We study the accuracy of the divide-and-conquer method for electronic structure calculations. The analysis is conducted for a prototypical subdomain problem in the method. We prove that the pointwise difference between electron densities of the global system and the subsystem decays exponentially as a function of the distance away from the boundary of the subsystem, under the gap assumption of ...

A notion of robust stability is developed for iterative learning control in the context of disturbance attenuation. The size of the unmodelled dynamics is captured via a gap distance, which in turn is related to the standardH gap metric, and the resulting robustness certificate is qualitatively equivalent to that obtained in classical robust H∞ theory. A bound on the robust stability margin for...

Let M be a connected, noncompact, complete Riemannian manifold, consider the operator L = ∆+∇V for some V ∈ C(M) with exp[V ] integrable w.r.t. the Riemannian volume element. This paper studies the existence of the spectral gap of L. As a consequence of the main result, let ρ be the distance function from a point o, then the spectral gap exists provided limρ→∞ supLρ < 0 while the spectral gap d...

In this paper we study the spectral properties of Markov-operator on L -spaces. Lawler and Sokal (Trans. Amer. Math. Soc., 1988, 309, pp. 557-580) used isoperimetric constants for discrete and continuous time Markov chains to obtain a spectral gap at 1. For time discrete Markov chains this does not exclude periodic behavior. We define a new constant measuring the distance from periodicity and g...

Russian and Polish lack ’unbounded’ syntactic dependencies that fall into the primary empirical domain of TAG-Adjoining, namely, long-distance movement/filler-gap dependencies across a tensed clause boundary. A theory that incorporates Adjoining as a recursive structure building device provides a novel and straightforward account of this gap, whereas existing theories of syntactic locality, e.g...

We review the non-Fermi or marginal liquid behavior of a relativistic QED plasma. In this medium a quasiparticle has a damping rate that depends linearly on the distance between its energy and the Fermi surface. We stress that this dependence is due to the long-range character of the magnetic interactions in the medium. Finally, we study how the quark damping rate modifies the gap equation of c...

Typical measures for closed loop systems are so-called gaps between two systems, classically either L2 or H2 gap. Here, the distance between to candidate models for a plant can be measured taking all possible combinations of bounded input and output signals into account. Rather recently, a variant of theses gaps, the ν − gap, gained interest in the “identification for control” community. This r...

A fabrication scheme to realize dense arrays of flexible, closed membranes with a small gap separating them from the substrate is presented. These membranes are the first step towards aquatic hair based flow sensors biomimicking fish lateral line. Electrodes are integrated underneath the membrane to avoid contact with the liquid. Arrays of membranes with a diameter of 100 μm, gap height of 3 μm...

BACKGROUND Angular stable plate fixation is a widely accepted treatment option for interprosthetic or periprosthetic femoral fractures with stable implants. This biomechanical study tries to establish a safe distance of the plate from the tip of a femoral prosthesis. METHODS A total of 38 composite femurs were reamed to an inner diameter of 23 mm to create an osteoporotic bone model. A Weber ...