In developing counties, efficiency of economic development has been determined by the analysis of industrial production. An examination of the characteristic of industrial sector is an essential aspect of growth studi...In developing counties, efficiency of economic development has been determined by the analysis of industrial production. An examination of the characteristic of industrial sector is an essential aspect of growth studies. The growth of a country can be measured by Gross Domestic Product (GDP). GDP is substantially affected by the industrial output. Industrial gross output is mainly a function of capital and labor input. If the effect of labor and capital input to output is at a satisfactory level in an industry or in a group of industries, then industrial investment will increase. As a result, the number of industries will increase, which will directly affect GDP and also will decrease the unemployment rate. This is why, industrial input-output relationship is so important for any industry as well as for the overall industrial sector of a country. To forecast the production of a firm is necessary to identify the appropriate model. MD. M. Hossain et al. [1] have shown that Cobb-Douglas production function with additive errors was more suitable for some selected manufacturing industries in Bangladesh. The main purpose of this paper is to detect the autocorrelation problem of Cobb-Douglas production model with additive errors. The result shows that autocorrelation is presented in some manufacturing industries. Finally, this paper removes the autocorrelation problem and re-estimates the parameters of the Cobb- Douglas production function with additive errors.展开更多
Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,ther...Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.展开更多
In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF...In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF that is suitable for expressing the dynamic correlations of words, we use the formula to calculate ACFs for frequent words in 12 books. The ACFs obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function;the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function. A word having the former ACF is called a Type-I word and a word with the latter ACF is called a Type-II word. It is also shown that the ACFs of Type-II words can be derived theoretically by assuming that the stochastic process governing word occurrence is a homogeneous Poisson point process. Based on the fitting of the ACFs by KWW and stepdown functions, we propose a measure of word importance which expresses the extent to which a word is important in a particular text. The validity of the measure is confirmed by using the Kleinburg’s burst detection algorithm.展开更多
Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated res...Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated respectively.The Maximum Sidelobe Ratio(MSR) of the kth coordinate sequence and the MSR of state output sequence are given respectively.The bounds of autocorrelation functions show that the values of autocorrelation functions are large when shifts are small.Comparisons of the autocorrelations between the state output sequence and coordinate output sequence are illustrated.The autocorrelation properties demonstrate that T-functions have cryptographic weaknesses and the illustration result shows coordinate output sequences have better autocorrelation than that of state output sequences.展开更多
This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of li...This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of linear frequency modulation, phase code, and frequency code. Firstly, it improves the coherent integration of LPI radar signals by adding the periodicity of the ambiguity function. Then, it develops a frequency domain detection method based on fast Fourier transform (FFT) and segmented autocorrelation function to detect signals without features of linear frequency modulation by virtue of the distribution characteristics of noise signals in the frequency domain. Finally, this paper gives a verification of the performance of the method for different signal-to-noise ratios by conducting simulation experiments, and compares the method with existing ones. Additionally, this method is characterized by the straightforward calculation and high real-time performance, which is conducive to better detecting all kinds of LPI radar signals.展开更多
Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphyll...Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphylla Sukaczev)in ten sub-regions of the Daxing’an Mountains,northeast China.Three commonly used taper functions were assessed using a diameter and height dataset comprising 1344 trees.A first-order continuous-time error structure accounted for the inherent autocorrelation.The segmented model of Max and Burkhart(For Sci 22:283–289,1976.https://doi.org/10.1093/fores tscie nce/22.3.283)and the variable exponent taper function of Kozak(For Chron 80:507–515,2004.https://doi.org/10.5558/tfc80507-4)described the data accurately.Owing to its lower multicollinearity,the Max and Burkhart(1976)model is recommended for diameter estimation at specific heights along the stem for the ten sub-regions.After comparison,the Max and Burkhart(1976)model was refitted using nonlinear mixed-effects techniques.Mixed-effects models would be used only when additional upper stem diameter measurements are available for calibration.Differences in region-specific taper functions were indicated by the method of the non-linear extra sum of squares.Therefore,the particular taper function should be adjusted accordingly for each sub-region in the Daxing’an Mountains.展开更多
Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as ...Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.展开更多
The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four...The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.展开更多
Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and m...Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and malfunction recovering.Unlike most detection methods based on the statistical analysis of the packet headers(Such as IP addresses and ports),a new approach only using network traffic volumes is proposed to detect anomalies reliably.Our method is based on autocorrelation function to judge whether anomalies have happened.In details,the correlation coefficients of normal and anomaly data fluctuate slightly respectively,while those of the overlapped data composed of them fluctuate greatly.Experimental results on network traffic volumes transformed from 1999 DARPA intrusion evaluation data set show that this method can effectively detect network anomalies,while avoiding the high false alarms rate.展开更多
Computational electrocardiogram (ECG) analysis is one of the most crucial topics in cardiovascular research domain especially in identifying abnormalities of heart condition through cardiac arrhythmia symptom. There a...Computational electrocardiogram (ECG) analysis is one of the most crucial topics in cardiovascular research domain especially in identifying abnormalities of heart condition through cardiac arrhythmia symptom. There are many existing works focusing on recognizing the abnormalities condition through arrhythmia symptom, however, the detection rate is still unsatisfied. Arrhythmia consists of more than 14 various types of symptoms. Therefore, most of the existing research found it difficult to classify the entire symptom and maintain the overall accuracy especially in long hour data. In this study, a new mechanism to overcome this issue is proposed: A combination between Autocorrelation methods with K-Nearest Neighbor (KNN) classifier method is introduced to accurately and robustly detect 14 types of Arrhythmia symptom regardless of the origin of the symptom in a long hour data. Moreover, variability analysis based on periodic autocorrelation result is proposed and used for classification procedure. 1 minute and 12 hours duration data was chosen to compare and signify the most suitable time duration to detect Arrhythmia symptom. In addition, an analytical result and discussion is done to provide justification behind each tendency of Arrhythmia and Normal Sinus symptom in autocorrelation result. As the result of proposed method performance evaluation, it was revealed that the accuracy of 95.5% in discriminating Arrhythmia from Normal Sinus data is achieved. Furthermore, it was confirmed that utilizing autocorrelation result in long hour data can help to generalize abnormalities characteristic of heart condition like Arrhythmia symptom. It is concluded that the proposed method can be useful to diagnose abnormalities of heart condition at any stage.展开更多
This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting mul...This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.展开更多
Under conditions differing from those subjected for central limit theorem, the spatial autocorrelation function of speckle pattern resulting from illuminated rough surface is investigated. Its dependence on different ...Under conditions differing from those subjected for central limit theorem, the spatial autocorrelation function of speckle pattern resulting from illuminated rough surface is investigated. Its dependence on different illuminating apertures and the average of the roughness heights is presented theoretically and experimentally. The experiments were carried out using a set of circular and square apertures having different sizes. The results indicate that, increasing the size of the illuminating aperture leads to a decrease in the width of the main lobe of the spatial autocorrelation function.展开更多
In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element ...In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF（2<sup>M</sup>）, rbe a positive integer, 1≤r≤2<sup>J</sup>, and（r, 2<sup>J</sup>-1）=1. Then the sequence b=b（0）b（1）…b（n）…is called GMW sequence over GF（2）. Here b（n）=tr<sub>1</sub><sup>J</sup>（tr<sub>J</sub><sup>M</sup>α<sup>n</sup>）<sup>r</sup>, for n=0, 1, 2….展开更多
In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator compl...In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator complexity and the autocorrelation function.In particular,we focus on a particular kind of operator complexity called the Krylov complexity.We find that a set of Lanczos coefficients{b_(n)}computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations,which are otherwise impossible.When the time axis is scaled by b1,different autocorrelation functions obey a universal function form at short time.We further propose a characteristic parameter deduced from{b_(n)}that can largely determine the behavior of autocorrelations at the intermediate time.This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time.We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations.We emphasize that these universal behaviors are held across different operators and different physical systems.展开更多
文摘In this paper, we obtain an explicit expression for the partial autocorrelation of an ARMA (1.1) process and discuss its asymptotic behaviour briefly.
文摘In developing counties, efficiency of economic development has been determined by the analysis of industrial production. An examination of the characteristic of industrial sector is an essential aspect of growth studies. The growth of a country can be measured by Gross Domestic Product (GDP). GDP is substantially affected by the industrial output. Industrial gross output is mainly a function of capital and labor input. If the effect of labor and capital input to output is at a satisfactory level in an industry or in a group of industries, then industrial investment will increase. As a result, the number of industries will increase, which will directly affect GDP and also will decrease the unemployment rate. This is why, industrial input-output relationship is so important for any industry as well as for the overall industrial sector of a country. To forecast the production of a firm is necessary to identify the appropriate model. MD. M. Hossain et al. [1] have shown that Cobb-Douglas production function with additive errors was more suitable for some selected manufacturing industries in Bangladesh. The main purpose of this paper is to detect the autocorrelation problem of Cobb-Douglas production model with additive errors. The result shows that autocorrelation is presented in some manufacturing industries. Finally, this paper removes the autocorrelation problem and re-estimates the parameters of the Cobb- Douglas production function with additive errors.
基金supported in part by the national natural science foundation of China (NSFC) under Grant61871193in part by the R&D Program of key science and technology fields in Guangdong province under Grant 2019B090912001in part by the Guangzhou Key Field R&D Program under Grant 202206030005
文摘Secret key generation(SKG)is a promising solution to the problem of wireless communications security.As the first step of SKG,channel probing affects it significantly.Although there have been some probing schemes,there is a lack of research on the optimization of the probing process.This study investigates how to optimize correlated parameters to maximize the SKG rate(SKGR)in the time-division duplex(TDD)mode.First,we build a probing model which includes the effects of transmitting power,the probing period,and the dimension of sample vectors.Based on the model,the analytical expression of the SKGR is given.Next,we formulate an optimization problem for maximizing the SKGR and give an algorithm to solve it.We conclude the SKGR monotonically increases as the transmitting power increases.Relevant mathematical proofs are given in this study.From the simulation results,increasing appropriately the probing period and the dimension of the sample vector could increase the SKGR dramatically compared to a yardstick,which indicates the importance of optimizing the parameters related to the channel probing phase.
文摘In this study, we regard written texts as time series data and try to investigate dynamic correlations of word occurrences by utilizing an autocorrelation function (ACF). After defining appropriate formula for the ACF that is suitable for expressing the dynamic correlations of words, we use the formula to calculate ACFs for frequent words in 12 books. The ACFs obtained can be classified into two groups: One group of ACFs shows dynamic correlations, with these ACFs well described by a modified Kohlrausch-Williams-Watts (KWW) function;the other group of ACFs shows no correlations, with these ACFs fitted by a simple stepdown function. A word having the former ACF is called a Type-I word and a word with the latter ACF is called a Type-II word. It is also shown that the ACFs of Type-II words can be derived theoretically by assuming that the stochastic process governing word occurrence is a homogeneous Poisson point process. Based on the fitting of the ACFs by KWW and stepdown functions, we propose a measure of word importance which expresses the extent to which a word is important in a particular text. The validity of the measure is confirmed by using the Kleinburg’s burst detection algorithm.
基金supported by National Natural Science Foundation of China under Grant No.60833008,60970119the Scientific Research Foundation of Education of Department of Shaanxi Provincial Government of China under Grant No.11JK0503+1 种基金Youth Science and Technology Foundation of Xi'an University of Architecture and Technology under Grant No.QN0831,QN1024Foundation of Guangxi Key Laboratory of Information and Communications under Grant No.20902
文摘Cryptographic properties of the single cycle T-function's output sequences are investigated.Bounds of autocorrelation functions of the kth coordinate sequence and bounds of state output sequence are calculated respectively.The Maximum Sidelobe Ratio(MSR) of the kth coordinate sequence and the MSR of state output sequence are given respectively.The bounds of autocorrelation functions show that the values of autocorrelation functions are large when shifts are small.Comparisons of the autocorrelations between the state output sequence and coordinate output sequence are illustrated.The autocorrelation properties demonstrate that T-functions have cryptographic weaknesses and the illustration result shows coordinate output sequences have better autocorrelation than that of state output sequences.
基金supported by the National Natural Science Foundation of China(61571462)Weapons and Equipment Exploration Research Project(7131464)
文摘This paper proposes a desirable method to detect different kinds of low probability of intercept (LPI) radar signals, targeted at the main intra-pulse modulation method of LPI radar signals including the signals of linear frequency modulation, phase code, and frequency code. Firstly, it improves the coherent integration of LPI radar signals by adding the periodicity of the ambiguity function. Then, it develops a frequency domain detection method based on fast Fourier transform (FFT) and segmented autocorrelation function to detect signals without features of linear frequency modulation by virtue of the distribution characteristics of noise signals in the frequency domain. Finally, this paper gives a verification of the performance of the method for different signal-to-noise ratios by conducting simulation experiments, and compares the method with existing ones. Additionally, this method is characterized by the straightforward calculation and high real-time performance, which is conducive to better detecting all kinds of LPI radar signals.
基金fi nancially supported by the National Natural Science Foundation of China(31570624)Applied Technology Research and Development Plan Project of Heilongjiang Province(GA19C006)Fundamental Research Funds for Central Universities(2572019CP15).
文摘Accurate prediction of stem diameter is an important prerequisite of forest management.In this study,an appropriate stem taper function was developed for upper stem diameter estimation of white birch(Betula platyphylla Sukaczev)in ten sub-regions of the Daxing’an Mountains,northeast China.Three commonly used taper functions were assessed using a diameter and height dataset comprising 1344 trees.A first-order continuous-time error structure accounted for the inherent autocorrelation.The segmented model of Max and Burkhart(For Sci 22:283–289,1976.https://doi.org/10.1093/fores tscie nce/22.3.283)and the variable exponent taper function of Kozak(For Chron 80:507–515,2004.https://doi.org/10.5558/tfc80507-4)described the data accurately.Owing to its lower multicollinearity,the Max and Burkhart(1976)model is recommended for diameter estimation at specific heights along the stem for the ten sub-regions.After comparison,the Max and Burkhart(1976)model was refitted using nonlinear mixed-effects techniques.Mixed-effects models would be used only when additional upper stem diameter measurements are available for calibration.Differences in region-specific taper functions were indicated by the method of the non-linear extra sum of squares.Therefore,the particular taper function should be adjusted accordingly for each sub-region in the Daxing’an Mountains.
文摘Considering the calculated result and higher degeneracy existing in the calculation of autocorrelation topological index totally depend on experimental parameters, a new group of autocorrelation topological index as A t, B t, C t and D t was designed and developed based on the vertex degree of molecular topology and autocorrelation function of mathematics. Autocorrelation function f(i) was calculated from the square root of the vertex degree, revised vertex degree and their combination, and they are (δ i) 1/2 , (δ V i) 1/2 ,(δ V i+δ i) 1/2 and (δ E i-δ i) 1/2 / N. With the matrix description method achieved, and the unit input in matrix of unsaturated bond and heteroatoms revised based on the adjacency matrix and distance matrix of organic molecular graph, the corresponding computer software has also been designed and developed. Better results have been obtained for the application of these indexes in QSAR study of organic chemicals.
基金Supported by the Natural Science Foundation of Anhui(1608085MF143)the National Natural Science Foundation of China(60573026,10101008)the Natural Science Foundation of Anhui Higher Education Institutions of China(KJ2018A0678)
文摘The sequences with good correlation properties are widely used in engineering applications, especially in the area of communications. In this paper, the relationships among crosscorrelation functions of arbitrary four binary sequences of period N are presented. Based on them, for a sequences set, the relationships between cross-correlation functions and autocorrelation functions are studied, by which we prove that they cannot keep optimal at the same time.
基金This work was supported by a grant from the National Natural Science Foundation of China(No.60773192).
文摘Network anomalies caused by network attacks can significantly degrade or even terminate network services.A Real-time and reliable detection of anomalies is essential to rapid anomaly diagnosis,anomaly mitigation,and malfunction recovering.Unlike most detection methods based on the statistical analysis of the packet headers(Such as IP addresses and ports),a new approach only using network traffic volumes is proposed to detect anomalies reliably.Our method is based on autocorrelation function to judge whether anomalies have happened.In details,the correlation coefficients of normal and anomaly data fluctuate slightly respectively,while those of the overlapped data composed of them fluctuate greatly.Experimental results on network traffic volumes transformed from 1999 DARPA intrusion evaluation data set show that this method can effectively detect network anomalies,while avoiding the high false alarms rate.
文摘Computational electrocardiogram (ECG) analysis is one of the most crucial topics in cardiovascular research domain especially in identifying abnormalities of heart condition through cardiac arrhythmia symptom. There are many existing works focusing on recognizing the abnormalities condition through arrhythmia symptom, however, the detection rate is still unsatisfied. Arrhythmia consists of more than 14 various types of symptoms. Therefore, most of the existing research found it difficult to classify the entire symptom and maintain the overall accuracy especially in long hour data. In this study, a new mechanism to overcome this issue is proposed: A combination between Autocorrelation methods with K-Nearest Neighbor (KNN) classifier method is introduced to accurately and robustly detect 14 types of Arrhythmia symptom regardless of the origin of the symptom in a long hour data. Moreover, variability analysis based on periodic autocorrelation result is proposed and used for classification procedure. 1 minute and 12 hours duration data was chosen to compare and signify the most suitable time duration to detect Arrhythmia symptom. In addition, an analytical result and discussion is done to provide justification behind each tendency of Arrhythmia and Normal Sinus symptom in autocorrelation result. As the result of proposed method performance evaluation, it was revealed that the accuracy of 95.5% in discriminating Arrhythmia from Normal Sinus data is achieved. Furthermore, it was confirmed that utilizing autocorrelation result in long hour data can help to generalize abnormalities characteristic of heart condition like Arrhythmia symptom. It is concluded that the proposed method can be useful to diagnose abnormalities of heart condition at any stage.
文摘This paper presents a new method of detecting multi-periodicities in a seasonal time series. Conventional methods such as the average power spectrum or the autocorrelation function plot have been used in detecting multiple periodicities. However, there are numerous cases where those methods either fail, or lead to incorrectly detected periods. This, in turn in applications, produces improper models and results in larger forecasting errors. There is a strong need for a new approach to detecting multi-periodicities. This paper tends to fill this gap by proposing a new method which relies on a mathematical instrument, called the Average Power Function of Noise (APFN) of a time series. APFN has a prominent property that it has a strict local minimum at each period of the time series. This characteristic helps one in detecting periods in time series. Unlike the power spectrum method where it is assumed that the time series is composed of sinusoidal functions of different frequencies, in APFN it is assumed that the time series is periodic, the unique and a much weaker assumption. Therefore, this new instrument is expected to be more powerful in multi-periodicity detection than both the autocorrelation function plot and the average power spectrum. Properties of APFN and applications of the new method in periodicity detection and in forecasting are presented.
文摘Under conditions differing from those subjected for central limit theorem, the spatial autocorrelation function of speckle pattern resulting from illuminated rough surface is investigated. Its dependence on different illuminating apertures and the average of the roughness heights is presented theoretically and experimentally. The experiments were carried out using a set of circular and square apertures having different sizes. The results indicate that, increasing the size of the illuminating aperture leads to a decrease in the width of the main lobe of the spatial autocorrelation function.
文摘In 1984, R. A. Scholtz and L. R. Welch constructed a series of new binary se-quences which are called GMW sequences by using the trace function as follows: LetM, J be positive integers, J|M, α be a primitive element of the finite field GF（2<sup>M</sup>）, rbe a positive integer, 1≤r≤2<sup>J</sup>, and（r, 2<sup>J</sup>-1）=1. Then the sequence b=b（0）b（1）…b（n）…is called GMW sequence over GF（2）. Here b（n）=tr<sub>1</sub><sup>J</sup>（tr<sub>J</sub><sup>M</sup>α<sup>n</sup>）<sup>r</sup>, for n=0, 1, 2….
基金supported by NSFC 12174300(RZ)the National Key R&D Program of China 2018YFA0307601(RZ)+3 种基金Tang Scholar(RZ)Innovation Program for Quantum Science and Technology 2021ZD0302005(HZ),2021ZD0302001(RZ)the Beijing Outstanding Young Scholar Program(HZ)the XPLORER Prize(HZ).
文摘In a quantum many-body system,autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium.In this letter,we bring out the connection between the operator complexity and the autocorrelation function.In particular,we focus on a particular kind of operator complexity called the Krylov complexity.We find that a set of Lanczos coefficients{b_(n)}computed for determining the Krylov complexity can reveal the universal behaviors of autocorrelations,which are otherwise impossible.When the time axis is scaled by b1,different autocorrelation functions obey a universal function form at short time.We further propose a characteristic parameter deduced from{b_(n)}that can largely determine the behavior of autocorrelations at the intermediate time.This parameter can also largely determine whether the autocorrelation function oscillates or monotonically decays in time.We present numerical evidences and physical intuitions to support these universal hypotheses of autocorrelations.We emphasize that these universal behaviors are held across different operators and different physical systems.
