虚二次域上不可分的正定Hermite型的构作

本文给出了构作虚二次域ＩＱ（－ｍ）上不可分的正定整Ｈｅｒｍｉｔｅ型的方法．对任意给定的自然数ｎ，ｄ和无平方因子的ｍ，当ｍ３（ｍｏｄ４），除了ｍ＝１时ｎ＝２，ｄ＝１；ｎ＝３，ｄ＝１，３；ｎ＝５，ｄ＝１和ｍ＝２时ｎ＝３，ｄ＝１这５个例外，证明了存在ＩＱ（－ｍ）上不可分的正定整Ｈｅｒｍｉｔｅ格，其秩为ｎ且判别式为ｄ，并给出它们的明确结构．在上述５个例外情形下，不存在具有上述性质的格．

不可分的正定Hermite型 (英文)

设Q（√-m）是类数为1的虚二次域，且Dm为它的整数环。本文证明了：对任给给定的自然数n和d，除了19个例外，常存在不可分的n秩正定HermiteDm一格，其判别式为d。在例外情形下，不存在具有上述性质的格。本文对二秩正定HermiteDm格处理的方法可应用于任意的m≡3（mod4）的情形。

虚二次域上的不可分正定整Hermite型

用格论方法证明了虚二次域 F=Q( mi) ( m≡ 3( mod4 )且 m无平方因子 )上存在任意秩 n判别式d(自然数 )的不可分正定整 Hermite型 ,但有下列例外 :Q( 3i) :n=2 ,d=1 ,2 ,4 ,1 0 ;n=3,d=1 ,2 ,5 ;n=4 ,d=1 ,2 ;n=5 ,d=1 ;n=7,d=1 ;Q( 7i) :n=2 ,d=1 ;Q( 1 1 i) :n=2 ,d=2 ;n=3,d=1 ,不存在相应的不可分正定整 Hermite型 .

Form Invariance and Conserved Quantity for Non-holonomic Systems with Variable Mass and Unilateral Constraints

The paper studies the form invariance and a type of non-Noether conserved quantity called Mei conserved quantity for non-holonomic systems with variable mass and unilateral constraints. Acoording to the invariance of the form of differential equations of motion under infinitesimal transformations, this paper gives the definition and criterion of the form invariance for non-holonomic systems with variable mass and unilateral constraints. The condition under which a form invariance can lead to Mei conservation quantity and the form of the conservation quantity are deduced. An example is given to illustrate the application of the results.

CONSTRUCTION OF INDECOMPOSABLEDEFINITE HERMITIAN FORMS

This Paper gives a method to construct indecomposable positive definite integral Hermitianforman imnginary quadratic field Q with gin discriminant and g。n rank.It is shown that for ally natural numbers n and a, there are n-ary Indecomposable positivedefinite intopal Herlllltian lattices over Q(resp. Q)with discriminant a, exceptfor four(resp. one) exceptions. In these exceptional cases there are no lattices with the desiredproperties.