In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional as...In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the Dirac operator on 4-dimensional manifolds with boundary.展开更多
In this paper,we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional.We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on e...In this paper,we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional.We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on evendimensional compact manifolds without boundary.Finally,several examples of the non-self-adjoint spectral triple are listed.展开更多
Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few wo...Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.展开更多
We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation...We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.展开更多
In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position e...In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position estimation,where the set of consecutive estimates provides the tracking trajectory,such as Two-step and direct position determination methods.However,duplicate estimates can be computationally expensive.In addition,these techniques suffer from data association problems.The PF algorithm is a tracking method that avoids these drawbacks,but the conventional PF algorithm is unable to construct a likelihood function from the received signals of multiple observatories to determine the weights of particles.Therefore,we developed an improved PF algorithm with the likelihood function modified by the projection approximation subspace tracking with deflation(PASTd)algorithm.The proposed algorithm uses the projection subspace and spectral function to replace the likelihood function of PF.Then,the weights of particles are calculated jointly by multiple likelihood functions.Finally,the tracking problem of multiple targets is solved by multiple sets of particles.Simulations demonstrate the effectiveness of the proposed method in terms of computational complexity and tracking accuracy.展开更多
The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium s...The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.展开更多
In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated w...In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators,particularly in the cases of on 4-dimensional manifolds with boundary.展开更多
This study introduces measures to identify resonant (concentration of energy in a single or a few frequencies) or unfavorable earthquake ground motions. Probabilistic measures based on the entropy rate and the geometr...This study introduces measures to identify resonant (concentration of energy in a single or a few frequencies) or unfavorable earthquake ground motions. Probabilistic measures based on the entropy rate and the geometric properties of the power spectral density function (PSDF) of the ground acceleration are developed first. Subsequently, deterministic measures for the frequency content of the ground acceleration are also developed. These measures are then used for identifying resonance and criticality in stochastic earthquake models and 110 acceleration records measured at rock, stiff, medium and soft soil sites. The unfavorable earthquake record for a given structure is defined as the record having a narrow frequency content and dominant frequency close to the structure fundamental natural frequency. Accordingly, the measures developed in this study may provide a basis for selecting records that are capable of producing the highest structural response. Numerical verifications are provided on damage caused to structures by identified resonant records.展开更多
The noise data in vertical component records of 85 seismic stations in Fujian Province during 2012 is used as the research object in this paper. The noise data is divided into fiveminute segments to calculate the powe...The noise data in vertical component records of 85 seismic stations in Fujian Province during 2012 is used as the research object in this paper. The noise data is divided into fiveminute segments to calculate the power spectra. The high reference line and low reference line of station are then identified by drawing a probability density function graph( PDF)using the power spectral probability density function. Moreover, according to the anomalies of PDF graphs in 85 seismic stations,the abnormal noise is divided into four categories: dropped packet, low noise, high noise, and median noise anomalies.Afterwards,four selection methods are found by the high or low noise reference line of the stations,and the system of real-time monitoring of seismic noise is formed by combining the four selection methods. Noise records of 85 seismic stations in Fujian Province in July2013 are selected for verification,and the results show that the anomalous noise-recognition system could reach a 90% success rate at most stations and the effect of selection are very good. Therefore,it could be applied to the seismic noise real-time monitoring in stations.展开更多
We investigate the unique properties of current-induced heat generation in nanojunctions,such as failed Q α I relation(where Q is the heat generation and I the current),threshold voltage required to generate heat,etc...We investigate the unique properties of current-induced heat generation in nanojunctions,such as failed Q α I relation(where Q is the heat generation and I the current),threshold voltage required to generate heat,etc.By employing the lead-quantum dot(QD)-lead system,we find these unique properties stem from(i) the discontinuity of Fermi distribution at chemical potentials of the leads and(ii) the satellite peaks in spectral function of the QD electron,which are induced by the electron-phonon interaction.展开更多
We present a systematic analysis on the role of the quantum dot （QD） shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representa...We present a systematic analysis on the role of the quantum dot （QD） shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes： spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains（≤2 ps）, and the oft-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.展开更多
This article lays out a unified theory for dynamics of vehicle-pavement interaction under moving and stochastic loads. It covers three major aspects of the subject： pavement surface, tire-pavement contact forces, and...This article lays out a unified theory for dynamics of vehicle-pavement interaction under moving and stochastic loads. It covers three major aspects of the subject： pavement surface, tire-pavement contact forces, and response of continuum media under moving and stochastic vehicular loads. Under the subject of pavement surface, the spectrum of thermal joints is analyzed using Fourier analysis of periodic function. One-dimensional and two-dimensional random field models of pavement surface are discussed given three different assumptions. Under the subject of tire-pavement contact forces, a vehicle is modeled as a linear system. At a constant speed of travel, random field of pavement surface serves as a stationary stochastic process exciting vehicle vibration, which, in turn, generates contact force at the interface of tire and pavement. The contact forces are analyzed in the time domain and the frequency domains using random vibration theory. It is shown that the contact force can be treated as a nonzero mean stationary process with a normal distribution. Power spectral density of the contact force of a vehicle with walking-beam suspension is simulated as an illustration. Under the subject of response of continuum media under moving and stochastic vehicular loads, both time-domain and frequency-domain analyses are presented for analytic treatment of moving load problem. It is shown that stochastic response of linear continuum media subject to a moving stationary load is a nonstationary process. Such a nonstationary stochastic process can be converted to a stationary stochastic process in a follow-up moving coordinate.展开更多
By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of t...By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.展开更多
This paper describes the finite element (FE) analysis technique to predict fatigue life using the narrow band frequency response approach. The life prediction results are useful for improving the component design meth...This paper describes the finite element (FE) analysis technique to predict fatigue life using the narrow band frequency response approach. The life prediction results are useful for improving the component design methodology at the very early development stage. The approach is found to be suitable for a periodic loading but requires very large time records to accurately describe random loading processes. This paper is aimed at investigating the effects of surface treatments on the fatigue life of the free piston linear engine’s components. Finite element modelling and frequency response analysis were conducted using computer aided design and finite element analysis commercial codes, respectively. In addition, the fatigue life prediction was carried out using finite element based fatigue analysis commercial code. Narrow band approach was specially applied to predict the fatigue life of the free piston linear engine cylinder block. Significant variation was observed between the surface treatments and untreated cylinder block of free piston engine. The obtained results indicated that nitrided treatment yielded the longest life. This approach can determine premature products failure phenomena, and therefore can reduce time to market, improve product reliability and customer confidence.展开更多
Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai...Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.展开更多
The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown th...The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).展开更多
Study is undertaken of spherical function spectral structures of long-term mean and anomaly patterns of the Northern Hemisphere 500 hPa monthly mean geopotential height together with the seasonal and interannual varia...Study is undertaken of spherical function spectral structures of long-term mean and anomaly patterns of the Northern Hemisphere 500 hPa monthly mean geopotential height together with the seasonal and interannual variations investigated.Results show that they are marked by low dimensions and low orders,and the mean and anomaly fields can be described in terms of 20 and 50 spherical function components,respectively.展开更多
We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral fu...We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.展开更多
Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWP...Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWPs that remain invariant under transverse Lorentz boosts. The Lorentz-invariant behavior of these STWPs is rigorously analyzed through their associated spectral line function, providing new insights into their fundamental properties. Furthermore, we quantify the limitations of this invariance and compare the robustness of the proposed nSTWPs against conventional nSTWPs.展开更多
文摘In this paper,we define the spectral Einstein functional associated with the Dirac operator for manifolds with boundary.And we give the proof of Kastler-Kalau-Walze type theorem for the spectral Einstein functional associated with the Dirac operator on 4-dimensional manifolds with boundary.
基金supported by the National Natural Science Foundation of China(Grant No.11771070).
文摘In this paper,we give the definitions of the non-self-adjoint spectral triple and its spectral Einstein functional.We compute the spectral Einstein functional associated with the nonminimal de Rham-Hodge operator on evendimensional compact manifolds without boundary.Finally,several examples of the non-self-adjoint spectral triple are listed.
基金the Postdoctoral ScienceFoundation of China(No.2023M730156)the NationalNatural Foundation of China(No.62301012).
文摘Hyper-and multi-spectral image fusion is an important technology to produce hyper-spectral and hyper-resolution images,which always depends on the spectral response function andthe point spread function.However,few works have been payed on the estimation of the two degra-dation functions.To learn the two functions from image pairs to be fused,we propose a Dirichletnetwork,where both functions are properly constrained.Specifically,the spatial response function isconstrained with positivity,while the Dirichlet distribution along with a total variation is imposedon the point spread function.To the best of our knowledge,the neural network and the Dirichlet regularization are exclusively investigated,for the first time,to estimate the degradation functions.Both image degradation and fusion experiments demonstrate the effectiveness and superiority of theproposed Dirichlet network.
基金Supported by the National Key Basic Research Program of China under Grant No 2013CB922304the National Natural Science Foundation of China under Grant Nos 11474275 and 11464034
文摘We report the observed photon bunching statistics of biexciton cascade emission at zero time delay in single quantum dots by second-order correlation function g（2） （T） measurements under continuous wave excitation. It is found that the bunching phenomenon is independent of the biexciton binding energy when it varies from 0.59 meV to nearly zero. The photon bunching takes place when the exeiton photon is not spectrally distinguishable from the biexciton photon, and either of them can trigger the %tart＇ in a Hanbury-Brown and Twiss setup. However, if the exciton energy is spectrally distinguishable from the biexciton, the photon statistics will become asymmetric and a cross-bunching lineshape can be obtained. The theoretical calculations based on a model of three-level rate-equation analysis are consistent with the result of g（2）（τ） correlation function measurements.
基金supported by China NSF Grants(62371225,62371227)Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX250590).
文摘In this paper,we present a novel particle filter(PF)-based direct position tracking method utilizing multiple distributed observation stations.Traditional passive tracking methods are anchored on repetitive position estimation,where the set of consecutive estimates provides the tracking trajectory,such as Two-step and direct position determination methods.However,duplicate estimates can be computationally expensive.In addition,these techniques suffer from data association problems.The PF algorithm is a tracking method that avoids these drawbacks,but the conventional PF algorithm is unable to construct a likelihood function from the received signals of multiple observatories to determine the weights of particles.Therefore,we developed an improved PF algorithm with the likelihood function modified by the projection approximation subspace tracking with deflation(PASTd)algorithm.The proposed algorithm uses the projection subspace and spectral function to replace the likelihood function of PF.Then,the weights of particles are calculated jointly by multiple likelihood functions.Finally,the tracking problem of multiple targets is solved by multiple sets of particles.Simulations demonstrate the effectiveness of the proposed method in terms of computational complexity and tracking accuracy.
基金supported by the National Natural Science Foundation of China(Grant No.12175318)the Natural Science Foundation of Guangdong Province of China(Grant No.2023A1515011704)。
文摘The observations of fully-charm tetraquark states in the LHCb,CMS,and ATLAS experiments suggested the existence of hadronic molecules of two-charmonium states,which may also imply bound states in the threecharmonium systems.In this work,we study the possible bound states in the triple-ηcand triple-J/ψsystems with J^(PC)=0^(-+)and 1^(--),respectively.In quantum chromodynamics sum rules,we calculate the two-point correlation functions and spectral functions up to the dimension-four gluon condensate.We use the iterative dispersion relation approach to deal with the five-loop banana integrals,which significantly improves computational efficiency.Our results show that the masses of triple-ηcand triple-J/ψstates lie below the corresponding mass thresholds,supporting the existence of such three-body bound states.
基金Supported by NSFC(Grant Nos.12301063 and 11771070)2024 Liaoning Provincial Natural Science Foundation Program(Ph.D.Research Start-up Project)(Grant No.2024-BS-205)。
文摘In this paper,we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary.Furthermore,we provide the proof of the Dabrowski–Sitarz–Zalecki type theorems associated with the spectral Einstein functionals for perturbations of Dirac operators,particularly in the cases of on 4-dimensional manifolds with boundary.
基金Project (No. JSPS-P-08073)supported by the Japanese Society for the Promotion of Science
文摘This study introduces measures to identify resonant (concentration of energy in a single or a few frequencies) or unfavorable earthquake ground motions. Probabilistic measures based on the entropy rate and the geometric properties of the power spectral density function (PSDF) of the ground acceleration are developed first. Subsequently, deterministic measures for the frequency content of the ground acceleration are also developed. These measures are then used for identifying resonance and criticality in stochastic earthquake models and 110 acceleration records measured at rock, stiff, medium and soft soil sites. The unfavorable earthquake record for a given structure is defined as the record having a narrow frequency content and dominant frequency close to the structure fundamental natural frequency. Accordingly, the measures developed in this study may provide a basis for selecting records that are capable of producing the highest structural response. Numerical verifications are provided on damage caused to structures by identified resonant records.
基金sponsored by the National Key Technology R&D Program of China(2009BAK55B00)the Earthquake Industry Research Project(201508012)
文摘The noise data in vertical component records of 85 seismic stations in Fujian Province during 2012 is used as the research object in this paper. The noise data is divided into fiveminute segments to calculate the power spectra. The high reference line and low reference line of station are then identified by drawing a probability density function graph( PDF)using the power spectral probability density function. Moreover, according to the anomalies of PDF graphs in 85 seismic stations,the abnormal noise is divided into four categories: dropped packet, low noise, high noise, and median noise anomalies.Afterwards,four selection methods are found by the high or low noise reference line of the stations,and the system of real-time monitoring of seismic noise is formed by combining the four selection methods. Noise records of 85 seismic stations in Fujian Province in July2013 are selected for verification,and the results show that the anomalous noise-recognition system could reach a 90% success rate at most stations and the effect of selection are very good. Therefore,it could be applied to the seismic noise real-time monitoring in stations.
基金Supported by the National Natural Science Foundation of China under Grant No.11164011the Provincial Nature Science Foundation of Jiangxi under Grant Nos.20122BAB212006 and 20132BAB212003
文摘We investigate the unique properties of current-induced heat generation in nanojunctions,such as failed Q α I relation(where Q is the heat generation and I the current),threshold voltage required to generate heat,etc.By employing the lead-quantum dot(QD)-lead system,we find these unique properties stem from(i) the discontinuity of Fermi distribution at chemical potentials of the leads and(ii) the satellite peaks in spectral function of the QD electron,which are induced by the electron-phonon interaction.
基金supported by the National Natural Science Foundation of China(Grant No.10974072)
文摘We present a systematic analysis on the role of the quantum dot （QD） shape in the influence of the phonon bath on the dynamics of a QD cavity QED system. The spectral functions of the phonon bath in three representative QD shapes： spherical, ellipsoidal, and disk, are calculated from the carrier wave functions subjected to the confinement potential provided by the corresponding shape. The obtained spectral functions are used to calculate three main effects brought by the phonon bath, i.e., the coupling renormalization, the off-resonance assisted feeding rate and the pure dephasing rate. It is found that the spectral function of a disk QD has the widest distribution, hence the phonon bath in a disk QD can lead to the smallest renormalization factor, the largest dephasing rate in the short time domains（≤2 ps）, and the oft-resonance assisted feeding can support the widest detuning. Except for the pure dephasing rate in the long time domains, all the influences brought by the phonon bath show serious shape dependence.
基金sponsored in part by the National Science Foundationby National Natural Science Foundation of China+1 种基金by Ministry of Communication of Chinaby Jiangsu Natural Science Foundation
文摘This article lays out a unified theory for dynamics of vehicle-pavement interaction under moving and stochastic loads. It covers three major aspects of the subject： pavement surface, tire-pavement contact forces, and response of continuum media under moving and stochastic vehicular loads. Under the subject of pavement surface, the spectrum of thermal joints is analyzed using Fourier analysis of periodic function. One-dimensional and two-dimensional random field models of pavement surface are discussed given three different assumptions. Under the subject of tire-pavement contact forces, a vehicle is modeled as a linear system. At a constant speed of travel, random field of pavement surface serves as a stationary stochastic process exciting vehicle vibration, which, in turn, generates contact force at the interface of tire and pavement. The contact forces are analyzed in the time domain and the frequency domains using random vibration theory. It is shown that the contact force can be treated as a nonzero mean stationary process with a normal distribution. Power spectral density of the contact force of a vehicle with walking-beam suspension is simulated as an illustration. Under the subject of response of continuum media under moving and stochastic vehicular loads, both time-domain and frequency-domain analyses are presented for analytic treatment of moving load problem. It is shown that stochastic response of linear continuum media subject to a moving stationary load is a nonstationary process. Such a nonstationary stochastic process can be converted to a stationary stochastic process in a follow-up moving coordinate.
基金Project supported by the National Natural Science Foundation of China(Grant No.12174101)the Fundamental Research Funds for the Central Universities(Grant No.2022MS051)。
文摘By using the numerical renormalization group(NRG)method,we construct a large dataset with about one million spectral functions of the Anderson quantum impurity model.The dataset contains the density of states(DOS)of the host material,the strength of Coulomb interaction between on-site electrons(U),and the hybridization between the host material and the impurity site(Γ).The continued DOS and spectral functions are stored with Chebyshev coefficients and wavelet functions,respectively.From this dataset,we build seven different machine learning networks to predict the spectral function from the input data,DOS,U,andΓ.Three different evaluation indexes,mean absolute error(MAE),relative error(RE)and root mean square error(RMSE),are used to analyze the prediction abilities of different network models.Detailed analysis shows that,for the two kinds of widely used recurrent neural networks(RNNs),gate recurrent unit(GRU)has better performance than the long short term memory(LSTM)network.A combination of bidirectional GRU(BiGRU)and GRU has the best performance among GRU,BiGRU,LSTM,and BiLSTM.The MAE peak of BiGRU+GRU reaches 0.00037.We have also tested a one-dimensional convolutional neural network(1DCNN)with 20 hidden layers and a residual neural network(ResNet),we find that the 1DCNN has almost the same performance of the BiGRU+GRU network for the original dataset,while the robustness testing seems to be a little weak than BiGRU+GRU when we test all these models on two other independent datasets.The ResNet has the worst performance among all the seven network models.The datasets presented in this paper,including the large data set of the spectral function of Anderson quantum impurity model,are openly available at https://doi.org/10.57760/sciencedb.j00113.00192.
基金Project (No. 03-02-02-0056 PR0025/04-03) supported by the Inten-sification of Research in Priority Areas (IRPA), Ministry of Science,Technology and Innovation, Malaysia
文摘This paper describes the finite element (FE) analysis technique to predict fatigue life using the narrow band frequency response approach. The life prediction results are useful for improving the component design methodology at the very early development stage. The approach is found to be suitable for a periodic loading but requires very large time records to accurately describe random loading processes. This paper is aimed at investigating the effects of surface treatments on the fatigue life of the free piston linear engine’s components. Finite element modelling and frequency response analysis were conducted using computer aided design and finite element analysis commercial codes, respectively. In addition, the fatigue life prediction was carried out using finite element based fatigue analysis commercial code. Narrow band approach was specially applied to predict the fatigue life of the free piston linear engine cylinder block. Significant variation was observed between the surface treatments and untreated cylinder block of free piston engine. The obtained results indicated that nitrided treatment yielded the longest life. This approach can determine premature products failure phenomena, and therefore can reduce time to market, improve product reliability and customer confidence.
文摘Let {vij}, i, j = 1, 2, …, be i.i.d, random variables with Ev11 = 0, Ev11^2 = 1 and a1 = （ai1,…, aiM） be random vectors with {aij} being i.i.d, random variables. Define XN =（x1,…, xk） and SN =XNXN^T,where xi=ai×si and si=1/√N（v1i,…, vN,i）^T. The spectral distribution of SN is proven to converge, with probability one, to a nonrandom distribution function under mild conditions.
文摘The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).
基金This work is sponsored by the Program on Long-Range Weather Forecasting Theory and Methodology of China.
文摘Study is undertaken of spherical function spectral structures of long-term mean and anomaly patterns of the Northern Hemisphere 500 hPa monthly mean geopotential height together with the seasonal and interannual variations investigated.Results show that they are marked by low dimensions and low orders,and the mean and anomaly fields can be described in terms of 20 and 50 spherical function components,respectively.
基金Natural Science Foundation of ChinaGrant for Returned Scholars of Shanxi
文摘We characterize the surjective additive maps compressing the spectral function Δ（·） between standard operator algebras acting on complex Banach spaces, where Δ（·） stands for any one of nine spectral functions σ（·）, σl（·）, σr（·）,σl（·） ∩ σr（·）, δσ（·）, ησ（·）, σap（·）, σs（·）, and σap（·） ∩ σs（·）.
文摘Non-diffractive space-time wave packets(nSTWPs) represent a broad class of optical pulses capable of propagating without diffraction or dispersion in linear media. In this work, we introduce a complete family of nSTWPs that remain invariant under transverse Lorentz boosts. The Lorentz-invariant behavior of these STWPs is rigorously analyzed through their associated spectral line function, providing new insights into their fundamental properties. Furthermore, we quantify the limitations of this invariance and compare the robustness of the proposed nSTWPs against conventional nSTWPs.
