioselective oxidative cyclization catalyzed by a palladium/(+)-sparteine system that had previously been developed by our group. The robustness of this method bodes well for further applications in the asymmetric total synthesis of natural products, particularly those with characteristic 6/5/5-fused pyrroloindole skeletons.     

Anti-inflammatory chromone alkaloids and glycoside from Dysoxylum binectariferum

Herein we report isolation of a new chromone alkaloid chrotacumine K (12) from fruits and a chromone glycoside schumaniofioside A (13) from leaves of Dysoxylum binectariferum Hook f. Schumaniofioside A is reported for the first time from Meliaceae family. Other known alkaloids isolated include rohitukine (1) and chrotacumine E (6). The structure of new alkaloid 12 was elucidated on the basis of extensive 1D and 2D NMR analysis, synthesis and chemical hydrolysis. Chemically, chrotacumine K (12) is a 3′-O-acetyl rohitukine which on chemical or enzymatic hydrolysis produces rohitukine. The new alkaloid 12 is also present in seeds and stem-barks of this plant. The glycoside schumaniofioside A (13) is present only in leaves, and in abundance (～1% w/w of dried leaves). The isolated compounds and extracts were evaluated for in vitro effect on the proinflammatory cytokines (TNF-α and IL-6) in human monocytic THP-1 cells. The alkaloid 12 displayed potent inhibition (57%) of TNF-α at 0.3 µM, and was non-toxic to THP-1 cells up to 40 µM, indicating its excellent therapeutic window. Furthermore, a nitrobenzoyl ester analog 15e showed better inhibition of IL-6 than parent natural product chrotacumine K.     

On a Serrin-Type Regularity Criterion for the Navier–Stokes Equations in Terms of the Pressure

We prove a Serrin-type regularity result for Leray–Hopf solutions to the Navier–Stokes equations, extending a recent result of Zhou [28].     

Spectral Element Discretization of the Circular Driven Cavity. Part IV: The Navier-Stokes Equations

This paper deals with the spectral element discretization of the Navier-Stokes equations in a disk with discontinuous boundary data, which is known as the driven cavity problem. The numerical treatment does not involve any regularization of these data. Relying on a variational formulation in the primitive variables of velocity and pressure, we describe a discretization of these equations and derive error estimates in appropriate weighted Sobolev spaces. We propose an algorithm to solve the nonlinear discrete system and present numerical experiments to verify its efficiency.     

碳纳米管-TiO_2修饰电极伏安法测定维生素K_3

利用碳纳米管、二氧化钛两种纳米材料制成碳纳米管-TiO2复合膜修饰电极,进行了维生素K3电化学行为的研究。维生素K3在碳纳米管-TiO2复合膜修饰电极的电化学响应优于碳纳米管修饰电极,表明前者具有更好的催化作用。通过条件实验的优化,结果表明维生素K3在pH=9.42的氨水-NH4Cl底液中,富集时间为10s,富集电位于-0.60V,扫描速度为0.1V/s时有稳定的灵敏的氧化还原峰。峰电流与维生素K3浓度在3.0×10-6～8.0×10-5mol/L范围内呈良好的线性关系,检出限为5.0×10-7 mol/L。考查了修饰电极的重现性,5次平行测量的RSD为1.78%。该方法用于片剂药品中维生素K3含量的测定,回收率在97.5%～102%之间。     

Ce掺杂K_2La_2Ti_3O_(10)催化剂的可见光高效催化制氢的研究

采用高温固相法合成了铈掺杂的K2La2Ti3O10催化剂,利用X射线衍射(XRD)、紫外-可见漫反射(UV-visDRS)、透射电镜(TEM)和X射线光电子能谱(XPS)对催化剂进行了表征.考察了催化剂的可见光催化分解甲醇水溶液制氢的活性,并对可见光催化机理进行了分析.研究表明,铈的掺杂没有改变K2La2Ti3O10的微晶结构,并使催化剂粒径有所减小.紫外可见漫反射分析表明禁带宽度为2.3eV左右,对可见光具有较高吸收.XPS表明La和Ti为+3和+4价,而Ce则是+3和+4的混合价态.担载2wt%Pt后,在可见光下光催化活性大大提高,当铈的掺杂量为0.5mol%(即Ce取代La的摩尔百分量)时,光催化活性达到最大,产氢速率为0.05mmol/h;光照5h后产氢量为0.22mmol,而纯K2La2Ti3O10的产氢量只有0.037mmol.     

4-氯-7H-吡咯并[2,3-d]嘧啶与2,4-二氯-7H-吡咯并[2,3-d]嘧啶的合成研究

报道了以廉价易得的丙二酸二乙酯为起始原料,经过α-烷基化、环合、氯化、烯键氧化和SNAr/环化五步反应,高收率地得到目标产物4-氯-7H-吡咯并[2,3-d]嘧啶(6)和2,4-二氯-7H-吡咯并[2,3-d]嘧啶(10)(总收率分别达到45.8%和44.8%)的合成方法,并对中间体和产物的化学结构进行了表征.