‎let $n$ and $k$ be two positive integers‎, ‎$kleq n$ and $a$ be an $n-$square quaternion matrix‎. ‎in this paper‎, ‎some results on the $k-$numerical range of $a$ are investigated‎. ‎moreover‎, ‎the notions of $k$-numerical radius‎, ‎right $k$-spectral radius and $k$-norm of $a$ are introduced‎, ‎and some of their algebraic properties are studied‎.

Lattice paths in the quarter plane have led to a large and varied set of results recent years. One major project has been classification step sets according properties corresponding generating functions, this involved variety techniques, some highly intricate specialised. The famous Kreweras reverse walk models are two particularly interesting models, as they among only four cases which algebra...

A permutation is said to be a square if it can be obtained by shuffling two order-isomorphic patterns. The definition is intended to be the natural counterpart to the ordinary shuffle of words and languages. In this paper, we tackle the problem of recognizing square permutations from both the point of view of algebra and algorithms. On the one hand, we present some algebraic and combinatorial p...

Various theoretical equations have been proposed to predict response rate as a function of the rate of reinforcement. If both the rate and probability of reinforcement are considered, a simple identity, defining equation, or "law" holds. This identity places algebraic constraints on the allowable forms of our mathematical models and can help identify the referents for certain empirical or theor...

Abstract A four-quadrant analog multiplier using a novel type of GaAs transistor is presented. This device, called 2-D MESFET, is dedicated to low power and high speed applications[1],[2]. A special architecture for the multiplier was designed by taking advantage of the dual-gate structure of the 2-D MESFET. The circuit relies on the square algebraic identity [8], with the squaring operation re...

In this paper, application of the complexity reduction approach based on halfand quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermo...