This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA+(n), a subgroup of the affine group in IRn and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to...

We study the set–theoretic combinatorics underlying the following two algebraic phenomena. (1) A subgroup G ≤ Z exhibits the Specker phenomenon iff every homomorphism G → Z maps almost all unit vectors to 0. Let se be the size of the smallest G ≤ Z exhibiting the Specker phenomenon. (2) Given an uncountably dimensional vector space E equipped with a symmetric bilinear form Φ over an at most cou...

This paper develops a method for generating smooth trajectories for a moving rigid body with specified boundary conditions. Our method involves two key steps: 1) the generation of optimal trajectories in GA+(n), a subgroup of the affine group in Rn and 2) the projection of the trajectories onto SE(3), the Lie group of rigid body displacements. The overall procedure is invariant with respect to ...

we call $h$ an $ss$-embedded subgroup of $g$ if there exists a‎ ‎normal subgroup $t$ of $g$ such that $ht$ is subnormal in $g$ and‎ ‎$hcap tleq h_{sg}$‎, ‎where $h_{sg}$ is the maximal $s$-permutable‎ ‎subgroup of $g$ contained in $h$‎. ‎in this paper‎, ‎we investigate the‎ ‎influence of some $ss$-embedded subgroups on the structure of a‎ ‎finite group $g$‎. ‎some new results were obtained.‎

Background: Cucumber mosaic virus (CMV) from the Bromoviridae family, is one of the most widespread plant viruses in the world. Objectives: In the present study tomato fields in Guilan, Isfahan, Khorasan Razavi, Khuzestan and Tehran provinces were surveyed to determine the presence of CMV subgroups during 2011-2012. Materials and Methods: Out of 305 symptomatic leaf samples ...

BACKGROUND Exercise test (ET) is the preferred initial noninvasive test for the diagnosis and risk stratification of coronary artery disease (CAD), however, its lower sensitivity may fail to identify patients at greater risk of adverse events. OBJECTIVE To assess the value of stress echocardiography (SE) for predicting all-cause mortality and major cardiac events (MACE) in patients with inter...

In this paper, methods of differential geometry and properties of Lie groups are used to show that in any conservative system subjected to a non zero external load, if one examines motions in SE(3), the special Euclidean group of rigid body motions in three dimensions, the resulting 6 ́6 stiffness matrix is asymmetric in any inertial (fixed) or body-fixed reference frame. We prove that in any su...