Titlebook: On Global Univalence Theorems; T. Parthasarathy Book 1983 Springer-Verlag Berlin Heidelberg 1983 Differenzierbare Abbildung.Finite.Funktio

intricacy

Ischemia

a big challenge in real-world applications due to the sparse, noisy and ambiguous nature of queries. In this paper, we present another important issue called “the pomegranate phenomenon”. This phenomenon is named for the gap between manually manageable small taxonomy and massive coherent topics in

生命

P-matrices and N-matrices,e global univalence results due to Gale, Nikaido and Inada. We will also see the interrelation between P-matrices and positive quasi-definite matrices. Finally we examine the question whether P-property holds good under multiplication (sum) of two P-matrices — this kind of result is useful in determ

Myofibrils

Adj異類的

Global homeomorphisms between finite dimensional spaces,y the line lifting property. We will show that this property is equivalent to a limiting condition (which in many cases easy to verify) which we call by L. We will use this condition L to derive several results on global homeomorphisms due to Roy Plastock. We will prove an approximation theorem due

頌揚(yáng)國家

eczema

Global univalent results in R2 and R3,ever the following two interesting open problems posed by Gale-Nikaido remain unanswered : (i) Suppose F is a differentiable map from a rectangular region μ ? R. to R.. Suppose the Jacobian is non-vanishing and every entry in the Jacobian is non-negative. Is F one-one? (ii) Suppose F is a differenti

羽飾

On the global stability of an autonomous system on the plane, system on the plane and extend a result of Olech using some of the recent global univalent theorems (see [52]). We present also a variety of examples to show the sharpness of the results. In the second half of this chapter we present the results obtained by Vidossich [71] in this direction.

呼吸

Univalence for mappings with Leontief type Jacobians, to Gale-Nikaido‘s theorem on univalence. Here we prove a result due to Gale-Nikaido and this says that if F and F. are differentiable and if F. is monotonic increasing then the Jacobian of F is a P-matrix provided the Jacobian matrix of F is of Leontief type. The second result due to Nikaido says t

CLAP