Question

某个函数是restricted variation ，在数学中是什么意思

Answer 1

程序设计里对函数的各种限定词，在数学里没有对应物，数学里的函数就是一个对应法则而已。

Answer 2

截断变分函数
这是例句
Using the modified saddle point method together with the restricted variationmethod, considering effects of the mass polariaztion and relativisitc corrections, the energies, fine structure splitting, and the mean transition wave lenghts of the (1s2s2p) 4P 0 and (1s2p2p) 4P e doubly excited states for the isoelectrons sequences of lithium like ions from Be to S have been investigated. These results are compared with theoretical and the experimental data in other literatures 利用改进的马鞍点方法，截断变分方法，并考虑能量的相对论修正和质量极化效应，计算和研究了类理等电子系列的两个四重态（1s2p2p）4P0和（1s2s2p）4Pe态的精细结构和平均跃迁波长，并与实验和其它理论计算结果进行了比较。 The Rayleigh Ritz variational method is used with a multiconfiguration interaction function and restricted variation method to obtain the energies of 2p 2 n p 4S o ( n =2,3,4) and 1s2p m p 4P( m =2,3,4) in lithiumlike B 2+ and N 4+ , including the mass polarization and relativistic corrections. 利用多组态相互作用方法及 Rayleigh- Ritz变分法 ,计算了类锂 B2 +,N4 +三激发态2 p2 np4 So( n=2 ,3,4 )和 1s2 pmp4 P态 ( m=2 ,3,4 )的能量 ,并运用截断变分方法得到能量的改进量及考虑相对论修正、质量极化效应 ,获得了高精度的能量计算值 . The Rayleigh\|Ritz variational method is used with a multiconfiguration\|interaction function and restricted variation method to obtain the energies of 2p 2 n p 4S o( n =2—4)and 1s2p m p 4P( m =2,3)in lithium\|like ions,including the mass polarization and relativistic corrections. 利用多组态相互作用方法及Rayleigh Ritz变分法 ,计算了类锂离子 2 p2 np4 So(n =2— 4)和 1s2 pmp4 P(m =2 ,3)的能量 . 运用截断变分方法得到能量的改进量 . The Rayleigh-Ritz variational method is used with a multiconfiguration-interaction function and restricted variation method to obtain the energies of 1s 22s 2 1S, 1s 22s2p 1P o, 1s 22s2p 3P o and 1s 22p 2 3P in beryllium-like boron, including the mass polarization and relativistic corrections. 利用多组态相互作用方法及Rayleigh Ritz变分法 ,计算了类铍BⅡ 1s2 2s2 1 S ,1s2 2s2p1 Po,1s2 2s2p3Po 和 1s2 2p2 3 P激发态的能量 . 运用截断变分方法得到能量的改进量 . The saddle-point variational method is used with restricted variation method to obtain the energies of the core-excited states 1s2smd 4D e (m=3—7) and 1s2pnd 4D o(n=3—5) for lithium, including the mass polarization and relativistic corrections. 采用鞍点变分方法计算了锂内壳高激发四重态 1s2smd4De(m =3— 7)和 1s2pnd4Do(n =3— 5 )的能量 ,利用截断变分方法得到能量改进量 ,并计算了相对论修正、质量极化效应 ,从而获得了高精度的能量计算值 .

这是数学含义：
Lavrentiev现象在变分问题中是广泛存在的,严格地证明其存在性并不容易.新截断法是求解具有Lavrentiev现象的变分问题的奇性解的一种数值方法.根据新截断法的数学原理,给出了数值判定变分问题是否具有Lavrentiev现象的过程,并举出三个一维变分问题作为算例,验证了数值判定的有效性.

​给定一个开的有界集合ΩRn和一个函数f:Ω×Rm×Rmn→R=R∪{+∞},泛函定义为I(u)=∫Ωf(x,u(x),Du(x))dx.(1)考虑问题infu∈Ap其中允许函数空间Ap=A1∩W1,p(Ω;Rm)且A1 W1,1(Ω;Rm),p∈[1,+∞].称此变分问题具有I(u),(2)Lavrentiev现象如果infu∈A∞I(u)infu∈A1I(u).从1926