in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...

Recursive modelling for the kinematics and dynamics of the known 3-PRR planar parallel robot is established in this paper. Three identical planar legs connecting to the moving platform are located in a vertical plane. Knowing themotion of the platform,we develop first the inverse kinematics and determine the positions, velocities and accelerations of the robot. Further, the principle of virtual...

Binary manipulators are powered by actuators which have only two stable states. Therefore, they can reach only a discrete (but possibly large) number of locations. Compared to a manipulator built with continuous actuators, a binary manipulator provides reasonable performance, and is relatively inexpensive (up to an order of magnitude cheaper). The number of states of a binary manipulator grows ...

In this paper, we study the existence of solution of the four-point boundary value problem for second-order differential equations with impulses by using leray-Schauder theory: ⎧⎨ ⎩ x′′(t) = f(t, x(t), x′(t)), t ∈ [0, 1], t = tk, k = 1, 2,··· ,m Δx(tk) = Ik(x(tk)), k = 1, 2,··· ,m Δx′(tk) = Ik(x(tk), x ′(tk)), k = 1, 2,··· ,m x′(0) = αx′(ξ), x(1) = βx(η), (E) where 0 < ξ ≤ η < 1, α ≥ 0, β ≥ 0 a...

The shift to modularized cars leads to the need for early and precise concept decisions for the development of modules. Many module definitions focus on the interaction between modules to make them upgradeable. The focus here is on modules that have to work with unknown restrictions in terms of uncertainty. In this paper, emphasis is put on unknown car styling in early design stages. Because of...

Abstract. Let Rk(n) be the number of representations of an integer n as the sum of a prime and a k-th power for k ≥ 2. Furthermore, set Ek(X) = |{n ≤ X, n ∈ Ik, n not a sum of a prime and a k-th power}|. In the present paper we use sieve techniques to obtain a strong upper bound on Rk(n) for n ≤ X with no exceptions, and we improve upon the results of A. Zaccagnini to prove Ek(X) ≪k X 1−181 log...

A complete proof of the quark Reggeization hypothesis in the leading logarithmic approximation for any quark–gluon inelastic process in the multi–Regge kinematics in all orders of α s is given. First, we show that the multi–Regge form of QCD amplitudes is guarantied if a set of conditions on the Reggeon vertices and the trajectories is fulfilled. Then, we examine these conditions and show that ...