Statistics of order 2 (variance, auto and cross-correlation functions, auto and cross-power spectra) and 3 (skewness, auto and cross-bicorrelation functions, auto and cross-bispectra) are used to analyze the wave-part...Statistics of order 2 (variance, auto and cross-correlation functions, auto and cross-power spectra) and 3 (skewness, auto and cross-bicorrelation functions, auto and cross-bispectra) are used to analyze the wave-particle interaction in space plasmas. The signals considered here are medium scale electron density irregularities and ELF/ULF electrostatic turbulence. Nonlinearities are mainly observed in the ELF range. They are independently pointed out in time series associated with fluctuations in electronic density and in time series associated with the measurement of one electric field component. Peaks in cross-bicorrelation function and in mutual information clearly show that, in well delimited frequency bands, the wave-particle interactions are nonlinear above a certain level of fluctuations. The way the energy is transferred within the frequencies of density fluctuations is indicated by a bi-spectra analysis.展开更多
This paper proposes a unified clutter model incorporating the effects of range walk and array rotation for space-time adaptive processing(STAP) in airborne multi-channel early-warning radar.Based on this clutter mod...This paper proposes a unified clutter model incorporating the effects of range walk and array rotation for space-time adaptive processing(STAP) in airborne multi-channel early-warning radar.Based on this clutter model,STAP performance is then analyzed from the perspective of covariance matrix tapering(CMT).For STAP performance degradation due to array rotation,a determinate compensation method is proposed based on the CMT method.Numerical examples are provided to verify the analysis and the proposed compensation method.展开更多
A convenient implementation approach to space-time adaptive processing for airborne radar has been proposed, which is added by some auxiliary array elements in the area of main-lobe clutter on the basis of 2-D Capon a...A convenient implementation approach to space-time adaptive processing for airborne radar has been proposed, which is added by some auxiliary array elements in the area of main-lobe clutter on the basis of 2-D Capon approach . It is of practical use for its small computational load. This approach possesses the ideal performance in the area of main-lobe clutter . In addition, the approach which is added by some auxiliary beams in the area of main-lobe clutter has also been discussed.展开更多
In non-homogeneous environment, traditional space-time adaptive processing doesn't effectively suppress interference and detect target, because the secondary data don' t exactly reflect the statistical characteristi...In non-homogeneous environment, traditional space-time adaptive processing doesn't effectively suppress interference and detect target, because the secondary data don' t exactly reflect the statistical characteristic of the range cell under test. A ravel methodology utilizing the direct data domain approach to space-time adaptive processing ( STAP ) in airbome radar non-homogeneous environments is presented. The deterministic least squares adaptive signal processing technique operates on a "snapshot-by-snapshot" basis to dethrone the adaptive adaptive weights for nulling interferences and estimating signal of interest (SOI). Furthermore, this approach eliminates the requirement for estimating the covariance through the data of neighboring range cell, which eliminates calculating the inverse of covariance, and can be implemented to operate in real-time. Simulation results illustrate the efficiency of interference suppression in non-homogeneous environment.展开更多
One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse ...One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.展开更多
This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected ...This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected through a data acquisition system for real time control. The interaction between the process variables is shown to be challenging for single variable controllers, therefore multi-variable control is worth considering. A multi-variable state space model is obtained from on-line experimental data. The controller design is translated into a Quadratic Programming (QP) problem, in which a cost function subject to actuators linear inequality constraints is minimized. The outcome of the experimental results is that the main control objectives, such as set-point tracking and perturbations rejection under actuators constraints, are well achieved for both controlled variables simultaneously.展开更多
For the slowly changed environment-range-dependent non-homogeneity, a new statistical space-time adaptive processing algorithm is proposed, which uses the statistical methods, such as Bayes or likelihood criterion to ...For the slowly changed environment-range-dependent non-homogeneity, a new statistical space-time adaptive processing algorithm is proposed, which uses the statistical methods, such as Bayes or likelihood criterion to estimate the approximative covariance matrix in the non-homogeneous condition. According to the statistical characteristics of the space-time snapshot data, via defining the aggregate snapshot data and corresponding events, the conditional probability of the space-time snapshot data which is the effective training data is given, then the weighting coefficients are obtained for the weighting method. The theory analysis indicates that the statistical methods of the Bayes and likelihood criterion for covariance matrix estimation are more reasonable than other methods that estimate the covariance matrix with the use of training data except the detected outliers. The last simulations attest that the proposed algorithms can estimate the covariance in the non-homogeneous condition exactly and have favorable characteristics.展开更多
A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphso...A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.展开更多
Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical meth...Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.展开更多
A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in...A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.展开更多
Specific challenges arise in the task of real-time automatic data reduction of optical space debris observations. Here we present an automatic technique that optimally detects and measures the sources from images of o...Specific challenges arise in the task of real-time automatic data reduction of optical space debris observations. Here we present an automatic technique that optimally detects and measures the sources from images of optical space debris ob- servations. We show that highly reliable and accurate results can be obtained on most images produced by our specific sensors, and due to optimizations, the whole pipeline works fast and efficiently. Tests demonstrate that the technique performs better than SExtractor from the point of view of fast and accurate detection, therefore it is well suited for data reduction of optical space debris observations.展开更多
This paper aims to present an intelligent system for parking space detection based on image processing technique. The proposed system captures and processes the rounded image drawn at parking lot and produces the info...This paper aims to present an intelligent system for parking space detection based on image processing technique. The proposed system captures and processes the rounded image drawn at parking lot and produces the information of the empty car parking spaces. In this work, a camera is used as a sensor to take photos to show the occupancy of car parks. The reason why a camera is used is because with an image it can detect the presence of many cars at once. Also, the camera can be easily moved to detect different car parking lots. By having this image, the particular car parks vacant can be known and then the processed information was used to guide a driver to an available car park rather than wasting time to find one. The proposed system has been developed in both software and hardware platform. An automatic parking system is used to make the whole process of parking cars more efficient and less complex for both drivers and administrators.展开更多
The Chang'e-3 (CE-3) mission is China's first exploration mission on the surface of the Moon that uses a lander and a rover. Eight instruments that form the scientific payloads have the following objectives: (1...The Chang'e-3 (CE-3) mission is China's first exploration mission on the surface of the Moon that uses a lander and a rover. Eight instruments that form the scientific payloads have the following objectives: (1) investigate the morphological features and geological structures at the landing site; (2) integrated in-situ analysis of minerals and chemical compositions; (3) integrated exploration of the structure of the lunar interior; (4) exploration of the lunar-terrestrial space environment, lunar sur- face environment and acquire Moon-based ultraviolet astronomical observations. The Ground Research and Application System (GRAS) is in charge of data acquisition and pre-processing, management of the payload in orbit, and managing the data products and their applications. The Data Pre-processing Subsystem (DPS) is a part of GRAS. The task of DPS is the pre-processing of raw data from the eight instruments that are part of CE-3, including channel processing, unpacking, package sorting, calibration and correction, identification of geographical location, calculation of probe azimuth angle, probe zenith angle, solar azimuth angle, and solar zenith angle and so on, and conducting quality checks. These processes produce Level 0, Level 1 and Level 2 data. The computing platform of this subsystem is comprised of a high-performance computing cluster, including a real-time subsystem used for processing Level 0 data and a post-time subsystem for generating Level 1 and Level 2 data. This paper de- scribes the CE-3 data pre-processing method, the data pre-processing subsystem, data classification, data validity and data products that are used for scientific studies.展开更多
This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance mi...This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.展开更多
Although tracking with a passive optical telescope is a powerful technique for space debris observation, it is limited by its sensitivity to dynamic background noise. Traditionally, in the field of astronomy, static b...Although tracking with a passive optical telescope is a powerful technique for space debris observation, it is limited by its sensitivity to dynamic background noise. Traditionally, in the field of astronomy, static background subtraction based on a median image technique has been used to extract moving space objects prior to the tracking operation, as this is computationally efficient. The main disadvantage of this technique is that it is not robust to variable illumination conditions. In this article, we propose an approach for tracking small and dim space debris in the context of a dynamic background via one of the optical telescopes that is part of the space surveillance network project, named the Asia- Pacific ground-based Optical Space Observation System or APOSOS. The approach combines a fuzzy running Gaussian average for robust moving-object extraction with dim-target tracking using a particle- filter-based track-before-detect method. The performance of the proposed algorithm is experimentally evaluated, and the results show that the scheme achieves a satisfactory level of accuracy for space debris tracking.展开更多
In order to implement an observing strategy, image degradation that occurs during optical observation of space debris is ineluctable and has distinct characteris- tics. Image restoration is presented as a way to remov...In order to implement an observing strategy, image degradation that occurs during optical observation of space debris is ineluctable and has distinct characteris- tics. Image restoration is presented as a way to remove the influence of degradation in CCD images of space debris, based on assumed PSF models with the same F-WHM as images of the object. In the process of image restoration, the maximum entropy method is adopted. The results of reduction using observed raw CCD images indi- cate that the precision in estimating positions of objects is improved and the effects of degradation are reduced. Improving the astrometry of space debris using image restoration is effective and feasible.展开更多
An optical survey is the main technique for detecting space debris. Due to the specific character- istics of observation, the pointing errors and tracking errors of the telescope as well as image degradation may be si...An optical survey is the main technique for detecting space debris. Due to the specific character- istics of observation, the pointing errors and tracking errors of the telescope as well as image degradation may be significant, which make it difficult for astrometric calibration. Here we present an improved method that corrects the pointing and tracking errors, and measures the image position precisely. The pipeline is tested on a number of CCD images obtained from a 1-m telescope administered by Xinjiang Astronomical Observatory while observing a GPS satellite. The results show that the position measurement error of the background stars is around 0.1 pixel, while the time cost for a single frame is about 7.5 s; hence the relia- bility and accuracy of our method are demonstrated. In addition, our method shows a versatile and feasible way to perform space debris observation utilizing non-dedicated telescopes, which means more sensors could be involved and the ability to perform surveys could be improved.展开更多
We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive...We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.展开更多
文摘Statistics of order 2 (variance, auto and cross-correlation functions, auto and cross-power spectra) and 3 (skewness, auto and cross-bicorrelation functions, auto and cross-bispectra) are used to analyze the wave-particle interaction in space plasmas. The signals considered here are medium scale electron density irregularities and ELF/ULF electrostatic turbulence. Nonlinearities are mainly observed in the ELF range. They are independently pointed out in time series associated with fluctuations in electronic density and in time series associated with the measurement of one electric field component. Peaks in cross-bicorrelation function and in mutual information clearly show that, in well delimited frequency bands, the wave-particle interactions are nonlinear above a certain level of fluctuations. The way the energy is transferred within the frequencies of density fluctuations is indicated by a bi-spectra analysis.
基金supported by the National Natural Science Foundation of China(60901056)
文摘This paper proposes a unified clutter model incorporating the effects of range walk and array rotation for space-time adaptive processing(STAP) in airborne multi-channel early-warning radar.Based on this clutter model,STAP performance is then analyzed from the perspective of covariance matrix tapering(CMT).For STAP performance degradation due to array rotation,a determinate compensation method is proposed based on the CMT method.Numerical examples are provided to verify the analysis and the proposed compensation method.
基金National Nature Science FoundationNational Deferise Research Funds
文摘A convenient implementation approach to space-time adaptive processing for airborne radar has been proposed, which is added by some auxiliary array elements in the area of main-lobe clutter on the basis of 2-D Capon approach . It is of practical use for its small computational load. This approach possesses the ideal performance in the area of main-lobe clutter . In addition, the approach which is added by some auxiliary beams in the area of main-lobe clutter has also been discussed.
文摘In non-homogeneous environment, traditional space-time adaptive processing doesn't effectively suppress interference and detect target, because the secondary data don' t exactly reflect the statistical characteristic of the range cell under test. A ravel methodology utilizing the direct data domain approach to space-time adaptive processing ( STAP ) in airbome radar non-homogeneous environments is presented. The deterministic least squares adaptive signal processing technique operates on a "snapshot-by-snapshot" basis to dethrone the adaptive adaptive weights for nulling interferences and estimating signal of interest (SOI). Furthermore, this approach eliminates the requirement for estimating the covariance through the data of neighboring range cell, which eliminates calculating the inverse of covariance, and can be implemented to operate in real-time. Simulation results illustrate the efficiency of interference suppression in non-homogeneous environment.
文摘One of the critical hurdles, and breakthroughs, in the field of Natural Language Processing (NLP) in the last two decades has been the development of techniques for text representation that solves the so-called curse of dimensionality, a problem which plagues NLP in general given that the feature set for learning starts as a function of the size of the language in question, upwards of hundreds of thousands of terms typically. As such, much of the research and development in NLP in the last two decades has been in finding and optimizing solutions to this problem, to feature selection in NLP effectively. This paper looks at the development of these various techniques, leveraging a variety of statistical methods which rest on linguistic theories that were advanced in the middle of the last century, namely the distributional hypothesis which suggests that words that are found in similar contexts generally have similar meanings. In this survey paper we look at the development of some of the most popular of these techniques from a mathematical as well as data structure perspective, from Latent Semantic Analysis to Vector Space Models to their more modern variants which are typically referred to as word embeddings. In this review of algoriths such as Word2Vec, GloVe, ELMo and BERT, we explore the idea of semantic spaces more generally beyond applicability to NLP.
文摘This paper investigates State Space Model Predictive Control (SSMPC) of an aerothermic process. It is a pilot scale heating and ventilation system equipped with a heater grid and a centrifugal blower, fully connected through a data acquisition system for real time control. The interaction between the process variables is shown to be challenging for single variable controllers, therefore multi-variable control is worth considering. A multi-variable state space model is obtained from on-line experimental data. The controller design is translated into a Quadratic Programming (QP) problem, in which a cost function subject to actuators linear inequality constraints is minimized. The outcome of the experimental results is that the main control objectives, such as set-point tracking and perturbations rejection under actuators constraints, are well achieved for both controlled variables simultaneously.
基金Supported by the National Post-doctor Fundation (No. 20090451251) the Shaanxi Industry Surmount Foundation (2009K08-31) of China
文摘For the slowly changed environment-range-dependent non-homogeneity, a new statistical space-time adaptive processing algorithm is proposed, which uses the statistical methods, such as Bayes or likelihood criterion to estimate the approximative covariance matrix in the non-homogeneous condition. According to the statistical characteristics of the space-time snapshot data, via defining the aggregate snapshot data and corresponding events, the conditional probability of the space-time snapshot data which is the effective training data is given, then the weighting coefficients are obtained for the weighting method. The theory analysis indicates that the statistical methods of the Bayes and likelihood criterion for covariance matrix estimation are more reasonable than other methods that estimate the covariance matrix with the use of training data except the detected outliers. The last simulations attest that the proposed algorithms can estimate the covariance in the non-homogeneous condition exactly and have favorable characteristics.
文摘A non-incremental time-space algorithm is proposed for numerical. analysis of forming process with the inclusion of geometrical, material, contact-frictional nonlinearities. Unlike the widely used Newton-Raphson counterpart, the present scheme features an iterative solution procedure on entire time and space domain. Validity and feasibility of foe present scheme are further justiced by the numerical investigation herewith presented.
文摘Let E be a uniformly smooth Banach space, K be a nonempty closed convex subset of E, and suppose: T: K --> K is a continuous Phi-strongly pseudocontractive operator with a bounded range. Using a new analytical method, under general cases, the Ishikawa iterative process {x(n)} converges strongly to the unique fixed point x* of the operator T were proved. The paper generalizes and extends a lot of recent corresponding results.
文摘A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.
基金funded by the National Natural Science Foundation of China(Grant Nos.11125315 and 11033009)
文摘Specific challenges arise in the task of real-time automatic data reduction of optical space debris observations. Here we present an automatic technique that optimally detects and measures the sources from images of optical space debris ob- servations. We show that highly reliable and accurate results can be obtained on most images produced by our specific sensors, and due to optimizations, the whole pipeline works fast and efficiently. Tests demonstrate that the technique performs better than SExtractor from the point of view of fast and accurate detection, therefore it is well suited for data reduction of optical space debris observations.
文摘This paper aims to present an intelligent system for parking space detection based on image processing technique. The proposed system captures and processes the rounded image drawn at parking lot and produces the information of the empty car parking spaces. In this work, a camera is used as a sensor to take photos to show the occupancy of car parks. The reason why a camera is used is because with an image it can detect the presence of many cars at once. Also, the camera can be easily moved to detect different car parking lots. By having this image, the particular car parks vacant can be known and then the processed information was used to guide a driver to an available car park rather than wasting time to find one. The proposed system has been developed in both software and hardware platform. An automatic parking system is used to make the whole process of parking cars more efficient and less complex for both drivers and administrators.
文摘The Chang'e-3 (CE-3) mission is China's first exploration mission on the surface of the Moon that uses a lander and a rover. Eight instruments that form the scientific payloads have the following objectives: (1) investigate the morphological features and geological structures at the landing site; (2) integrated in-situ analysis of minerals and chemical compositions; (3) integrated exploration of the structure of the lunar interior; (4) exploration of the lunar-terrestrial space environment, lunar sur- face environment and acquire Moon-based ultraviolet astronomical observations. The Ground Research and Application System (GRAS) is in charge of data acquisition and pre-processing, management of the payload in orbit, and managing the data products and their applications. The Data Pre-processing Subsystem (DPS) is a part of GRAS. The task of DPS is the pre-processing of raw data from the eight instruments that are part of CE-3, including channel processing, unpacking, package sorting, calibration and correction, identification of geographical location, calculation of probe azimuth angle, probe zenith angle, solar azimuth angle, and solar zenith angle and so on, and conducting quality checks. These processes produce Level 0, Level 1 and Level 2 data. The computing platform of this subsystem is comprised of a high-performance computing cluster, including a real-time subsystem used for processing Level 0 data and a post-time subsystem for generating Level 1 and Level 2 data. This paper de- scribes the CE-3 data pre-processing method, the data pre-processing subsystem, data classification, data validity and data products that are used for scientific studies.
基金supported by the National Natural Science Foundation of China(10801056)the Natural Science Foundation of Ningbo(2010A610094)
文摘This paper studies the limit average variance criterion for continuous-time Markov decision processes in Polish spaces. Based on two approaches, this paper proves not only the existence of solutions to the variance minimization optimality equation and the existence of a variance minimal policy that is canonical, but also the existence of solutions to the two variance minimization optimality inequalities and the existence of a variance minimal policy which may not be canonical. An example is given to illustrate all of our conditions.
基金support from The World Academy of Sciences(TWAS)the Chinese Academy of Sciences(CAS)+1 种基金the AsiaPacific Space Cooperation Organization(APSCO)supported as part of a national major scientific research equipment development project of China(No.ZDYZ2013-2)
文摘Although tracking with a passive optical telescope is a powerful technique for space debris observation, it is limited by its sensitivity to dynamic background noise. Traditionally, in the field of astronomy, static background subtraction based on a median image technique has been used to extract moving space objects prior to the tracking operation, as this is computationally efficient. The main disadvantage of this technique is that it is not robust to variable illumination conditions. In this article, we propose an approach for tracking small and dim space debris in the context of a dynamic background via one of the optical telescopes that is part of the space surveillance network project, named the Asia- Pacific ground-based Optical Space Observation System or APOSOS. The approach combines a fuzzy running Gaussian average for robust moving-object extraction with dim-target tracking using a particle- filter-based track-before-detect method. The performance of the proposed algorithm is experimentally evaluated, and the results show that the scheme achieves a satisfactory level of accuracy for space debris tracking.
基金funded by the National Natural Science Foundation of China (Grant Nos.11125315 and 11033009)
文摘In order to implement an observing strategy, image degradation that occurs during optical observation of space debris is ineluctable and has distinct characteris- tics. Image restoration is presented as a way to remove the influence of degradation in CCD images of space debris, based on assumed PSF models with the same F-WHM as images of the object. In the process of image restoration, the maximum entropy method is adopted. The results of reduction using observed raw CCD images indi- cate that the precision in estimating positions of objects is improved and the effects of degradation are reduced. Improving the astrometry of space debris using image restoration is effective and feasible.
基金funded by the National Natural Science Foundation of China(Grant Nos.11125315,11403108 and 11273069)the Youth Innovation Promotion Association of CAS(2015252)
文摘An optical survey is the main technique for detecting space debris. Due to the specific character- istics of observation, the pointing errors and tracking errors of the telescope as well as image degradation may be significant, which make it difficult for astrometric calibration. Here we present an improved method that corrects the pointing and tracking errors, and measures the image position precisely. The pipeline is tested on a number of CCD images obtained from a 1-m telescope administered by Xinjiang Astronomical Observatory while observing a GPS satellite. The results show that the position measurement error of the background stars is around 0.1 pixel, while the time cost for a single frame is about 7.5 s; hence the relia- bility and accuracy of our method are demonstrated. In addition, our method shows a versatile and feasible way to perform space debris observation utilizing non-dedicated telescopes, which means more sensors could be involved and the ability to perform surveys could be improved.
文摘We continue studying systems whose state depends on time and whose resources are renewably based on functional operators with shift. In previous articles, we considered the term which described results of reproductive processes as a linear expression or as a shift summand. In this work, the reproductive term is represented using an integral with a degenerate kernel. A cyclic model of evolution of the system with a renewable resource is developed. We propose a method for solving the balance equation and we determine an equilibrium state of the system. Having applied this model, we can investigate problems of natural systems and their resource production.