Based on a study of basic properties of cyclic graphs of prime order, we give an algorithm for computing lower bounds of classical Ramsey numbers. Our algorithm reduces certain amount of computation of cyclic graphs of prime order, since only some of them normalized cyclic graphs require computation in our method. Using the algorithm, we construct ten cyclic graphs of prime order to obtain new ...

Previous research has shown that stimuli rendered invisible through masking can be sufficiently processed to induce nonconscious influences and facilitate subsequent recognition. However, masking paradigms are methodologically restricted such that stimuli cannot be presented for longer than a few tens of milliseconds, potentially restricting the strength of nonconscious influences. By adapting ...

The purpose of this paper is to introduce new concepts in a module  over ring , the first one called e*- small essential submodule, which generalization second concept called e*-radical submodule radical and last e* - hollow module. We will prove some properties all these concepts.

We obtain character formulas of minimal affinizations of representations of quantum groups when the underlying simple Lie algebra is orthogonal and the support of the highest weight is contained in the first three nodes of the Dynkin diagram. We also give a framework for extending our techniques to a more general situation. In particular, for the orthogonal algebras and a highest weight support...

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

The modularity of a modular multilevel dc converter (MMDC) makes it attractive for medium voltage distribution systems. Inherent balance submodule (SM) capacitor voltages is considered as an ideal property which avoids complex sorting process based on many measurements thereby reducing costs and enhancing reliability. This paper extends the inherent concept previously shown square-wave modulati...

Many observations about coalgebras were inspired by comparable situations for algebras. Despite the prominent role of prime algebras, the theory of a corresponding notion for coalgebras was not well understood so far. Coalgebras C over fields may be called coprime provided the dual algebra C∗ is prime. This definition, however, is not intrinsic it strongly depends on the base ring being a field...

We show that the classical discrete logarithm problem over prime fields can be reduced to that of solving a system of linear modular equations.