The paper deals with a comprehensive theory of mappings, whose local behavior can be described by means linear subspaces, contained in the graphs two (primal and dual) generalized derivatives. This class mappings includes graphically Lipschitzian thus number multifunctions, frequently arising optimization equilibrium problems. developed makes use new derivatives, provides us some calculus rules...

The relation between two–dimensional integrable systems and four–dimen-sional self–dual Yang–Mills equations is considered. Within the twistor description and the zero–curvature representation a method is given to associate self–dual Yang-Mills connections with integrable systems of the Korteweg–de Vries and non–linear Schrödinger type or principal chiral models. Examples of self–dual connectio...

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat R. We show how all such connections lie in the orbit of the flat connection on R under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mill...

A one to one correspondence between regular generalized bent functions from Fn2 to Z2m , and m−tuples of Boolean bent functions is established. This correspondence maps selfdual (resp. anti-self-dual) generalized bent functions to m−tuples of self-dual (resp. anti self-dual) Boolean bent functions. An application to the classification of regular generalized bent functions under the extended aff...

Let $A_1$, $A_2$ be unital Banach algebras and $X$ be an $A_1$-$A_2$- module. Applying the concept of module maps, (inner) modulegeneralized derivations and  generalized first cohomology groups, wepresent several results concerning the relations between modulegeneralized derivations from $A_i$ into the dual space $A^*_i$ (for$i=1,2$) and such derivations  from  the triangular Banach algebraof t...

In the field of deep neural network, model compression has been widely used. As a method, knowledge distillation studied more and widely. Most existing methods need lot data to train teacher in advance, interaction between their student is often weak. The such as DML are constrained by loss realize soft weight sharing, there little work discuss hard sharing. Therefore, new interactive online me...

In this paper we start developing the so-called Klein’s formalism on dual Lie algebroids. The nonlinear connection associated to a regular section is naturally obtained. Particularly, this connection is found for the Hamiltonian case. Mathematics Subject Classification: 17B66, 53C05.

We introduce some approximate optimal solutions and a generalized augmented Lagrangian in nonlinear programming, establish dual function and dual problem based on the generalized augmented Lagrangian, obtain approximate KKT necessary optimality condition of the generalized augmented Lagrangian dual problem, prove that the approximate stationary points of generalized augmented Lagrangian problem...