Statistical Energy Analysis(SEA) is one of the conventional tools for predicting vehicle high-frequency acoustic responses.This study proposes a new method that can provide customized optimization solutions to meet NV...Statistical Energy Analysis(SEA) is one of the conventional tools for predicting vehicle high-frequency acoustic responses.This study proposes a new method that can provide customized optimization solutions to meet NVH targets based on the specific needs of different project teams during the initial project stages.This approach innovatively integrates dynamic optimization,Radial Basis Function(RBF),and Fuzzy Design Variables Genetic Algorithm(FDVGA) into the optimization process of Statistical Energy Analysis(SEA),and also takes vehicle sheet metal into account in the optimization of sound packages.In the implementation process,a correlation model is established through Python scripts to link material density with acoustic parameters,weight,and cost.By combining Optimus and VaOne software,an optimization design workflow is constructed and the optimization design process is successfully executed.Under various constraints related to acoustic performance,weight and cost,a globally optimal design is achieved.This technology has been effectively applied in the field of Battery Electric Vehicle(BEV).展开更多
A microphone and a seismic sensor always become a basic unit of UGS(unattended ground sensors) system. The mechanism of acoustic and seismic property of target and its propagation are described. The acoustic and seism...A microphone and a seismic sensor always become a basic unit of UGS(unattended ground sensors) system. The mechanism of acoustic and seismic property of target and its propagation are described. The acoustic and seismic signals of targets are analyzed with time frequency distribution according to its non stationary property. Narrow band energy function (NEF) and local power spectral density (LPSD) are proposed to extract features for target identification. Experiment results show that local power spectral density indicates corresponding target clearly.展开更多
To suppress the strong noise in seismic data with wide range of amplitudes, commonly used methods often yield unsatisfactory denoising results owing to inappropriate thresholds and require parametric testing as well a...To suppress the strong noise in seismic data with wide range of amplitudes, commonly used methods often yield unsatisfactory denoising results owing to inappropriate thresholds and require parametric testing as well as iterations to achieve the anticipated results. To overcome these problems, a data-driven strong amplitude suppression method based on the decibel criterion in the wavelet domain (ISANA) is proposed. The method determines the denoising threshold based on the decibel criterion and statistically analyzes the amplitude index rather than the abnormally high amplitudes. The method distinguishes the frequency band distributions of the valid signals in the time-frequency domain based on the wavelet transformation and then calculates thresholds in selected time windows, eventually achieving frequency-divided noise attenuation for better denoising. Simulations based on theoretical and real-world data verify the adaptability and low dependence of the method on the size of the time window. The method suppresses noise without energy loss in the signals.展开更多
By calculating the energy distribution of electrons reaching the photocathode surface and solving the Schrodinger equation that describes the behavior of an electron tunneling through the surface potential barrier,we ...By calculating the energy distribution of electrons reaching the photocathode surface and solving the Schrodinger equation that describes the behavior of an electron tunneling through the surface potential barrier,we obtain an equation to calculate the emitted electron energy distribution of transmission-mode NEA GaAs photocathodes. Accord- ing to the equation,we study the effect of cathode surface potential barrier on the electron energy distribution and find a significant effect of the barrier-Ⅰ thickness or end height,especially the thickness,on the quantum efficiency of the cath- ode. Barrier Ⅱ has an effect on the electron energy spread, and an increase in the vacuum level will lead to a narrower electron energy spread while sacrificing a certain amount of cathode quantum efficiency. The equation is also used to fit the measured electron energy distribution curve of the transmission-mode cathode and the parameters of the surface barri- er are obtained from the fitting. The theoretical curve is in good agreement with the experimental curve.展开更多
This paper mainly deals with the reservoir on the heat and mass transfer and mass and energy balance in a geothermal field.On the basis of briefing the general characteristics of the reservoir and the supposition of t...This paper mainly deals with the reservoir on the heat and mass transfer and mass and energy balance in a geothermal field.On the basis of briefing the general characteristics of the reservoir and the supposition of the reservoir modeling,the paper emphasizes the mathematical descriptions of hydra thermal transportation and convection by two methods according to the different models,such as lumped parameter model and distributed parameter model.It is effective to use these models in simulating the heterogeneous,and anisotropical fracture reservoir for the designed lifetime of 15 years.展开更多
Mg-9Al-xPr(x=0.4,0.8 and 1.2,mass fraction,%)magnesium alloys were prepared by high-pressure die-casting technique.The effects of Pr on the microstructures of die-cast Mg-9Al based alloy were investigated by XRD and S...Mg-9Al-xPr(x=0.4,0.8 and 1.2,mass fraction,%)magnesium alloys were prepared by high-pressure die-casting technique.The effects of Pr on the microstructures of die-cast Mg-9Al based alloy were investigated by XRD and SEM.Needle-like Al11Pr3 phase and polygon Al6Mn6Pr phase are found in the microstructure.With 0.4%Pr addition,fine needle-like Al11Pr3 phase and a small amount of polygon Al6Mn6Pr phase near the grain boundary are found in the microstructure.Increasing Pr addition to 0.8%, lots of coarse needle-like Al11Pr3 phase within grain and polygon Al6Mn6Pr phase on grain boundary are observed.Further increasing Pr addition,the size of needle-like Al11Pr3 phase decreases,while the size of polygon Al6Mn6Pr relatively increases.The mass fraction of Pr at around 0.8%is considered to be suitable to obtain the optimal mechanical properties.The optimal mechanical properties are mainly resulted from grain boundary strengthening obtained by precipitates and solid solution.展开更多
The model of heat source(MHS) which reflects the thermal interaction between materials and laser during processing determines the accuracy of simulation results. To acquire desirable simulations results, although vari...The model of heat source(MHS) which reflects the thermal interaction between materials and laser during processing determines the accuracy of simulation results. To acquire desirable simulations results, although various modifications of heat sources in the aspect of absorption process of laser by materials have been purposed, the distribution of laser power density(DLPD) in MHS is still modeled theoretically. However, in the actual situations of laser processing, the DLPD is definitely different from the ideal models. So, it is indispensable to build MHS using actual DLPD to improve the accuracy of simulation results. Besides, an automatic modeling method will be benefit to simplify the tedious pre-processing of simulations. This paper presents a modeling method and corresponding algorithm to model heat source using measured DLPD. This algorithm automatically processes original data to get modeling parameters and provides a step MHS combining with absorption models. Simulations and experiments of heat transfer in steel plates irradiated by laser prove the mothed and the step MHS. Moreover, the investigations of laser induced thermal-crack propagation in glass highlight the signification of modeling heat source based on actual DLPD and demonstrate the enormous application of this method in the simulation of laser processing.展开更多
Functionalized graphene nano-sheets(FGN) of 0.01%-0.05%(mass fraction) were added to produce FGN-cement composites in the form of mortars. Flow properties, mechanical properties and microstructure of the cementitious ...Functionalized graphene nano-sheets(FGN) of 0.01%-0.05%(mass fraction) were added to produce FGN-cement composites in the form of mortars. Flow properties, mechanical properties and microstructure of the cementitious material were then investigated. The results indicate that the addition of FGN decreases the fluidity slightly and improves mechanical properties of cement-based composites significantly. The highest strength is obtained with FGN content of 0.02% where the flexural strength and compressive strength at 28 days are 12.917 MPa and 52.42 MPa, respectively. Besides, scanning electron micrographs show that FGN can regulate formation of massive compact cross-linking structures and thermo gravimetric analysis indicates that FGN can accelerate the hydration reaction to increase the function of the composite effectively.展开更多
In our previous theoretical studies [Meng-Tao Sun, Yong-Qing Lee, and Feng-Cai Ma, Chem. Phys.Left. 371 (2003) 342], we have reported the quantum interference on collision-induced rotational energy transfer on CO (...In our previous theoretical studies [Meng-Tao Sun, Yong-Qing Lee, and Feng-Cai Ma, Chem. Phys.Left. 371 (2003) 342], we have reported the quantum interference on collision-induced rotational energy transfer on CO (A ^1 Π,v = 3) with inert gases, which originates from the difference between the two A-related collision potential energy surfaces. The interference angle, which measures the degree of coherence, is presented in this paper. Based on the time-dependent first order Born approximation, taking into account the anisotropic Lennard-Jones interaction potentials, the relation of the interference angle with the factors, including experimental temperature, partner, and rotational quantum number, are obtained. The changing tendencies with them are discussed. This theoretical model is important to understanding and performing this kind of experiment.展开更多
Energy efficiency(EE) is a key requirement for the design of short-range communication network.In order to alleviate energy consumption(EC) constraint,a novel layered heterogeneous mobile cloud architecture is propose...Energy efficiency(EE) is a key requirement for the design of short-range communication network.In order to alleviate energy consumption(EC) constraint,a novel layered heterogeneous mobile cloud architecture is proposed in this paper.Based on the proposed layered heterogeneous mobile cloud architecture,we establish an appropriate energy consumption model,and design an energy efficiency scheme based on joint data packet fragmentation and cooperative transmission and analyze the energy efficiency corresponding to different packet sizes and the cloud size.Simulation results show that,when all nodes of the cloud are accessing the same size of data packet fragmentation,the proposed layered heterogeneous mobile cloud architecture can provide significant energy savings.The results provide useful insights into the possible operation of the strategies and show that significant energy consumption reductions are possible.展开更多
The effects of Ca addition on the as-cast microstructure and mechanical properties of the Mg-5Zn-5Sn (mass fraction,%) alloy were investigated.The results indicate that an addition of 0.5%-1.5% (mass fraction) Ca to t...The effects of Ca addition on the as-cast microstructure and mechanical properties of the Mg-5Zn-5Sn (mass fraction,%) alloy were investigated.The results indicate that an addition of 0.5%-1.5% (mass fraction) Ca to the Mg-5Zn-5Sn alloy not only refines the as-cast microstructure of the alloy but also causes the formation of the primary and/or eutectic CaMgSn phases with high thermal stability;an increase in Ca amount from 0.5% to 1.5% (mass fraction) increases the amount and size of the CaMgSn phase.In addition,Ca addition to the Mg-5Zn-5Sn alloy improves not only the tensile properties at room temperature and 150 ℃ but also the creep properties.Among the Ca-containing Mg-5Zn-5Sn alloys,the one added 0.5% (mass fraction) Ca obtains the optimum ultimate tensile strength and elongation at room temperature and 150 ℃,however,the alloy added 1.5% (mass fraction) Ca exhibits the optimum yield strength and creep properties.展开更多
The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical ra...The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical radius is determined by the growth rate, the mass transfer coefficient and the mass balance, and is independent of whether the limiting stationary growth regime has been obtained.展开更多
A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the expone...A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.展开更多
Recently, content-centric networking (CCN) has become a hot research topic for the diffusion of contents over the Internet. Most existing works on CCN focus on the improvement of network resource utilization. Conseq...Recently, content-centric networking (CCN) has become a hot research topic for the diffusion of contents over the Internet. Most existing works on CCN focus on the improvement of network resource utilization. Consequently, the energy consumption aspect of CCN is largely ignored. In this paper, we propose a distributed energyefficient in-network caching scheme for CCN, where each content router only needs locally available information to make caching decisions considering both caching energy consumption and transport energy consumption. We formulate the in-network caching problem as a non-cooperative game. Through rigorous mathematical analysis, we prove that pure strategy Nash equilibria exist in the proposed scheme, and it always has a strategy profile that implements the socially optimal configuration, even if the touters are self-interested in nature. Simulation results are presented to show that the distributed solution is competitive to the centralized scheme, and has superior performance compared to other popular caching schemes in CCN. Besides, it exhibits a fast convergence speed when the capacity of content routers varies.展开更多
We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distribution...We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.展开更多
文摘Statistical Energy Analysis(SEA) is one of the conventional tools for predicting vehicle high-frequency acoustic responses.This study proposes a new method that can provide customized optimization solutions to meet NVH targets based on the specific needs of different project teams during the initial project stages.This approach innovatively integrates dynamic optimization,Radial Basis Function(RBF),and Fuzzy Design Variables Genetic Algorithm(FDVGA) into the optimization process of Statistical Energy Analysis(SEA),and also takes vehicle sheet metal into account in the optimization of sound packages.In the implementation process,a correlation model is established through Python scripts to link material density with acoustic parameters,weight,and cost.By combining Optimus and VaOne software,an optimization design workflow is constructed and the optimization design process is successfully executed.Under various constraints related to acoustic performance,weight and cost,a globally optimal design is achieved.This technology has been effectively applied in the field of Battery Electric Vehicle(BEV).
文摘A microphone and a seismic sensor always become a basic unit of UGS(unattended ground sensors) system. The mechanism of acoustic and seismic property of target and its propagation are described. The acoustic and seismic signals of targets are analyzed with time frequency distribution according to its non stationary property. Narrow band energy function (NEF) and local power spectral density (LPSD) are proposed to extract features for target identification. Experiment results show that local power spectral density indicates corresponding target clearly.
基金supported by the National Science and Technology Major Project(No.2011ZX05002-004-002)the National Natural Science Foundation of China(No.41304111)+3 种基金Key Project of Science and Technology Department of Sichuan Province(No.2016JY0200)Natural Science project of Education Department of Sichuan Province(Nos.16ZB0101 and 14ZA0061)the Sichuan Provincial Youth Science&Technology Innovative Research Group Fund(No.2016TD0023)the Cultivating Program of Excellent Innovation Team of Chengdu University of Technology(No.KYTD201410)
文摘To suppress the strong noise in seismic data with wide range of amplitudes, commonly used methods often yield unsatisfactory denoising results owing to inappropriate thresholds and require parametric testing as well as iterations to achieve the anticipated results. To overcome these problems, a data-driven strong amplitude suppression method based on the decibel criterion in the wavelet domain (ISANA) is proposed. The method determines the denoising threshold based on the decibel criterion and statistically analyzes the amplitude index rather than the abnormally high amplitudes. The method distinguishes the frequency band distributions of the valid signals in the time-frequency domain based on the wavelet transformation and then calculates thresholds in selected time windows, eventually achieving frequency-divided noise attenuation for better denoising. Simulations based on theoretical and real-world data verify the adaptability and low dependence of the method on the size of the time window. The method suppresses noise without energy loss in the signals.
文摘By calculating the energy distribution of electrons reaching the photocathode surface and solving the Schrodinger equation that describes the behavior of an electron tunneling through the surface potential barrier,we obtain an equation to calculate the emitted electron energy distribution of transmission-mode NEA GaAs photocathodes. Accord- ing to the equation,we study the effect of cathode surface potential barrier on the electron energy distribution and find a significant effect of the barrier-Ⅰ thickness or end height,especially the thickness,on the quantum efficiency of the cath- ode. Barrier Ⅱ has an effect on the electron energy spread, and an increase in the vacuum level will lead to a narrower electron energy spread while sacrificing a certain amount of cathode quantum efficiency. The equation is also used to fit the measured electron energy distribution curve of the transmission-mode cathode and the parameters of the surface barri- er are obtained from the fitting. The theoretical curve is in good agreement with the experimental curve.
文摘This paper mainly deals with the reservoir on the heat and mass transfer and mass and energy balance in a geothermal field.On the basis of briefing the general characteristics of the reservoir and the supposition of the reservoir modeling,the paper emphasizes the mathematical descriptions of hydra thermal transportation and convection by two methods according to the different models,such as lumped parameter model and distributed parameter model.It is effective to use these models in simulating the heterogeneous,and anisotropical fracture reservoir for the designed lifetime of 15 years.
基金Project(2006AA03Z520)supported by National High-tech Research and Development Program of ChinaProject(20080508)supported bythe Science and Technology Program of Jilin Province of China+2 种基金Project(2007094)supported by the Science and Technology Program of Education Department of Jilin Province of ChinaProject(2007101)supported by the Science&Technology Development ProgramProject supported by the Basic Research Program of Changchun University of Technology,China
文摘Mg-9Al-xPr(x=0.4,0.8 and 1.2,mass fraction,%)magnesium alloys were prepared by high-pressure die-casting technique.The effects of Pr on the microstructures of die-cast Mg-9Al based alloy were investigated by XRD and SEM.Needle-like Al11Pr3 phase and polygon Al6Mn6Pr phase are found in the microstructure.With 0.4%Pr addition,fine needle-like Al11Pr3 phase and a small amount of polygon Al6Mn6Pr phase near the grain boundary are found in the microstructure.Increasing Pr addition to 0.8%, lots of coarse needle-like Al11Pr3 phase within grain and polygon Al6Mn6Pr phase on grain boundary are observed.Further increasing Pr addition,the size of needle-like Al11Pr3 phase decreases,while the size of polygon Al6Mn6Pr relatively increases.The mass fraction of Pr at around 0.8%is considered to be suitable to obtain the optimal mechanical properties.The optimal mechanical properties are mainly resulted from grain boundary strengthening obtained by precipitates and solid solution.
基金Project(2021YFF0500200) supported by the National Key R&D Program of ChinaProject(52105437) supported by the National Natural Science Foundation of China+1 种基金Project(202006120184) supported by the Heilongjiang Provincial Postdoctoral Science Foundation,ChinaProject(LBH-Z20054) supported by the China Scholarship Council。
文摘The model of heat source(MHS) which reflects the thermal interaction between materials and laser during processing determines the accuracy of simulation results. To acquire desirable simulations results, although various modifications of heat sources in the aspect of absorption process of laser by materials have been purposed, the distribution of laser power density(DLPD) in MHS is still modeled theoretically. However, in the actual situations of laser processing, the DLPD is definitely different from the ideal models. So, it is indispensable to build MHS using actual DLPD to improve the accuracy of simulation results. Besides, an automatic modeling method will be benefit to simplify the tedious pre-processing of simulations. This paper presents a modeling method and corresponding algorithm to model heat source using measured DLPD. This algorithm automatically processes original data to get modeling parameters and provides a step MHS combining with absorption models. Simulations and experiments of heat transfer in steel plates irradiated by laser prove the mothed and the step MHS. Moreover, the investigations of laser induced thermal-crack propagation in glass highlight the signification of modeling heat source based on actual DLPD and demonstrate the enormous application of this method in the simulation of laser processing.
基金Project(51102035)supported by the National Natural Science Foundation of China
文摘Functionalized graphene nano-sheets(FGN) of 0.01%-0.05%(mass fraction) were added to produce FGN-cement composites in the form of mortars. Flow properties, mechanical properties and microstructure of the cementitious material were then investigated. The results indicate that the addition of FGN decreases the fluidity slightly and improves mechanical properties of cement-based composites significantly. The highest strength is obtained with FGN content of 0.02% where the flexural strength and compressive strength at 28 days are 12.917 MPa and 52.42 MPa, respectively. Besides, scanning electron micrographs show that FGN can regulate formation of massive compact cross-linking structures and thermo gravimetric analysis indicates that FGN can accelerate the hydration reaction to increase the function of the composite effectively.
基金The project supported by National Natural Science Foundation of China under Grant No. 10374040
文摘In our previous theoretical studies [Meng-Tao Sun, Yong-Qing Lee, and Feng-Cai Ma, Chem. Phys.Left. 371 (2003) 342], we have reported the quantum interference on collision-induced rotational energy transfer on CO (A ^1 Π,v = 3) with inert gases, which originates from the difference between the two A-related collision potential energy surfaces. The interference angle, which measures the degree of coherence, is presented in this paper. Based on the time-dependent first order Born approximation, taking into account the anisotropic Lennard-Jones interaction potentials, the relation of the interference angle with the factors, including experimental temperature, partner, and rotational quantum number, are obtained. The changing tendencies with them are discussed. This theoretical model is important to understanding and performing this kind of experiment.
基金jointly supported by the Chongqing Municipal Natural Science Foundation under Grant No.CSTC2013jjB40001)the National High Technology Research and Development Program of China(863Program)under Grant No.20140908the Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT1299
文摘Energy efficiency(EE) is a key requirement for the design of short-range communication network.In order to alleviate energy consumption(EC) constraint,a novel layered heterogeneous mobile cloud architecture is proposed in this paper.Based on the proposed layered heterogeneous mobile cloud architecture,we establish an appropriate energy consumption model,and design an energy efficiency scheme based on joint data packet fragmentation and cooperative transmission and analyze the energy efficiency corresponding to different packet sizes and the cloud size.Simulation results show that,when all nodes of the cloud are accessing the same size of data packet fragmentation,the proposed layered heterogeneous mobile cloud architecture can provide significant energy savings.The results provide useful insights into the possible operation of the strategies and show that significant energy consumption reductions are possible.
基金Project(50725413) supported by the National Natural Science Foundation of ChinaProject (2007CB613704) supported by the National Basic Research Program of China Projects(2006AA4012-9-6,2007BB4400) supported by Chongqing Science and Technology Commission,China
文摘The effects of Ca addition on the as-cast microstructure and mechanical properties of the Mg-5Zn-5Sn (mass fraction,%) alloy were investigated.The results indicate that an addition of 0.5%-1.5% (mass fraction) Ca to the Mg-5Zn-5Sn alloy not only refines the as-cast microstructure of the alloy but also causes the formation of the primary and/or eutectic CaMgSn phases with high thermal stability;an increase in Ca amount from 0.5% to 1.5% (mass fraction) increases the amount and size of the CaMgSn phase.In addition,Ca addition to the Mg-5Zn-5Sn alloy improves not only the tensile properties at room temperature and 150 ℃ but also the creep properties.Among the Ca-containing Mg-5Zn-5Sn alloys,the one added 0.5% (mass fraction) Ca obtains the optimum ultimate tensile strength and elongation at room temperature and 150 ℃,however,the alloy added 1.5% (mass fraction) Ca exhibits the optimum yield strength and creep properties.
基金Project (No. 20076039) supported by the National Science Founda-tion of China
文摘The relation between the critical radius and the particle size distribution for generalized Ostwald type ripening processes whereby the mass transfer coefficient is modelled by a power law was derived. The critical radius is determined by the growth rate, the mass transfer coefficient and the mass balance, and is independent of whether the limiting stationary growth regime has been obtained.
文摘A modified Olami Feder-Christensen model of self-organized criticality on a square lattice with the properties of small world networks has been studied.We find that our model displays power-law behavior and the exponent τ of the model depends on φ,the density of long-range connections in our network.
基金supported under the National Basic Research Program(973) of China(Project Number: 2012CB315801)the National Natural Science Fund(Project Number:61300184)the fundamental research funds for the Central Universities(Project Number:2013RC0113)
文摘Recently, content-centric networking (CCN) has become a hot research topic for the diffusion of contents over the Internet. Most existing works on CCN focus on the improvement of network resource utilization. Consequently, the energy consumption aspect of CCN is largely ignored. In this paper, we propose a distributed energyefficient in-network caching scheme for CCN, where each content router only needs locally available information to make caching decisions considering both caching energy consumption and transport energy consumption. We formulate the in-network caching problem as a non-cooperative game. Through rigorous mathematical analysis, we prove that pure strategy Nash equilibria exist in the proposed scheme, and it always has a strategy profile that implements the socially optimal configuration, even if the touters are self-interested in nature. Simulation results are presented to show that the distributed solution is competitive to the centralized scheme, and has superior performance compared to other popular caching schemes in CCN. Besides, it exhibits a fast convergence speed when the capacity of content routers varies.
基金National Natural Science Foundation of China under Grant Nos.10775097,10874174 and 10647133the Natural Science Foundation of Jiangxi Province under Grant Nos.2007GQS1906 and 2007GZS1871the Research Foundation of the Education Department of Jiangxi Province under Grant No.[2007]22
文摘We find that the squeezed two-mode number state is just a two-variable Hermite polynomial excitation of thetwo-mode squeezed vacuum state (THPES).We find that the Wigner function of THPES and its marginal distributionsare just related to two-variable Hermite polynomials (or Laguerre polynomials) and that the tomogram of THPES canbe expressed by one-mode Hermite polynomial.