Let $mathfrak{A}$ be an algebra. A linear mapping $delta:mathfrak{A}tomathfrak{A}$ is called a textit{derivation} if $delta(ab)=delta(a)b+adelta(b)$ for each $a,binmathfrak{A}$. Given two derivations $delta$ and $delta'$ on a $C^*$-algebra $mathfrak A$, we prove that there exists a derivation $Delta$ on $mathfrak A$ such that $deltadelta'=Delta^2$ if and only if either $delta'=0$ or $delta=sdel...

in this article a new and an accurate method for kinematic and dynamic analysis of a parallel robot 3prs and a hybrid robot (parallel and serial) 3prs-rrp are presented, which is based on the denavit-hartenberg transformation matrix algebra. first, basic properties of various kinds of robots are compared, and then the denavit-hartenberg parameters and their table are introduced. next, the metho...

The paper focuses on simulation tools for parallel kinematics using Augmented Reality. AR is used in the design of new equipment for reasons of clarity in testing the physical model of parallel kinematics (linking real and virtual scene model). The article describes the process of the model creation and its further processing. The article focuses on other possible solutions which could be benef...

let $r$ be a 2-torsion free ring and $u$ be a square closed lie ideal of $r$. suppose that $alpha, beta$ are automorphisms of $r$. an additive mapping $delta: r longrightarrow r$ is said to be a jordan left $(alpha,beta)$-derivation of $r$ if $delta(x^2)=alpha(x)delta(x)+beta(x)delta(x)$ holds for all $xin r$. in this paper it is established that if $r$ admits an additive mapping $g : rlongrigh...

Certain high speed industrial assembly robots share a peculiar three legged parallel architecture wherein three “hips”, attached to a fixed upper base or “pelvis”, actuate “thighs” connected by “knees” to “shins”. Each shin is a parallelogramic four-bar linkage. “Ankles” are connected to a common end effector “foot” which executes spatial translatory motion. Inverse and direct kinematic analyse...