Some local--global phenomena in locally finite graphs

In this paper we present some results for a connected infinite graph $G$ with finite degrees where the properties of balls of small radii guarantee the existence of some Hamiltonian and connectivity properties of $G$. (For a vertex $w$ of a graph $G$ the ball of radius $r$ centered at $w$ is the subgraph of $G$ induced by the set $M_r(w)$ of vertices whose distance from $w$ does not exceed $r$). In particular, we prove that if every ball of radius 2 in $G$ is 2-connected and $G$ satisfies the condition $d_G(u)+d_G(v)\geq |M_2(w)|-1$ for each path $uwv$ in $G$, where $u$ and $v$ are non-adjacent vertices, then $G$ has a Hamiltonian curve, introduced by K\"undgen, Li and Thomassen (2017). Furthermore, we prove that if every ball of radius 1 in $G$ satisfies Ore's condition (1960) then all balls of any radius in $G$ are Hamiltonian.Comment: 18 pages, 6 figures; journal accepted versio

Could any black holes be produced at the LHC?

We introduce analytical quantum gravity modifications of the production cross section for terascale black holes by employing an effective ultraviolet cut off $l$. We find the new cross sections approach the usual "black disk" form at high energy, while they differ significantly near the fundamental scale from the standard increase with respect to $s$. We show that the heretofore discontinuous step function used to represent the cross section threshold can realistically be modeled by two functions representing the incoming and final parton states in a high energy collision. The growth of the cross section with collision energy is thus a unique signature of $l$ and number of spatial dimensions $d$. Contrary to the classical black disk result, our cross section is able to explain why black holes might not be observable in LHC experiments while they could be still at the reach of ultra-high energy cosmic ray events.Comment: v1: 10 pages, 1 figure; v2: 11 pages, 1 figure, additional references, minor modifications; v3: new title, expanded discussion with updated production estimates, additional references, 4 figures, 19 pages, version accepted for publication on Physical Review

Rhodium complexes bearing tetradentate diamine-bis(phenolate) ligands

Using tetradentate, dianionic ligands, several new rhodium complexes have been prepared. Some of these diamine-bis(phenolate) compounds, are active for C–H activation of benzene. These complexes are air and thermally stable. All four complexes were characterized by X-ray diffraction

Noise Thermometry with Two Weakly Coupled Bose-Einstein Condensates

Here we report on the experimental investigation of thermally induced fluctuations of the relative phase between two Bose-Einstein condensates which are coupled via tunneling. The experimental control over the coupling strength and the temperature of the thermal background allows for the quantitative analysis of the phase fluctuations. Furthermore, we demonstrate the application of these measurements for thermometry in a regime where standard methods fail. With this we confirm that the heat capacity of an ideal Bose gas deviates from that of a classical gas as predicted by the third law of thermodynamics.Comment: 4 pages, 4 figure

Primary beam effects of radio astronomy antennas -- II. Modelling the MeerKAT L-band beam

After a decade of design and construction, South Africa's SKA-MID precursor MeerKAT has begun its science operations. To make full use of the widefield capability of the array, it is imperative that we have an accurate model of the primary beam of its antennas. We have taken available L-band full-polarization 'astro-holographic' observations of three antennas and a generic electromagnetic simulation and created sparse representations of the beams using principal components and Zernike polynomials. The spectral behaviour of the spatial coefficients has been modelled using discrete cosine transform. We have provided the Zernike-based model over a diameter of 10 deg averaged over the beams of three antennas in an associated software tool (EIDOS) that can be useful in direction-dependent calibration and imaging. The model is more accurate for the diagonal elements of the beam Jones matrix and at lower frequencies. As we get more accurate beam measurements and simulations in the future, especially for the cross-polarization patterns, our pipeline can be used to create more accurate sparse representations of MeerKAT beams.Comment: 16 pages, 18 figures. This is a pre-copyedited, author-produced PDF of an article accepted for publication in MNRAS following peer review. The version of record [K. M. B. Asad et al., 2021] is available online at: https://doi.org/10.1093/mnras/stab10

Tunneling through nanosystems: Combining broadening with many-particle states

We suggest a new approach for transport through finite systems based on the Liouville equation. By working in a basis of many-particle states for the finite system, Coulomb interactions are taken fully into account and correlated transitions by up to two different contact states are included. This latter extends standard rate equation models by including level-broadening effects. The main result of the paper is a general expression for the elements of the density matrix of the finite size system, which can be applied whenever the eigenstates and the couplings to the leads are known. The approach works for arbitrary bias and for temperatures above the Kondo temperature. We apply the approach to standard models and good agreement with other methods in their respective regime of validity is found.Comment: 9 pages, 5 figures included to tex

Age effect on retina and optic disc normal values

Purpose: To investigate retinal thickness and optic disc parameters by the Retinal Thickness Analyzer (RTA) glaucoma program in older normal subjects and to determine any age effect. Methods: Subjects over 40 years of age without any prior history of eye diseases were recruited. Only subjects completely normal on clinical ophthalmologic examination and on visual field testing by Humphrey Field Analyzer (HFA) using the SITA 24-2 program were included. A total of 74 eyes from 74 subjects with even age distribution over the decades were enrolled and underwent topographic measurements of the posterior pole and of the optic disc by RTA. The `glaucoma full' program in software version 4.11B was applied. Results: Mean patient age was 59.9 +/- 10.3 years with a range from 40 to 80 years. The only parameter intraocular pressure (IOP) correlated with was retinal posterior pole asymmetry (r=0.27, p=0.02). IOP itself increased significantly with age (r=0.341, p=0.003). Mean defect and pattern standard deviation of the HFA did not correlate with any of the retinal or optic disc measurements. Increasing age correlated significantly with some of the morphologic measurements of the RTA: decreasing perifoveal minimum thickness (r=-0.258, p=0.026), increased cup-to-disc area ratio (r=0.302, p=0.016) and increased cup area (r=0.338 p=0.007). Conclusions: An age effect exists for some of the retina and optic disc measurements obtained by the RTA. Copyright (C) 2005 S. Karger AG, Basel