Based on the Buşneag’s model ([2, 3, 4]), the notion of pseudovaluations (valuations) on a BE-algebra is introduced, and a pseudometric is induced by a pseudo-valuation on BE-algebras. Related properties are investigated, and conditions for a real-valued function on a BE-algebra to be a pseudo-valuation are discussed. Using the notion of (pseudo) valuation, we show that the binary operation in ...

OBJECTIVE When researchers evaluate brain-computer interface (BCI) systems, we want quantitative answers to questions such as: How good is the system's performance? How good does it need to be? and: Is it capable of reaching the desired level in future? In response to the current lack of objective, quantitative, study-independent approaches, we introduce methods that help to address such questi...

The goal of this paper is to describe, in as much detail as possible, the structure of the algebra of differential invariants of a Lie pseudo-group. Under the assumption of local freeness of the prolonged pseudo-group action, we develop algorithms for locating a finite generating set of differential invariants, establishing the recurrence relations for the differentiated invariants, and fixing ...

Our study shows that subjects can implicitly learn to use a steady-state visually-evoked potential (SSVEP) based brain computer interface (BCI). The SSVEP stimuli were presented in an immersive star field virtual environment. Within the star field the SSVEP stimuli appeared in a pseudo random order. Participants’ attention to the stimuli resulted in stars moving within the immersive space. Part...

The conjugacy problem for the pseudo-Anosov automorphisms of a compact surface is studied. To each pseudo-Anosov automorphism φ, we assign an AF -algebra Aφ (an operator algebra). It is proved that the assignment is functorial, i.e. every φ, conjugate to φ, maps to an AF algebra Aφ′ , which is stably isomorphic to Aφ. The new invariants of the conjugacy of the pseudo-Anosov automorphisms are ob...

The aim of this paper is to introduce the notions of (∈,∈ ∨ q)fuzzy p-ideals, (∈,∈ ∨ q)-fuzzy q-ideals and (∈,∈ ∨ q)-fuzzy a-ideals in BCIalgebras and to investigate some of their properties. Several characterization theorems for these generalized fuzzy ideals are proved and the relationship among these generalized fuzzy ideals of BCI-algebras is discussed. It is shown that a fuzzy set of a BCI...

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.