Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Cross sections for geodesic flows and \alpha-continued fractions

We adjust Arnoux's coding, in terms of regular continued fractions, of the geodesic flow on the modular surface to give a cross section on which the return map is a double cover of the natural extension for the \alpha-continued fractions, for each $\alpha$ in (0,1]. The argument is sufficiently robust to apply to the Rosen continued fractions and their recently introduced \alpha-variants.Comment: 20 pages, 2 figure

Multilevel Analysis of Oscillation Motions in Active Regions of the Sun

We present a new method that combines the results of an oscillation study made in optical and radio observations. The optical spectral measurements in photospheric and chromospheric lines of the line-of-sight velocity were carried out at the Sayan Solar Observatory. The radio maps of the Sun were obtained with the Nobeyama Radioheliograph at 1.76 cm. Radio sources associated with the sunspots were analyzed to study the oscillation processes in the chromosphere-corona transition region in the layer with magnetic field B=2000 G. A high level of instability of the oscillations in the optical and radio data was found. We used a wavelet analysis for the spectra. The best similarities of the spectra of oscillations obtained by the two methods were detected in the three-minute oscillations inside the sunspot umbra for the dates when the active regions were situated near the center of the solar disk. A comparison of the wavelet spectra for optical and radio observations showed a time delay of about 50 seconds of the radio results with respect to optical ones. This implies a MHD wave traveling upward inside the umbral magnetic tube of the sunspot. Besides three-minute and five-minute ones, oscillations with longer periods (8 and 15 minutes) were detected in optical and radio records.Comment: 17 pages, 9 figures, accepted to Solar Physics (18 Jan 2011). The final publication is available at http://www.springerlink.co

Natural extensions and entropy of α\alpha-continued fractions

We construct a natural extension for each of Nakada's $\alpha$-continued fractions and show the continuity as a function of $\alpha$ of both the entropy and the measure of the natural extension domain with respect to the density function $(1+xy)^{-2}$. In particular, we show that, for all $0 < \alpha \le 1$, the product of the entropy with the measure of the domain equals $\pi^2/6$. As a key step, we give the explicit relationship between the $\alpha$-expansion of $\alpha-1$ and of $\alpha$

Multi-level Dynamical Systems: Connecting the Ruelle Response Theory and the Mori-Zwanzig Approach

In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response theory on such a weakly coupled system to construct a surrogate dynamics, such that the expectation value of any observable agrees, up to second order in the coupling strength, to its expectation evaluated on the full dynamics. We show here that such surrogate dynamics agree up to second order to an expansion of the Mori-Zwanzig projected dynamics. This implies that the parametrizations of unresolved processes suited for prediction and for the representation of long term statistical properties are closely related, if one takes into account, in addition to the widely adopted stochastic forcing, the often neglected memory effects.Comment: 14 pages, 1 figur

Влияние индол-3-масляной кислоты и хлормеквата хлорида на рост растений томата

Relevance. This study aimed to improve fruit set and plant performance to increase tomato productivity by studying the effect of plant growth regulators on tomato plants.Methods. A specific experiment has been carried out to study the effect of plant growth regulators Milagro (1% indol-3-butric acid) and Atlet active substances indol-3-butric acid and chloromequate chloride with applied doses (0.6 M/L, 1.0 M/L and 1.5 M/L) and (1.0, 1.5 and 2.0 M/L) on growth and physiological characteristics of plants (Big Beef F1). The experimental design was a Complete Randomized Blocks Design. Both Hemo bles was applied three times (spraying on plants at 30 DAP, spraying on plants at 60 DAP and spraying on plants 90 DAP).Results. The obtained results showed that, Applying Milagro (1% indol-3-butric acid) had the highest significant Plant height (80.13, 128.77 and 239 cm), number of leaves/plant (18.0, 34.67 and 44.3) and stem diameter (1.07, 1.5 and 2.03 cm), fruit weight (122.0 and 136 g), Flower Clusters number in the plant (4.64, 13.33 and 16.33) and Fruits Number (61.67, 62.0 and 67) Over the three years of study. The results were analyzed using one-way analysis of variance (ANOVA) followed by Tukey’s HSD test with α = 0.05 with the help of MINITAB (v. 19.0) program.Актуальность. Исследование было направлено на улучшение плодоношения и продуктивности растений для увеличения урожайности томатов путем изучения влияния регуляторов роста растений.Материал и методы. Проведен эксперимент по изучению влияния регуляторов роста растений Милагро (1% индол-3-масляная кислота) и активных веществ Атлет – индол-3-масляной кислоты и хлормеквата хлорида, применяемых в дозах (0,6 м/л, 1,0 м/л) и 1,5 м/л) и (1,0, 1,5 и 2,0 м/л) по росту и физиологическим характеристикам растений (Big Beef F1). Оба регулятора роста наносили три раза (опрыскивание растений при 30 DAP, опрыскивание растений при 60 DAP и опрыскивание растений при 90 DAP).Результаты. Применение Милагро (1% индол-3-масляной кислоты) оказало наибольшее влияние на высоту растений (80,13, 128,77 и 239 см), количество листьев / растений (18,0, 34,67 и 44,3) и диаметр стебля (1,07, 1,5 и 2,03 см), массу плодов (122,0 и 136 г), количество цветочных кистей на растении (4,64, 13,33 и 16,33) и количество плодов (61,67, 62,0 и 67) в течение трех лет исследования. Результаты были проанализированы с использованием одностороннего дисперсионного анализа (ANOVA) с последующим HSD-тестом Тьюки с α = 0,05 с помощью программы MINITAB (v. 19,0)