It is known that the hybrid numbers are generalizations of complex, hyperbolic and dual numbers. Recently, they have attracted attention many scientists. At this paper, we provide Euler’s De Moivre’s formulas for 4×4 matrices associated with by using trigonometric identities. Also, give roots Moreover, some illustrative examples to support main formulas.

A recursive dynamic modeling of a three-DOF parallel robot, namely, threeRevolute-Prismatic-Spherical (3-RPS) parallel manipulator is reported in this work. Euler parameters are utilized to define the 3-DOF orientation of its moving platform, because the coordinates are free of singularity. For the dynamic modeling, the concept of the Decoupled Natural Orthogonal complement (DeNOC) matrices is ...

<abstract><p>In this note, we approximate the von Neumann and Rényi entropies of high-dimensional graphs using Euler-Maclaurin summation formula. The obtained estimations have a considerable degree accuracy. performed experiments suggest some entropy problems concerning whose Laplacians are $ g $-circulant matrices, i.e., circulant matrices with $-periodic diagonals, or quasi-Toepli...

The dynamics of rigid bodies coupled by holonomic and non-holonomic constraints are formulated by the Newton Euler method employing a compact notation. The compact notation involves the use of two three by three matrices A and B and the totality of constraint vector C. The Lagrangian and Newton Euler methods are related for a one link rigid body in order to introduce the methodology of the pape...

In this paper we study matrices A = (aij) whose (i, j) -entry is a function of i/j; that is, aij = f(i/j) for some f : Q → C. We obtain a formula for the truncated determinants in the case where f is multiplicative, linking them to determinants of truncated Toeplitz matrices. We apply our formula to obtain several determinants of number-theoretic matrices. Mathematics Subject Classification 200...

In this paper we show that standard preconditioners for parabolic PDEs discretized by implicit Euler or Crank–Nicolson schemes can be reused for higher–order fully implicit Runge–Kutta time discretization schemes. We prove that the suggested block diagonal preconditioners are order–optimal for A–stable and irreducible Runge–Kutta schemes with invertible coefficient matrices. The theoretical inv...

In his 1984 Ph.D. thesis, J. Greene defined an analogue of the Euler integral transform for finite field hypergeometric series. Here we consider a special family of matrices which arise naturally in the study of this transform and prove a conjecture of Ono about the decomposition of certain finite field hypergeometric functions into functions of lower dimension.