A global model of intensity autocorrelation to determine laser pulse duration

We present a new global model of collinear autocorrelation based on second harmonic generation nonlinearity.The model is rigorously derived from the nonlinear coupled wave equation specific to the autocorrelation measurement configuration,without requiring a specific form of the incident pulse function.A rigorous solution of the nonlinear coupled wave equation is obtained in the time domain and expressed in a general analytical form.The global model fully accounts for the nonlinear interaction and propagation effects within nonlinear crystals,which are not captured by the classical local model.To assess the performance of the global model compared to the classic local model,we investigate the autocorrelation signals obtained from both models for different incident pulse waveforms and different full-widthes at half-maximum(FWHMs).When the incident pulse waveform is Lorentzian with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 399.9 fs,while the classic local model predicts an FWHM of 331.4 fs.The difference between the two models is 68.6 fs,corresponding to an error of 17.2%.Similarly,for a sech-type incident pulse with an FWHM of 200 fs,the global model predicts an autocorrelation signal FWHM of 343.9 fs,while the local model predicts an FWHM of 308.8 fs.The difference between the two models is 35.1 fs,with an error of 10.2%.We further examine the behavior of the models for Lorentzian pulses with FWHMs of 100 fs,200 fs and 500 fs.The differences between the global and local models are 17.1 fs,68.6 fs and 86.0 fs,respectively,with errors approximately around 17%.These comparative analyses clearly demonstrate the superior accuracy of the global model in intensity autocorrelation modeling.

A Probing Model of Secret Key Generation Based on Channel Autocorrelation Function

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.

A multi-scale second-order autoregressive recursive filter approach for the sea ice concentration analysis

To effectively extract multi-scale information from observation data and improve computational efficiency,a multi-scale second-order autoregressive recursive filter(MSRF)method is designed.The second-order autoregressive filter used in this study has been attempted to replace the traditional first-order recursive filter used in spatial multi-scale recursive filter(SMRF)method.The experimental results indicate that the MSRF scheme successfully extracts various scale information resolved by observations.Moreover,compared with the SMRF scheme,the MSRF scheme improves computational accuracy and efficiency to some extent.The MSRF scheme can not only propagate to a longer distance without the attenuation of innovation,but also reduce the mean absolute deviation between the reconstructed sea ice concentration results and observations reduced by about 3.2%compared to the SMRF scheme.On the other hand,compared with traditional first-order recursive filters using in the SMRF scheme that multiple filters are executed,the MSRF scheme only needs to perform two filter processes in one iteration,greatly improving filtering efficiency.In the two-dimensional experiment of sea ice concentration,the calculation time of the MSRF scheme is only 1/7 of that of SMRF scheme.This means that the MSRF scheme can achieve better performance with less computational cost,which is of great significance for further application in real-time ocean or sea ice data assimilation systems in the future.

Coordinated Control of Second-order Harmonic Voltage and Current Fluctuations in Cascaded H-bridge Inverter with Supercapacitor and DC-DC Stage at Variable Output Frequencies

In the cascaded H-bridge inverter(CHBI)with supercapacitor and dc-dc stage,inherent second-order harmonic power flows through each submodule(SM),causing fluctuations in both the dc-link voltage and the dc-dc current.There exist limitations in handling these fluctuations at variable output frequencies when employing proportional-integral(PI)control to the dc-dc stage.This paper aims to coordinately control these second-order harmonic voltage and current fluctuations in the CHBI.The presented method configures a specific second-order harmonic voltage reference,equipped with a maximum voltage fluctuation constraint and a suitable phase,for the dc-dc stage.A PI-resonant controller is used to track the configured reference.This allows for regulating the second-order harmonic fluctuation in the average dc-link voltage among the SMs within a certain value.Importantly,the second-order harmonic fluctuation in the dc-dc current can also be reduced.Simulation and experimental results demonstrate the effectiveness of the presented method.

The Convergence Rate of Fréchet Distribution under the Second-Order Regular Variation Condition

In this article we consider the asymptotic behavior of extreme distribution with the extreme value index γ>0 . The rates of uniform convergence for Fréchet distribution are constructed under the second-order regular variation condition.

Second-Order Raman Scattering from n- and p-Type 4H-SiC

The results of second-order Raman-scattering experiments on n- and p-type 4H-SiC are presented,covering the acoustic and the optical overtone spectral regions.Some of the observed structures in the spectra are assigned to particular phonon branches and the points in the Brillouin zone from which the scattering originates.There exists a doublet at 626/636cm -1 with energy difference about 10cm -1 in both n- and p-type 4H-SiC,which is similar to the doublet structure with the same energy difference founded in hexagonal GaN,ZnO, and AlN.The cutoff frequency at 1926cm -1 of the second-order Raman is not the overtone of the A 1(LO) peak of the n-type doping 4H-SiC,but that of the undoping one.The second-order Raman spectrum of 4H-SiC can hardly be affected by doping species or doping density.

Measurement of spatiotemporal characteristics of femtosecond laser pulses by a modified single-shot autocorrelation

To overcome the shortcomings of the single-shot autocorrelation SSA where only one pulse width is obtained when the SSA is applied to measure the pulse width of ultrashort laser pulses a modified SSA for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions is proposed. The spatiotemporal characteristics of femtosecond laser pulses output from the Ti sapphire regenerative amplifier system are experimentally measured by the proposed method. It was found that the complex spatial characteristics are measured accurately.The pulse widths at different spatial positions are various which obey the Gaussian distribution.The pulse width at the same spatial position becomes narrow with the increase in input average power when femtosecond laser pulses pass through a carbon disulfide CS2 nonlinear medium.The experimental results verify that the proposed method is valid for measuring the spatiotemporal characteristics of ultrashort laser pulses at different spatial positions.

Anti-periodic solutions to a class of second-order evolution equations

In this paper we discuss the anti-periodic problem for a class of abstractnonlinear second-order evolution equations associated with maximal monotone operators in Hilbertspaces and give some new assumptions on operators. We establish the existence and uniqueness ofanti-periodic solutions, which improve andgeneralize the results that have been obtained. Finally weillustrate the abstract theory by discussing a simple example of an anti-periodic problem fornonlinear partial differential equations.

Anti-interference beam pattern design based on second-order cone programming optimization

When signal-to-interference ratio is low, the energy of strong interference leaked from the side lobe of beam pattern will infect the detection of weak target. Therefore, the beam pattern needs to be optimized. The existing Dolph-Chebyshev weighting method can get the lowest side lobe level under given main lobe width, but for the other non-uniform circular array and nonlinear array, the low side lobe pattern needs to be designed specially. The second order cone programming optimization （SOCP） algorithm proposed in the paper transforms the optimization of the beam pattern into a standard convex optimization problem. Thus there is a paradigm to follow for any array formation, which not only achieves the purpose of Dolph-Chebyshev weighting, but also solves the problem of the increased side lobe when the signal is at end fire direction The simulation proves that the SOCP algorithm can detect the weak target better than the conventional beam forming.

Design of a spatial sampling scheme considering the spatial autocorrelation of crop acreage included in the sampling units

Information on crop acreage is important for formulating national food polices and economic planning. Spatial sampling, a combination of traditional sampling methods and remote sensing and geographic information system （GIS） technology, provides an efficient way to estimate crop acreage at the regional scale. Traditional sampling methods require that the sampling units should be independent of each other, but in practice there is often spatial autocorrelation among crop acreage contained in the sampling units. In this study, using Dehui County in Jilin Province, China, as the study area, we used a thematic crop map derived from Systeme Probatoire d＇Observation de la Terre （SPOT-5） imagery, cultivated land plots and digital elevation model data to explore the spatial autocorrelation characteristics among maize and rice acreage included in sampling units of different sizes, and analyzed the effects of different stratification criteria on the level of spatial autocorrelation of the two crop acreages within the sampling units. Moran＇s/, a global spatial autocorrelation index, was used to evaluate the spatial autocorrelation among the two crop acreages in this study. The results showed that although the spatial autocorrelation level among maize and rice acreages within the sampling units generally decreased with increasing sampling unit size, there was still a significant spatial autocorrelation among the two crop acreages included in the sampling units （Moran＇s / varied from 0.49 to 0.89）, irrespective of the sampling unit size. When the sampling unit size was less than 3000 m, the stratification design that used crop planting intensity （CPI） as the stratification criterion, with a stratum number of 5 and a stratum interval of 20% decreased the spatial autocorrelation level to almost zero for the maize and rice area included in sampling units within each stratum. Therefore, the traditional sampling methods can be used to estimate the two crop acreages. Compared with CPI, there was still a strong spatial correlation among the two crop acreages included in the sampling units belonging to each stratum when cultivated land fragmentation and ground slope were used as stratification criterion. As far as the selection of stratification criteria and sampling unit size is concerned, this study provides a basis for formulating a reasonable spatial sampling scheme to estimate crop acreage.

Stability analysis for a second-order continuous finite-time control system subject to a disturbance

In this paper, using finite-time control method, we consider the disturbance analysis of a second-order system with unknown but bounded disturbance. We show that the states of the second-order system will be stabilized to a region containing the origin. The radius of this region is determined by the control parameters and can be rendered as small as desired. The rigorous stability analysis is also given. Compared with the conventional PD control law, the finite-time control law yields a better disturbance rejection performance. Numerical simulation results show the effectiveness of the method.

LPI radar signal detection based on the combination of FFT and segmented autocorrelation plus PAHT

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.

Second-Order Analytic Solutions of Nonlinear Interactions of Edge Waves on A Plane Sloping Bottom

Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.

STUDY ON SPATIAL AUTOCORRELATION OF URBAN LAND PRICE DISTRIBUTION IN CHANGZHOU CITY OF JIANGSU PROVINCE

This paper uses a spatial statistics method based on the calculation of spatial autocorrelation as a possible approach for modeling and quantifying the distribution of urban land price in Changzhou City, Jiangsu Province. GIS and spatial statistics provide a useful way for describing the distribution of urban land price both spatially and temporally, and have proved to be useful for understanding land price distribution pattern better. In this paper, we apply the statistical analysis method to 8379 urban land price samples collected from Changzhou Land Market, and it is turned out that the proposed approach can effectively identify the spatial clusters and local point patterns in dataset and forms a general method for conceptualizing the land price structure. The results show that land price structure in Changzhou City is very complex and that even where there is a high spatial autocorrelation, the land price is still relatively heterogeneous. Furthermore, lands for different uses have different degrees of spatial autocorrelation. Spatial autocorrelation of commercial lands is more intense than that of residential and industrial lands in regional central district. This means that treating land price as integration of homogeneous units can limit analysis of pattern, over-simplifying the structure of land price, but the methods, just as the autocorrelation approaches, are useful tools for quantifying the variables of land price.

Vertex degree autocorrelation topological index and its application in QSAR study of organic chemicals

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.

Cluster consensus of second-order multi-agent systems via pinning control

This paper investigates the cluster consensus problem for second-order multi-agent systems by applying the pinning control method to a small collection of the agents. Consensus is attained independently for different agent clusters according to the community structure generated by the group partition of the underlying graph and sufficient conditions for both cluster and general consensus are obtained by using results from algebraic graph theory and the LaSalle Invariance Principle. Finally, some simple simulations are presented to illustrate the technique.

Improved design of reconfigurable frequency response masking filters based on second-order cone programming

In order to improve the design results for the reconfigurable frequency response masking FRM filters an improved design method based on second-order cone programming SOCP is proposed.Unlike traditional methods that separately design the proposed method takes all the desired designing modes into consideration when designing all the subfilters. First an initial solution is obtained by separately designing the subfilters and then the initial solution is updated by iteratively solving a SOCP problem. The proposed method is evaluated on a design example and simulation results demonstrate that jointly designing all the subfilters can obtain significantly lower minimax approximation errors compared to the conventional design method.

Eigenstructure assignment in a class of second-order dynamic systems

Eigenstructure assignment using the proportional-plus-derivative feedback controller in a class of secondorder dynamic system is investigated. Simple, general, complete parametric expressions for both the closed-loop eigenvector matrix and the feedback gains are established based on two simple Smith form reductions. The approach utilizes directly the original system data and involves manipulations only on n-dimensional matrices. Furthermore, it reveals all the degrees of freedom which can be further utilized to achieve additional system specifications. An example shows the effect of the proposed approach.

Consensus problem of second-order multi-agent systems with time-varying communication delay and switching topology

Leader-following stationary consensus problem is investigated for the second-order multi-agent systems with timevarying communication delay and switching topology. Based on Lyapunov-Krasovskii functional and Lyapunov-Razumikhin functions respectively, consensus criterions in the form of linear matrix inequality （LMI） are obtained for the system with time-varying communication delays under static interconnection topology con- verging to the leader＇s states. Moreover, the delay-dependent consensus criterion in the form of LMI is also obtained for the system with time-invariant communication delay and switching topologies by constructing Lyapunov-Krasovskii functional. Numerical simulations present the correctness of the results.

Linear complexity and autocorrelation of a new class of binary generalized cyclotomic sequences of order two and length pqr

Cyclotomic sequences have good cryptographic properties and are closely related to difference sets.This paper proposes a new class of binary generalized cyclotomic sequences of order two and length pqr.Its linear complexity,minimal polynomial,and autocorrelation are investigated.The results show that these sequences have a large linear complexity when 2∈D1,which means they can resist the Berlekamp-Massey attack.Furthermore,the autocorrelation values are close to 0 with a probability of approximately 1?1/r.Therefore,when r is a big prime,the new sequence has a good autocorrelation.