COUNTING ROOTED EULERIAN MAPS ON THE PROJECTIVE PLANE

1IntroductionAsurfaceisacompactclosed2-manifold.Theorielltable(non-orielltable)surfaceofgenuskisthespherewitllkhandles(crosscaPs)denotedbySk(Nk).AmapMollSk(Nk)meansthatitsunderlyinggraphnlaybedrownou(embeddedin)itsuchthatllthpairofedgesintersectataninnerpoilltalldeachfaceishomeomorphictothedisc.Amapisrootedifanedgewithadirectiollalongtheedge,alldasideoftl1eedgeisdistinguisl1ed.Tworootedmapsareconsideredtobethesal11eifthereisanisomorphismpreserviIlgtl1erooting.ArootedEuleriall1llapissuchaon…     

Inversion Properties of n-Alkane Phosphonic Acids Stabilized Emulsions: HLB Dependence

The emulsifier properties of n-alkane phosphonic acids (C10H21PO3H2; C12H25PO3H2 and C13H27PO3H2) and their mono- and di-sodic salts were studied, with emphasis on the morphological and dynamical inversion properties as a function of their neutralization degree. Maximum stabilization properties were appreciated for C10PO3H2 and C12PO3H2 while not for C13PO3H2. Such fact is associated to their odd number of carbon atoms chain, which is the origin of the intrachain constraints on the tail-chain flexibility.     

Some Alternating Double Binomial Sums

We consider some new alternating double binomial sums. By using the Lagrange inversion formula, we obtain explicit expressions of the desired results which are related to a third-order linear recursive sequence. Furthermore, their recursive relation and generating functions are obtained.     

类克尔介质对二能级原子与压缩相干态相互作用的影响

通过研究原子反转和光子数统计分布,讨论包含类克尔介质的双光子二能级原子与压缩相干态相互作用的量予特性.结果表明,在类克尔介质与模场的耦合强度为原子与模场耦合强度的两倍以上时,原子与模场耦合的作用不明显.     

A new matrix inverse

We compute the inverse of a specific infinite-dimensional matrix, thus unifying a number of previous matrix inversions. Our inversion theorem is applied to derive a number of summation formulas of hypergeometric type.

     

The role of crystallographic angle in characterizing and modeling apatite fission-track length data

Recent experimental work on apatite fission-track length measurement has documented a number of factors that can exert a considerable influence on determinations of mean length. The principal source of length variation is anisotropy of annealing and etching behavior with respect to crystallographic angle. Procedural and environmental factors that influence which angular populations are preferentially sampled during measurement lead to variations in mean length that exceed standard statistical predictions. This paper evaluates the possibility of using c-axis projection to remove angular effects, and thus make length data more reproducible and informative.     

混合结构的闭环光纤陀螺研究

提出并研制了混合结构的闭环光纤陀螺系统。详细分析了该系统的结构特点、信号检测方法以及反馈信号对系统的影响。该系统具有低损耗、长期低漂移特性。实现了３００ｄｅｇ．／ｓ的动态范围及小于３００×１０－６的线性误差。     

Heptaphyrins: Expanded porphyrins with seven heterocyclic rings

Expanded porphyrins containing seven pyrrole/heterocyclic rings linked in a cyclic fashion are termed heptaphyrins. The number ofπ-electrons in heptaphyrins depends on the number ofmeso carbon bridges used to link the heterocyclic rings, accordingly heptaphyrins with 28π-electrons and 30π-electrons are reported to date. Both condensation reactions of the appropriate precursors and acid-catalysed oxidative coupling reactions have been utilized to synthesise the heptaphyrins. The 30π heptaphyrins exhibit rich structural diversity where some of the heterocyclic rings in the macrocycle undergo a 180° ring flipping. An overview of the synthetic methods employed for the synthesis of heptaphyrins, their spectroscopic properties, structural behaviour and aromatic properties are highlighted in this paper. Dedicated to Professor C N R Rao on his 70th birthday