For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflect...For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.展开更多
Context: The advent of Artificial Intelligence (AI) requires modeling prior to its implementation in algorithms for most human skills. This observation requires us to have a detailed and precise understanding of the i...Context: The advent of Artificial Intelligence (AI) requires modeling prior to its implementation in algorithms for most human skills. This observation requires us to have a detailed and precise understanding of the interfaces of verbal and emotional communications. The progress of AI is significant on the verbal level but modest in terms of the recognition of facial emotions even if this functionality is one of the oldest in humans and is omnipresent in our daily lives. Dysfunction in the ability for facial emotional expressions is present in many brain pathologies encountered by psychiatrists, neurologists, psychotherapists, mental health professionals including social workers. It cannot be objectively verified and measured due to a lack of reliable tools that are valid and consistently sensitive. Indeed, the articles in the scientific literature dealing with Visual-Facial-Emotions-Recognition (ViFaEmRe), suffer from the absence of 1) consensual and rational tools for continuous quantified measurement, 2) operational concepts. We have invented a software that can use computer-morphing attempting to respond to these two obstacles. It is identified as the Method of Analysis and Research of the Integration of Emotions (M.A.R.I.E.). Our primary goal is to use M.A.R.I.E. to understand the physiology of ViFaEmRe in normal healthy subjects by standardizing the measurements. Then, it will allow us to focus on subjects manifesting abnormalities in this ability. Our second goal is to make our contribution to the progress of AI hoping to add the dimension of recognition of facial emotional expressions. Objective: To study: 1) categorical vs dimensional aspects of recognition of ViFaEmRe, 2) universality vs idiosyncrasy, 3) immediate vs ambivalent Emotional-Decision-Making, 4) the Emotional-Fingerprint of a face and 5) creation of population references data. Methods: M.A.R.I.E. enables the rational, quantified measurement of Emotional Visual Acuity (EVA) in an individual observer and a population aged 20 to 70 years. Meanwhile, it can measure the range and intensity of expressed emotions through three Face- Tests, quantify the performance of a sample of 204 observers with hypernormal measures of cognition, “thymia” (defined elsewhere), and low levels of anxiety, and perform analysis of the six primary emotions. Results: We have individualized the following continuous parameters: 1) “Emotional-Visual- Acuity”, 2) “Visual-Emotional-Feeling”, 3) “Emotional-Quotient”, 4) “Emotional-Decision-Making”, 5) “Emotional-Decision-Making Graph” or “Individual-Gun-Trigger”, 6) “Emotional-Fingerprint” or “Key-graph”, 7) “Emotional-Fingerprint-Graph”, 8) detecting “misunderstanding” and 9) detecting “error”. This allowed us a taxonomy with coding of the face-emotion pair. Each face has specific measurements and graphics. The EVA improves from ages of 20 to 55 years, then decreases. It does not depend on the sex of the observer, nor the face studied. In addition, 1% of people endowed with normal intelligence do not recognize emotions. The categorical dimension is a variable for everyone. The range and intensity of ViFaEmRe is idiosyncratic and not universally uniform. The recognition of emotions is purely categorical for a single individual. It is dimensional for a population sample. Conclusions: Firstly, M.A.R.I.E. has made possible to bring out new concepts and new continuous measurements variables. The comparison between healthy and abnormal individuals makes it possible to take into consideration the significance of this line of study. From now on, these new functional parameters will allow us to identify and name “emotional” disorders or illnesses which can give additional dimension to behavioral disorders in all pathologies that affect the brain. Secondly, the ViFaEmRe is idiosyncratic, categorical, and a function of the identity of the observer and of the observed face. These findings stack up against Artificial Intelligence, which cannot have a globalist or regionalist algorithm that can be programmed into a robot, nor can AI compete with human abilities and judgment in this domain. *Here “Emotional disorders” refers to disorders of emotional expressions and recognition.展开更多
Transient Rayleigh wave detection is a high-precision nondestructive detection method.At present,it has been widely used in shallow exploration,but rarely used in tunnel lining quality detection.Through the tunnel lin...Transient Rayleigh wave detection is a high-precision nondestructive detection method.At present,it has been widely used in shallow exploration,but rarely used in tunnel lining quality detection.Through the tunnel lining physical model experiment,the layout defects of the double-layer reinforcement lining area were detected and the Rayleigh wave velocity profile and dispersion curve were analyzed after data process-ing,which finally verified the feasibility and accuracy of Rayleigh wave method in detecting the tunnel lining void area.The results show that the method is not affected by the reinforcement inside the lining,the shallow detection is less disturbed and the accuracy is higher,and the data will fluctuate slightly with the deepening of the detection depth.At the same time,this method responds quite accurately to the thickness of the concrete,allowing for the assessment of the tunnel lining’s lack of compactness.This method has high efficiency,good reliability,and simple data processing,and is suitable for nondestructive detection of internal defects of tun-nel lining structure.展开更多
The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when th...The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.展开更多
基金supported by the Scientific Research Fund of Hunan Provincial Education Department(21B0070)the Natural Science Foundation of Jiangsu Province(BK20231452)+1 种基金the Fundamental Research Funds for the Central Universities(30922010809)the National Natural Science Foundation of China(11801591,11971195,12071171,12171107,12201207,12371072)。
文摘For each real number x∈(0,1),let[a_(1)(x),a_(2)(x),…,a_n(x),…]denote its continued fraction expansion.We study the convergence exponent defined byτ(x)=inf{s≥0:∞∑n=1(a_(n)(x)a_(n+1)(x))^(-s)<∞},which reflects the growth rate of the product of two consecutive partial quotients.As a main result,the Hausdorff dimensions of the level sets ofτ(x)are determined.
文摘Context: The advent of Artificial Intelligence (AI) requires modeling prior to its implementation in algorithms for most human skills. This observation requires us to have a detailed and precise understanding of the interfaces of verbal and emotional communications. The progress of AI is significant on the verbal level but modest in terms of the recognition of facial emotions even if this functionality is one of the oldest in humans and is omnipresent in our daily lives. Dysfunction in the ability for facial emotional expressions is present in many brain pathologies encountered by psychiatrists, neurologists, psychotherapists, mental health professionals including social workers. It cannot be objectively verified and measured due to a lack of reliable tools that are valid and consistently sensitive. Indeed, the articles in the scientific literature dealing with Visual-Facial-Emotions-Recognition (ViFaEmRe), suffer from the absence of 1) consensual and rational tools for continuous quantified measurement, 2) operational concepts. We have invented a software that can use computer-morphing attempting to respond to these two obstacles. It is identified as the Method of Analysis and Research of the Integration of Emotions (M.A.R.I.E.). Our primary goal is to use M.A.R.I.E. to understand the physiology of ViFaEmRe in normal healthy subjects by standardizing the measurements. Then, it will allow us to focus on subjects manifesting abnormalities in this ability. Our second goal is to make our contribution to the progress of AI hoping to add the dimension of recognition of facial emotional expressions. Objective: To study: 1) categorical vs dimensional aspects of recognition of ViFaEmRe, 2) universality vs idiosyncrasy, 3) immediate vs ambivalent Emotional-Decision-Making, 4) the Emotional-Fingerprint of a face and 5) creation of population references data. Methods: M.A.R.I.E. enables the rational, quantified measurement of Emotional Visual Acuity (EVA) in an individual observer and a population aged 20 to 70 years. Meanwhile, it can measure the range and intensity of expressed emotions through three Face- Tests, quantify the performance of a sample of 204 observers with hypernormal measures of cognition, “thymia” (defined elsewhere), and low levels of anxiety, and perform analysis of the six primary emotions. Results: We have individualized the following continuous parameters: 1) “Emotional-Visual- Acuity”, 2) “Visual-Emotional-Feeling”, 3) “Emotional-Quotient”, 4) “Emotional-Decision-Making”, 5) “Emotional-Decision-Making Graph” or “Individual-Gun-Trigger”, 6) “Emotional-Fingerprint” or “Key-graph”, 7) “Emotional-Fingerprint-Graph”, 8) detecting “misunderstanding” and 9) detecting “error”. This allowed us a taxonomy with coding of the face-emotion pair. Each face has specific measurements and graphics. The EVA improves from ages of 20 to 55 years, then decreases. It does not depend on the sex of the observer, nor the face studied. In addition, 1% of people endowed with normal intelligence do not recognize emotions. The categorical dimension is a variable for everyone. The range and intensity of ViFaEmRe is idiosyncratic and not universally uniform. The recognition of emotions is purely categorical for a single individual. It is dimensional for a population sample. Conclusions: Firstly, M.A.R.I.E. has made possible to bring out new concepts and new continuous measurements variables. The comparison between healthy and abnormal individuals makes it possible to take into consideration the significance of this line of study. From now on, these new functional parameters will allow us to identify and name “emotional” disorders or illnesses which can give additional dimension to behavioral disorders in all pathologies that affect the brain. Secondly, the ViFaEmRe is idiosyncratic, categorical, and a function of the identity of the observer and of the observed face. These findings stack up against Artificial Intelligence, which cannot have a globalist or regionalist algorithm that can be programmed into a robot, nor can AI compete with human abilities and judgment in this domain. *Here “Emotional disorders” refers to disorders of emotional expressions and recognition.
基金Supported by Project of Natural Science Foundation of Jilin Province(No.20220101172JC).
文摘Transient Rayleigh wave detection is a high-precision nondestructive detection method.At present,it has been widely used in shallow exploration,but rarely used in tunnel lining quality detection.Through the tunnel lining physical model experiment,the layout defects of the double-layer reinforcement lining area were detected and the Rayleigh wave velocity profile and dispersion curve were analyzed after data process-ing,which finally verified the feasibility and accuracy of Rayleigh wave method in detecting the tunnel lining void area.The results show that the method is not affected by the reinforcement inside the lining,the shallow detection is less disturbed and the accuracy is higher,and the data will fluctuate slightly with the deepening of the detection depth.At the same time,this method responds quite accurately to the thickness of the concrete,allowing for the assessment of the tunnel lining’s lack of compactness.This method has high efficiency,good reliability,and simple data processing,and is suitable for nondestructive detection of internal defects of tun-nel lining structure.
基金Project supported by the National Natural Science Foundation of China(No.12102131)the Natural Science Foundation of Henan Province of China(No.242300420248)the International Science and Technology Cooperation Project of Henan Province of China(No.242102521010)。
文摘The Laguerre polynomial method has been successfully used to investigate the dynamic responses of a half-space.However,it fails to obtain the correct stress at the interfaces in a layered half-space,especially when there are significant differences in material properties.Therefore,a coupled Legendre-Laguerre polynomial method with analytical integration is proposed.The Rayleigh waves in a one-dimensional(1D)hexagonal quasicrystal(QC)layered half-space with an imperfect interface are investigated.The correctness is validated by comparison with available results.Its computation efficiency is analyzed.The dispersion curves of the phase velocity,displacement distributions,and stress distributions are illustrated.The effects of the phonon-phason coupling and imperfect interface coefficients on the wave characteristics are investigated.Some novel findings reveal that the proposed method is highly efficient for addressing the Rayleigh waves in a QC layered half-space.It can save over 99%of the computation time.This method can be expanded to investigate waves in various layered half-spaces,including earth-layered media and surface acoustic wave(SAW)devices.
