Let K be a field and G a finite group. The question of 'admissibility' of G over K was originally posed by Schacher, who gave partial results in the case K = Q. In this paper, we give necessary conditions for admissibility of a finite group G over function fields of curves over complete discretely valued fields. Using this criterion, we give an example of a finite group which is not admissible over Q p (t). We also prove a certain Hasse principle for division algebras over such fields.
In this paper, we consider impulsive integro-differential equations in Banach space and we establish the bound on the difference between two approximate solutions. We also discuss nearness and convergence of solutions of the problem under consideration. The impulsive integral inequality of Grownwall type is used to obtain results.
Mathematical Subject Classification
Soft set theory introduced by D. Molodstov is a new theory which deals with uncertainty. Connected graphs can be represented by using soft sets called soft graphs. In the present paper, we introduce the tabular representation of soft graph and define radius, diameter, center and degree of soft graph. We also define union, product of soft graphs and soft trees. We then derive some properties of radius, degree of vertex in soft graph and soft trees.
The theory of soft set offers a mathematical tool to deal with uncertainty. Nowadays, work on soft graph theory is progressing rapidly. In this paper, we define connected soft graph and derive some results. We also define cut vertex and bridge of soft graph along with some results on it.
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