Let H be a subgroup of a finite group G and p be a prime.We say H is S_(p)-c-normal in G if there is a subnormal subgroup T of G such that G=HT and(H∩T)HG/HG is contained in the p-soluble hypercenter Z_(S_(p))(G/H_(G...Let H be a subgroup of a finite group G and p be a prime.We say H is S_(p)-c-normal in G if there is a subnormal subgroup T of G such that G=HT and(H∩T)HG/HG is contained in the p-soluble hypercenter Z_(S_(p))(G/H_(G))of G/H_(G),where S_(p)denotes the class of p-soluble groups.In this paper,we prove that G is p-soluble if certain classes of subgroups of G are S_(p)-c-normal in G,which generalizes the related known results.展开更多
An exact closed form of solution to the hyperradial Schrdinger equation is constructed for any generalcase comprising any hypercentral power and inverse-power potential.The hypercentral potential depends only on thehy...An exact closed form of solution to the hyperradial Schrdinger equation is constructed for any generalcase comprising any hypercentral power and inverse-power potential.The hypercentral potential depends only on thehyperradius,which itself is a function of Jacobi relative coordinates that are functions of particle positions(r_1,r_2,…...,r_N).This article is mainly devoted to the dernonstrat of the fact that any ψ of the form ψ=power series×exp(polynomial)=[f(x)exp(g(x))]is potentially a solution of the Schrdinger equation,where the polynomial g(x)is an ansatz dependingon the interaction potential.展开更多
基金supported in part by NSF of China(12071093,12071092)NSF of Guangdong Province(2021A1515010217).
文摘Let H be a subgroup of a finite group G and p be a prime.We say H is S_(p)-c-normal in G if there is a subnormal subgroup T of G such that G=HT and(H∩T)HG/HG is contained in the p-soluble hypercenter Z_(S_(p))(G/H_(G))of G/H_(G),where S_(p)denotes the class of p-soluble groups.In this paper,we prove that G is p-soluble if certain classes of subgroups of G are S_(p)-c-normal in G,which generalizes the related known results.
文摘An exact closed form of solution to the hyperradial Schrdinger equation is constructed for any generalcase comprising any hypercentral power and inverse-power potential.The hypercentral potential depends only on thehyperradius,which itself is a function of Jacobi relative coordinates that are functions of particle positions(r_1,r_2,…...,r_N).This article is mainly devoted to the dernonstrat of the fact that any ψ of the form ψ=power series×exp(polynomial)=[f(x)exp(g(x))]is potentially a solution of the Schrdinger equation,where the polynomial g(x)is an ansatz dependingon the interaction potential.
