The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel functio...The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel function is of the form Ke(ξ,t)=exp(−iξt). Joseph Fourier, the famous French Mathematician and Engineer, was the pioneer and he studied the properties in his seminal works. This important tool created an avenue of research later and it is very important in tackling problems in strong differential form and studying spectral properties of various ordinary and partial differential operators. In our article, we will obtain explicit bounds for the modified Fourier transform and derive some corollaries using in the Kernel function a multiple of the Euler-Mascheroni constant γ. The bounds obtained involve the Riemann zeta function for positive integers at the right-hand side.展开更多
The reverse transformation temperature and recovery strain ratio of the martensite formed during the cooling process under a constant stress in TiNi shape memory alloy wires are studied in this paper. Results sh...The reverse transformation temperature and recovery strain ratio of the martensite formed during the cooling process under a constant stress in TiNi shape memory alloy wires are studied in this paper. Results show that a higher level of the applied constant stress during the cooling process will induce martensite with a higher reverse martensitic transformation start temperature As and a smaller recovery strain ratio. Similarly, a prestrain at the room temperature elevates the As temperature and decreases the recovery strain ratio. However, the As temperature and the recovery strain ratio of the martensite formed during the cooling process under a constant stress are lower than those of the martensite formed by prestrain at the room temperature.展开更多
The conformal transformation solution is presented for the attenuation constant ofTEM transmission lines which can be mapped into the coaxial or the parallel plate lines by certainconformal transformations including t...The conformal transformation solution is presented for the attenuation constant ofTEM transmission lines which can be mapped into the coaxial or the parallel plate lines by certainconformal transformations including the numerical ones.The analytic and numerical results ofsome examples are also given.展开更多
Epilepsy is one of the most prevalent neurological disorders affecting 70 million people worldwide.The present work is focused on designing an efficient algorithm for automatic seizure detection by using electroenceph...Epilepsy is one of the most prevalent neurological disorders affecting 70 million people worldwide.The present work is focused on designing an efficient algorithm for automatic seizure detection by using electroencephalogram(EEG) as a noninvasive procedure to record neuronal activities in the brain.EEG signals' underlying dynamics are extracted to differentiate healthy and seizure EEG signals.Shannon entropy,collision entropy,transfer entropy,conditional probability,and Hjorth parameter features are extracted from subbands of tunable Q wavelet transform.Efficient decomposition level for different feature vector is selected using the Kruskal-Wallis test to achieve good classification.Different features are combined using the discriminant correlation analysis fusion technique to form a single fused feature vector.The accuracy of the proposed approach is higher for Q=2 and J=10.Transfer entropy is observed to be significant for different class combinations.Proposed approach achieved 100% accuracy in classifying healthy-seizure EEG signal using simple and robust features and hidden Markov model with less computation time.The proposed approach efficiency is evaluated in classifying seizure and non-seizure surface EEG signals.The system has achieved 96.87% accuracy in classifying surface seizure and nonseizure EEG segments using efficient features extracted from different J level.展开更多
In this paper,we introduce and study a(p,q)-Mellin transform and its corresponding convolution and inversion.In terms of applications of the(p,q)-Mellin transform,we solve some integral equations.Moreover,a(p,q)-analo...In this paper,we introduce and study a(p,q)-Mellin transform and its corresponding convolution and inversion.In terms of applications of the(p,q)-Mellin transform,we solve some integral equations.Moreover,a(p,q)-analogue of the Titchmarsh theorem is also derived.展开更多
The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved dele...The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.展开更多
The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency(i.e.,the Q value is independent of the frequency).For seismic waves propagating in viscoelastic media,the ...The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency(i.e.,the Q value is independent of the frequency).For seismic waves propagating in viscoelastic media,the wave equation is determined by the viscoelastic media model.Equivalence relations exist between various frequency domain mathematical models and physical rheological models for the constant Q property.Considering two elastic moduli and three attenuation variables,24 kinds of wave equations based on diff erent generalized rheological models are divided into six classes in this study,and the 12 kinds of specifi c representation for the wave equations in the time domain are derived.On the basis of the equivalence relations between the generalized rheological models,the diff erence and equivalence relation between diff erent wave equations are proven and clarifi ed.Results show that the high-order generalized rheological model can accurately characterize the attenuation characteristics of seismic waves and has advantages in characterizing the dispersion characteristics in viscoelastic media.Lastly,the seismic refl ection characteristics caused by the diff erence of Q value are verifi ed by the forward modeling of the constant Q wave equation in this study,thereby providing a theoretical basis for the analysis and inversion of the formation Q value from refl ection seismic data.展开更多
The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-co...The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.展开更多
文摘The exponential transform or modified Fourier transform is an integral transform where the Kernel function is Ka(ξ,t)=a−iξt, and a∈] 1,+∞ [. This is a general case of the Fourier transform where the Kernel function is of the form Ke(ξ,t)=exp(−iξt). Joseph Fourier, the famous French Mathematician and Engineer, was the pioneer and he studied the properties in his seminal works. This important tool created an avenue of research later and it is very important in tackling problems in strong differential form and studying spectral properties of various ordinary and partial differential operators. In our article, we will obtain explicit bounds for the modified Fourier transform and derive some corollaries using in the Kernel function a multiple of the Euler-Mascheroni constant γ. The bounds obtained involve the Riemann zeta function for positive integers at the right-hand side.
基金supported by the National Natural Science Foundation of the People’s Republic of China under grant No.50071037.
文摘The reverse transformation temperature and recovery strain ratio of the martensite formed during the cooling process under a constant stress in TiNi shape memory alloy wires are studied in this paper. Results show that a higher level of the applied constant stress during the cooling process will induce martensite with a higher reverse martensitic transformation start temperature As and a smaller recovery strain ratio. Similarly, a prestrain at the room temperature elevates the As temperature and decreases the recovery strain ratio. However, the As temperature and the recovery strain ratio of the martensite formed during the cooling process under a constant stress are lower than those of the martensite formed by prestrain at the room temperature.
文摘The conformal transformation solution is presented for the attenuation constant ofTEM transmission lines which can be mapped into the coaxial or the parallel plate lines by certainconformal transformations including the numerical ones.The analytic and numerical results ofsome examples are also given.
文摘Epilepsy is one of the most prevalent neurological disorders affecting 70 million people worldwide.The present work is focused on designing an efficient algorithm for automatic seizure detection by using electroencephalogram(EEG) as a noninvasive procedure to record neuronal activities in the brain.EEG signals' underlying dynamics are extracted to differentiate healthy and seizure EEG signals.Shannon entropy,collision entropy,transfer entropy,conditional probability,and Hjorth parameter features are extracted from subbands of tunable Q wavelet transform.Efficient decomposition level for different feature vector is selected using the Kruskal-Wallis test to achieve good classification.Different features are combined using the discriminant correlation analysis fusion technique to form a single fused feature vector.The accuracy of the proposed approach is higher for Q=2 and J=10.Transfer entropy is observed to be significant for different class combinations.Proposed approach achieved 100% accuracy in classifying healthy-seizure EEG signal using simple and robust features and hidden Markov model with less computation time.The proposed approach efficiency is evaluated in classifying seizure and non-seizure surface EEG signals.The system has achieved 96.87% accuracy in classifying surface seizure and nonseizure EEG segments using efficient features extracted from different J level.
文摘In this paper,we introduce and study a(p,q)-Mellin transform and its corresponding convolution and inversion.In terms of applications of the(p,q)-Mellin transform,we solve some integral equations.Moreover,a(p,q)-analogue of the Titchmarsh theorem is also derived.
文摘The use of [1] Box-Cox power transformation in regression analysis is now common;in the last two decades there has been emphasis on diagnostics methods for Box-Cox power transformation, much of which has involved deletion of influential data cases. The pioneer work of [2] studied local influence on constant variance perturbation in the Box-Cox unbiased regression linear mode. Tsai and Wu [3] analyzed local influence method of [2] to assess the effect of the case-weights perturbation on the transformation-power estimator in the Box-Cox unbiased regression linear model. Many authors noted that the influential observations on the biased estimators are different from the unbiased estimators. In this paper I describe a diagnostic method for assessing the local influence on the constant variance perturbation on the transformation in the Box-Cox biased ridge regression linear model. Two real macroeconomic data sets are used to illustrate the methodologies.
基金This work was supported by National Natural Science Foundation of China(No.41774137)111 project(No.B18055),and the Fundamental Research Funds for the Central Universities(No.19CX02002A).
文摘The constant Q property in viscoelastic media assumes that the quality factor Q does not change with frequency(i.e.,the Q value is independent of the frequency).For seismic waves propagating in viscoelastic media,the wave equation is determined by the viscoelastic media model.Equivalence relations exist between various frequency domain mathematical models and physical rheological models for the constant Q property.Considering two elastic moduli and three attenuation variables,24 kinds of wave equations based on diff erent generalized rheological models are divided into six classes in this study,and the 12 kinds of specifi c representation for the wave equations in the time domain are derived.On the basis of the equivalence relations between the generalized rheological models,the diff erence and equivalence relation between diff erent wave equations are proven and clarifi ed.Results show that the high-order generalized rheological model can accurately characterize the attenuation characteristics of seismic waves and has advantages in characterizing the dispersion characteristics in viscoelastic media.Lastly,the seismic refl ection characteristics caused by the diff erence of Q value are verifi ed by the forward modeling of the constant Q wave equation in this study,thereby providing a theoretical basis for the analysis and inversion of the formation Q value from refl ection seismic data.
文摘The aim of the present paper is to introduce and study a new type of q-Mellin transform [11], that will be called q-finite Mellin transform. In particular, we prove for this new transform an inversion formula and q-convolution product. The application of this transform is also earlier proposed in solving procedure for a new equation with a new fractional differential operator of a variational type.
