Abstract : this paper provides the functional equation of general rooted maps with the number of inner faces , the rooted face valency and the number of non - rooted vertices as parameters on the torus , and gives an explicit expression of the enumerating function of these maps with the number of inner faces and of non - rooted vertices , then the number of these maps with the size as a parameter whose asymptotic result had been obtained in [ 2 ] is obtained as a corollary 文摘:这篇文章给出了环面上以内面个数,根面次和非根节点个数为参数的一般有根地图的计数方程,导出了以内面个数和非根节点个数为参数的这类地图的计数方程的精确解.作为推论,推出了以边数为参数的这类地图的个数,其近似解在文献[ 2 ]中已讨论
In manganite perovskites , substitution of divalent ions ( alkaline earth metals viz . ca , sr , ba ) in the a sublattice , introduces mn4 + ions or holes into the system . it is generally considered that the concentration of holes is equal to the concentration of divalent cations because of the charge compensation by controlled valencies 在类钙钛矿型晶体结构中通过掺入二价碱土金属(如ca ， sr ， ba )可以在系统中产生mn ~ ( 4 + )或氧空位，由价格补偿的原理，理论上掺入的二价离子的浓度和氧空位的浓度相等。
Ca , sr , ba ) in the a sublattice , introduces mn4 + ions or holes into the system . it is generally considered that the concentration of holes is equal to the concentration of divalent cations because of the charge compensation by controlled valencies . a number of publications exist in the literature on the synthesis of manganite perovskites 在类钙钛矿型晶体结构中通过掺入二价碱土金属(如ca ， sr ， ba )可以在系统中产生mn ~ ( 4 + )或氧空位，由价位补偿的原理，理论上掺入的二价离子的浓度和氧空位的浓度相等。
