Related papers: Singularity Analysis of Lower-Mobility Parallel Ma…
We apply scattering theory on asymptotically hyperbolic manifolds to singular Yamabe metrics, applying the results to the study of the conformal geometry of compact manifolds with boundary. In particular, we define extrinsic versions of the…
Parallel manipulators, also called parallel kinematics machines (PKM), enable robotic solutions for highly dynamic handling and machining applications. The safe and accurate design and control necessitates high-fidelity dynamics models.…
The aim of this paper is to find higher order geometrical corrections to the Einstein-Hilbert action that can lead to only second order equations of motion. The metric formalism is used, and static spherically symmetric and…
The pseudo-inverse of a graph Laplacian matrix, denoted as $L^\dagger$, finds extensive application in various graph analysis tasks. Notable examples include the calculation of electrical closeness centrality, determination of Kemeny's…
The paper addresses kinematic and geometrical aspects of the Orthoglide, a three-DOF parallel mechanism. This machine consists of three fixed linear joints, which are mounted orthogonally, three identical legs and a mobile platform, which…
A class of CW-complexes, called self-similar complexes, is introduced, together with C*-algebras A_j of operators, endowed with a finite trace, acting on square-summable cellular j-chains. Since the Laplacian Delta_j belongs to A_j,…
On finite metric graphs the set of all realizations of the Laplace operator in the edgewise defined $L^2$-spaces are studied. These are defined by coupling boundary conditions at the vertices most of which define non-self-adjoint operators.…
We study the null-controllability of some hypoelliptic quadratic parabolic equations posed on the whole Euclidean space with moving control supports, and provide necessary or sufficient geometric conditions on the moving control supports to…
This paper extends the Bakry-\'{E}mery theorem connecting the Ricci curvature and log-Sobolev inequalities to the matrix-valued setting. Using tools from noncommuative geometry, it is shown that for a right invariant second order…
Based on the theory of Poisson vertex algebras we calculate skew-symmetry conditions and Jacobi identities for a class of third-order nonlocal operators of differential-geometric type. Hamiltonian operators within this class are defined by…
The paper presents a novel modular hybrid parallel robot for pancreatic surgery and its higher-order kinematics derived based on various formalisms. The classical vector, homogeneous transformation matrices and dual quaternion approaches…
This work studies collections of Hilbert space operators which possess a strict monoid structure under composition. These collections can be thought of as discrete unital semigroups for which no subset of the collection is closed under…
Series elastic actuators (SEA) were introduced for serial robotic arms. Their model-based trajectory tracking control requires the second time derivatives of the inverse dynamics solution, for which algorithms were proposed. Trajectory…
A family of reconfigurable parallel robots can change motion modes by passing through constraint singularities by locking and releasing some passive joints of the robot. This paper is about the kinematics, the workspace and singularity…
We investigate the dynamical equivalence of quadratic Lagrangians and its relation to separation of variables. We show that requiring two quadratic Lagrangians to generate the same Euler--Lagrange equations imposes a compatibility condition…
The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of…
An algebra ${\cal G}$ of symmetric {\em one-particle} operators is constructed for the Calogero model. This is an infinite-dimensional Lie-algebra, which is independent of the interaction parameter $\lambda$ of the model. It is constructed…
Much of the structure of cosmological correlators is controlled by their singularities, which in turn are fixed in terms of flat-space scattering amplitudes. An important challenge is to interpolate between the singular limits to determine…
We develop the notions of connections and curvature for general Lie-Rinehart algebras without using smoothness assumptions on the base space. We present situations when a connection exists. E.g., this is the case when the underlying module…
We study the coupled Einstein-Klein-Gordon equations for a complex scalar field with and without a quartic self-interaction in a curvatureless Friedman-Lema\^{\i}\-tre Universe. The equations can be written as a set of four coupled first…