In this paper, we studied the category of EQ-algebras and showed that it is complete, but not cocomplete, in general. We proved multiplicatively relative have coequlizers calculated coproduct pushout a special case. Also, constructed free EQ-algebra on singleton.

A special algebra called EQ-algebra has been recently introduced by Vilém Novák. Its original motivation comes from fuzzy type theory, in which the main connective is fuzzy equality. EQ-algebras have three binary operations meet, multiplication, fuzzy equality and a unit element. They open the door to an alternative development of fuzzy (manyvalued) logic with the basic connective being fuzzy e...

It is well-known that the Macfarlane-Biedenharn q-oscillator and its generalization has no Hopf structure, whereas the Hong Yan q-oscillator can be endowed with a Hopf structure. In this letter, we demonstrate that it is possible to construct a general q-oscillator algebra which includes the Macfarlane-Biedenharn oscillator algebra and the Hong Yan oscillator algebra as special cases. E-mail ad...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

We show that the arguments proposed by Park and Yee against our recent derivation of the statistical entropy of 2D black holes do not apply to the case under consideration PACS: 04.70. Dy, 04.50. +h E-Mail: [email protected] E-Mail: [email protected] In a recent Comment [1] Park and Yee claimed that derivation of the statistical entropy of 2D (two-dimensional) black holes proposed by us in Ref...

Using a formalism of minitwistors, we derive infinitely many conserved charges for the sl(∞)-Toda equation which accounts for gravitational instantons with a rotational Killing symmetry. These charges are shown to form an infinite dimensional algebra through the Poisson bracket which is isomorphic to two dimensional area preserving diffeomorphism with central extentions. E-mail address; be10@dk...

In this paper, we study and classify Hilbert space representations of cross product ∗-algebras of the quantized enveloping algebra Uq(e2) with the coordinate algebras O(Eq(2)) of the quantum motion group and O(Cq) of the complex plane, and of the quantized enveloping algebra Uq(su1,1) with the coordinate algebras O(SUq(1, 1)) of the quantum group SUq(1, 1) and O(Uq) of the quantum disc. Invaria...

EQ-algebras were introduced by Novak (2006) as an algebraic structure of truth values for fuzzy-type theory (FFT). Novák and De Baets (2009) various kinds such good, residuated, IEQ-algebras. In this paper, we define the notion (pre)ideal in bounded (BEQ-algebras) investigate some properties. Then, introduce a congruence relation on good BEQ-algebras using ideals, then, solve open problem Paad ...