The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the...The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref. [5]found a base for establishing an expert system of spatial mechanism analysis in the future.展开更多
In this study, we explored the neural mechanism of global topological perception in the human visual system. We showed strong evidence that the retinotectal pathway in the archicortex of the human brain is responsible...In this study, we explored the neural mechanism of global topological perception in the human visual system. We showed strong evidence that the retinotectal pathway in the archicortex of the human brain is responsible for global topological perception, and for modulating the local feature processing in the classical ventral visual pathway. Inspired by this recent cognitive discovery,we developed a novel CogNet architecture to emulate the global-local dichotomy of human visual cognitive mechanisms. The thorough experimental results indicate that the proposed CogNet not only significantly improves image classification accuracies but also effectively addresses the texture bias problem observed in baseline CNN models. We have also conducted mathematical analysis for the generalization gap for general neural networks. Our theoretical derivations suggest that the Hurst parameter, a measure of the curvature of the loss landscape, can closely bind the generalization gap. A larger Hurst parameter corresponds to a better generalization ability. We found that our proposed CogNet achieves a lower test error and attains a larger Hurst parameter,strengthening its superiority over the baseline CNN models further.展开更多
In this paper, we conduct research on the developmental trend and characteristics of the modern oil painting from perspectives ofthe texture and color. Image oil painting is not just a simple art genre and style, it i...In this paper, we conduct research on the developmental trend and characteristics of the modern oil painting from perspectives ofthe texture and color. Image oil painting is not just a simple art genre and style, it is a western oil painting the foreign art in the Chinese culturalenvironment to generate the types of oil painting is a kind of Chinese national culture characteristic of painting art for the purpose of art topresent true feelings and true feelings should be created by the artist’s technique, form, style, texture effects such as external factors. And manyof the current oil painting art works are showing the true feelings, because of the wrong style, texture and other external factors as the purpose ofart. Master of art means the long-term growth path is essentially in express their true feelings, and to form the style need to constantly supplementand perfect process. We provide the novel perspective on the corresponding issues that will be meaningful and important.展开更多
An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, clo...An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.展开更多
The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addit...The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.展开更多
Sentiment analysis is the computational study of how opinions, attitudes, emotions, and perspectives are expressed in language, and has been the important task of natural language processing. Sentiment analysis is hig...Sentiment analysis is the computational study of how opinions, attitudes, emotions, and perspectives are expressed in language, and has been the important task of natural language processing. Sentiment analysis is highly valuable for both research and practical applications. The focuses were put on the difficulties in the construction of sentiment classifiers which normally need tremendous labeled domain training data, and a novel unsupervised framework was proposed to make use of the Chinese idiom resources to develop a general sentiment classifier. Furthermore, the domain adaption of general sentiment classifier was improved by taking the general classifier as the base of a self-training procedure to get a domain self-training sentiment classifier. To validate the effect of the unsupervised framework, several experiments were carried out on publicly available Chinese online reviews dataset. The experiments show that the proposed framework is effective and achieves encouraging results. Specifically, the general classifier outperforms two baselines(a Na?ve 50% baseline and a cross-domain classifier), and the bootstrapping self-training classifier approximates the upper bound domain-specific classifier with the lowest accuracy of 81.5%, but the performance is more stable and the framework needs no labeled training dataset.展开更多
For LAMOST, the largest sky survey program in China, the solution of the problem of automatic discrimination of stars from galaxies by spectra has shown that the results of the PSF test can be significantly refined. H...For LAMOST, the largest sky survey program in China, the solution of the problem of automatic discrimination of stars from galaxies by spectra has shown that the results of the PSF test can be significantly refined. However, the problem is made worse when the redshifts of galaxies are not available. We present a new automatic method of star/(normal) galaxy separation, which is based on Statistical Mixture Modeling with Radial Basis Function Neural Networks (SMM-RBFNN). This work is a continuation of our previous one, where active and non-active celestial objects were successfully segregated. By combining the method in this paper and the previous one, stars can now be effectively separated from galaxies and AGNs by their spectra-a major goal of LAMOST, and an indispensable step in any automatic spectrum classification system. In our work, the training set includes standard stellar spectra from Jacoby's spectrum library and simulated galaxy spectra of EO, SO, Sa, Sb types with redshift ranging from 0 to 1.2, and the test set of stellar spectra from Pickles' atlas and SDSS spectra of normal galaxies with SNR of 13. Experiments show that our SMM-RBFNN is more efficient in both the training and testing stages than the BPNN (back propagation neural networks), and more importantly, it can achieve a good classification accuracy of 99.22% and 96.52%, respectively for stars and normal galaxies.展开更多
The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the...The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices(ESAI)elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI's yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.展开更多
Embedded clusters are ideal laboratories for understanding the early phase of the dynamical evolution of clusters as well as massive star formation. An interesting observational phenomenon is that some of the embedded...Embedded clusters are ideal laboratories for understanding the early phase of the dynamical evolution of clusters as well as massive star formation. An interesting observational phenomenon is that some of the embedded clusters show mass segregation, i.e., the most massive stars are preferentially found near the cluster center. We develop a new approach to describe mass segregation. Using this approach and the Two Micron All Sky Survey Point Source Catalog (2MASS PSC), we analyze 18 embedded clusters in the Galaxy. We find that 11 of them are mass-segregated and that the others are not mass-segregated. No inversely mass-segregated cluster is found.展开更多
The quality of full-disk solar Hα images is significantly degraded by stripe interference. In this paper, to improve the analysis of morphological evolution, a robust solution for stripe interference removal in a par...The quality of full-disk solar Hα images is significantly degraded by stripe interference. In this paper, to improve the analysis of morphological evolution, a robust solution for stripe interference removal in a partial full-disk solar Hα image is proposed. The full-disk solar image is decomposed into a set of support value images on different scales by convolving the image with a sequence of multiscale support value filters, which are calculated from the mapped least-squares support vector machines (LS-SVMs). To match the resolution of the support value images, a scale-adaptive LS-SVM regression model is used to remove stripe interference from the support value images. We have demonstrated the advantages of our method on solar Hα images taken in 2001-2002 at the Huairou Solar Observing Station. Our experimental results show that our method can remove the stripe interference well in solar Hα images and the restored image can be used in morphology researches.展开更多
There are two methods on option pricing, no-arbitrage and equilibrium analysis. We construct a simple economy with continuous consumption, in which we “endogenize” the stochastic process of prices in the option pric...There are two methods on option pricing, no-arbitrage and equilibrium analysis. We construct a simple economy with continuous consumption, in which we “endogenize” the stochastic process of prices in the option pricing model based on no-arbitrage analysis. With constant relative risk aversion type utility function assumption, we present Merton (1973) option pricing model and find the consistency of the model with a general equilibrium framework. We extend the model to the market with m securities and it turns out similar results.展开更多
Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructi...Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.展开更多
Searching for new resonances and finding out their properties is an essential part of any existing or future particle physics experiment. The nature of a new resonance is characterized by its spin, charge conjugation,...Searching for new resonances and finding out their properties is an essential part of any existing or future particle physics experiment. The nature of a new resonance is characterized by its spin, charge conjugation,parity, and its couplings with the existing particles of the Standard Model. If a new resonance is found in the four lepton final state produced via two intermediate Z bosons, the resonance could be a new heavy scalar or a Z boson or even a higher spin particle. In such cases a step by step methodology as enunciated in this paper can be followed to determine the spin, parity and the coupling to two Z bosons of the parent particles, in a fully model-independent way. In our approach we show how three uni-angular distributions and a few experimentally measurable observables can conclusively tell us about the spin, parity as well as the couplings of the new resonance to two Z bosons. We have performed a numerical analysis to validate our approach and showed how the uni-angular observables can be used to disentangle the spin parity as well as the coupling of the resonance.展开更多
文摘The displacement, velocity and acceleration analysis of the general spatial 7R mechanism is discussed in this paper, fused on the method proposed in Ref. [2], an input-output algebra equation of the 16th degree in the tan-half-angle of the output angular displacement is derived. The derivation process and computation are considerably simple. A program written in Allanguage is used to derive the coefficients of displacement equations: therefore the amount of manual work is greatly decreased. The results are verified by a numerical example. The researches of this paper and Ref. [5]found a base for establishing an expert system of spatial mechanism analysis in the future.
基金supported by the National Key Research and Development Project of China (Grant No. 2020AAA0105600)the National Natural Science Foundation of China (Grant Nos. U21B2048 and 62276208)+1 种基金Shenzhen Key Technical Projects (Grant No. CJGJZD2022051714160501)the Chinese Academy of Sciences (Grant Nos. 2021091 and YSBR-068)。
文摘In this study, we explored the neural mechanism of global topological perception in the human visual system. We showed strong evidence that the retinotectal pathway in the archicortex of the human brain is responsible for global topological perception, and for modulating the local feature processing in the classical ventral visual pathway. Inspired by this recent cognitive discovery,we developed a novel CogNet architecture to emulate the global-local dichotomy of human visual cognitive mechanisms. The thorough experimental results indicate that the proposed CogNet not only significantly improves image classification accuracies but also effectively addresses the texture bias problem observed in baseline CNN models. We have also conducted mathematical analysis for the generalization gap for general neural networks. Our theoretical derivations suggest that the Hurst parameter, a measure of the curvature of the loss landscape, can closely bind the generalization gap. A larger Hurst parameter corresponds to a better generalization ability. We found that our proposed CogNet achieves a lower test error and attains a larger Hurst parameter,strengthening its superiority over the baseline CNN models further.
文摘In this paper, we conduct research on the developmental trend and characteristics of the modern oil painting from perspectives ofthe texture and color. Image oil painting is not just a simple art genre and style, it is a western oil painting the foreign art in the Chinese culturalenvironment to generate the types of oil painting is a kind of Chinese national culture characteristic of painting art for the purpose of art topresent true feelings and true feelings should be created by the artist’s technique, form, style, texture effects such as external factors. And manyof the current oil painting art works are showing the true feelings, because of the wrong style, texture and other external factors as the purpose ofart. Master of art means the long-term growth path is essentially in express their true feelings, and to form the style need to constantly supplementand perfect process. We provide the novel perspective on the corresponding issues that will be meaningful and important.
基金Project(51274250)supported by the National Natural Science Foundation of ChinaProject(2012BAK09B02-05)supported by the National Key Technology R&D Program during the 12th Five-year Plan of China
文摘An integration processing system of three-dimensional laser scanning information visualization in goaf was developed. It is provided with multiple functions, such as laser scanning information management for goaf, cloud data de-noising optimization, construction, display and operation of three-dimensional model, model editing, profile generation, calculation of goaf volume and roof area, Boolean calculation among models and interaction with the third party soft ware. Concerning this system with a concise interface, plentiful data input/output interfaces, it is featured with high integration, simple and convenient operations of applications. According to practice, in addition to being well-adapted, this system is favorably reliable and stable.
基金National Natural Science Foundation of China(NSFC)(11274083,61405067)Guandong Natural Science Foundation(2015A030313748)Shenzhen Municipal Science and Technology Plan(JCYJ20150513151706573)
文摘The exceptional point(EP)is one of the typical properties of parity–time-symmetric systems,arising from modes coupling with identical resonant frequencies or propagation constants in optics.Here we show that in addition to two different modes coupling,a nonuniform distribution of gain and loss leads to an offset from the original propagation constants,including both real and imaginary parts,resulting in the absence of EP.These behaviors are examined by the general coupled-mode theory from the first principle of the Maxwell equations,which yields results that are more accurate than those from the classical coupled-mode theory.Numerical verification via the finite element method is provided.In the end,we present an approach to achieve lossless propagation in a geometrically symmetric waveguide array.
基金Projects(61170156,60933005)supported by the National Natural Science Foundation of China
文摘Sentiment analysis is the computational study of how opinions, attitudes, emotions, and perspectives are expressed in language, and has been the important task of natural language processing. Sentiment analysis is highly valuable for both research and practical applications. The focuses were put on the difficulties in the construction of sentiment classifiers which normally need tremendous labeled domain training data, and a novel unsupervised framework was proposed to make use of the Chinese idiom resources to develop a general sentiment classifier. Furthermore, the domain adaption of general sentiment classifier was improved by taking the general classifier as the base of a self-training procedure to get a domain self-training sentiment classifier. To validate the effect of the unsupervised framework, several experiments were carried out on publicly available Chinese online reviews dataset. The experiments show that the proposed framework is effective and achieves encouraging results. Specifically, the general classifier outperforms two baselines(a Na?ve 50% baseline and a cross-domain classifier), and the bootstrapping self-training classifier approximates the upper bound domain-specific classifier with the lowest accuracy of 81.5%, but the performance is more stable and the framework needs no labeled training dataset.
基金Supported by "863" National High Technology R&D program.
文摘For LAMOST, the largest sky survey program in China, the solution of the problem of automatic discrimination of stars from galaxies by spectra has shown that the results of the PSF test can be significantly refined. However, the problem is made worse when the redshifts of galaxies are not available. We present a new automatic method of star/(normal) galaxy separation, which is based on Statistical Mixture Modeling with Radial Basis Function Neural Networks (SMM-RBFNN). This work is a continuation of our previous one, where active and non-active celestial objects were successfully segregated. By combining the method in this paper and the previous one, stars can now be effectively separated from galaxies and AGNs by their spectra-a major goal of LAMOST, and an indispensable step in any automatic spectrum classification system. In our work, the training set includes standard stellar spectra from Jacoby's spectrum library and simulated galaxy spectra of EO, SO, Sa, Sb types with redshift ranging from 0 to 1.2, and the test set of stellar spectra from Pickles' atlas and SDSS spectra of normal galaxies with SNR of 13. Experiments show that our SMM-RBFNN is more efficient in both the training and testing stages than the BPNN (back propagation neural networks), and more importantly, it can achieve a good classification accuracy of 99.22% and 96.52%, respectively for stars and normal galaxies.
基金supported by the National Natural Science Foundation of China(11573065 and 11633008)the Specialized Research Fund for State Key Laboratories and the Chinese Academy of Sciences
文摘The latitudinal migration of sunspots toward the equator,which implies there is propagation of the toroidal magnetic flux wave at the base of the solar convection zone,is one of the crucial observational bases for the solar dynamo to generate a magnetic field by shearing of the pre-existing poloidal magnetic field through differential rotation.The Extended time series of Solar Activity Indices(ESAI)elongated the Greenwich observation record of sunspots by several decades in the past.In this study,ESAI's yearly mean latitude of sunspots in the northern and southern hemispheres during the years 1854 to 1985 is utilized to statistically test whether hemispherical latitudinal migration of sunspots in a solar cycle is linear or nonlinear.It is found that a quadratic function is statistically significantly better at describing hemispherical latitudinal migration of sunspots in a solar cycle than a linear function.In addition,the latitude migration velocity of sunspots in a solar cycle decreases as the cycle progresses,providing a particular constraint for solar dynamo models.Indeed,the butterfly wing pattern with a faster latitudinal migration rate should present stronger solar activity with a shorter cycle period,and it is located at higher latitudinal position,giving evidence to support the Babcock-Leighton dynamo mechanism.
基金project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technologyfunded by the National Aeronautics and Space Administration and the National Science Foundationsupported by the National Natural Science Foundation of China(Grant Nos.10873037,10921063,10733030 and 10833001)
文摘Embedded clusters are ideal laboratories for understanding the early phase of the dynamical evolution of clusters as well as massive star formation. An interesting observational phenomenon is that some of the embedded clusters show mass segregation, i.e., the most massive stars are preferentially found near the cluster center. We develop a new approach to describe mass segregation. Using this approach and the Two Micron All Sky Survey Point Source Catalog (2MASS PSC), we analyze 18 embedded clusters in the Galaxy. We find that 11 of them are mass-segregated and that the others are not mass-segregated. No inversely mass-segregated cluster is found.
基金supported in part by the National Natural Science Fund Committee and the Chinese Academy of Sciences astronomical union funds (Grant U1331113)the Special Program for Basic Research of the Ministry of Science and Technology,China (Grant 2014FY120300)
文摘The quality of full-disk solar Hα images is significantly degraded by stripe interference. In this paper, to improve the analysis of morphological evolution, a robust solution for stripe interference removal in a partial full-disk solar Hα image is proposed. The full-disk solar image is decomposed into a set of support value images on different scales by convolving the image with a sequence of multiscale support value filters, which are calculated from the mapped least-squares support vector machines (LS-SVMs). To match the resolution of the support value images, a scale-adaptive LS-SVM regression model is used to remove stripe interference from the support value images. We have demonstrated the advantages of our method on solar Hα images taken in 2001-2002 at the Huairou Solar Observing Station. Our experimental results show that our method can remove the stripe interference well in solar Hα images and the restored image can be used in morphology researches.
文摘There are two methods on option pricing, no-arbitrage and equilibrium analysis. We construct a simple economy with continuous consumption, in which we “endogenize” the stochastic process of prices in the option pricing model based on no-arbitrage analysis. With constant relative risk aversion type utility function assumption, we present Merton (1973) option pricing model and find the consistency of the model with a general equilibrium framework. We extend the model to the market with m securities and it turns out similar results.
基金The Scientific Research Project of Hunan Education Department(18C0964)The 2016 Scientific Research Fund Project for Young Teachers of Hunan University of Finance and Economics(Q201604)
文摘Nowadays more and more people reside in metropolitan areas,and the impact of this phenomenon is clearly creating challenges for the environment,the economy and the society at large.It is therefore useful and instructive to consider the issue of optimal city size and review the literature over the past decades on optimal city size theory.Based on the progress in recent years of comparative analysis and inductive research,from both theoretical and empirical perspectives,this paper outlines the original definitions proposed for optimal city size and discusses some of the advantages and disadvantages of the various theories.The two prevailing models in the classical analysis of optimal city size,the Henry George Theorem(HGT)and the neoclassical approach,are examined later.This paper then introduces the supply oriented dynamic model(SOUDY model)and offers a plausible model for optimal city size based on the general equilibrium analysis,which is related to sustainable development.The results show that:(1)Simple optimal city size theories come from the cost-benefit analysis developed by main stream economics,and therefore cannot overcome the defect that the optimal size of cities is the same since the same production function;(2)The Henry George Theorem,which is one of the classical analysis paradigms of optimal city size,has been used more frequently in recent years to research the issues of optimal tax and public goods and has gradually lost its connection to the topic of optimal city size;(3)The neoclassical approach to optimal city size consists of externalities influencing optimal city size,the equilibrium and optimal models for city size,the optimal town,product variety and city size distribution.This kind of research is still in the mainstream of the study of optimal city size.Compared to single optimal city size,more attention is paid to the optimal distribution of city size;and(4)The supply-oriented dynamic model allows for the integration of a spatial dimension into the economic research of optimal city size,and the constraint between city level and city size is relaxed and this has more power to explain real-world problems.At the same time,the general equilibrium analysis,as a significant economic research method,provides a new perspective for the study of optimal city size.The supply-oriented dynamic model and general equilibrium analysis are two new research paradigms that deserve more attention in the analysis of optimal city size.
基金Supported in part by MOST(Taiwan)(103-2112-M-001-005(HYC),101-2112-M-001-005-MY3(TCY))
文摘Searching for new resonances and finding out their properties is an essential part of any existing or future particle physics experiment. The nature of a new resonance is characterized by its spin, charge conjugation,parity, and its couplings with the existing particles of the Standard Model. If a new resonance is found in the four lepton final state produced via two intermediate Z bosons, the resonance could be a new heavy scalar or a Z boson or even a higher spin particle. In such cases a step by step methodology as enunciated in this paper can be followed to determine the spin, parity and the coupling to two Z bosons of the parent particles, in a fully model-independent way. In our approach we show how three uni-angular distributions and a few experimentally measurable observables can conclusively tell us about the spin, parity as well as the couplings of the new resonance to two Z bosons. We have performed a numerical analysis to validate our approach and showed how the uni-angular observables can be used to disentangle the spin parity as well as the coupling of the resonance.