A new type additive was added to the non-self-fluxing copper powdered alloy, and the powder showed satisfactory performance of spraying and fusing, self-protecting, and self-fluxing in the oxygen-acetylene flame spray...A new type additive was added to the non-self-fluxing copper powdered alloy, and the powder showed satisfactory performance of spraying and fusing, self-protecting, and self-fluxing in the oxygen-acetylene flame spraying and fusing process. The additive was melted and could absorb copper oxide when spraying, then it created a layer of film to cover the copper liquid, which protected the copper liquid from oxidizing efficiently and promoted it wetting on iron surface. Thus it lead to real diffusion between Cu and Fe, which resolved the diffwulty of combining Cu with Fe and reduced the limitation of the powder, and it promoted the usage value of general powder. Through analysis of microstructures, it was found that the fastness and compactness of the combining interface was excellent as well as the diffusing of transition area, and the hardness was suitable, which meant that the performance could meet the needs of high quality valves completely.展开更多
In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators,in two and three spatial dimensions.Indeed,in the multidimensional case very few results are known on t...In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators,in two and three spatial dimensions.Indeed,in the multidimensional case very few results are known on the location of the eigenvalues.This leads to solve nonlinear eigenvalue problems.In introduction we begin with a review of theoretical results and numerical results obtained for the one dimensional case.Then we present the numerical methods developed to compute the spectra(finite difference discretization)for the two and three dimensional cases.The numerical results obtained are presented and analyzed.One difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are unstable.This work is in continuity of a previous work in one spatial dimension[3].展开更多
Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A...Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.展开更多
In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a resi...In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.展开更多
A version of the ＂Fredholm index = spectral flow＂ theorem is proved for general families of elliptic operators （A（t）}t∈R on closed （compact and without boundary） manifolds. Here we do not require that A（t）,...A version of the ＂Fredholm index = spectral flow＂ theorem is proved for general families of elliptic operators （A（t）}t∈R on closed （compact and without boundary） manifolds. Here we do not require that A（t）, t ∈R or its leading part is self-adjoint.展开更多
Ellis and Branton introduced a class of non-self-similar sete;they gave an upper bound of Hausdorff dimension for such sets,and a conjecture of the lower bound for these sets.This paper gives a proof of this conjectur...Ellis and Branton introduced a class of non-self-similar sete;they gave an upper bound of Hausdorff dimension for such sets,and a conjecture of the lower bound for these sets.This paper gives a proof of this conjecture by using the lemma of Frostman.展开更多
文摘A new type additive was added to the non-self-fluxing copper powdered alloy, and the powder showed satisfactory performance of spraying and fusing, self-protecting, and self-fluxing in the oxygen-acetylene flame spraying and fusing process. The additive was melted and could absorb copper oxide when spraying, then it created a layer of film to cover the copper liquid, which protected the copper liquid from oxidizing efficiently and promoted it wetting on iron surface. Thus it lead to real diffusion between Cu and Fe, which resolved the diffwulty of combining Cu with Fe and reduced the limitation of the powder, and it promoted the usage value of general powder. Through analysis of microstructures, it was found that the fastness and compactness of the combining interface was excellent as well as the diffusing of transition area, and the hardness was suitable, which meant that the performance could meet the needs of high quality valves completely.
基金supported by the Fédération de Mathématiques des Pays de la Loire,CNRS FR 2962。
文摘In this article we are interested in the numerical computation of spectra of non-self adjoint quadratic operators,in two and three spatial dimensions.Indeed,in the multidimensional case very few results are known on the location of the eigenvalues.This leads to solve nonlinear eigenvalue problems.In introduction we begin with a review of theoretical results and numerical results obtained for the one dimensional case.Then we present the numerical methods developed to compute the spectra(finite difference discretization)for the two and three dimensional cases.The numerical results obtained are presented and analyzed.One difficulty here is that we have to compute eigenvalues of strongly non-self-adjoint operators which are unstable.This work is in continuity of a previous work in one spatial dimension[3].
基金Supported by the National Natural Science Foundation of China (Grant Nos. 10872084, 10472040)the Outstanding Young Talents Training Fund of Liaoning Province of China (Grant No. 3040005)the Research Program of Higher Educa-tion of Liaoning Province of China (Grant No. 2008S098)
文摘Non-self-adjoint dynamical systems, e.g., nonholonomic systems, can admit an almost Poisson structure, which is formulated by a kind of Poisson bracket satisfying the usual properties except for the Jacobi identity. A general theory of the almost Poisson structure is investigated based on a decompo- sition of the bracket into a sum of a Poisson one and an almost Poisson one. The corresponding rela- tion between Poisson structure and symplectic structure is proved, making use of Jacobiizer and symplecticizer. Based on analysis of pseudo-symplectic structure of constraint submanifold of Chaplygin’s nonholonomic systems, an almost Poisson bracket for the systems is constructed and decomposed into a sum of a canonical Poisson one and an almost Poisson one. Similarly, an almost Poisson structure, which can be decomposed into a sum of canonical one and an almost "Lie-Poisson" one, is also constructed on an affine space with torsion whose autoparallels are utilized to describe the free motion of some non-self-adjoint systems. The decomposition of the almost Poisson bracket di- rectly leads to a decomposition of a dynamical vector field into a sum of usual Hamiltionian vector field and an almost Hamiltonian one, which is useful to simplifying the integration of vector fields.
基金We thank the anonymous referees for their valuable comments and suggestions which lead to an improved presentation of this paper. This work was supported by NSFC under the grant 11371199, 11226334 and 11301275, the Jiangsu Provincial 2011 Program （Collaborative Innovation Center of Climate Change）, the Program of Natural Science Research of Jiangsu Higher Education Institutions of China （Grant No. 12KJB110013）, Natural Science Foundation of Guangdong Province of China （Grant No. S2012040007993） and Educational Commission of Guangdong Province of China （Grant No. 2012LYM0122）.
文摘In this paper, we study a weakly over-penalized interior penalty method for non-self- adjoint and indefinite problems. An optimal a priori error estimate in the energy norm is derived. In addition, we introduce a residual-based a posteriori error estimator, which is proved to be both reliable and efficient in the energy norm. Some numerical testes are presented to validate our theoretical analysis.
文摘A version of the ＂Fredholm index = spectral flow＂ theorem is proved for general families of elliptic operators （A（t）}t∈R on closed （compact and without boundary） manifolds. Here we do not require that A（t）, t ∈R or its leading part is self-adjoint.
文摘Ellis and Branton introduced a class of non-self-similar sete;they gave an upper bound of Hausdorff dimension for such sets,and a conjecture of the lower bound for these sets.This paper gives a proof of this conjecture by using the lemma of Frostman.
