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In the present study, the computer simulation has been used to generate the (1+1) and (2+1) surfaces with two types of correlation function Gaussian and correlation function Exponential forms. For this aim, a random number generator is used to generate the surfaces with Gaussian height distribution with zero mean, and their correlation functions were assumed to have Gaussian and exponential formulas. The calculations have been done for isotropic and anisotropic surfaces. For monofractal evaluation of rough surfaces, skewness and kurtosis values have been calculated for these (1+1) and (2+1) dimensional surfaces. Moreover, these values have been analyzed by the behavior of probability distribution of height. Also, the Hurst exponents of surfaces have been evaluated to study the irregularity and jaggedness of produced surfaces. Furthermore, the fractal dimension of these rough surfaces has been obtained to describe the complexity of the irregular fractal surfaces.

Correlated and uncorrelated Debye-Waller factors and correlation function in atomic vibrations described by mean square relative displacement, mean square displacement, and displacement displacement correlation function, respectively, have been studied based on correlated and uncorrelated Einstein models, including many-body effects. The impact of many-body effects in the derived analytical expressions of the above-considered quantities is realized by using the effective potentials of the derived Einstein models, which take into account the contributions of all nearest neighbors of vibrating atoms. The Morse potential is used to describe the single-pair atomic interactions. The difference between the correlated Debye-Waller factor and the uncorrelated one is considered to be the source of the correlation effect described by the correlation function, which is temperature and crystal-type-dependent. The larger such difference is, the stronger the correlation effect it generates. The numerical results for the Cu crystal agree with experimental results and with those calculated using other theories. [ABSTRACT FROM AUTHOR]

We find the scaling limits of a general class of boundary-to-boundary connection probabilities and multiple interfaces in the critical planar FK-Ising model, thus verifying predictions from the physics literature. We also discuss conjectural formulas using Coulomb gas integrals for the corresponding quantities in general critical planar random-cluster models with cluster-weight q ∈ [ 1 , 4) . Thus far, proofs for convergence, including ours, rely on discrete complex analysis techniques and are beyond reach for other values of q than the FK-Ising model ( q = 2 ). Given the convergence of interfaces, the conjectural formulas for other values of q could be verified similarly with relatively minor technical work. The limit interfaces are variants of SLE κ curves (with κ = 16 / 3 for q = 2 ). Their partition functions, that give the connection probabilities, also satisfy properties predicted for correlation functions in conformal field theory (CFT), expected to describe scaling limits of critical random-cluster models. We verify these properties for all q ∈ [ 1 , 4) , thus providing further evidence of the expected CFT description of these models. [ABSTRACT FROM AUTHOR]

Context: The prediction of freshwater quality is important for detecting pollution risks and assessing changes in freshwater ecosystems. As a high-precision interpolation method, Kriging was able to predict freshwater quality by using previously monitored data. However, how to select the key parameters, regression functions and correlation functions of Kriging method in the process of improving prediction accuracy is still a bottleneck. Aims: This study aims to propose an adaptive weighted-average Kriging (AWAK) method to further enhance the accuracy of freshwater-quality predictions. Methods: The AWAK method consists of four main steps. First, the key parameters influencing pollution indicators are selected by FPS method. Subsequently, six different Kriging candidate models are constructed by using regression and correlation functions with different characteristics. Then, an enhanced-likelihood function is used to determine the weights of the six Kriging candidate models. Finally, AWAK is built by weighted sum of these six Kriging models. Key results: The AWAK outperformed traditional Kriging in predicting pH and dissolved oxygen, significantly reducing prediction errors. Conclusions: By employing the AWAK method, this study successfully improved the accuracy of freshwater-quality predictions. Implications: The introduction of the AWAK provides an effective approach in the field of freshwater ecology. Freshwater-quality prediction is crucial for monitoring pollution risks and assessing changes in freshwater ecosystems. Whereas Kriging is a precise interpolation method for predicting freshwater quality, selecting key parameters, regression functions and correlation functions remains challenging. Therefore, this study proposed an adaptive weighted-average Kriging (AWAK) method that outperforms traditional Kriging in predicting pH and dissolved oxygen, reducing prediction errors significantly. Overall, AWAK improved freshwater-quality prediction and provided an effective approach in freshwater-ecology research. This article belongs to the collection Ecological Monitoring and Assessment of Freshwater Ecosystems. [ABSTRACT FROM AUTHOR]

A modification of the Klyshko method is proposed for the reference-free calibration of analog photodetectors. It is shown that the photocurrent distribution of an analog detector can be approximated by a convolution of the Poisson distribution of the number of photoelectrons with a function describing single photopulses, and the number of photons incident on the detector can be determined from the statistical properties of biphoton radiation. The ratio of the number of photoelectrons to the number of photons gives the efficiency of the analog photodetector, which can be used to measure the intensity of the radiation incident on the detector in units of photon numbers. [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]

We have analyzed the photon blockade effect in a double-cavity optomechanical system. We have explained the conventional and unconventional photon blockade effects in both weak and strong Kerr-nonlinear regimes. Through the analytical solution of the non-Hermitian Hamiltonian and the numerical solution of the master equation, the second-order correlation function of the cavity field has been calculated. We can control photon blockade effects under a small value of external pump amplitude. In this theoretical simulation, both numerical and analytical results are agreed well. The photon blockade effect is visualized by using a different contour plot. In this study, we achieve the optimal conditions for red detuning and blue detuning. We can control the rate of transmission and minimal points to locate g 2 0 . This proposal may be used to generate a single photon source with sub-Poissonian distribution and can also be useful for quantum information processing in quantum communication technology. [ABSTRACT FROM AUTHOR]

Polymer matrix tablets are an important drug-delivery system widely used for oral drug administration. Understanding the tablet hydration process, both experimentally and theoretically, is, thus, very important for the development of drug delivery systems that exhibit high drug loading capacity and controlled release potential. In this study, we used magnetic resonance microscopy (MRM) to nondestructively and dynamically analyze the water hydration process of xanthan-based tablets. The swelling process was characterized by well-resolved fronts of erosion, swelling, and penetration. The experimental results were complemented by numerical simulations of the polymer matrix hydration process. In the simulations, the polymer tablet matrix was modeled as an assembly of interacting chains with embedded drug particles, while its hydration process was mediated by interaction with solvent particles. The swelling dynamics were modeled within a Monte Carlo-based bond fluctuation model (BFM) that elegantly accounted for steric and nearest-neighbor interactions. This study provides an efficient experimental–theoretical approach for the study of polymer matrix swelling processes. [ABSTRACT FROM AUTHOR]

The paper presents an online version of the identification method for estimating the impulse responses in the case of a two-input single-output linear empirical model of type 1 diabetes that allows us to adapt the model parameters due to the intra-subject time variability in real time. The method builds on and augments our original research by providing important enhancements concerning the online parameter estimation, recursive formulation of essential equations, improved regularization, and new effective approaches to numerically solve the estimation problem. Recursive equations are derived to update the covariance matrix of the sample cross-correlation function, as well as the inverse of this covariance matrix, where the customized Sherman-Morrison formula was considered. To efficiently update the parameter estimate at each sample while avoiding direct calculation of the Hessian matrix inverse, two alternative strategies are proposed to be applied instead. The first is based on the numeric minimization by the conjugate gradient method, whereas the second takes advantage of the Schulz method to approximate the inverse Hessian matrix. As a result, all steps of the identification algorithm were designed so that only basic linear operations are required. Features to robustify the estimate were also involved, as the optimal regularization strategies based on the inverse of the covariance matrix of the actual parameter distribution and the inter-sample parameter drift were applied. In the end of the paper, a series of simulation-based experiments was carried out to assess the effectiveness of the proposed method and to demonstrate all of its aspects and important characteristics. The documented results showed that the method can yield valid estimates of impulse responses and also effectively adapt parameters in real time under the influence of time-varying physiology.

The postoccupancy performance and operation management level of green building largely determines the overall sustainability level of green buildings. It is necessary to evaluate the degree of success of green buildings in the operation stage to ensure the implementation effect of the whole life cycle. However, the current green building evaluation system is incomplete, and the research on the degree of success evaluation of green buildings is very lacking. It is necessary to establish a scientific and effective evaluation index system to evaluate the degree of success of green buildings. This article applies the extension matter‐element theory and entropy method to evaluate the degree of success of green building projects, taking a green building project in Nanchang as an example, and seven experts were invited to score and evaluate the project's degree of success by calculating the relevance degree of each evaluation index. The results show that this green building's degree of success emerged as at level II, that is, the "generally successful" level, and each first‐level indicator, respectively, lay at level III, level II, level II, and level II. The case study proves that the evaluation method of green building determined in this article is scientific and reliable. [ABSTRACT FROM AUTHOR]

One of the most modern technologies for growing row crops is strip-till. Currently, it occupies an intermediate position between conventional tillage and no-till technologies. Special complex and expensive machines are used to implement strip-till technology practically. To avoid this, a combined unit is proposed, including a tractor and two simple machines: a front-disc harrow and a chisel plough mounted behind the tractor. As experimental studies have shown, this unit makes implementing the strip-till one-pass technology possible. In this case, the oscillations process in the soil-loosening depth of strips is low-frequency since at least 95% of this statistical parameter variance is concentrated in the frequency range of 0–16.8 s−1 or 0–2.7 Hz, and its maximum falls at a frequency of 0.4 Hz. The soil-loosening depth in the strips can deviate from the mean value by ±2 cm once per 7.1 m of the combined unit's path. With a mean speed of its movement of 2.1 m·s−1, the release frequency of the mean value of the soil-loosening depth exceeding ±2 cm is only 0.29 s or 0.05 Hz. Not less than 95% of the loosened strips' non-straightness oscillations variance is in the frequency range of 0–0.25 m−1, and the value of the variance itself is small and amounts to 1.08 cm2. Proceeding from this, the non-straightness of the loosened strips by the combined unit can be considered satisfactory since its indicators meet the requirements for the non-straightness of row crops in terms of variance and frequency oscillations. [ABSTRACT FROM AUTHOR]

This paper describes a methodological analysis of the Brillouin precursor formation to understand the impairments undergone by like-noise and random noise waveforms propagating through naturally dispersive media commonly found in radar applications. By means of a frequency-domain methodology based on considering the frequency response of the medium under study, the effect of these dispersive media on the evolution of an input signal can be seen as frequency filtering. The simulations were performed at a center frequency of 1.5 GHz and for a signal bandwidth of 3 GHz. Four random noise signals were considered: Barker codes, PRBS codes, Frank codes, Costas codes and additive white Gaussian noise. The experienced impairments were assessed in terms of cross-correlation function (CCF) degradation. The differences in the behavior of each type of phase and frequency coded signal to face the dispersive propagation have been demonstrated in terms of parameters used for information retrieval: peak amplitude decay, CCF secondary sidelobe level and multipath detectability. Finally, a frequency filtering approach is proposed to mitigate the impairments due to dispersive propagation under multipath conditions. [ABSTRACT FROM AUTHOR]

One of the most modern technologies for growing row crops is strip-till. Currently, it occupies an intermediate position between conventional tillage and no-till technologies. Special complex and expensive machines are used to implement strip-till technology practically. To avoid this, a combined unit is proposed, including a tractor and two simple machines: a front-disc harrow and a chisel plough mounted behind the tractor. As experimental studies have shown, this unit makes implementing the strip-till one-pass technology possible. In this case, the oscillations process in the soil-loosening depth of strips is low-frequency since at least 95% of this statistical parameter variance is concentrated in the frequency range of 0–16.8 s−1 or 0–2.7 Hz, and its maximum falls at a frequency of 0.4 Hz. The soil-loosening depth in the strips can deviate from the mean value by ±2 cm once per 7.1 m of the combined unit’s path. With a mean speed of its movement of 2.1 m·s−1, the release frequency of the mean value of the soil-loosening depth exceeding ±2 cm is only 0.29 s or 0.05 Hz. Not less than 95% of the loosened strips’ non-straightness oscillations variance is in the frequency range of 0–0.25 m−1, and the value of the variance itself is small and amounts to 1.08 cm2. Proceeding from this, the non-straightness of the loosened strips by the combined unit can be considered satisfactory since its indicators meet the requirements for the non-straightness of row crops in terms of variance and frequency oscillations.

Accurate identification of the source of water gushing in closed coal mines and correct division of water gushing modes are of great significance for scientific disposal of water resources waste and water environment pollution caused by closed coal mine drainage. A comprehensive method for water inflow characterization, source identification, and model research for closed coal mines by multivariate analysis of “water quantity–hydrochemistry–microorganism–hydrogeological conditions” is proposed. The method is based on the dynamic monitoring data of water inflow and the water chemical and microbial indexes of several closed coal mines in the Songzao mining area of Chongqing in a hydrological year. Water quality analysis methods, such as flow dynamic analysis of water inflow and flow–rainfall hydro-logical series correlation function, descriptive statistics of water chemical indexes, and the Pearson correla-tion function of water chemical indexes between mine water samples are also used as bases. The method is further coupled with the hydrogeological conditions of the mining area. Results show that there are three types of fluctuations in the response of water inflow from closed coal mines to rainfall: sudden rise and slow drop, slow rise and slow drop, and stable. The difference in water inflow source and water diversion medium is the main reason for the dynamic change in mine water inflow and the temporal and spatial differences in its response to rainfall. It also causes the characteristics of large variability in TDS, pH, chemical correlation degree, and microbial content of mine water. Based on water source identification, four types, rainfall infiltration type, aquifer release type, old empty water overflow type, and compound type, of water gushing modes of closed coal mines in mining areas are proposed. The multivariate comprehensive analysis method identifies the source of water inrush from closed coal mines in karst mining areas effectively, deepens the understanding of the characteristics of water inrush from closed coal mines, and provides theoretical support for the scientific prevention and control of closed coal mine water inrush in Songzao mining area and the coordinated development of environment and resources.

The research article demonstrates that agricultural transport and technological systems are susceptible to external random influences during their operation. By accurately describing and modeling these effects, the performance of the tool can be enhanced during the research and design stages. (Research purpose) The objective of this research is to generate random processes with predefined correlation functions that simulate the profile of the supporting surface under the wheels of agricultural transport and technological systems during operations. Additionally, the study aims to visually represent the resulting random implementations of the support surface profile height. (Materials and methods) The proposed approach considers the variation in support surface profile height along the trajectory of agricultural transport and technological systems, while maintaining a constant speed, as a stationary random process. The selection of the correlation function type and its parameters is dependent on the specific characteristics of the support surface. Subsequently, using the Matlab environment, the model for the support surface profile height under the wheels is developed. (Results and discussion) Successful implementations of support surface profile height have been achieved for two distinct scenarios: asphalt and wheat stubble. A comparative analysis is conducted between the correlation function of the simulated implementation of the random process and the original correlation function. (Conclusions) The proposed algorithm has demonstrated its capability to generate a random process with specified correlation function properties, accurately describing the height fluctuations of the support surface profile under the wheels of agricultural transport and technological systems. The adequacy of the algorithm has been confirmed through a comprehensive analysis of at least 50 implementations, highlighting its effectiveness and reliability.

We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval. Estimation of the covariance function for functional snippets is challenging since information for the far off-diagonal regions of the covariance structure is completely missing. We address this difficulty by decomposing the covariance function into a variance function component and a correlation function component. The variance function can be effectively estimated nonparametrically, while the correlation part is modeled parametrically, possibly with an increasing number of parameters, to handle the missing information in the far off-diagonal regions. Both theoretical analysis and numerical simulations suggest that this hybrid strategy is effective. In addition, we propose a new estimator for the variance of measurement errors and analyze its asymptotic properties. This estimator is required for the estimation of the variance function from noisy measurements.

In the background of economic informationization, the integration and development of enterprise refinement management and financial integration have become the mainstream management direction of modern enterprise management. In this paper, the correlation function and judgment matrix are firstly determined by the entropy-weighted elementary topologizable evaluation model, while the initial judgment matrix V is standardized, and the differences in the correlation degree of indicators of different natures should be noted. The entropy power method is applied to calculate the change of relevant evaluation indexes, and the value of information utility in the evaluation system is determined through the change of entropy value. Then the initial data are obtained by means of questionnaires, and data analysis is performed on the first-level indicators in the evaluation system of enterprise financial management capability. The results show that the three indicators of financial risk control capability, financial management informationization level and financial personnel capability, and total budget management level have more room for improvement, but the score of financial risk control capability is only 5.04 points different from the total score, indicating that the specific situation of the enterprise itself for specific analysis. This study improves the level of financial management of enterprises and promotes their development of enterprises.

This paper firstly proposes a digital resource system of university libraries oriented to knowledge service for digital library resource evaluation research, which mainly consists of a knowledge service diamond system and digital resource diamond system, and studies the evaluation elements and evaluation process of this system, then constructs the evaluation system of library digital resources from quantitative evaluation and qualitative evaluation, etc., and through multi-level topologizable theory, the evaluation indexes and The evaluation indexes and the correlation function are calculated by multi-level topology theory, to derive the weight coefficients and comprehensive superiority of the evaluation indexes, and an example analysis of the digital library based on multi-level topology optimization decision making is conducted. The results show that the users’ comprehensive evaluation of digital library decision-making is excellent, S2, S5 is good, S3 is medium, and S4 is average, where S5 has a higher comprehensive correlation degree in the good level than the correlation degree of S2, indicating that this study improves the quality of digital library decision making in universities and then better serves the users.

In this letter, we present the first study of Hawking radiation as a tunneling process within the framework of non-commutative (NC) gauge theory of gravity. First, we reconstruct the non-commutative Schwarzschild black hole (NC SBH) within the gauge theory of gravity, employing the Seiberg-Witten (SW) map and the star product. Then, we compute the emission spectrum of outgoing massless particles using the quantum tunneling mechanism. In the first scenario, we calculate the tunneling rate of massless particles crossing the event horizon of the NC SBH with lower frequencies. Our results reveal pure thermal radiation. Notably, we find that the Hawking temperature remains consistent in both the classical thermodynamics and the quantum tunneling approach, suggesting equivalence between these two approaches in NC spacetime. However, in the case of massless particle emission with higher frequencies, we account for energy conservation resulting in the tunneling rate to deviate from pure thermal radiation. This tunneling rate remains consistent with an underlying unitary quantum theory. We establish a relationship between this deviation and the change in the black hole entropy, revealing a logarithmic correction to the entropy within this geometry. Furthermore, we demonstrate that non-commutativity enhances the correlations between two successively emitted particles. Additionally, we determine the NC density number of particle emission and conclude by discussing the implications of our findings.

In momentum space, we investigate the correlation properties of the ground state of Tonks–Girardeau gases. With Bose–Fermi mapping method, the exact ground state wavefunction in coordinate space can be obtained based on the wavefunction of spin-polarized Fermions. By Fourier transformation we obtain the ground state wavefunction in momentum space, and therefore the pair correlation and the reduced one-body density matrix (ROBDM) in momentum space, whose diagonal part is the momentum distribution. The ROBDM in momentum space is the Fourier transformation of the ROBDM in coordinate space and the pair correlation in momentum space is the Fourier transformation of the reduced two-body density matrix in coordinate space. The correlations in momentum space display larger values only in small momentum region and vanish in most other regions. The lowest natural orbital and occupation distribution in momentum space are also obtained. [ABSTRACT FROM AUTHOR]

Tchebyscheff map is a typical chaotic map and the correlation functions play a key role in the study of its statistical properties. This paper aims at the solutions of a class of exponential Diophantine equations arising in the calculation of correlation functions of the Tchebyscheff map. To solve the equation, we firstly reduce it to a new Diophantine equation with strictly increasing exponentials and nonzero coefficients. Then we introduce the definition of "block" and classify the reduced equations based on the number of blocks constructing the equation, thus transform the problem of solving the equation to solve the new equations constructed by blocks. Finally we solve the equations constructed by one block and two blocks and exemplify the application of the main results. [ABSTRACT FROM AUTHOR]

Aiming at the troubles of difficult extraction of fault features and low fault recognition rate in rotating equipment fault detection approach, a new technique for intelligent diagnosis based on modified hierarchical diversity entropy (MHDE) and extension theory (ET) is proposed in the thesis. Firstly, MHDE employs to comprehensively describe the fault information of the given signals. Secondly, the MHDE feature sets are regarded as the characteristic parameters of the extension matter element model, and the matter element model in various states is established. Finally, the testing datasets are fed into the matter element model for each operating conditions, and the correlation function is used to compute the comprehensive correlation between the testing datasets and the various conditions of the rotating machinery, so as to realize the qualitative and quantitative identification of the testing datasets. The reliability and superiority of the proposed new approach is validated by real experimental datasets on various rotating machinery types. The analysis results show that the proposed novel technology can effectively excavate the feature information and accurately identify various fault conditions of rotating machinery. In addition, compared with other combined model technology in the paper, the proposed intelligent fault diagnosis technology has better classification performance. [ABSTRACT FROM AUTHOR]

We evaluate the correlation function of a radar signal scattered by inhomogeneities of turbulent medium and received by a radar station at the output of the matched filter. For the turbulent medium, we employ the model of wandering inhomogeneities, which is a generalization of the 'frozen' turbulence. The concepts of strong and weak wanderings are introduced. The case of bistatic radar station is considered. For a monostatic radar station, simple asymptotic formulas are obtained. It is shown that, in the short-wavelength limit, wanderings are almost always strong, and in the long-wavelength limit, the weak wandering limit takes place mainly in the long-wavelength approximation. [ABSTRACT FROM AUTHOR]

Copyright of Coal Science & Technology (0253-2336) is the property of Coal Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Scientific Bulletin of National Mining University is the property of National Mining University, State Higher Educational Institution and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangdong University of Technology is the property of Journal of Guangdong University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The object of this study is the material flow incoming the conveyor. The actual problem of calculating the stochastic characteristics of the input material flow of a transport system, based on the typification of the input material flow, is being solved. When constructing a model of the input material flow, methods of similarity theory were used. A criterion has developed for dividing the realization of the input material flow into a deterministic and stochastic component, which makes it possible to represent the stochastic component of the input flow in the form of an realization of a centered ergodic process. A method is presented for calculating amplitude and phase frequency spectra for the components of the input material flow, based on specified types of theoretical correlation functions. The calculating accuracy of the normalized correlation function values is e~0.05. Distinctive features of the obtained results are that the typification method of the input material flow is based on the use of the amplitude spectrum for the input material flow. A special feature of the results obtained is that a single realization of the input material flow was used to model the input material flow. The scope of application of the obtained results is the mining industry. The developed methodology for calculating the statistical characteristics of the input material flow allow to improve the accuracy of algorithms for optimal control of the flow parameters of the transport system for a mining enterprise. The condition for the practical application of the obtained results is the presence in the sections of the transport conveyor of measuring sensors that determine the speed of the belt and the amount of material in the bunker. [ABSTRACT FROM AUTHOR]

To effectively receive a useful broadband signal, it is necessary to compensate for distortions caused by the complex frequency-dependent coefficient of the receiving and transmitting antenna, multiplicative interference and noise from the heterogeneity of the propagation medium, additive interference and noise. Using only correlation processing under certain conditions will not allow receiving a useful broadband signal with the required quality. The article develops a mathematical model of spatio-temporal processing of broadband signals in satellite broadband access systems, showing that spatio-temporal processing should be carried out in two stages. At the first stage, space-time processing is carried out in the channel adaptively to the antenna array based on the formation of a complex frequency-dependent vector of weighting coefficients, which should change with a change in the signal-interference situation in real time, taking into account the change in the direction of radiation sources. At the second stage, correlation processing of the broadband signal is performed based on the use of long-length code sequences. This model is the basis for the development of methods for the formation and correlation (temporal) processing of broadband signals and methods of spatio-temporal processing of broadband signals under conditions of intentional and unintentional exposure. Based on the presented mathematical model of spatio-temporal processing of broadband signals, the main directions of increasing the noise immunity of radio-electronic systems are determined.

Spherical Bessel functions (sBFs) appear commonly in many areas of physics wherein there is both translation and rotation invariance, and often integrals over products of several arise. Thus, analytic evaluation of such integrals with different weighting functions (which appear as toy models of a given physical observable, such as the galaxy power spectrum) is useful. Here, we present a generalization of a recursion-based method for evaluating such integrals. It gives relatively simple closed-form results in terms of Legendre functions (for the exponentially damped case) and Gamma, incomplete Gamma, and hypergeometric functions (for the Gaussian-damped case). We also present a new, non-recursive method to evaluate integrals of products of sBFs with Gaussian damping in terms of incomplete Gamma functions and hypergeometric functions. [ABSTRACT FROM AUTHOR]

We are interested in the phase transition of the correlation function of local densities of states at mesoscopic scales of random band matrices of width W in dimension 2. As a result, we show that the local densities of states are alternately positively and negatively correlated in the diffusive regime O (log (L / W)) times, L being the size of the system. [ABSTRACT FROM AUTHOR]

This work introduces a new, compactly supported correlation function that can be inhomogeneous over Euclidean three‐space, anisotropic when restricted to the sphere, and compactly supported on regions other than spheres of fixed radius. This function, which we call the Generalized Gaspari–Cohn (GenGC) correlation function, is a generalization of the compactly supported, piecewise rational approximation to a Gaussian introduced by Gaspari and Cohn in 1999 and its subsequent extension by Gaspari et al in 2006. The GenGC correlation function is a parametric correlation function that allows two parameters a$$ a $$ and c$$ c $$ to vary, as functions, over space, whereas the earlier formulations either keep both a$$ a $$ and c$$ c $$ fixed or only allow a$$ a $$ to vary. Like these earlier formulations, GenGC is a sixth‐order piecewise rational function (fifth‐order near the origin), while the coefficients now depend explicitly on the values of both a$$ a $$ and c$$ c $$ at each pair of points being correlated. We show that, by allowing both a$$ a $$ and c$$ c $$ to vary, the correlation length of GenGC also varies over space and introduces inhomogeneous and anisotropic features that may be useful in data assimilation applications. Covariances produced using GenGC are computationally tractable due to their compact support and have the added flexibility of generating compact support regions that adapt to the input c$$ c $$ field. These features can be useful for covariance modeling and covariance tapering applications in data assimilation. We derive the GenGC correlation function using convolutions, discuss continuity properties relating to a$$ a $$ and c$$ c $$ and its correlation length, and provide one‐ and two‐dimensional examples that highlight its anisotropy and variable regions of compact support. [ABSTRACT FROM AUTHOR]

Copyright of Ordnance Industry Automation is the property of Editorial Board for Ordnance Industry Automation and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A mathematical modeling of contaminate transportation has been presented in the current paper. The time-dependent dispersion has been considered in the transportation of contaminant in a finite homogeneous porous medium. The study of contaminants concentration has been presented for the uniform unsteady ow of ground-water. Instead of a constant dispersion, in order to consider the effect of groundwater velocity on contaminant transportation, dispersion has been considered as a groundwater velocity-dependent quantity. As found in the many practical aspects, a linear increase in concentration at a source point with time has been assumed for the present modeling. The spread of the initial contaminant concentration has been considered linearly decreasing along the direction of one-dimensional ow. The contaminant transport equation for the above-mentioned conditions and environment has been solved. The Laplace transform variation iteration method (LVIM) has been adopted to obtain a solution. Spatial and temporal variations of concentration for a developed model have been presented graphically by varying dispersion. The LVIM has been found suitable for the present study of contaminant transport modeling. The MATHEMATICA package has been used for the present study. [ABSTRACT FROM AUTHOR]

The manipulation of photons is a key technology for obtaining optical quantum information. In this study, we present a phase-modulated optomechanical system comprising two coupled cavity resonators and illustrate the phase-controlled photon blockade in the system. The coupling phase of the cavities reveals the interference of photons and introduces an unconventional photon-blockade effect. We also study the influence of the energy level fineness on the photon blockade and resonant frequency of the mechanical mode. Numerical simulations demonstrate that photon blockade can occur over a wide range of system parameters. These results have several implications for understanding the role of the state phase in quantum cavity optomechanics and provide a promising method for the realization of optomechanical quantum devices using photon blockade.

The objective of this work is to measure the influence of the Mth coherent state on the optics model of two atoms interacting with two-mode quantized field. Also, two atoms interacting together is included in this optics model. The time-dependent wave function is computed analytically. The two-mode quantized field is in the Mth coherent state while the two atoms have two levels. The influence of the Mth coherent state on the quantum model is measured via studying the atomic inversion, von Neumann entropy, variance squeezing, correlation function and Husimi function. The influence of each mode of the quantized field separately and both modes together are discussed. The statistical measures indicate that the nonclassical quantized features increase in the presence of the Mth coherent state, and it features a controlling mechanism. This study opens up a wide range of a large number of serious applications for the quantum optics models.

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

Using a new method of correlation function for amplitude and phase fluctuations (APCF), records of geomagnetic field component fluctuations (observatories Mondy and Borok) have been processed for a number of hour zones of the nightside magnetosphere. This method is meant to detect groups of equidistant frequencies inside the spectrum of source signal and also to measure a difference between two neighbor frequencies in each of these groups.

The descriptions of a radially phased-locked Hermite–Gaussian correlated beam array are introduced, the equation of this beam array in oceanic turbulence is derived, and the intensity profiles of this beam array are shown and analyzed. The results imply that the evolutions of the sub-beam of this beam array in free space are the same as the Hermite–Gaussian correlated beam, while the intensity of this beam array can be adjusted by controlling the initial beam radius R and the coherence length. The intensity profiles of this beam array in free space have multiple spots during propagation, while the same beam array in oceanic turbulence can become a beam spot due to the influences of R and oceanic turbulence. The beam array with smaller coherence length in oceanic turbulence retains the splitting properties better during propagation. [ABSTRACT FROM AUTHOR]