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AbstractThe main objective of this paper is to introduce a new class of time series that extends a specific fractional models, including fractional autoregressive integrated moving average, Gegenbauer autoregressive moving average and Humbert autoregressive moving average (HARMA). The generalized HARMA is constructed using an orthogonal polynomial called generalized Humbert polynomial. The process is constructed to enhance the ability to capture complex patterns such as long memory and seasonal components. In this study, we present several properties including stationarity, invertibility, spectral density, and autocovariance function. In the simulation study, we check the validity of the theoretical findings. [ABSTRACT FROM AUTHOR]

While the statistical inference of first-order autoregressive processes driven by independent and identically distributed noises has a long history, the statistical analysis for first-order autoregressive processes driven by dependent noises is more recent. This paper considers the problem of estimating all the unknown parameters in first-order autoregressive processes driven by the fractional Gaussian noise, which is a self-similar stochastic process used to model persistent or anti-persistent dependency structures in observed time series. The estimation procedure is built upon the marriage of the log-periodogram regression and the method of moments. The usual asymptotic properties, including consistency and asymptotic normality, are established under some mild conditions. Monte Carlo simulations are performed to demonstrate the feasibility and effectiveness of the proposed method. Finally, the estimation methods are applied to model some realized volatility time series, where we find that the realized volatility is rough. Moreover, the proposed model is compared with some alternative models, including the first-order autoregressive process driven by the standard Gaussian noise, the heterogeneous autoregression model with lag structure (1,5,21) (HAR(1,5,21)), the autoregressive fractionally integrated moving average model (ARFIMA(1,d,0)) and the scaled fractional Brownian motion, in forecasting the logarithmic realized volatility. [ABSTRACT FROM AUTHOR]

A new efficient nonparametric estimator for Toeplitz covariance matrices is proposed. This estimator is based on a data transformation that translates the problem of Toeplitz covariance matrix estimation to the problem of mean estimation in an approximate Gaussian regression. The resulting Toeplitz covariance matrix estimator is positive definite by construction, fully data driven and computationally very fast. Moreover, this estimator is shown to be minimax optimal under the spectral norm for a large class of Toeplitz matrices. These results are readily extended to estimation of inverses of Toeplitz covariance matrices. Also, an alternative version of the Whittle likelihood for the spectral density based on the discrete cosine transform is proposed. [ABSTRACT FROM AUTHOR]

Central limit theorems (CLTs) for frequency‐domain statistics are fundamental tools in frequency‐domain analysis. However, for irregularly spaced data, they are still limited. In both the pure increasing domain and the mixed increasing domain asymptotic frameworks, three CLTs of frequency‐domain statistics are established for the observations at uniformly distributed sampling locations over a rectangular sampling region. One is for discrete Fourier transforms (DFTs), while the other two pertain to generalized spectral means (GSMs). The asymptotic joint normality and independence of the DFT at any finite number of standard frequencies are derived. Additionally, the asymptotic normalities of two GSMs are set up, with asymptotic variances given in different forms, according to the Gaussian or non‐Gaussian model assumption. Three established CLTs are very useful in investigating the sampling properties of many important frequency‐domain statistics, such as periodogram, non‐negative definite auto‐covariance estimator, spectral density estimator, and Whittle likelihood estimator as well. [ABSTRACT FROM AUTHOR]

Objective. Longitudinal forced harmonic vibrations of vertical rods with a concentrated mass at the end are considered.Method. The mathematical model of forced kinematically excited longitudinal vibrations is described by a differential equation and boundary conditions arising from the condition of fixing the ends of the rod. The problem will be solved using the finite difference method.Result. With near-resonance oscillation there is a significant difference between the amplitudes and standard deviations. The closeness of β to the natural frequency and the smallness of the value of α make almost all values of the frequencies of seismic action almost resonant. The reliability of the results of problems in deterministic and stochastic formulations has been confirmed. It has been established that the forms and parameters of forced deterministic oscillations significantly depend on the combination of the frequencies of the forcing disturbances with the natural frequencies of the oscillatory system. It has been established that the forms and parameters of forced random oscillations significantly depend on the combination of the spectral density of the random process of disturbances with the discrete spectrum of eigenvalues.Conclusion. It is necessary to expand the scope of research to include other types of vibrations: combinations of longitudinal with transverse, angular, torsional, parametric, etc.

In this article, we introduce a Gegenbauer autoregressive tempered fractionally integrated moving average process. We work on the spectral density and autocovariance function for the introduced process. The parameter estimation is done using the empirical spectral density with the help of the nonlinear least square technique and the Whittle likelihood estimation technique. The performance of the proposed estimation techniques is assessed on simulated data. Further, the introduced process is shown to better model the real-world data in comparison to other time series models. [ABSTRACT FROM AUTHOR]

Holographic processing of hydroacoustic noise signals in randomly inhomogeneous ocean environment is presented. A method of hologram purification from a perturbed field is described. An algorithm of resolving signals using a single detector is presented. Focusing of signal spectral density on a hologram is considered. Criteria of signal resolution are proposed. Results of numerical simulation of the resolution of two hydroacoustic signals against the background of intense internal waves, conditioning coupling of sound field modes, are shown. [ABSTRACT FROM AUTHOR]

In this scientific paper, we have considered a method for determining the complex reflection coefficient based on spectral analysis of the output voltage of a parametric microwave converter. [ABSTRACT FROM AUTHOR]

The analytical method for the synthesis of a generator of a random process with a given spectrum in the form of a linear system of Itô's equations is proposed. The stationarity of a random process is assumed, the spectral and corresponding transfer functions of which are defined in the form of rational fractions. The coefficients of the system of Itô's equations of the generator are found from recurrent algebraic relations. The method is focused on working with mathematical models of nature random processes, such as the Dryden's wind model. The transformation of the spectra of the wind gust model in three directions is presented in detail and the corresponding stochastic equations are given. [ABSTRACT FROM AUTHOR]

From a continuous-time long memory stochastic process, a discrete-time randomly sampled one is drawn using a renewal sampling process. We establish the existence of the spectral density of the sampled process, and we give its expression in terms of that of the initial process. We also investigate different aspects of the statistical inference on the sampled process. In particular, we obtain asymptotic results for the periodogram, the local Whittle estimator of the memory parameter and the long run variance of partial sums. We mainly focus on Gaussian continuous-time process. The challenge being that the randomly sampled process will no longer be jointly Gaussian. [ABSTRACT FROM AUTHOR]

This extends our new study of the automatic selfadjoint ideal property for B(H) -operator semigroups introduced to us by Heydar Radjavi (SI semigroups for short). Our investigation here of singly generated SI semigroups led to unexpected algebraic and analytic phenomena on the simplicity of SI semigroups and on the spectral density of their generators. In particular: the SI property yields for a hyponormal operator, zero planar area measure of its approximate point spectrum; the same for the essential spectrum of an essentially normal operator; and that SI semigroups generated by unilateral weighted shifts with periodic nonzero weights are simple. We also characterized the simplicity of the SI semigroups generated by certain commuting classes of normal operators. [ABSTRACT FROM AUTHOR]

The dams and banks of small water reservoirs face significant erosion from wind-generated oscillatory waves. Proper design of structure height is crucial to protect such banks against erosion, considering the maximum characteristics of wind waves. Long-term measurements at the Hulín reservoir revealed that the wave spectrum aligns best with the Bretschneider type. This spectrum serves as a basis for simulating oscillatory waves and their impact on shore protection structure design. Empirical models were evaluated using wind and wave data from Hulín reservoir in the Czech Republic. The measured wind speeds attained a maximum of 8 m/s, and wave heights reached up to 15 cm. The Bretschneider (SMB) empirical formula provided the most accurate estimation of wave height (Hm0), with an average underestimate of RMSE = 0.038 m. On the other hand, Wilson revisited (WIL rev.) performed less effectively, with an average RMSE = 0.304 m. For wave period (T) estimation, Bretschneider (SMB) yielded the best results, with an average RMSE = 0.062 s. Conversely, Wilson revisited (WIL rev.) showed poorer performance, with an average underestimate of RMSE = 2.196 s. The discrepancy between the empirical formulas and measured values, particularly in underestimating Hm0, can be attributed to inaccurate determination of fetch length and wind speed.

This article introduces a discrete‐time fractional stochastic volatility model (FSV) based on fractional Gaussian noise. The new model includes the standard stochastic volatility model as a special case and has the same limit as the fractional integrated stochastic volatility (FISV) model, which is the continuous‐time fractional Ornstein–Uhlenbeck process. A simulated maximum likelihood method, which maximizes the time‐domain log‐likelihood function calculated by the importance sampling technique, and a frequency‐domain quasi maximum likelihood method (or quasi Whittle) are employed to estimate the model parameters. Simulation studies suggest that, while both estimation methods can accurately estimate the model, the simulated maximum likelihood method outperforms the quasi Whittle method. As an illustration, we fit the FSV and FISV models with the proposed estimation techniques to the S&P 500 composite index over a sample period spanning 45 years. [ABSTRACT FROM AUTHOR]

In this paper we study point processes on the complex plane and illustrate their uses in several statistical areas, where the quantities of interest requiring estimation involve Fourier expansions. In particular, for any problem where we can describe a quantity in terms of its Fourier expansion, we propose modeling the coefficients of the expansion using a point process on the complex plane. We utilize the Poisson complex point process and model its intensity function using log-linear and mixture models. The proposed models are exemplified via applications to general density approximation, via modeling of the characteristic function, and time series analysis, via modeling of the spectral density. [ABSTRACT FROM AUTHOR]

This paper studies the second-order asymptotics of maximum likelihood estimator (MLE) and Whittle estimator under ε -contaminated model for Gaussian stationary processes. We evaluate the robustness of MLE and Whittle estimator based on the second-order Edgeworth expansion with an ε -disturbance spectral density. The measures of second-order robustness of MLE and Whittle estimator are investigated for concrete models with numerical study. The findings show that the MLE of Gaussian autoregressive process is robust in second-order term to a disturbance in spectral density under the middle level of spectral frequency, while it is more sensitive to a contamination under a too low frequency spectral mass. The Whittle estimator is robust to a moving average contamination when the Gaussian autoregressive process is not near unit root case, while it is sensitive to the disturbance under a nonregular situation in the case of near unit root. [ABSTRACT FROM AUTHOR]

The correlation structure of the vibration signal of the decanter bearing assembly was analyzed using the theory and methods of statistics of periodically non-stationary random processes. Indicators for detecting and evaluating the propagation of the defects have been developed. The relationship between the width of the filtering bandwidth and the parameters of the amplitude spectrum of the signal variation was investigated. [ABSTRACT FROM AUTHOR]

This study examines the possible utilization of machine learning and decision-making in the woodworking sector. This refers to the recognition of certain sounds produced during tool idling. The physical and geometric properties of the circular saw blade result in different noises being generated during idling. It was assumed that the respective circular saw blades can be recognized by these noises. The noises of three different circular saw blades were examined while idling at the same speed. In order to obtain useful data for the deep learning process, the coarse signals were subjected to frequency analysis. A total of 240 noise samples were taken for each circular saw blade and later subjected to signal processing. Frequency-power spectra were created using a custom program in Matlab Campus Edition software, such as for the spectrograms. A short Fourier transform was used to create the average spectral density plot using self-made software. The input data for the deep learning network was created in Matlab using a custom program. The GoogleNet deep learning network was used as a data classifier. After training the network, an accuracy of 97.5% was achieved in recognizing circular saw blades.

Exponential Frequency-Modulated (EFM) signals, characterized by their exponentially changing instantaneous frequency, are valuable in radar, sonar, and communication systems. This paper explores the application of EFM signals for measuring impulse response and nonlinear distortions in electronic devices. The EFM signal testing method, which involves recording and analyzing the device's output in response to EFM signals, provides insights into amplitude-frequency, phase-frequency responses, and impulse response. The spectral density analysis reveals a 3 dB/octave decrease in high-frequency regions. An innovative measurement method is proposed, involving convolution with a time-reversed and amplitude-modulated EFM signal, simplifying traditional approaches. MATLAB simulations validate the method, highlighting its efficacy in comprehensive device performance assessment. [ABSTRACT FROM AUTHOR]

The paper is concerned with the statistical estimation of the spectral parameters of stationary models with tapered data. As estimators of the unknown parameters we consider the tapered Whittle estimator and the simplified tapered Whittle estimators. We show that under broad regularity conditions on the spectral density of the model these estimators are asymptotically statistically equivalent, in the sense that these estimators possess the same asymptotic properties. The processes considered will be discrete-time and continuous-time Gaussian, linear or Lévy-driven linear processes with memory. [ABSTRACT FROM AUTHOR]

This study examines the possible utilization of machine learning and decision-making in the woodworking sector. This refers to the recognition of certain sounds produced during tool idling. The physical and geometric properties of the circular saw blade result in different noises being generated during idling. It was assumed that the respective circular saw blades can be recognized by these noises. The noises of three different circular saw blades were examined while idling at the same speed. In order to obtain useful data for the deep learning process, the coarse signals were subjected to frequency analysis. A total of 240 noise samples were taken for each circular saw blade and later subjected to signal processing. Frequency-power spectra were created using a custom program in Matlab Campus Edition software, such as for the spectrograms. A short Fourier transform was used to create the average spectral density plot using self-made software. The input data for the deep learning network was created in Matlab using a custom program. The GoogleNet deep learning network was used as a data classifier. After training the network, an accuracy of 97.5% was achieved in recognizing circular saw blades. [ABSTRACT FROM AUTHOR]

At the present stage, with the current demands for the accuracy of motion control processes for a moving object on a specified or programmable trajectory, it is necessary to synthesize the optimal structure and parameters of the stabilization system (controller) of the object, taking into account both real controlled and uncontrolled stochastic disturbing factors. Also, in the process of synthesizing the optimal controller structure, it is necessary to assess and consider multidimensional dynamic models, including those of the object itself, its basic components, controlled and uncontrolled disturbing factors that affect the object in its actual motion. Objective. The aim of the research, the results of which are presented in this article, is to obtain and assess the accuracy of the Stewart platform dynamic model using a justified algorithm for the multidimensional moving object dynamics identification. Method. The article employs a frequency-domain identification method for multidimensional stochastic stabilization systems of moving objects with arbitrary dynamics. The proposed algorithm for multidimensional moving object dynamics model identification is constructed using operations of polynomial and fractional-rational matrices addition, multiplication, Wiener factorization, Wiener separation, and determination of dispersion integrals. Results. As a result of the conducted research, the problem of identifying the dynamic model of a multidimensional moving object is formalized, illustrated by the example of a test stand based on the Stewart platform. The outcomes encompass the identification of the dynamic model of the Stewart platform, its transfer function, and the transfer function of the shaping filter. The verification of the identification results confirms the sufficient accuracy of the obtained models. Conclusions. The justified identification algorithm allows determining the order and parameters of the linearized system of ordinary differential equations for a multidimensional object and the matrix of spectral densities of disturbances acting on it under operating conditions approximating the real functioning mode of the object prototype. The analysis of the identification results of the dynamic models of the Stewart platform indicates that the primary influence on the displacement of the center of mass of the moving platform is the variation in control inputs. However, neglecting the impact of disturbances reduces the accuracy of platform positioning. Therefore, for the synthesis of the control system, methods should be applied that enable determining the structure and parameters of a multidimensional controller, considering such influences. [ABSTRACT FROM AUTHOR]

Recent research has demonstrated the success of employing neural networks for the purpose of detecting image tampering. Nevertheless, the utilization of referencefree steganalysis has become increasingly popular as a result of the challenges associated with obtaining an annotated dataset. This dataset is crucial for the classification process using neural networks, which aims to detect and identify instances of tampering. This paper introduces a robust approach to blind steganalysis, utilizing image spectral density and differential histogram correlative power spectral density. The proposed method employed two distinct forms of image data, namely a gray-scale image and true-color image data. The results indicate that the proposed methodology successfully achieved the anticipated outcomes in identifying manipulated images as evidenced by its successful application on the two distinct datasets. In the experiment results, the proposed technique succeeded quite well in terms of accuracy at low embedding ratios. Also, it successfully recognized sequential and random least significant bit steganography. [ABSTRACT FROM AUTHOR]

The species structure of the dominant community of unicellular algae inhabiting the spawning and feeding salmon lake was studied in the Kurile Lake (southern Kamchatka Peninsula). It has been shown that this structure is well described by the Motomura model. The geometric progression coefficient does not differ significantly from the value prescribed by the model, which is based on the stochastic remainder hypothesis. Several integral indicators characterizing the species structure have been calculated. The study has revealed some typical and unusual correlations between these integral indices. Inter-annual and intra-annual cyclical fluctuations in the value of indicators have been found. [ABSTRACT FROM AUTHOR]

Subject and Purpose. The sporadic radio emissions coming from the Sun in a broad frequency range contain a lot of important information concerning the solar corona, parameters of the radio frequency sources therein, and the parameter variations resulting from active processes on and about the Sun. These have been the reasons for recent launches of the space missions intended for stud- ying the Sun and its corona, such as the Parker Solar Probe (PSP) and the Solar Orbiter. The present work is aimed at demonstrating effectiveness of the ground-based support for the space missions, the PSP before all, which is provided by the large Ukrainian radio telescopes of the decameter wavelength range. Another purpose has been cross-calibration of the space-borne radiometer against calibrated data from a ground-based instrument. Methods and Methodology. One of the remote diagnosis techniques widely used with respect to the solar corona is to analyze parameters of the radio frequency emissions from sources lying at a variety of altitudes within the corona. The methodology of such joint, space-borne/terrestrial investigations suggests simultaneous observations of certain individual events during closest approach of the space probe PSP to the Sun, with analysis over a widest possible frequency range. The data obtainable within overlapping fre- quency bands are proposed for calibrating the on-board radio receivers of the space probe. Results. The methodology proposed for joint, space-based / terrestrial observations has been substantiated. Data from the UTR-2 and URAN-2 radio telescopes and the space probe PSP have been used to plot the dynamic and the polarization spectra of the June 9, 2020 solar bursts, with identification and comparison of the relevant individual events. A joint dynamic spectrum of these bursts has been obtained for the frequency band of 0.5 to 32 MHz. The calibrated data from the ground-based radio telescopes have allowed performing cross-calibration of the HF receiver in the FIELDS-PSP data taking module within the frequency band of 10 to 18 MHz. Conclusions. The paper has provided evidence of an effective ground-based support for the space mission PSP on the part of large Ukrainian radio telescopes. Examples of joint observations have been given, and a methodology described which is employed for cross-calibrating the HF receivers of the FIELD-PSP module. Prospects are outlined of further ground-based support for solar space research missions.

Existing methods and equipment for determining the dynamic characteristics of devices and systems are considered. A new method for estimating the dynamic error of navigation devices is proposed. It makes it possible to simplify the experimental assessment of the dynamic error of serial products as well as to evaluate its value under conditions of real disturbing influences corresponding to operating conditions using test equipment. The method is based on the measurement by the device of pseudo-random test effects reproduced by the stand in a given frequency spectrum corresponding to the operating conditions of the instrument. In this case, the variance of the dynamic error of the device under study is determined as the area under the graph of its power spectral density. To implement the method, it is proposed to use a specialized stand that allows to reproduce oscillations in a given frequency spectrum. The results of the application of the developed method in solving the problems of estimating the dynamic errors of the electronic inclinometer are presented. The results of experimental studies are consistent with the results of field tests obtained earlier. The developed method makes it possible to reduce the time for estimating the dynamic error of sensors and devices to 15–20 minutes because it does not require measurements at each frequency separately, and also allows to evaluate the error of devices in real modes of its operation.

Taking the BTA deep hole boring bar as the object of axial flow and axial feed movement, the dynamic characteristics of the fluid-structure coupling boring bar are systematically studied. The influence of complex deformation (bending, torsion, tension, and compression) factors are considered in the derivation of dynamic characteristics. According to the force situation of the BTA deep hole boring bar, the transverse vibration equation of the BTA deep hole boring bar is established. The transverse vibration equation is discretized by Galerkin method, and then its characteristic root, response variance, and spectral density are solved to realize the transverse vibration analysis of the boring bar. Research has found that the correlation between system stability and boring bar speed is no longer monotonous. System stability is positively correlated with the equivalent stiffness and the equivalent shear modulus. There is a negative correlation between system stability and axial force, but it is not significant. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the frequency domain approach to describe some probabilistic properties of the GARCH (p , q) processes using the associated transfer functions which seem more informative. So, in the first part, we propose an appropriate bilinear representation of GARCH (p , q) model governed by a second-order Hermite polynomial with leading coefficient 1, and we give a necessary and sufficient condition for the causal and second-order stationary solution. In a second part, we establish the autocovariance and the associated spectral density function of such a representation, and for its squared version in terms of transfer functions. As a consequence, it is observed that the second-order properties are similar to an ARMA process with uncorrelated innovations and hence the resort to higher-order properties however becomes inevitable. Therefore, the explicit expressions of bispectral densities of the process and its squared version are given and several illustrative examples are emphasized. Our results are related to the work of Terdik (2000, §3) for the GARCH(1, 1) model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new frequency domain test for pairwise time reversibility at any specific couple of quantiles of two-dimensional marginal distribution. The proposed test is applicable to a very broad class of time series, regardless of the existence of moments and Markovian properties. By varying the couple of quantiles, the test can detect any violation of pairwise time reversibility. Our approach is based on an estimator of the L 2 -distance between the imaginary part of copula spectral density kernel and its value under the null hypothesis. We show that the limiting distribution of the proposed test statistic is normal and investigate the finite sample performance by means of a simulation study. We illustrate the use of the proposed test by applying it to stock price data. [ABSTRACT FROM AUTHOR]

Context. The article is devoted to overcoming the contradictions between the assumptions adopted in known methods of closedloop control system identification and the design and conditions of its operation. The article presents a new method of identifying the transfer functions matrix of a two-level closed-loop control system element, which functions under the conditions of multidimensional stationary centered random influences. Objective. The purpose of the study, the results of which are presented in this paper, is to extend the indirect identification method to the case of estimating one of the two-level closed-loop control system elements, dynamics model based on passive experiment data. Method. To solve the optimal identification problem, a variational method for minimizing the quality functional on the class of fractional-rational transfer function matrices was used. Results. As a result of the research, the identification problem formulation was formalized, the rules for obtaining experimental information about the input and output signals were determined, the rules for identifying the transfer functions matrix of a two-level closed-loop control system element, which minimizes the sum of the variances of identification errors in the frequency domain, and the verification of these rules was carried out. Conclusions. Justified rules allow to correctly determine transfer functions matrices of the closed-loop systems selected element when fulfilling the defined list of conditions. The closed-loop systems control paths signals analysis proves the possibility of the effect of changing these signals statistical means, even under conditions of only centered stationary input influences actions on the system. Based on this, the further development of research can be aimed at overcoming such effects. [ABSTRACT FROM AUTHOR]

In order to establish multifactorial empirical energy models of low-frequency (EНЧК) and toothed (EЗК) oscillations of the dynamic component of the torque on the bit, experimental studies are conducted at the stand of the Ivano-Frankivsk National State University of Oil and Gas, using the method of rational planning of experiments. According to this method, the combination of variable factors, which include the axial static load Fст, bit rotation frequency n, stiffness C, and damping coefficient β of the drilling tool, occurs only once. The studied parameter is the amplitude value of the dispersion (energy) at local maxima, which are fixed on the low-frequency and jagged fluctuations of the spectral density (energy spectrum) of the internal structure of the dynamic component. General multidimensional functions are represented by the product of individual dependences on variable factors: EНЧК = Bсрf(n)f(Fст)f(C)f(β) and EЗК = Bсрf(n)f(Fст)f(C)f(β), where Bср is the average value of the numerical coefficient for the set of all experiments. Constant factors during the planned experiment are both the type and the diameter of the three-layer bit and the consumption of flushing fluid (water). The planned factorial experiment is carried out in blocks of sandstone of the Horodyshche strata with a stamp hardness of 1440 MPa. According to the results of the experiment, the equations of multifactor empirical models of energy EНЧК and EЗК fluctuations of the dynamic component of the torque on the bit are constructed, and the influence of external independent factors on this energy is analysed. [ABSTRACT FROM AUTHOR]

We introduce, in the dual Macaev ideal of compact operators of a Hilbert space, the spectral weight ρ(L) of a positive, self-adjoint operator L having discrete spectrum away from zero. We provide criteria for its measurability and unitarity of its Dixmier traces (ρ(L) is then called spectral density) in terms of the growth of the spectral multiplicities of L or in terms of the asymptotic continuity of the eigenvalue counting function NL. Existence of meromorphic extensions and residues of the ζ-function ζL of a spectral density are provided under summability conditions on spectral multiplicities. The hypertrace property of the states ΩL(·) = Trω(·ρ(L)) on the norm closure of the Lipschitz algebra AL follows if the relative multiplicities of L vanish faster than its spectral gaps or if NL is asymptotically regular. [ABSTRACT FROM AUTHOR]

Let p, d be positive integers, with d odd. Let ϕ : [ 0 , + ∞) → R p × p be the isotropic part of a matrix-valued and isotropic covariance function (a positive semidefinite matrix-valued function) that is defined over the d-dimensional Euclidean space. If ϕ is compactly supported over [ 0 , π ] , then we show that the restriction of ϕ to [ 0 , π ] is the isotropic part of a matrix-valued covariance function defined on a d-dimensional sphere, where isotropy in this case means that the covariance function depends on the geodesic distance. Our result does not need any assumption of continuity for the mapping ϕ . Further, when ϕ is continuous, we provide an analytical expression of the d-Schoenberg sequence associated with the compactly-supported covariance on the sphere, which only requires knowledge of the Fourier transform of its isotropic part, and illustrate with the Gauss hypergeometric covariance model, which encompasses the well-known spherical, cubic, Askey and generalized Wendland covariances, and with a hole effect covariance model. Special cases of the results presented in this paper have been provided by other authors in the past decade. [ABSTRACT FROM AUTHOR]

This study investigates the effect of small random transverse wall roughness on electromagnetohydrodynamic (EMHD) flow is in a microchannel, employing the perturbation method based upon stationary random function theory. An exact solution of a random corrugation function ξ, which is a measure of the flow rate deviated from the case without the roughness of two plates, is obtained by integrating the spectral density. After the sinusoidal, triangular, rectangular, and sawtooth functions that satisfy the Dirichlet condition are expanded into the Fourier sine series, the spectral density of the sine function is used to represent the corrugation function. Interestingly, for sinusoidal roughness, the final expression of the corrugation function is in good agreement with our previous work. Results show that no matter the shape of the wall roughness, the flow rate always decreases due to the existence of wall corrugation. Variations of the corrugation function and the flow rate strongly depend on fluid wavenumber λ and Hartmann number Ha. Finally, the flow resistance is found to become small, and the flow rate increases with roughness that is in phase (θ = 0) compared with the one that is out of phase (θ = π). [ABSTRACT FROM AUTHOR]

In this paper, we propose tests for the existence of random effects and interactions for two-way models with dependent errors. We prove that the proposed tests are asymptotically distribution-free which have asymptotically size τ and are consistent. We elucidate the nontrivial power under the local alternative when a sample size tends to infinity and the number of groups is fixed. A simulation study is performed to investigate the finite-sample performance of the proposed tests. In the real data analysis, we apply our tests to the daily log-returns of 24 stock prices from six countries and four sectors. We find that there is no strong evidence to support the existence of substantial differences in the log-return across countries, nor to the existence of interactions between countries and sectors. However, there exists random effect differences in the daily log-return series across different sectors. [ABSTRACT FROM AUTHOR]

Long-memory models are frequently used in finance and other fields to capture long-range dependence in time series data. However, correctly identifying whether a process has long memory is crucial. This paper highlights a significant limitation in using the sample autocorrelation function (ACF) to identify long-memory processes. While the ACF establishes the theoretical definition of a long-memory process, it is not possible to determine long memory by summing the sample ACFs. Hassani's − 1 2 theorem demonstrates that the sum of the sample ACF is always − 1 2 for any stationary time series with any length, rendering any diagnostic or analysis procedures that include this sum open to criticism. The paper presents several cases where discrepancies between the empirical and theoretical use of a long-memory process are evident, based on real and simulated time series. It is critical to be aware of this limitation when developing models and forecasting. Accurately identifying long-memory processes is essential in producing reliable predictions and avoiding incorrect model specification. [ABSTRACT FROM AUTHOR]

The study of issues related to the study of the state of the soil on the surface of the most constant technological track is relevant, since the movement of the running wheels along narrow tracks determines the traction and coupling properties of machine-tractor units, their vibrations, the stability of movement and the controllability of movement. The рurpose of this study was to increase the efficiency of the process of profiling microroughnesses of the soil surface located in areas that form a track along which the running wheels of machine-tractor units will move, by substantiating a new scheme of an automated profilograph and developing methods for its use. For this study, modern methods of experimental research based on IT technologies were used. In particular, an automated complex has been developed for measuring and evaluating the microprofile of soil surface irregularities on the very track of the tramline. The results of the experimental studies in this matter showed that the standard deviation of the soil surface irregularities reaches ±0.84 cm. This gives reason to consider the harmonic components of these functions as damped, having normalized correlation functions. The graphs constructed using PC showed that most of the dispersions of soil surface irregularities on the ruts themselves are concentrated in the range of 0…0.3 sm-1. It was established that the generator of the formation of irregularities in the longitudinal profile of traces of a permanent technological track is the parameters of the treads of the wheels of the machines moving along it. The obtained results of the study can be used in the selection of protectors of pneumatic tires of the running wheels of machine-tractor units moving on two tracks