Lyapunov vs. Geometrical Stability Analysis of the Kepler and the Restricted Three Body Problem

In this letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al [1] predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well.Comment: 9 pages, 14 figure

Professional trade in property

Zasadniczo, definicyjnie, profesjonalny obrót majątkiem odnosi się do wykonywania działalności gospodarczej w celach zarobkowych, w sposób zorganizowany i ciągły. Jednak w regulacjach podatkowych nie zawsze pojęcie to odnosić się będzie do wykonywanej, rejestrowanej działalności. Konstrukcja systemu podatkowego dotyczącego opodatkowania czynności profesjonalnych wprowadza bowiem szczególne, różniące się od ogólnie przyjętej, definicje działalności gospodarczej dla własnych potrzeb podatkowych, przez co zdarzyć się może wykonywanie profesjonalnego obrotu majątkiem np. przez osobę fizyczną nieprowadzącą działalności gospodarczej w sposób zorganizowany i ciągły. Poniższy tekst ma przedstawić zasady opodatkowania profesjonalnego obrotu majątkiem w systemie polskiego prawa podatkowego z uwzględnieniem jego specyfiki na gruncie tych przepisów.University of Bialysto

The Impact of The European Court of Justice Case-Law on Indirect Taxes System in Poland – Selected Problems

Wpływ orzecznictwa Europejskiego Trybunału Sprawiedliwości na stosowanie prawa podatkowego w zakresie podatków pośrednich w Polsce jest niezmiernie istotny i orzecznictwo to jest wykorzystywane w pełni przez sądownictwo administracyjne. Znacznie gorzej jest z korzystaniem z doświadczeń Trybunału na płaszczyźnie pierwszoinstancyjnej przez organy podatkowe, chociaż już zauważa się takie decyzje, w których to orzecznictwo jest wykorzystywane. Powoli, lecz systematycznie, likwidowane są także niezgodności polskich ustaw z przepisami wspólnotowymi na etapie tworzenia prawa podatkowego. Chociaż można mieć zastrzeżenia do tempa tego postępowania, sam proces należy uznać za jednoznacznie pozytywny.The University of Bialystok (Poland

Development of multisensory spatial integration and perception in humans

Previous studies have shown that adults respond faster and more reliably to bimodal compared to unimodal localization cues. The current study investigated for the first time the development of audiovisual (A‐V) integration in spatial localization behavior in infants between 1 and 10 months of age. We observed infants’ head and eye movements in response to auditory, visual, or both kinds of stimuli presented either 25° or 45° to the right or left of midline. Infants under 8 months of age intermittently showed response latencies significantly faster toward audiovisual targets than toward either auditory or visual targets alone They did so, however, without exhibiting a reliable violation of the Race Model, suggesting that probability summation alone could explain the faster bimodal response. In contrast, infants between 8 and 10 months of age exhibited bimodal response latencies significantly faster than unimodal latencies for both eccentricity conditions and their latencies violated the Race Model at 25° eccentricity. In addition to this main finding, we found age‐dependent eccentricity and modality effects on response latencies. Together, these findings suggest that audiovisual integration emerges late in the first year of life and are consistent with neurophysiological findings from multisensory sites in the superior colliculus of infant monkeys showing that multisensory enhancement of responsiveness is not present at birth but emerges later in life

Discrimination of the Healthy and Sick Cardiac Autonomic Nervous System by a New Wavelet Analysis of Heartbeat Intervals

We demonstrate that it is possible to distinguish with a complete certainty between healthy subjects and patients with various dysfunctions of the cardiac nervous system by way of multiresolutional wavelet transform of RR intervals. We repeated the study of Thurner et al on different ensemble of subjects. We show that reconstructed series using a filter which discards wavelet coefficients related with higher scales enables one to classify individuals for which the method otherwise is inconclusive. We suggest a delimiting diagnostic value of the standard deviation of the filtered, reconstructed RR interval time series in the range of $\sim 0.035$ (for the above mentioned filter), below which individuals are at risk.Comment: 5 latex pages (including 6 figures). Accepted in Fractal

Ballistic transport, chiral anomaly and emergence of the neutral electron - hole plasma in graphene

The process of coherent creation of particle - hole excitations by an electric field in graphene is quantitatively described using a dynamic "first quantized" approach. We calculate the evolution of current density, number of pairs and energy in ballistic regime using the tight binding model. The series in electric field strength $E$ up to third order in both DC and AC are calculated. We show how the physics far from the two Dirac points enters various physical quantities in linear response and how it is related to the chiral anomaly. The third harmonic generation and the imaginary part of conductivity are obtained. It is shown that at certain time scale $t_{nl}\propto E^{-1/2}$ the physical behaviour dramatically changes and the perturbation theory breaks down. Beyond the linear response physics is explored using an exact solution of the first quantized equations. While for small electric fields the I-V curve is linear characterized by the universal minimal resistivity $\sigma =\pi /2(e^{2}/h)$%, at $t>t_{nl}$ the conductivity grows fast. The copious pair creation (with rate $E^{3/2}$), analogous to Schwinger's electron - positron pair creation from vacuum in QED, leads to creation of the electron - hole plasma at ballistic times of order $t_{nl}$. This process is terminated by a relaxational recombination.Comment: 15 pages, 5 figures

Development of multisensory spatial integration and perception in humans

Previous studies have shown that adults respond faster and more reliably to bimodal compared to unimodal localization cues. The current study investigated for the first time the development of audiovisual (A‐V) integration in spatial localization behavior in infants between 1 and 10 months of age. We observed infants’ head and eye movements in response to auditory, visual, or both kinds of stimuli presented either 25° or 45° to the right or left of midline. Infants under 8 months of age intermittently showed response latencies significantly faster toward audiovisual targets than toward either auditory or visual targets alone They did so, however, without exhibiting a reliable violation of the Race Model, suggesting that probability summation alone could explain the faster bimodal response. In contrast, infants between 8 and 10 months of age exhibited bimodal response latencies significantly faster than unimodal latencies for both eccentricity conditions and their latencies violated the Race Model at 25° eccentricity. In addition to this main finding, we found age‐dependent eccentricity and modality effects on response latencies. Together, these findings suggest that audiovisual integration emerges late in the first year of life and are consistent with neurophysiological findings from multisensory sites in the superior colliculus of infant monkeys showing that multisensory enhancement of responsiveness is not present at birth but emerges later in life