the main purpose of this paper is to define a new regular matrix by using fibonacci numbers and to investigate its matrix domain in the classical sequence spaces $ell _{p},ell _{infty },c$ and $c_{0}$, where $1leq p

We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations. Local Lorentz invariance is treated as a gauge theory with the spin connection field taken in the so(3,1) enveloping algebra. The resulting theory appears to be...

We present a syntactic proof of cut-elimination for weak Grzegorczyk logic Go. The logic has a syntactically similar axiomatisation to Gödel–Löb logic GL (provability logic) and Grzegorczyk’s logic Grz. Semantically, GL can be viewed as the irreflexive counterpart of Go, and Grz can be viewed as the reflexive counterpart of Go. Although proofs of syntactic cut-elimination for GL and Grz have ap...

In this paper general mechanisms and syntactic restrictions are explored in order to specify and merge rule bases in the Semantic Web. Rule bases are expressed by extended logic programs having two forms of negation, namely strong (or explicit) and weak (also known as default negation or negation-as-failure). The proposed mechanisms are defined by very simple modular program transformations, an...

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...

In this paper general mechanisms and syntactic restrictions are explored in order to specify and merge rule bases in the Semantic Web. Rule bases are expressed by extended logic programs having two forms of negation, namely strong (or explicit) and weak (also known as default negation or “negation as failure”). The proposed mechanisms are defined by very simple modular program transformations, ...