Related papers: Observable diameters with varying screens
We study non-compact scaling limits of uniform random planar quadrangulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe…
We study the observability of the one-dimensional Schr{\"o}dinger equation and of the beam and plate equations by moving or oblique observations. Applying different versions and adaptations of Ingham's theorem on nonharmonic Fourier series,…
We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…
We have developed a perturbative approach to microlensing due to an extrasolar planetary lens. In particular, we have found analytic formulae for triple images. We have used the formulae to investigate the astrometric microlensing due to…
The problem of leak detection in a pipeline with nonlinear friction is considered. A distributed observer-based method is proposed which applies a linearised, distributed adaptive observer design to the nonlinear model. The methodology is…
Nonlinear interactions are recognized as potential resources for quantum metrology, facilitating parameter estimation precisions that scale as the exponential Heisenberg limit of $2^{-N}$. We explore such nonlinearity and propose an…
We prove a limit theorem for the the maximal interpoint distance (also called the diameter) for a sample of n i.i.d. points in the unit ball of dimension 2 or more. The exact form of the limit distribution and the required normalisation are…
A simplified direct method is described for obtaining massless scalar functional determinants on the Euclidean ball. The case of odd dimensions is explicitly discussed.
Oriented circular cylinders in an opaque medium are used to represent certain microstructural objects in steel. The opaque medium is sliced parallel to the cylinder axes of symmetry and the cut-plane contains the observable rectangular…
The classical isoperimetric inequality can be extended to a general normed plane. In the Euclidean plane, the defect in the isoperimetric inequality can be calculated in terms of the signed areas of some singular sets. In this paper we…
We consider mappings satisfying an upper bound for the distortion of families of curves. We establish lower bounds for the distortion of distances under such mappings. As applications, we obtain theorems on the discreteness of the limit…
Calibrating displays is a basic and regular task that content creators must perform to maintain optimal visual experience, yet it remains a troublesome issue. Measuring display characteristics from different viewpoints often requires…
We put constraints on unparticle physics, specifically on the scale $\Lambda_\U$ and the scale dimension $d_\U$ of unparticle operators, using (i) measurements of atomic parity violation as well as (ii) branching ratio and CP asymmetry…
We theoretically investigate the apparent contact angle of droplets on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited droplet. We provide an intuitive geometrical interpretation whereby the…
This paper proposes a simple interval observer which can generate tighter interval estimates of variables in transient states than the standard interval observer. The simple nonlinear dynamics shrinks the estimated intervals to true state…
Nonlinear imaging systems can surpass the limits of linear optics, but to date they have all relied on physical media (e.g. crystals) to work. These materials are all constrained by their physical properties, such as frequency selectivity,…
The diffraction of electromagnetic waves by screens (apertures in screens) with time-varying dimensions is studied. The generalized vector Kirchhoff's representation for this case is obtained. It is also shown that with accuracy up to the…
We propose an optical read-out scheme allowing a demonstration of principle of information extraction below the diffraction limit. This technique, which could lead to improvement in data read-out density onto optical discs, is independent…
I describe the manifestation of the non-Euclidean geometry in the behavior of collective observables of some complex physical systems. Specifically, I consider the formation of equilibrium shapes of plants and statistics of sparse random…
This paper introduces a new nonlinear observer for state estimation of linear time invariant systems. The proposed observer contains a (nonlinear) cubic term in its error dynamics. "For the final version of this article, please refer to the…