Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the i...Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.展开更多
To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound the...To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound theorem of limit analysis and the Hoek-Brown nonlinear failure criterion, the supporting pressure derived from the virtual work rate equation is regarded as an objective function to achieve optimal calculation. By employing variational calculation to optimize the objective function, an upper bound solution for the supporting pressure and the collapsing block shape of a shallow square tunnel are obtained. To evaluate the validity of the failure mechanism proposed in this paper, the solutions computed by the curved failure mechanism are compared with the results calculated by the linear multiple blocks failure mechanism when the Hoek-Brown nonlinear failure criterion is converted into the Mohr-Coulomb linear criterion. The influences of rock mass parameters on the supporting pressure and collapsing block shape are discussed.展开更多
The main purpose of this article is to establish an effective version of the Grunwald-Wang theorem, which asserts that given a family of local characters Xv of Kv of exponent m, where v C S for a finite set S of prime...The main purpose of this article is to establish an effective version of the Grunwald-Wang theorem, which asserts that given a family of local characters Xv of Kv of exponent m, where v C S for a finite set S of primes of K, there exists a global character X of the idele class group CK of exponent m （unless some special case occurs, when it is 2m） whose local component at v is Xv. The effectiveness problem for this theorem is to bound the norm N（X） of the conductor of X in terms of K, m, S and N（Xv） （v C S）. The Kummer case （when K contains pro） is easy since it is almost an application of the Chinese remainder theorem. In this paper, we solve this problem completely in general case, and give three versions of bound, one is with GRH, and the other two are unconditional bounds. These effective results have some interesting applications in concrete situations. To give a simple example, if we fix p and l, one gets a good least upper bound for N such that p is not an /-th power rood N. One also gets the least upper bound for N such that lr ｜φ｜（N） and p is not an/-th power mod N. Some part of this article is adopted （with some revision） from the unpublished thesis by Wang （2001）.展开更多
文摘Let H be a separable infinite dimensional complex Hilbert space, and L（H） the algebra of all bounded linear operators on 3-t＇. The class of finite operators is the class of operators for which the distance of the identity operator I and the derivation range is maximal; where the derivation range of the operator A is defined by δA;δA ： L（H） -L（H） X- AX - XA. In this paper we present some properties of finite operators and give some classes of operators which are in the class of finite operators, and find for witch condition A ~ W is a finite operator in L（2-H H）, and gave a g6neralisation of Stampflli theorem.
基金supported by the National Natural Science Foundation of China (No. 51178468)the National Basic Research Program (973) of China (No. 2011CB013800)
文摘To analyze the stability of a shallow square tunnel, a new curved failure mechanism, representing the mechanical characteristics and collapsing form of this type of tunnel, is constructed. Based on the upper bound theorem of limit analysis and the Hoek-Brown nonlinear failure criterion, the supporting pressure derived from the virtual work rate equation is regarded as an objective function to achieve optimal calculation. By employing variational calculation to optimize the objective function, an upper bound solution for the supporting pressure and the collapsing block shape of a shallow square tunnel are obtained. To evaluate the validity of the failure mechanism proposed in this paper, the solutions computed by the curved failure mechanism are compared with the results calculated by the linear multiple blocks failure mechanism when the Hoek-Brown nonlinear failure criterion is converted into the Mohr-Coulomb linear criterion. The influences of rock mass parameters on the supporting pressure and collapsing block shape are discussed.
基金supported by National Basic Research Program of China(973 Program)(Grant No.2013CB834202)National Natural Science Foundation of China(Grant No.11321101)the One Hundred Talent’s Program from Chinese Academy of Sciences
文摘The main purpose of this article is to establish an effective version of the Grunwald-Wang theorem, which asserts that given a family of local characters Xv of Kv of exponent m, where v C S for a finite set S of primes of K, there exists a global character X of the idele class group CK of exponent m （unless some special case occurs, when it is 2m） whose local component at v is Xv. The effectiveness problem for this theorem is to bound the norm N（X） of the conductor of X in terms of K, m, S and N（Xv） （v C S）. The Kummer case （when K contains pro） is easy since it is almost an application of the Chinese remainder theorem. In this paper, we solve this problem completely in general case, and give three versions of bound, one is with GRH, and the other two are unconditional bounds. These effective results have some interesting applications in concrete situations. To give a simple example, if we fix p and l, one gets a good least upper bound for N such that p is not an /-th power rood N. One also gets the least upper bound for N such that lr ｜φ｜（N） and p is not an/-th power mod N. Some part of this article is adopted （with some revision） from the unpublished thesis by Wang （2001）.
