Higher order numerical methods for solving fractional differential equations

The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-013-0443-3In this paper we introduce higher order numerical methods for solving fractional differential equations. We use two approaches to this problem. The first approach is based on a direct discretisation of the fractional differential operator: we obtain a numerical method for solving a linear fractional differential equation with order 0 0. The order of convergence of the numerical method is O(h^3) for α ≥ 1 and O(h^(1+2α)) for 0 < α ≤ 1 for sufficiently smooth solutions. Numerical examples are given to show that the numerical results are consistent with the theoretical results

Four-colour photometry of eclipsing binaries. XLI uvby light curves for AD Bootis, HW Canis Majoris, SW Canis Majoris, V636 Centauri, VZ Hydrae, and WZ Ophiuchi

CONTEXT: Accurate mass, radius, and abundance determinations from binaries provide important information on stellar evolution, fundamental to central fields in modern astrophysics and cosmology. AIMS: Within the long-term Copenhagen Binary Project, we aim to obtain high-quality light curves and standard photometry for double-lined detached eclipsing binaries with late A, F, and G type main-sequence components, needed for the determination of accurate absolute dimensions and abundances, and for detailed comparisons with results from recent stellar evolutionary models. METHODS: Between March 1985 and July 2007, we carried out photometric observations of AD Boo, HW CMA, SW CMa, V636 Cen, VZ Hya, and WZ Oph at the Str"omgren Automatic Telescope at ESO, La Silla. RESULTS: We obtained complete uvby light curves, ephemerides, and standard uvby\beta indices for all six systems.For V636 Cen and HW CMa, we present the first modern light curves, whereas for AD Boo, SW CMa, VZ Hya, and WZ Oph, they are both more accurate and more complete than earlier data. Due to a high orbital eccentricity (e = 0.50), combined with a low orbital inclination (i = 84.7), only one eclipse, close to periastron, occurs for HW CMa. For the two other eccentric systems, V636 Cen (e = 0.134) and SW CMa (e = 0.316), apsidal motion has been detected with periods of 5270 +/- 335 and 14900 +/- 3600 years, respectively.Comment: Only change is: Bottom lines (hopefully) not truncated anymore. Accepted for publication in Astonomy & Astrophysic

Absolute properties of the binary system BB Pegasi

We present a ground based photometry of the low-temperature contact binary BB Peg. We collected all times of mid-eclipses available in literature and combined them with those obtained in this study. Analyses of the data indicate a period increase of 3.0(1) x 10^{-8} days/yr. This period increase of BB Peg can be interpreted in terms of the mass transfer 2.4 x 10^{-8} Ms yr^{-1} from the less massive to the more massive component. The physical parameters have been determined as Mc = 1.42 Ms, Mh = 0.53 Ms, Rc = 1.29 Rs, Rh = 0.83 Rs, Lc = 1.86 Ls, and Lh = 0.94 Ls through simultaneous solution of light and of the radial velocity curves. The orbital parameters of the third body, that orbits the contact system in an eccentric orbit, were obtained from the period variation analysis. The system is compared to the similar binaries in the Hertzsprung-Russell and Mass-Radius diagram.Comment: 17 pages, 3 figures, accepted for Astronomical Journa

Why did Swiss citizens vote to ban tobacco advertising?

In February 2022, Swiss citizens agreed to modify the Swiss Constitution to ban tobacco advertising reaching children and adolescents. This case study analyses the arguments used by both opponents and supporters of the constitutional amendment. Opponents argued that the proposed regulation went too far, threatened the economy, restricted personal freedom, was superfluous as the current law already protected youth and that it opened the door to marketing bans of other harmful products. Proponents focused on youth protection and invoked the burden of smoking on public health and the fact that advertising bans are an effective evidence-based measure. A comparison with previous campaigns to ban tobacco advertising that had failed suggests factors accounting for the positive vote in 2022. These include the strategic framing of youth protection, the separation of tobacco from other issues (such as alcohol advertising), the deteriorating image of the tobacco industry and the ability of the proponents to mobilise a broad coalition of health and youth organisations, with improved funding and communication. The lessons may be instructive for other campaigns seeking to regulate commercial determinants of health

GU Boo: A New 0.6 Msun Detached Eclipsing Binary

We have found a new low-mass, double-lined, detached eclipsing binary, GU Boo, among a sample of new variables from the ROTSE-I database. The binary has an orbital period of 0.488728 +/- 0.000002 days, and estimated apparent magnitudes Vrotse = 13.7 and I = 11.8. Our analysis of the light and radial velocity curves of the system yields individual masses and radii of M1= 0.610 +/- 0.007 Msun, M2 = 0.599 +/- 0.006 Msun, R1= 0.623 +/- 0.016 Rsun, R2= 0.620 +/- 0.020 Rsun. The stars in GU Boo are therefore very similar to the components of the eclipsing binary YY Gem. For this study we have adopted a mean effective temperature for the binary of Teff = 3870 +/- 130 K. Based on its space velocities we suggest that GU Boo is a main sequence binary, possibly with an age of several Gyr. The metallicity of the binary is not well constrained at this point but we speculate that it should not be very different from solar. We have compared the physical parameters of GU Boo with current low-mass stellar models, where we accounted for uncertainties in age and metallicity by considering a wide range of values for those parameters. Our comparisons reveal that all the models underestimate the radii of the components of GU Boo by at least 10-15%. This result is in agreement with the recent studies of YY Gem and CU Cnc.Comment: 41 pages, 10 figures, 11 tables; accepted by Ap

Detailed error analysis for a fractional adams method with graded meshes

The final publication is available at Springer via http://dx.doi.org/10.1007/s11075-017-0419-5We consider a fractional Adams method for solving the nonlinear fractional differential equation \, ^{C}_{0}D^{\alpha}_{t} y(t) = f(t, y(t)), \, \alpha >0, equipped with the initial conditions $y^{(k)} (0) = y_{0}^{(k)}, k=0, 1, \dots, \lceil \alpha \rceil -1$. Here $\alpha$ may be an arbitrary positive number and $\lceil \alpha \rceil$ denotes the smallest integer no less than $\alpha$ and the differential operator is the Caputo derivative. Under the assumption \, ^{C}_{0}D^{\alpha}_{t} y \in C^{2}[0, T], Diethelm et al. \cite[Theorem 3.2]{dieforfre} introduced a fractional Adams method with the uniform meshes $t_{n}= T (n/N), n=0, 1, 2, \dots, N$ and proved that this method has the optimal convergence order uniformly in $t_{n}$, that is $O(N^{-2})$ if $\alpha > 1$ and $O(N^{-1-\alpha})$ if $\alpha \leq 1$. They also showed that if \, ^{C}_{0}D^{\alpha}_{t} y(t) \notin C^{2}[0, T], the optimal convergence order of this method cannot be obtained with the uniform meshes. However, it is well known that for $y \in C^{m} [0, T]$ for some $m \in \mathbb{N}$ and $0 < \alpha 1$, we show that the optimal convergence order of this method can be recovered uniformly in $t_{n}$ even if \, ^{C}_{0}D^{\alpha}_{t} y behaves as $t^{\sigma}, 0< \sigma <1$. Numerical examples are given to show that the numerical results are consistent with the theoretical results

The Chemical Compositions of the Type II Cepheids -- The BL Her and W Vir Variables

Abundance analyses from high-resolution optical spectra are presented for 19 Type II Cepheids in the Galactic field. The sample includes both short-period (BL Her) and long-period (W Vir) stars. This is the first extensive abundance analysis of these variables. The C, N, and O abundances with similar spreads for the BL Her and W Vir show evidence for an atmosphere contaminated with $3\alpha$-process and CN-cycling products. A notable anomaly of the BL Her stars is an overabundance of Na by a factor of about five relative to their presumed initial abundances. This overabundance is not seen in the W Vir stars. The abundance anomalies running from mild to extreme in W Vir stars but not seen in the BL Her stars are attributed to dust-gas separation that provides an atmosphere deficient in elements of high condensation temperature, notably Al, Ca, Sc, Ti, and $s$-process elements. Such anomalies have previously been seen among RV Tau stars which represent a long-period extension of the variability enjoyed by the Type II Cepheids. Comments are offered on how the contrasting abundance anomalies of BL Her and W Vir stars may be explained in terms of the stars' evolution from the blue horizontal branch.Comment: 41 pages including 11 figures and 4 tables; Accepted for publication in Ap

The Distribution of the Elements in the Galactic Disk III. A Reconsideration of Cepheids from l = 30 to 250 Degrees

This paper reports on the spectroscopic investigation of 238 Cepheids in the northern sky. Of these stars, about 150 are new to the study of the galactic abundance gradient. These new Cepheids bring the total number of Cepheids involved in abundance distribution studies to over 400. In this work we also consider systematics between various studies and also those which result from the choice of models. We find systematic variations exist at the 0.06 dex level both between studies and model atmospheres. In order to control the systematic effects our final gradients depend only on abundances derived herein. A simple linear fit to the Cepheid data from 398 stars yields a gradient d[Fe/H]/dRG = -0.062 \pm 0.002 dex/kpc which is in good agreement with previously determined values. We have also reexamined the region of the "metallicity island" of Luck et al. (2006). With the doubling of the sample in that region and our internally consistent abundances, we find there is scant evidence for a distinct island. We also find in our sample the first reported Cepheid (V1033 Cyg) with a pronounced Li feature. The Li abundance is consistent with the star being on its red-ward pass towards the first giant branch.Comment: 66 pages including tables, 12 figures, Accepted Astronomical Journa

Clinical aspects of Mayer-Rokitansky-Kuester-Hauser syndrome: recommendations for clinical diagnosis and staging

BACKGROUND: The Mayer-Rokitansky-Kuester-Hauser (MRKH) syndrome is a malformation of the female genitals (occurring in one in 4000 female live births) as a result of interrupted embryonic development of the Müllerian (paramesonephric) ducts. This retrospective study examined the issue of associated malformations, subtyping, and the frequency distribution of subtypes in MRKH syndrome. METHODS: Fifty-three MRKH patients were investigated using a newly developed standardized questionnaire. Together with the results of clinical and diagnostic examinations, the patients were classified into the three recognized subtypes [typical, atypical and MURCS (Müllerian duct aplasia, renal aplasia, and cervicothoracic somite dysplasia)]. RESULTS: The typical form was diagnosed in 25 patients (47%), the atypical form in 11 patients (21%), and the most marked form—the MURCS type—in 17 patients (32%). Associated malformations were notably frequent among the patients. Malformations of the renal system were the most frequent type of accompanying malformation, with 23 different malformations in 19 patients, followed by 18 different skeletal changes in 15 patients. CONCLUSIONS: In accordance with the literature, this study shows that associated malformations are present in more than a third of cases. Therefore, new basic guidelines for standard diagnostic classification involving patients with suspected MRKH are presente

Retarding Sub- and Accelerating Super-Diffusion Governed by Distributed Order Fractional Diffusion Equations

We propose diffusion-like equations with time and space fractional derivatives of the distributed order for the kinetic description of anomalous diffusion and relaxation phenomena, whose diffusion exponent varies with time and which, correspondingly, can not be viewed as self-affine random processes possessing a unique Hurst exponent. We prove the positivity of the solutions of the proposed equations and establish the relation to the Continuous Time Random Walk theory. We show that the distributed order time fractional diffusion equation describes the sub-diffusion random process which is subordinated to the Wiener process and whose diffusion exponent diminishes in time (retarding sub-diffusion) leading to superslow diffusion, for which the square displacement grows logarithmically in time. We also demonstrate that the distributed order space fractional diffusion equation describes super-diffusion phenomena when the diffusion exponent grows in time (accelerating super-diffusion).Comment: 11 pages, LaTe