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1.
In the paper [1], the author told us that he provides new proofs for the three classical theorems on real singularity theory: Mather′s two theorms, and the splitting lemma. And in the paper[2], the author used this method to catastrophe theory. The journal "Mathematical Reviews" ever commented the above papers successivelly in Vol.57, No.3 (1979) and Vol.58, No.3 (1979). This paper points out that the proofs about Mather's theorems I and Ⅱ in [1] are wrong, and then presents an counter-example to show that the corollary and conjecture are false.  相似文献   

2.
ON VECTOR VALUED ORLICZ SPACES   总被引:2,自引:0,他引:2  
The theory of vector valued Orlicz spaces generated by generalized N-functions wasintroduced by M.S.Skaff(see[1,2]).But the proofs of two main theorems in [2] areincorrect.In this paper,the author exhibits an example to show the incorrectness,givesthe correct proofs and improves one of those theorems.  相似文献   

3.
In this paper,the author introduces the concept of rotated vector fields in higher-dimensional spaces and proves some theorems which are similar to those in theory of rotatedvector fields in plane.Besides,some applications are given.  相似文献   

4.
In this paper, the author uses the topological degree theory to investigate the multiple solutions of nonlinear Fredholm integral equations in Banach spaces. Two new theorems aro obtained and two examples are given.  相似文献   

5.
In this paper, it is the first time ever to suggest that we study the model theory of all finite structures and to put the equal sign in the same situtation as the other relations. Using formulas of infinite lengths we obtain new theorems for the preservation of model extensions, submodels, model homomorphisms and inverse homomorphisms. These kinds of theorems were discussed in Chang and Keisler's Model Theory, systematically for general models, but Gurevich obtained some different theorems in this direction for finite models. In our paper the old theorems manage to survive in the finite model theory. There are some differences between into homomorphisms and onto homomorphisms in preservation theorems too. We also study reduced models and minimum models. The characterization sentence of a model is given, which derives a general result for any theory T to be equivalent to a set of existential-universal sentences. Some results about completeness and model completeness are also given.  相似文献   

6.
The main purpose of this paper is to generalize the study of the Hecke-Rogers type series,which are the extensions of truncated theorems obtained by Andrews,Merca,Wang and Yee.Our proofs rely heavily on the theory of Bailey pairs.  相似文献   

7.
In this note, the author discusses the problem of best simultaneous approximation by function pairs. The existence and characterization theorems of the best simultaneous approximation in L1 and L norms are obtained respectively, and some rezults of [ 1 ] are the special case of the theorems of the paper.  相似文献   

8.
We prove an oscillation theorem of two meromorphic functions whose derivatives share four values IM. From this we obtain some uniqueness theorems, which improve the corresponding results given by Yang [16] and Qiu [10], and supplement results given by Nevanlinna [9] and Gundersen [3, 4]. Some examples are provided to show that the results in this paper are best possible.  相似文献   

9.
This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.  相似文献   

10.
In this paper the author discusses the vector fields satisfying the conditions (C1) and (C2) and proves some theorems for the number of limit cycles of the plane autonomous systems. Some applications of the theorems and lemmas in §1 are given in §2.  相似文献   

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