Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge t...Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.展开更多
A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power...A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.展开更多
This paper aims to formalize a general definition of intelligence beyond human intelligence. We accomplish this by re-imagining the concept of equality as a fundamental abstraction for relation. We discover that the c...This paper aims to formalize a general definition of intelligence beyond human intelligence. We accomplish this by re-imagining the concept of equality as a fundamental abstraction for relation. We discover that the concept of equality = limits the sensitivity of our mathematics to abstract relationships. We propose a new relation principle that does not rely on the concept of equality but is consistent with existing mathematical abstractions. In essence, this paper proposes a conceptual framework for general interaction and argues that this framework is also an abstraction that satisfies the definition of Intelligence. Hence, we define intelligence as a formalization of generality, represented by the abstraction ∆∞Ο, where each symbol represents the concepts infinitesimal, infinite, and finite respectively. In essence, this paper proposes a General Language Model (GLM), where the abstraction ∆∞Ο represents the foundational relationship of the model. This relation is colloquially termed “The theory of everything”.展开更多
The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactio...The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactions than the four fundamental interactions, and these basic interaction gauge fields are only the projection components to the base manifold, that is our universe, from a unified gauge potential or connection of the principal associated bundle manifold on the base manifold. These components can satisfy the transformation of gauge potential, and can even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, that is, the generalized gauge Equation (GGE), but the gauge potential or connection on the principal bundle is invariant, corresponding to the invariance of gauge transformation [1]. In this paper, we will continue to discuss this aspect concretely, and specifically construct a spatiotemporal model with the frame bundle as the principal bundle, and the tensor bundle as the associated bundle, so that the four fundamental interactions, especially the electromagnetic interaction and the gravitational interaction, can be reflected in the bottom manifold, that is, the regional distributions in our universe. Furthermore, this paper studies the existence of gauge transformation across basic interactions by establishing a model of gauge transformation of basic interaction field;it is found that the unified expression formula is GGE and the expression relation on the curvature of space-time. Therefore, the author discusses the feasibility of the generalized gauge transformation across the basic electromagnetic interaction and the basic gravitational interaction, and on this basis, specifically determines a method or way to find the generalized gauge transformation, so as to try to realize the last step of the “unification” of the four fundamental interactions in physics, that is, the “unification” of electromagnetism and gravity.展开更多
由于水下环境的多样性和光在水中受到的散射及选择性吸收作用,采集到的水下图像通常会产生严重的质量退化问题,如颜色偏差、清晰度低和亮度低等,为解决以上问题,本文提出了一种基于Transformer和生成对抗网络的水下图像增强算法。以生...由于水下环境的多样性和光在水中受到的散射及选择性吸收作用,采集到的水下图像通常会产生严重的质量退化问题,如颜色偏差、清晰度低和亮度低等,为解决以上问题,本文提出了一种基于Transformer和生成对抗网络的水下图像增强算法。以生成对抗网络为基础架构,结合编码解码结构、基于空间自注意力机制的全局特征建模Transformer模块和通道级多尺度特征融合Transformer模块构建了TGAN(generative adversarial network with transformer)网络增强模型,重点关注水下图像衰减更严重的颜色通道和空间区域,有效增强了图像细节并解决了颜色偏差问题。此外,设计了一种结合RGB和LAB颜色空间的多项损失函数,约束网络增强模型的对抗训练。实验结果表明,与CLAHE(contrast limited adaptive histogram equalization)、UDCP(underwater dark channel prior)、UWCNN(underwater based on convolutional neural network)、FUnIE-GAN(fast underwater image enhancement for improved visual perception)等典型水下图像增强算法相比,所提算法增强后的水下图像在清晰度、细节纹理和色彩表现等方面都有所提升,客观评价指标如峰值信噪比、结构相似性和水下图像质量度量的平均值分别提升了5.8%、1.8%和3.6%,有效地提升了水下图像的视觉感知效果。展开更多
We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic...We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic record is performed in the S domain to restore the amplitude spectrum of reflection. We use spectral simulation methods to fit the time-dependent amplitude spectrum and compensate for the amplitude attenuation owing to absorption. We use phase scanning to select the time-, space-, and frequencydependent phases correction based on the parsimony criterion and eliminate the residual phase effect of the wavelet in the S domain. The method does not directly calculate the Q value; thus, it can be applied to the case of variable Q. The comparison of the theory model and field data verify that the proposed method can recover the amplitude spectrum of the strata reflectivity, while eliminating the effect of the residual phase of the wavelet. Thus, the wavelet approaches the zero-phase wavelet and, the seismic resolution is improved.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12326305,11931017,and 12271490)the Excellent Youth Science Fund Project of Henan Province(Grant No.242300421158)+2 种基金the Natural Science Foundation of Henan Province(Grant No.232300420119)the Excellent Science and Technology Innovation Talent Support Program of ZUT(Grant No.K2023YXRC06)Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。
文摘Under investigation is an integrable generalization of the Fokas–Lenells equation, which can be derived from the negative power flow of a 2 × 2 matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas–Lenells system is constructed. As a reduction, the N-fold Darboux transformation for the generalized Fokas–Lenells equation is obtained, from which the N-soliton solution in a compact Vandermonde-like determinant form is given. Particularly,the explicit one-and two-soliton solutions are presented and their dynamical behaviors are shown graphically.
文摘A generalized form of the error function, Gp(x)=pΓ(1/p)∫0xe−tpdt, which is directly associated with the gamma function, is evaluated for arbitrary real values of p>1and 0x≤+∞by employing a fast-converging power series expansion developed in resolving the so-called Grandi’s paradox. Comparisons with accurate tabulated values for well-known cases such as the error function are presented using the expansions truncated at various orders.
文摘This paper aims to formalize a general definition of intelligence beyond human intelligence. We accomplish this by re-imagining the concept of equality as a fundamental abstraction for relation. We discover that the concept of equality = limits the sensitivity of our mathematics to abstract relationships. We propose a new relation principle that does not rely on the concept of equality but is consistent with existing mathematical abstractions. In essence, this paper proposes a conceptual framework for general interaction and argues that this framework is also an abstraction that satisfies the definition of Intelligence. Hence, we define intelligence as a formalization of generality, represented by the abstraction ∆∞Ο, where each symbol represents the concepts infinitesimal, infinite, and finite respectively. In essence, this paper proposes a General Language Model (GLM), where the abstraction ∆∞Ο represents the foundational relationship of the model. This relation is colloquially termed “The theory of everything”.
文摘The author of this paper has put forward a unified program of gauge field from the mathematical and physical picture of the principal associated bundles: thinking that our universe may have more fundamental interactions than the four fundamental interactions, and these basic interaction gauge fields are only the projection components to the base manifold, that is our universe, from a unified gauge potential or connection of the principal associated bundle manifold on the base manifold. These components can satisfy the transformation of gauge potential, and can even be transformed from one basic interaction gauge potential to another basic interaction gauge potential, and can be summarized into a unified equation, that is, the generalized gauge Equation (GGE), but the gauge potential or connection on the principal bundle is invariant, corresponding to the invariance of gauge transformation [1]. In this paper, we will continue to discuss this aspect concretely, and specifically construct a spatiotemporal model with the frame bundle as the principal bundle, and the tensor bundle as the associated bundle, so that the four fundamental interactions, especially the electromagnetic interaction and the gravitational interaction, can be reflected in the bottom manifold, that is, the regional distributions in our universe. Furthermore, this paper studies the existence of gauge transformation across basic interactions by establishing a model of gauge transformation of basic interaction field;it is found that the unified expression formula is GGE and the expression relation on the curvature of space-time. Therefore, the author discusses the feasibility of the generalized gauge transformation across the basic electromagnetic interaction and the basic gravitational interaction, and on this basis, specifically determines a method or way to find the generalized gauge transformation, so as to try to realize the last step of the “unification” of the four fundamental interactions in physics, that is, the “unification” of electromagnetism and gravity.
文摘由于水下环境的多样性和光在水中受到的散射及选择性吸收作用,采集到的水下图像通常会产生严重的质量退化问题,如颜色偏差、清晰度低和亮度低等,为解决以上问题,本文提出了一种基于Transformer和生成对抗网络的水下图像增强算法。以生成对抗网络为基础架构,结合编码解码结构、基于空间自注意力机制的全局特征建模Transformer模块和通道级多尺度特征融合Transformer模块构建了TGAN(generative adversarial network with transformer)网络增强模型,重点关注水下图像衰减更严重的颜色通道和空间区域,有效增强了图像细节并解决了颜色偏差问题。此外,设计了一种结合RGB和LAB颜色空间的多项损失函数,约束网络增强模型的对抗训练。实验结果表明,与CLAHE(contrast limited adaptive histogram equalization)、UDCP(underwater dark channel prior)、UWCNN(underwater based on convolutional neural network)、FUnIE-GAN(fast underwater image enhancement for improved visual perception)等典型水下图像增强算法相比,所提算法增强后的水下图像在清晰度、细节纹理和色彩表现等方面都有所提升,客观评价指标如峰值信噪比、结构相似性和水下图像质量度量的平均值分别提升了5.8%、1.8%和3.6%,有效地提升了水下图像的视觉感知效果。
基金supported by the National Natural Science Foundation of China(No.41204091)New Teachers’ Fund for Doctor Stations,the Ministry of Education(No.20105122120001)Science and Technology Support Program from Science and Technology Department of Sichuan Province(No.2011GZ0244)
文摘We propose a method for the compensation and phase correction of the amplitude spectrum based on the generalized S transform. The compensation of the amplitude spectrum within a reliable frequency range of the seismic record is performed in the S domain to restore the amplitude spectrum of reflection. We use spectral simulation methods to fit the time-dependent amplitude spectrum and compensate for the amplitude attenuation owing to absorption. We use phase scanning to select the time-, space-, and frequencydependent phases correction based on the parsimony criterion and eliminate the residual phase effect of the wavelet in the S domain. The method does not directly calculate the Q value; thus, it can be applied to the case of variable Q. The comparison of the theory model and field data verify that the proposed method can recover the amplitude spectrum of the strata reflectivity, while eliminating the effect of the residual phase of the wavelet. Thus, the wavelet approaches the zero-phase wavelet and, the seismic resolution is improved.
