Approximate Minimum Diameter

We study the minimum diameter problem for a set of inexact points. By inexact, we mean that the precise location of the points is not known. Instead, the location of each point is restricted to a contineus region (\impre model) or a finite set of points (\indec model). Given a set of inexact points in one of \impre or \indec models, we wish to provide a lower-bound on the diameter of the real points. In the first part of the paper, we focus on \indec model. We present an $O(2^{\frac{1}{\epsilon^d}} \cdot \epsilon^{-2d} \cdot n^3 )$ time approximation algorithm of factor $(1+\epsilon)$ for finding minimum diameter of a set of points in $d$ dimensions. This improves the previously proposed algorithms for this problem substantially. Next, we consider the problem in \impre model. In $d$-dimensional space, we propose a polynomial time $\sqrt{d}$-approximation algorithm. In addition, for $d=2$, we define the notion of $\alpha$-separability and use our algorithm for \indec model to obtain $(1+\epsilon)$-approximation algorithm for a set of $\alpha$-separable regions in time $O(2^{\frac{1}{\epsilon^2}}\allowbreak . \frac{n^3}{\epsilon^{10} .\sin(\alpha/2)^3} )$

ESR Study of (C_5H_{12}N)_2CuBr_4

ESR studies at 9.27, 95.4, and 289.7 GHz have been performed on (C$_5$H$_{12}$N)$_2$CuBr$_4$ down to 3.7 K. The 9.27 GHz data were acquired with a single crystal and do not indicate the presence of any structural transitions. The high frequency data were collected with a polycrystalline sample and resolved two absorbances, consistent with two crystallographic orientations of the magnetic sites and with earlier ESR studies performed at 300 K. Below $B_{C1}=6.6$ T, our data confirm the presence of a spin singlet ground state.Comment: 2 pages, 4 figs., submitted 23rd International Conference on Low Temperature Physics (LT-23), Aug. 200

Laser induced magnetization switching in films with perpendicular anisotropy: a comparison between measurements and a multi-macrospin model

Thermally-assisted ultra-fast magnetization reversal in a DC magnetic field for magnetic multilayer thin films with perpendicular anisotropy has been investigated in the time domain using femtosecond laser heating. The experiment is set-up as an optically pumped stroboscopic Time Resolved Magneto-Optical Kerr Effect magnetometer. It is observed that a modest laser fluence of about 0.3 mJ/square-cm induces switching of the magnetization in an applied field much less than the DC coercivity (0.8 T) on the sub-nanosecond time-scale. This switching was thermally-assisted by the energy from the femtosecond pump-pulse. The experimental results are compared with a model based on the Landau Lifschitz Bloch equation. The comparison supports a description of the reversal process as an ultra-fast demagnetization and partial recovery followed by slower thermally activated switching due to the spin system remaining at an elevated temperature after the heating pulse.Comment: 8 pages, 10 figures, to be submitted to PR

A Note on the Slim Accretion Disk Model

We show that when the gravitational force is correctly calculated in dealing with the vertical hydrostatic equilibrium of black hole accretion disks, the relationship that is valid for geometrically thin disks, i.e., $c_s/\Omega_K H =$ constant, where $c_s$ is the sound speed, $\Omega_K$ is the Keplerian angular velocity, and $H$ is the half-thickness of the disk, does not hold for slim disks. More importantly, by adopting the correct vertical gravitational force in studies of thermal equilibrium solutions, we find that there exists a maximally possible accretion rate for each radius in the outer region of optically thick accretion flows, so that only the inner region of these flows can possibly take the form of slim disks, and strong outflows from the outer region are required to reduce the accretion rate in order for slim disks to be realized.Comment: 14 pages, 5 figures, accepted by Ap

Observational Evidence of Accretion Disk-Caused Jet Precession in Galactic Nuclei

We show that the observational data of extragalactic radio sources tend to support the theoretical relationship between the jet precession period and the optical luminosity of the sources, as predicted by the model in which an accretion disk causes the central black hole to precess.Comment: 13 pages, 1 figure, accepted for publication in ApJ Letter

Rayleigh scattering in fused silica samples for gravitational wave detectors

Laser interferometer gravitational wave detectors require very high optical quality test masses. We report the bulk Rayleigh scattering in high quality fused silica samples. Results show that the scattering of the high quality fused silica is similar for various grades of fused silica from Heraeus. The total integrated scattering is about 0.7 ppm cm− 1at 1064 nm wavelength, which agrees with the theoretical value calculated using known fused silica parameters. All samples show Rayleigh scattering ratio inhomogeneity of ~ 4%

Upregulation of Anti-Angiogenic miR-106b-3p Correlates Negatively with IGF-1 and Vascular Health Parameters in a Model of Subclinical Cardiovascular Disease: Study with Metformin Therapy

\ua9 2024 by the authors.Well-controlled type 1 diabetes mellitus (T1DM) is regarded as a model of subclinical cardiovascular disease (CVD), characterized by inflammation and adverse vascular health. However, the underlying mechanisms are not fully understood. We investigated insulin-like growth factor-1 (IGF-1) and IGF-binding protein-3 (IGFBP-3) levels, their correlation to miR-106b-3p expression in a subclinical CVD model, and the cardioprotective effect of metformin. A total of 20 controls and 29 well-controlled T1DM subjects were studied. Plasma IGF-1, IGFBP-3 levels, and miR-106b-3p expression in colony-forming unit-Hills were analyzed and compared with vascular markers. miR-106b-3p was upregulated in T1DM (p < 0.05) and negatively correlated with pro-angiogenic markers CD34+/100-lymphocytes (p < 0.05) and IGF-1 (p < 0.05). IGF-1 was downregulated in T1DM (p < 0.01), which was associated with increased inflammatory markers TNF-α, CRP, and IL-10 and reduced CD34+/100-lymphocytes. IGFBP-3 had no significant results. Metformin had no effect on IGF-1 but significantly reduced miR-106b-3p (p < 0.0001). An Ingenuity Pathway analysis predicted miR-106b-3p to inhibit PDGFA, PIK3CG, GDNF, and ADAMTS13, which activated CVD. Metformin was predicted to be cardioprotective by inhibiting miR-106b-3p. In conclusion: Subclinical CVD is characterized by a cardio-adverse profile of low IGF-1 and upregulated miR-106b-3p. We demonstrated that the cardioprotective effect of metformin may be via downregulation of upregulated miR-106b-3p and its effect on downstream targets

The role of N∗(1535)N^*(1535) in pp→ppϕpp \to pp \phi and π−p→nϕ\pi^- p \to n \phi reactions

The near threshold $\phi$ meson production in proton-proton and $\pi^- p$ collisions is studied with the assumption that the production mechanism is due to the sub-$N\phi$-threshold $N^*(1535)$ resonance. The $\pi^0$, $\eta$ and $\rho^0$-meson exchanges for proton-proton collisions are considered. It is shown that the contribution to the $pp \to pp \phi$ reaction from the t-channel $\pi^0$ meson exchange is dominant. With a significant $N^*(1535)N\phi$ coupling ($g^2_{N^*(1535)N \phi}/4 \pi$ = 0.13), both $pp \to pp \phi$ and $\pi^- p \to n \phi$ data are very well reproduced. The significant coupling of the $N^*(1535)$ resonance to $N \phi$ is compatible with previous indications of a large $s \bar{s}$ component in the quark wave function of the $N^*(1535)$ resonance and may be the real origin of the significant enhancement of the $\phi$ production over the naive OZI-rule predictions.Comment: 15 pages, 6 figure