Derivation of baroclinic Ertel–Rossby invariant-based thermally-coupled vorticity equation in moist flow

For the potential vorticity （PV） invariant, there is a PV-based complete-form vorticity equation, which we use heuris- tically in the present paper to answer the following question： for the Ertel-Rossby invariant （ERI）, is there a corresponding vorticity tendency equation？ Such an ERI-based thermally-coupled vorticity equation is derived and discussed in detail in this study. From the obtained new vorticity equation, the vertical vorticity change is constrained by the vertical velocity term, the term associated with the slope of the generalized momentum surface, the term related to the horizontal vorticity change, and the baroclinic or solenoid term. It explicitly includes both the dynamical and thermodynamic factors＇ influence on the vorticity change. For the ERI itself, besides the traditional PV term, the ERI also includes the moisture factor, which is excluded in dry ERI, and the term related to the gradients of pressure, kinetic energy, and potential energy that reflects the fast-manifold property. Therefore, it is more complete to describe the fast motions off the slow manifold for severe weather than the PV term. These advantages are naturally handed on and inherited by the ERI-based thermally-coupled vorticity equation. Then the ERI-based thermally-coupled vorticity equation is further transformed and compared with the traditional vorticity equation. The main difference between the two equations is the term which describes the contribution of the solenoid term to the vertical vorticity development. In a barotropic flow, the solenoid term disappears, then the ERI-based thermally-coupled vorticity equation can regress to the traditional vorticity equation.     

超高效液相色谱-串联质谱法定量分析尿液中色氨酸及其代谢产物

基于超高效液相色谱-串联质谱(UPLC-MS/MS)建立定量分析色氨酸(Trp)及代谢产物3-OH-犬尿氨酸(3-OH-Kyn)、3-OH-邻氨基苯甲酸(3-OH-AA)、黄尿酸(XA)、犬尿氨酸(Kyn)、5-羟基吲哚乙酸(5-HIAA)、犬尿喹啉酸(KA)和5-羟色胺(5-HT)的方法,应用该方法分析其在尿样中的含...     

On the finiteness of differential invariants

In this paper we show how Weil's theory of near points yields a new light on the classical approaches to the study of the differential invariants of a sheaf of tangent vector fields. We give conditions for the existence of invariant derivations for a sheaf of tangent vector fields, which allows to apply Lie's algorithm to obtain new differential invariants as quotients of Jacobian determinants of known ones. We give sufficient conditions for the asymptotic stability of the symbol of a sheaf of tangent vector fields and prove our main result, a finiteness theorem for the differential invariants of a sheaf of Lie algebras which simplifies and improves on the treatment given in J. Differential Geom. 10 (1975) 249-416.     

形式三角矩阵环的导子和自同构

本文研究了形式上三角矩阵环Tri(A,M,B)的导子和自同构,利用与单位元相乘的方法,获得了形式上三角矩阵环Tri(A,M,B)的导子和自同构的结构形式.     

论平面上的可求长曲线

本文利用Hausdorff分数型导数与积分理论给出平面上可求长曲线的积分表 达式.     

Central simple Poisson algebras

Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded.     

N，N′-二苄基-苯并咪唑四氯合铜(Ⅱ)化合物的合成、结构和性能研究(英)

A novel N，N′-dibenzyl-benzimidazolium tetrachlorocuprate(Ⅱ) complex, [C₂₁H₁₉N₂]₂[CuCl₄], was synthesized and its crystal structure was determined by X-ray diffraction. It crystallizes in monoclinic system, space group P2/c, a=1.203 9(2) nm, b=0.975 0(2) nm, c=1.878 2(6) nm, β=114.12(2)°, V=2.012 2(8) nm³. Its structure was identified by EA, IR and UV spectra and characterized by electrochemistry, thermal and magnetic property. The Cu(Ⅱ) atom of [CuCl₄]^2- has distorted tetrahedral coordination geometry. In the crystal structure, there are strong extensive C-H…Cl hydrogen bonds and π-π stacking interactions, which stabilized the crystal structure. CCDC: 221570.     

Basic Derivations for Subarrangements of Coxeter Arrangements

We prove that various subarrangements of Coxeter hyperplane arrangements are free. We do this by exhibiting a basis for the corresponding module of derivations. Our method uses a theorem of Saito [24] and Terao [30] which checks for a basis using certain divisibility and determinantal criteria. As a corollary, we find the roots of the characteristic polynomials for these arrangements, since they are just one more than the degrees in any basis of the module. We will also see some interesting applications of symmetric and supersymmetric functions along the way.