In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating fun...In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.展开更多
Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevan...Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevant conclusions in singularity theory, the plastic yield criterion is discussed in detail. We found that the most general form of the plastic yield criterionshould be f(J1,J2,J23 ) = 0.Obviously, this form is more precise than the form f(J1,J2,J3) = 0which is given in the usual literature. Finally, we shall also give some practical examples forexplanation.展开更多
Whitney＇s theorem is a famous theorem in the local singularity theory. In this paper, as an application of Malgrange preparation theorem, a generalized form of Whitney＇s theorem will be derived.
文摘In this paper, we define the generalized r-Whitney numbers of the first and second kind. Moreover, we drive the generalized Whitney numbers of the first and second kind. The recurrence relations and the generating functions of these numbers are derived. The relations between these numbers and generalized Stirling numbers of the first and second kind are deduced. Furthermore, some special cases are given. Finally, matrix representation of the relations between Whitney and Stirling numbers is given.
文摘Whitney's lemma is an important theorem in local singularity theory of germs of C∞functions.In this paper, we are going to prove the global version of this lemma. Based on thisgenerailized theorem and the relevant conclusions in singularity theory, the plastic yield criterion is discussed in detail. We found that the most general form of the plastic yield criterionshould be f(J1,J2,J23 ) = 0.Obviously, this form is more precise than the form f(J1,J2,J3) = 0which is given in the usual literature. Finally, we shall also give some practical examples forexplanation.
文摘Whitney＇s theorem is a famous theorem in the local singularity theory. In this paper, as an application of Malgrange preparation theorem, a generalized form of Whitney＇s theorem will be derived.
