A New Method for Estimating Starspot Lifetimes Based on Autocorrelation Functions

We present a method that utilizes autocorrelation functions from long-term precision broadband differential light curves to estimate the average lifetimes of starspot groups for two large samples of Kepler stars: stars with and without previously known rotation periods. Our method is calibrated by comparing the strengths of the first few normalized autocorrelation peaks using ensembles of models that have various starspot lifetimes. We find that we must mix models of short and long lifetimes together (in heuristically determined ratios) to align the models with the Kepler data. Our fundamental result is that short starspot-group lifetimes (one to four rotations) are implied when the first normalized peak is weaker than about 0.4, long lifetimes (15 or greater) are implied when it is greater than about 0.7, and in between are the intermediate cases. Rotational lifetimes can be converted to physical lifetimes if the rotation period is known. Stars with shorter rotation periods tend to have longer rotational (but not physical) spot lifetimes, and cooler stars tend to have longer physical spot lifetimes than warmer stars with the same rotation period. The distributions of the physical lifetimes are log-normal for both samples and generally longer in the first sample. The shorter lifetimes in the stars without known periods probably explain why their periods are difficult to measure. Some stars exhibit longer than average physical starspot lifetimes; their percentage drops with increasing temperature from nearly half at 3000 K to nearly zero for hotter than 6000 K.

Comparative analysis of the profile variability of black soil water-physical properties when long-term applying plowing and no-till technologies use (the case of Panfily Research Station)

The results of actual research on profile variability of soil water-physical properties of undisturbed structure at the plots, where traditional plowing and no-till technology have been applied for 11 years, are given. The comparative research was conducted based on a stationary field experiment, which is carried out at Panfily Research Station of the National Scientific Center "Institute of Agriculture NAAS" when applying a system of laboratory diagnostics of water-physical properties created in the Institute of Water Problems and Land Reclamation of NAAS based on hydrophysical methods. The characteristics of main hydrophysical functions, namely moisture conductivity and water holding capacity, as well as hydrological constants - maximum hygroscopic moisture, withering point, minimal water holding capacity, maximum water holding capacity, specific surface area and active moisture range were obtained for three different depths. Based on the results of comparison, it was found that mesoporosity was more developed in the soil on the plots under plowing, while macroporosity was more developed on the no-till plots. The fundamental result is determining the inversion type of profile distribution of moisture conductivity in unsaturated soil. Thus, under on the no-till plots the highest values of moisture conductivity were observed in the deepest soil layer (0,70-0,85 m), decreasing to the soil surface, while on the plots under plowing the highest values of moisture conductivity were observed in cultivated soil layer (0,00-0,15 m), which naturally decreased in depth. The profile distribution of moisture conductivity on the no-till plots contributed to the infiltration supply of groundwater and capillary feeding of soil root layers from the deeper ones.

A Meeting Point of Probability, Graphs, and Algorithms: The Lovász Local Lemma and Related Results—A Survey

A classic and fundamental result, known as the Lovász Local Lemma, is a gem in the probabilistic method of combinatorics. At a high level, its core message can be described by the claim that weakly dependent events behave similarly to independent ones. A fascinating feature of this result is that even though it is a purely probabilistic statement, it provides a valuable and versatile tool for proving completely deterministic theorems. The Lovász Local Lemma has found many applications; despite being originally published in 1973, it still attracts active novel research. In this survey paper, we review various forms of the Lemma, as well as some related results and applications.

Extensional and Intensional Semantics of Bounded and Unbounded Nondeterminism

We give extensional and intensional characterizations of functional programs with nondeterminism: as structure preserving functions between biorders, and as nondeterministic sequential algorithms on ordered concrete data structures which compute them. A fundamental result establishes that these extensional and intensional representations are equivalent, by showing how to construct the unique sequential algorithm which computes a given monotone and stable function, and describing the conditions on sequential algorithms which correspond to continuity with respect to each order. We illustrate by defining may-testing and must-testing denotational semantics for sequential functional languages with bounded and unbounded choice operators. We prove that these are computationally adequate, despite the non-continuity of the must-testing semantics of unbounded nondeterminism. In the bounded case, we prove that our continuous models are fully abstract with respect to may-testing and must-testing by identifying a simple universal type, which may also form the basis for models of the untyped {\lambda}-calculus. In the unbounded case we observe that our model contains computable functions which are not denoted by terms, by identifying a further "weak continuity" property of the definable elements, and use this to establish that it is not fully abstract.

Decomposition of Random Sequences into Mixtures of Simpler Ones and Its Application in Network Analysis

A classic and fundamental result about the decomposition of random sequences into a mixture of simpler ones is de Finetti’s Theorem. In its original form, it applies to infinite 0–1 valued sequences with the special property that the distribution is invariant to permutations (called an exchangeable sequence). Later it was extended and generalized in numerous directions. After reviewing this line of development, we present our new decomposition theorem, covering cases that have not been previously considered. We also introduce a novel way of applying these types of results in the analysis of random networks. For self-containment, we provide the introductory exposition in more detail than usual, with the intent of making it also accessible to readers who may not be closely familiar with the subject.

Constructal design of top metallic contacts on a disc-shaped solar cell

Trends in crystalline silicon photovoltaic improvements demonstrate that some of the key factors that have contributed to reaching efficiency values up to 23 % are the introduction of the passivated emitter and rear cell structure with local rear contacts in low-cost large-volume fabrication; the reduction of the width of the front metallization fingers, from about 100 microm to less than 30 micro m in large volume production, and the re-emergence of mono-crystalline silicon wafers as a consequence of cost reduction in the Czochralski silicon ingot fabrication process. In the present work, we have developed a theoretical model that defines the geometric arrangement of a branched top metallic contacts network over a solar cell with a disc-shaped body. The solar cell considers two main regions: the solar cell material and an insert of metallic material for the collection of the photogenerated electrical current. The geometric characteristics of the network are defined from the minimization of the resistive power losses applying the constructal design method. As a fundamental result, the optimal lengths, branching angles, and geometrical relationships of the n-branched network are determined. The numerical results show that the dimensionless power losses of the branched arrangement of contacts present minimum values for the allocation of the metallic material and the disc size of the solar cell.

Consilience in the Peripheral Sensory Adaptation Response

Measurements of the peripheral sensory adaptation response were compared to a simple mathematical relationship involving the spontaneous, peak, and steady-state activities. This relationship is based on the geometric mean and is found to be obeyed to good approximation in peripheral sensory units showing a sustained response to prolonged stimulation. From an extensive review of past studies, the geometric mean relationship is shown to be independent of modality and is satisfied in a wide range of animal species. The consilience of evidence, from nearly 100 years of experiments beginning with the work of Edgar Adrian, suggests that this is a fundamental result of neurophysiology.

Fixed point property of amenable planar vortexes

This article introduces free group representations of planar vortexes in a CW space that are a natural outcome of results for amenable groups and fixed points found by M.M. Day during the 1960s and a fundamental result for fixed points given by L.E.J. Brouwer.

On the practical h-stabilization of nonlinear time-varying systems: application to separately excited DC motor

Purpose The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems.

Existence of Solutions for a Singular Fractional q-Differential Equations under Riemann–Liouville Integral Boundary Condition

We investigate the existence of solutions for a system of m-singular sum fractional q-differential equations in this work under some integral boundary conditions in the sense of Caputo fractional q-derivatives. By means of a fixed point Arzelá–Ascoli theorem, the existence of positive solutions is obtained. By providing examples involving graphs, tables, and algorithms, our fundamental result about the endpoint is illustrated with some given computational results. In general, symmetry and q-difference equations have a common correlation between each other. In Lie algebra, q-deformations can be constructed with the help of the symmetry concept.