Nagymennyiségű változócsillagászati észlelések feldolgozása és analízise = Reduction and analysis of large-scale variable star data sets

A következő három fő témakört vizsgáltuk: (a) periodikus tranzit detektálás és extraszolaris bolygók vizsgálata a HATNet es a WHAT automata távcsövek észlelései alapján; (b) a MACHO adatbázis RR Lyrae csillagainak periódus analízise; (c) pulzáló változócsillagok elméleti és empirikus vizsgálata. A következő eredményeket kaptuk. Téma (a): kis apertúrájú, teljesen automatizált távcsövek alkalmasak néhány millimagnitúdó pontosságú észlelésekre és forró Jupiterek (HJ-k) detektálására; a BLS algoritmusunk hatásos eszköz periodikus tranzitok keresésében; az adatfeldolgozás miatt fellépő szisztematikák kiszűrésének hatékony eszköze a TFA algoritmusunk; a HD 189733 HJ rendszer valójában egy hármas rendszer, K fő- es M másod-komponensekkel, valamint a főkomponens körül keringő bolygóval. Téma (b): az LMC-ben található alapmódusú RR Lyrae csillagok 12%-a mutat Blashko jelenséget. Ez az érték szignifikánsan magasabb, mint az újabb analizisünk alapján az első felhangú csillagokra kapott gyakoriság, amely a rendelkezésre álló adatok felhasználásával 7.5%-nak adódott. Téma (c): nincs ellentmondás az RR Lyrae és a Cepheida változók alapján a Baade-Wesselink módszer segítségével számított távolságok között. Az LMC távolságára konzisztens értékeket kaptunk; több irreguláris változó fénygörbéjének analizálása alapján további megerősítést kaptunk ezen csillagok kaotikus pulzációjára. | We have investigated the following three major topics: (a) periodic transit detection and extrasolar planetary studies based on large-scale photometric databases of the HATNet and WHAT automated telescopes; (b) frequency analysis of RR Lyrae stars in the MACHO database; (c) theoretical and empirical stellar pulsation studies. We obtained the following results. Topic (a): small aperture fully automated telescopes are able to gather few millimag precision photometric data and detect transits caused by hot Jupiters; our BLS algorithm is very efficient in searching for periodic transits; the effects of systematics due to errors in the data acquisition can be successfully filtered by our TFA algorithm; the hot Jupiter system HD 189733 is a triple system with a K primary and M secondary and the planet orbiting the primary. Topic (b): the incidence rate of the Blazhko stars pulsating in the fundamental mode is 12% in the LMC. This is significantly higher than that of the first overtone Blazhko stars (which is 7.5%, according to our new analysis of all available data. Topic (c): there is no contradiction between the distances derived by Baade-Wesselink analyses of RR Lyrae and Cepheid variables and they both yield consistent distances for the LMC; by analyzing the archival data of several irregular variables, we got further support for the presence of chaotic pulsations in these stars

Testing the Titius-Bode law predictions for Kepler multi-planet systems

We use three and half years of Kepler Long Cadence data to search for the 97 predicted planets of Bovaird & Lineweaver (2013) in 56 of the multi-planet systems, based on a general Titius-Bode relation. Our search yields null results in the majority of systems. We detect five planetary candidates around their predicted periods. We also find an additional transit signal beyond those predicted in these systems. We discuss the possibility that the remaining predicted planets are not detected in the Kepler data due to their non-coplanarity or small sizes. We find that the detection rate is beyond the lower boundary of the expected number of detections, which indicates that the prediction power of the TB relation in general extra solar planetary systems is questionable. Our analysis of the distribution of the adjacent period ratios of the systems suggests that the general Titius-Bode relation may over-predict the presence of planet pairs near the 3:2 resonance.Comment: Accepted by MNRA

Resonantly Forced Inhomogeneous Reaction-Diffusion Systems

The dynamics of spatiotemporal patterns in oscillatory reaction-diffusion systems subject to periodic forcing with a spatially random forcing amplitude field are investigated. Quenched disorder is studied using the resonantly forced complex Ginzburg-Landau equation in the 3:1 resonance regime. Front roughening and spontaneous nucleation of target patterns are observed and characterized. Time dependent spatially varying forcing fields are studied in the 3:1 forced FitzHugh-Nagumo system. The periodic variation of the spatially random forcing amplitude breaks the symmetry among the three quasi-homogeneous states of the system, making the three types of fronts separating phases inequivalent. The resulting inequality in the front velocities leads to the formation of ``compound fronts'' with velocities lying between those of the individual component fronts, and ``pulses'' which are analogous structures arising from the combination of three fronts. Spiral wave dynamics is studied in systems with compound fronts.Comment: 14 pages, 19 figures, to be published in CHAOS. This replacement has some minor changes in layout for purposes of neatnes

Big and little Lipschitz one sets

Given a continuous function $f: {{\mathbb R}}\to {{\mathbb R}}$ we denote the so-called "big Lip" and "little lip" functions by ${{\mathrm {Lip}}} f$ and ${{\mathrm {lip}}} f$ respectively}. In this paper we are interested in the following question. Given a set $E {\subset} {{\mathbb R}}$ is it possible to find a continuous function $f$ such that ${{\mathrm {lip}}} f=\mathbf{1}_E$ or ${{\mathrm {Lip}}} f=\mathbf{1}_E$? For monotone continuous functions we provide the rather straightforward answer. For arbitrary continuous functions the answer is much more difficult to find. We introduce the concept of uniform density type (UDT) and show that if $E$ is $G_\delta$ and UDT then there exists a continuous function $f$ satisfying ${{\mathrm {Lip}}} f =\mathbf{1}_E$, that is, $E$ is a ${{\mathrm {Lip}}} 1$ set. In the other direction we show that every ${{\mathrm {Lip}}} 1$ set is $G_\delta$ and weakly dense. We also show that the converse of this statement is not true, namely that there exist weakly dense $G_{{\delta}}$ sets which are not ${{\mathrm {Lip}}} 1$. We say that a set $E\subset \mathbb{R}$ is ${{\mathrm {lip}}} 1$ if there is a continuous function $f$ such that ${{\mathrm {lip}}} f=\mathbf{1}_E$. We introduce the concept of strongly one-sided density and show that every ${{\mathrm {lip}}} 1$ set is a strongly one-sided dense $F_\sigma$ set.Comment: This is the final preprint version accepted to appear in European Journal of Mathematic

Multicriteria cruise control design considering geographic and traffic conditions

The paper presents the design of cruise control systems considering road and traffic information during the design of speed trajectories. Several factors are considered such as road inclinations, traffic lights, preceding vehicles, speed limits, engine emissions and travel times. The purpose of speed design is to reduce longitudinal energy, fuel consumption and engine emissions without a significant increase in travel time. The signals obtained from the road and traffic are handled jointly with the dynamic equations of the vehicle and built into the control design of reference speed. A robust H∞ control is designed to achieve the speed of the cruise control, guaranteeing the robustness of the system against disturbances and uncertainties