This paper deals with generalized semi-infinite optimization problems where the (infinite) index set of inequality constraints depends on the state variables and all involved functions are twice continuously differentiable. Necessary and sufficient second order optimality conditions for such problems are derived under assumptions which imply that the corresponding optimal value function is seco...

Generalized semi-infinite optimization problems (GSIP) are considered. It is investigated how the numerical methods for standard semi-infinite programming (SIP) can be extended to GSIP. Newton methods can be extended immediately. For discretization methods the situation is more complicated. These difficulties are discussed and convergence results for a discretizationand an exchange method are d...

The direct product of two Fibonacci tilings can be described as a genuine stone inflation rule with four prototiles. This admits various modifications, which lead to 48 different rules, known the variations. They all result in that are measure-theoretically isomorphic by Halmos–von Neumann theorem. cut and project sets characteristic windows two-dimensional Euclidean internal space. Here, we an...

The purpose of this study is to construct the concept direct product bitonic algebras, and investigate some respective features. Also, commutative homomorphism are studied. Then notion algebras expanded finite family their qualifications practised.

We propose a generalization of the external direct product concept to polyadic algebraic structures which introduces novel properties in two ways: arity can differ from that constituents, and elements different multipliers be \textquotedblleft entangled\textquotedblright\ such is no longer componentwise. The main property we want preserve associativity, gained by using associativity quiver tech...