Let B n be the unit ball in C n, we study ε-starlike mappings on B n. The upper bounds of second order item coefficients of homogeneous expansion for ε-starlike mappings are obtained.
A method of three-dimensional loaded slope stability for anisotropic and nonhomogeneous slopes was presented based on the upper-bound theorem of the limit analysis approach. The approach can be considered as a modific...A method of three-dimensional loaded slope stability for anisotropic and nonhomogeneous slopes was presented based on the upper-bound theorem of the limit analysis approach. The approach can be considered as a modification and extension of the solutions. The influences of friction angle, anisotropy factor, nonhomogeneous factor, slope angle, ratio of width to depth, and load on the slope crest were investigated. The results show that solutions are suitable to deal with the purely cohesive soils and frictional/cohesive soils, isotropic and anisotropic, homogeneous and nonhomogeneous, loaded and unloaded cases.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 B n be the unit ball in C n, we study ε-starlike mappings on B n. The upper bounds of second order item coefficients of homogeneous expansion for ε-starlike mappings are obtained.
基金Projects(41002095,41172251,41272317) supported by the National Natural Science Foundation of China
文摘A method of three-dimensional loaded slope stability for anisotropic and nonhomogeneous slopes was presented based on the upper-bound theorem of the limit analysis approach. The approach can be considered as a modification and extension of the solutions. The influences of friction angle, anisotropy factor, nonhomogeneous factor, slope angle, ratio of width to depth, and load on the slope crest were investigated. The results show that solutions are suitable to deal with the purely cohesive soils and frictional/cohesive soils, isotropic and anisotropic, homogeneous and nonhomogeneous, loaded and unloaded cases.
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）.
