In this note first we define a BCK‐algebra on the states of a deterministic finite automaton. Then we show that it is a BCK‐algebra with condition (S) and also it is a positive implicative BCK‐algebra. Then we find some quotient BCK‐algebras of it. After that we introduce a hyper BCK‐algebra on the set of all equivalence classes of an equivalence relation on the states of a deterministic finite...

We construct a Teichmüller curve uniformized by the Fuchsian triangle group ∆(m, n, ∞) for every m < n ≤ ∞. Our construction includes the Teichmüller curves constructed by Veech and Ward as special cases. The construction essentially relies on properties of hypergeometric differential operators. For small m, we find bil-liard tables that generate these Teichmüller curves. We interprete some of ...

This paper presents a fast algorithm for generating triangle strips from triangulated meshes, providing a compact representation suitable for transmission and rendering of the models. A data structure that allows efficient triangle strip generation is also described. The method is based on simple heuristics, significantly reducing the number of vertices used to describe the triangulated models....

Let R be an Artin algebra and e idempotent of R. Assume that Tor (Re, G) = 0 for any G ∈ Gproj eRe i sufficiently large. Necessary sufficient conditions are given the Schur functor Se to induce a triangle-equivalence ⅅdef(R) ≃ ⅅdef(eRe). Combining this with result Psaroudakis et al. (2014), we provide necessary singular equivalence ⅅsg(R) ⅅsg(eRe) restrict GprojR GprojeRe. Applying these triang...

Let B(H) be the algebra of all bounded linear operators on a Hilbert space H and let N(⋅) norm B(H). For every 0≤ν≤1, we introduce w(N,ν)(A) as an extension classical numerical radius byw(N,ν)(A):=supθ∈R⁡N(νeiθA+(1−ν)e−iθA⁎) investigate basic properties this notion prove inequalities involving it. In particular, when is Hilbert–Schmidt ‖⋅‖2, present several weighted for operator matrices. Furth...

Abstract By rewriting the relation 1 + 2 = 3 {1+2=3} as {\sqrt{1}^{2}+\sqrt{2}^{2}=\sqrt{3}^{2}} , a right triangle is looked at. Some geometrical observations in connection with plane parqueting lead to an in...

In this paper, we introduce a notion of generalized states from an EQ-algebra E1 to another EQ-algebra E2, which is a generalization of internal states (or state operators) on an EQ-algebra E. Also we give a type of special generalized state from an EQ-algebra E1 to E1, called generalized internal states (or GI-state). Then we give some examples and basic properties of generalized (internal) st...

A C *-algebra A is called an ideal C * -algebra (or equally a dual algebra) if it is an ideal in its bidual A**. M.C.F. Berglund proved that subalgebras and quotients of ideal C*-algebras are also ideal C*-algebras, that a commutative C *-algebra A is an ideal C *-algebra if and only if it is isomorphicto C (Q) for some discrete space ?. We investigate ideal J*-algebras and show that the a...

With the aid of computer algebra systems COCO and GAP with its packages we are investigating all seven known primitive triangle-free strongly regular graphs on 5, 10, 16, 50, 56, 77 and 100 vertices. These graphs are rank 3 graphs, having a rich automorphism group. The embeddings of each graph from this family to other ones are described, the automorphic equitable partitions are classified, all...

let $a$ be a banach algebra and $x$ be a banach $a$-bimodule. then ${mathcal{s}}=a oplus x$, the $l^1$-direct sum of $a$ and $x$ becomes a module extension banach algebra when equipped with the algebra product $(a,x).(a',x')=(aa',ax'+xa').$ in this paper, we investigate biflatness and biprojectivity for these banach algebras. we also discuss on automatic continuity of derivations on ${mathcal{s...