An experiment was carried out to estimate the effect of sound feedback on the work of a plant operator. Eight students of computer science operated a process simulation program of an assembly line with computer numeric controlled (CNC) robots. Relevant information of disturbances and machine breakdowns was given only in a visual (test condition 1), and in visual and audible form (test condition...

Small perturbations of the Jacobi matrix with weights √ n and zero diagonal are considered. A formula relating the asymptotics of polynomials of the first kind to the spectral density is obtained, which is analogue of the classical Weyl-Titchmarsh formula for the Schrödinger operator on the half-line with summable potential. Additionally a base of generalized eigenvectors for ”free” Hermite ope...

By using the Deift–Trubowitz transformations for adding or removing bound states to the spectrum of the Schrödinger operator on the line we construct a simple algorithm allowing one to reduce the problem of deriving symplectic expansions to its simplest case when the spectrum is purely continuous, and vice versa. We also obtain the transformation formulas for the correponding recursion operator...

I describe a new way of constructing a gauge action that eliminates scaling artifacts, by writing the continuum formalism in terms of “gauge links” (Schwinger line integrals) and using the optimal SLAC representation of the lattice derivative. Computational performance can be maintained by implementing the action as a “stochastic” operator, as has been recently implemented in the MILC code for ...

We study the resonant set of a two-level Schrödinger operator with a linear conical intersection. This model operator can be decomposed into a direct sum of first order systems on the real half-line. For these ordinary differential systems we locally construct exact WKB solutions, which are connected to global solutions, amongst which are resonant states. The main results are a generalized Bohr...

In this note we present a operator formulation of gauge theories in a quantum phase space which is specified by a operator algebra. For simplicity we work with the Heisenberg algebra. We introduce the notion of the derivative (transport) and Wilson line (parallel transport) which enables us to construct a gauge theory in a simple way. We illustrate the formulation by a discussion of the Higgs m...

In this paper we construct the scattering operator for the forced non-linear Schrödinger equation with a potential on the half-line. Moreover, in the case where the force is zero, and the solutions satisfy the homogeneous Dirichlet boundary condition at zero, we prove that the scattering operator determines uniquely the potential and the non-linearity and we give a method for the reconstruction...

We consider a compact Riemannian manifold with a Hermitian line bundle whose curvature is non-degenerate. The Laplacian acting on high tensor powers (the semiclassical regime) of the bundle exhibits a cluster of low-energy states. We demonstrate that the orthogonal projectors onto these states are the Fourier components of an operator with the structure of the Szegö projector, i.e. a Fourier in...

We give an explicit realization of the 4d local operator / 2d conformal block correspondence Costello and Paquette in case gauge theories. This is accomplished by lifting operators to non-local twistor space using a holomorphic generalization Wilson line. procedure automatically constructs blocks corresponding operator. interpret this as effectively integrating out degrees freedom living on def...

‎in this paper we try to extend geometric concepts in the context of operator valued tensors‎. ‎to this end‎, ‎we aim to replace the field of scalars $ mathbb{r} $ by self-adjoint elements of a commutative $ c^star $-algebra‎, ‎and reach an appropriate generalization of geometrical concepts on manifolds‎. ‎first‎, ‎we put forward the concept of operator-valued tensors and extend semi-riemannian...