An admissible Poisson algebra (or briefly, an adm-Poisson algebra) gives equivalent presentation with only one operation for a algebra. We establish bialgebra theory algebras independently and systematically, including but beyond the corresponding results on bialgebras given in [27]. Explicitly, we introduce notion of which are to Manin triples as well bialgebras. The direct correspondence betw...

We establish the Leray–Schauder type theorems for very general classes of multifunctions, which are called admissible. Our admissible classes contain compositions of important multifunctions in nonlinear analysis and algebraic topology. Moreover, our arguments are elementary, without using the concept of degree of maps or theory of homotopy extensions. The Leray–Schauder principle [LS], one of ...

Classification is a learning function that maps a given data item into one of several predefined classes. It is a data analysis technique that extracts models describing important data classes and predicts future values. Basically, classification techniques have better capability to handle a wider variety of datasets than regression. It can also be described as a supervised learning algorithm i...

We introduce methods for identifying operator preconditions that need not be expanded further. The methods are proved to be admissible , that is, they will not cause a solution to be missed when one exists. In certain cases, the methods also identify operator reformulations that increase the number of nonexpandable preconditions. This approach provides effective loop control in common situation...