Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed ...Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed in the complexity of the character strokes, style variations and general layouts. Determining how Chinese calligraphy aesthetic patterns emerged from the general layout of artworks is a challenging objective for researchers. Here we investigate the statistical fluctuation structure of Chinese calligraphy characters sizes using characters obtained from the calligraphy artwork "Preface to the Poems Collected from the Orchid Pavilion" which was praised as the best running script under heaven. We found that the character size distribution is a stretched exponential distribution. Moreover, the variations in the local correlation features in character size fluctuations can accurately reflect expressions of the calligrapher's complex feelings. The fractal dimensions of character size fluctuations are close to the Fibonacci sequence. The Fibonacci number is first discovered in the Chinese calligraphy artworks, which inspires the aesthetics of Chinese calligraphy artworks and maybe also provides an approach to creating Chinese calligraphy artworks in multiple genres.展开更多
With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent dec...With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent decades.The intrinsic mathematical reasons for the studies on inverse problems come from the fact that most of the inverse problems are ill-posed,i.e.,the existence,uniqueness and stability of the solution cannot be ensured due to the configurations of the problems themselves.The characteristic of the ill-posedness for inverse problems makes it hard to construct the(generalized)solutions,especially to keep the solutions stable with respect to the noisy input data.To overcome these difficulties,some regularizing techniques should be introduced,which are closely related to many mathematical branches such as partial differential equations(PDEs),functional analysis,optimizations and numerical analysis.展开更多
基金funded by the National Natural Science Foundation of China (No. 41465010, 41977245)。
文摘Chinese calligraphy is a thousand-year-old writing art. The question of how Chinese calligraphy artworks convey emotion has cast its spell over people for millennia. Calligraphers' joys and sorrows were expressed in the complexity of the character strokes, style variations and general layouts. Determining how Chinese calligraphy aesthetic patterns emerged from the general layout of artworks is a challenging objective for researchers. Here we investigate the statistical fluctuation structure of Chinese calligraphy characters sizes using characters obtained from the calligraphy artwork "Preface to the Poems Collected from the Orchid Pavilion" which was praised as the best running script under heaven. We found that the character size distribution is a stretched exponential distribution. Moreover, the variations in the local correlation features in character size fluctuations can accurately reflect expressions of the calligrapher's complex feelings. The fractal dimensions of character size fluctuations are close to the Fibonacci sequence. The Fibonacci number is first discovered in the Chinese calligraphy artworks, which inspires the aesthetics of Chinese calligraphy artworks and maybe also provides an approach to creating Chinese calligraphy artworks in multiple genres.
文摘With the promotion by both mathematics itself and the practical requirements from modern society,the interest of studies on inverse problems and ill-posed problems,at home and abroad,has been flourishing in recent decades.The intrinsic mathematical reasons for the studies on inverse problems come from the fact that most of the inverse problems are ill-posed,i.e.,the existence,uniqueness and stability of the solution cannot be ensured due to the configurations of the problems themselves.The characteristic of the ill-posedness for inverse problems makes it hard to construct the(generalized)solutions,especially to keep the solutions stable with respect to the noisy input data.To overcome these difficulties,some regularizing techniques should be introduced,which are closely related to many mathematical branches such as partial differential equations(PDEs),functional analysis,optimizations and numerical analysis.
