The study of light-scattering intensity on the dew-bubble curve of a binary mixture in the framework of scaling theory

In the framework of scaling theory and the principle of isomorphism of critical phenomena in mixtures, the analytical expression for the light-scattering intensity in a binary fluid mixture has been obtained in rather wide vicinity of its liquid–gas critical point. The deduced validity condition for the light-scattering intensity as an explicit function of temperature or density reveals the adequacy of the description of the obtained experimental data for the methane–pentane binary mixture. The good agreement between the theory and the experiment has been demonstrated. The critical temperature and density values were obtained as a result of optimization procedure.

Wavelet transformation on a finite interval

Integral transformations on a finite interval with a singular basis wavelet are considered. Using a sequence of such transformations, the problem of nonparametric approximation of a function is solved. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet must be zero). The paper develops the previously proposed method of singular wavelets when the tolerance condition is not met. In this case Delta-shaped functions that participate in Parzen – Rosenblatt and Nadaray – Watson estimations can be used as a basic wavelet. The set of wavelet transformations for a function defined on a numeric axis, defined locally, and on a finite interval were previously investigated. However, the study of the convergence of the decomposition on a finite interval was carried out only in one particular case. It was due to technical difficulties when trying to solve this problem directly. In the paper the idea of evaluating the periodic continuation of a function defined initially on a finite interval is implemented. It allowed to formulate sufficient convergence conditions for the expansion of the function in a series. An example of approximation of a function defined on a finite interval using the sum of discrete wavelet transformations is given.

CONFIRMATION OF ADS-B DATA IN THE AERODROME TRAFFIC ZONE BY GATING METHOD

The low cost of ADS-B stations in comparison with radars and multi-position surveillance systems allows to consider them as promising means, including for the airfield zone. However, at present, the ICAO does not recommend the use of the ADS-B as the main means of observation, since confirmation of the accuracy of the received coordinate information is required. The article presents a method of algorithmic confirmation of the ADS-B data, while providing flights in the aerodrome traffic zone. It is suggested to use method of the gating to estimate the fidelity of the ADS-B data by selecting the area of space around he extrapolated coordinate of the aircraft. According to the required flight procedure, request of the enhanced surveillance a Mode S is transmitted to the aircraft. On the coordinates of assigned track, according to the maneuvering scheme, aircraft trajectory is built, relative to which the calculation of location errors is performed. Estimation of the mathematical expectation and the mean square deviation of the location error is performed for different levels of reliability. Based on the size of the gate area, a check is performed for compliance of the obtained interval estimates with the data validity condition. The check is performed sequentially for reliability levels 0.9, 0.95, and 0.999. On exit the values of estimate of the error beyond the limit of tolerance for a target level of reliability, information about the unreliability of the received data is displayed, which allows to detect large deviations of the measured coordinates for a smaller number of observations. When performing imitation modelling for the obtained data were set various inaccuracy values: the mathematical expectation from 10 to 48 m and the mean square deviation from 20 to 100 m. The error estimation for the reliability level of 0.999 required from 5 to 22 observations, which corresponds to a time interval of 3 to 11 s real time. At values systematic error of 10 m and mean square deviation of 70 m, the accepted coordinates will be identified as untrusted and will display the information on prohibiting the use of ADS-B and necessary to use other surveillance equipment.

The impact of retro-cue validity on working memory representation: Evidence from electroencephalograms

Memory performance can be improved by retrospectively cueing an item maintained in visual working memory (VWM). Different hypotheses have been proposed to explain the mechanisms behind retro-cueing and VWM. Previous behavioral studies suggest that different retro-cue validities may lead individuals to implement retro-cues in different ways to obtain a retro-cue effect. However, there is still no clear electroencephalogram (EEG) evidence to support that the retro-cue effect under different validity conditions is triggered by different mechanisms. Herein, we investigated whether retro-cue validity modulated the mechanisms underlying the retro-cue effect in VWM by using EEGs. We manipulated retro-cue validity by using blocks in a color change detection task. Contralateral delay activity (CDA) and lateralized alpha power were used assess spatial attention and memory storage, respectively. Significant retro-cue effects were observed under both high- and low-validity conditions. More importantly, although the retro-cue could redirect spatial attention under both high- and low-validity conditions, we found that participants maintained the non-cued items during a measured time interval under the low-validity condition, but dropped them out of VWM under the high-validity condition. Our results resolve previous contradictory findings. The retro-cue effect in our study can be explained by the removal hypothesis, prioritization hypothesis, and protection-during-retrieval hypothesis. This work suggests that the mechanisms underlying the retro-cue effect are not mutually exclusive, but determined by the cue validity. Individuals can voluntarily choose different mechanisms based on the expected retro-cue validity.

Isolation of a periodic component by singular wavelet decomposition

In this paper, we propose to use a discrete wavelet transform with a singular wavelet to isolate the periodic component from the signal. Traditionally, it is assumed that the validity condition must be met for a basic wavelet (the average value of the wavelet is zero). For singular wavelets, the validity condition is not met. As a singular wavelet, you can use the Delta-shaped functions, which are involved in the estimates of Parzen-Rosenblatt, Nadaraya-Watson. Using singular value of a wavelet is determined by the discrete wavelet transform. This transformation was studied earlier for the continuous case. Theoretical estimates of the convergence rate of the sum of wavelet transformations were obtained; various variants were proposed and a theoretical justification was given for the use of the singular wavelet method; sufficient conditions for uniform convergence of the sum of wavelet transformations were formulated. It is shown that the wavelet transform can be used to solve the problem of nonparametric approximation of the function. Singular wavelet decomposition is a new method and there are currently no examples of its application to solving applied problems. This paper analyzes the possibilities of the singular wavelet method. It is assumed that in some cases a slow and fast component can be distinguished from the signal, and this hypothesis is confirmed by the numerical solution of the real problem. A similar analysis is performed using a parametric regression equation, which allows you to select the periodic component of the signal. Comparison of the calculation results confirms that nonparametric approximation based on singular wavelets and the application of parametric regression can lead to similar results.

Estimation of Wave Reflection Coefficient by Semi-Analytical Method in an Acoustic Black Hole Beam

Acoustic Black Hole (ABH) has been deployed into beam-plate structures with the passive damping system to enhance its performance in absorbing flexural waves. The wave reflection coefficient can be used to measure this performance. This paper proposes a semi-analytical method to estimate the wave reflection coefficient, which is based on the Finite Element Method (FEM). The proposed method is validated by the exact solution for the wave analysis on the quadratic ABH beam. By this method, this study also investigates the performances of power-law ABH beams with exponent [Formula: see text] and 10. The numerical results indicate that the wave reflection coefficient of ABH shows a decreasing trend as frequency increases. Moreover, the validity condition of the geometrical acoustic approach (GAA) is explored through error analysis on the estimated wave reflection coefficient. An envelope of this condition is presented to recommend conservative criteria for GAA.

Control of Output and Circulating Current of Modular Multilevel Converter Using a Sliding Mode Approach

The modular multilevel converter (MMC) has been prominently used in medium- and high-power applications. This paper presents the control of output and circulating current of MMC using sliding mode control (SMC). The design of the proposed controller and the relation between control parameters and validity condition are based on the system dynamics. The proposed designed controller enables the system to track its reference values. The controller is designed to control both output current and circulating current along with suppression of second harmonics contents in circulating current. Furthermore, the capacitor voltage and energy of the converter are also regulated. The control of output current is carried out in dq-axis as well as in αβ-axis with first-order switching law. However, a second-order switching law-based super twisting algorithm is used for controlling circulating current and suppression of its second harmonics contents. The stability of the controlled system is numerically calculated and verified by Lyapunov stability conditions. Moreover, the simulation results of the proposed controller are critically compared with the conventional proportional resonant (PR) controller to verify the effectiveness of the proposed control strategy. The proposed controller attains faster dynamic response and minimizes steady-state error comparatively. The simulation of the MMC model is carried out in MATLAB/Simulink

On the Convexity Correction Approximation in Pricing Volatility Swaps and VIX Futures

Convexity correction is a well-known approximation technique used in pricing volatility swaps and VIX futures. However, the accuracy of the technique itself and the validity condition of this approximation have hardly been addressed and discussed in the literature. This paper shows that, through both theoretical analysis and numerical examples, this type of approximations is not necessarily accurate and one should be very careful in using it. We also show that a better accuracy cannot be achieved by extending the convexity correction approximation from a second-order Taylor expansion to third-order or fourth-order Taylor expansions. We then analyze why and when it deteriorates, and provide a validity condition of applying the convexity correction approximation. Finally, we propose a new approximation, which is an extension of the convexity correction approximation, to achieve better accuracies.

Stochastic Interest Model Based on Compound Poisson Process and Applications in Actuarial Science

Considering stochastic behavior of interest rates in financial market, we construct a new class of interest models based on compound Poisson process. Different from the references, this paper describes the randomness of interest rates by modeling the force of interest with Poisson random jumps directly. To solve the problem in calculation of accumulated interest force function, one important integral technique is employed. And a conception called the critical value is introduced to investigate the validity condition of this new model. We also discuss actuarial present values of several life annuities under this new interest model. Simulations are done to illustrate the theoretical results and the effect of parameters in interest model on actuarial present values is also analyzed.

Brans–Dicke theory and thermodynamical laws on apparent and event horizons

In this work, we describe the Brans–Dicke (BD) theory of gravity and give a particular solution by choosing a power law form for the scalar field [Formula: see text] and constant ω. If we assume that the first law of thermodynamics and the entropy formula hold on the apparent horizon, then we recover the Friedmann equations. Next, assuming the first law of thermodynamics holds, the validity conditions of the generalized second law (GSL) on the event horizon are presented. If we impose the entropy relation on the horizon, without using the first law, then we also obtain the validity condition of the GSL on the event horizon. The validity of the GSL completely depends on the BD model scalar field solutions. We have justified that the two processes are equivalent on the apparent horizon, but on the event horizon they are not equivalent. If the first law is valid on the event horizon, then the GSL may be satisfied by the BD solution, but if the first law is not satisfied then the GSL is not satisfied by the BD solution. Therefore, the first law always favours the GSL on the event horizon. In our effective approach, the first law and the GSL are always satisfied on the apparent horizon, which does not depend on the BD theory of gravity.