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This paper presents an adaptive enhancement model with selective smoothing for restoration of degraded document images with blur, noise and bleed-through, which involves adaptive shock filtering and selective diffusion processes. A novel hybrid scheme is developed to solve the proposed model numerically, which combines explicit finite difference and exponential smoothing. Numerical experiments show that the proposed model is very effective for restoration of degraded document images with blur, noise and bleed-through, and has averagely the best performance on the DIBCO (Document Image Binarization Competition) series datasets, compared to five PDE (partial differential equation)-based models for restoration of degraded document images. 相似文献
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《Discrete Mathematics》2022,345(3):112739
A ballot permutation is a permutation π such that in any prefix of π the descent number is not more than the ascent number. By using a reversal-concatenation map, we (i) give a formula for the joint distribution (pk, des) of the peak and descent statistics over ballot permutations, (ii) connect this distribution and the joint distribution (pk, des) over ordinary permutations in terms of generating functions, and (iii) confirm Spiro's conjecture which finds the equidistribution of the descent statistic for ballot permutations and an analogue of the descent statistic for odd order permutations. 相似文献
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《Journal of Pure and Applied Algebra》2022,226(11):107116
It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2. 相似文献
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《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3735-3744
This paper deals with a synchronization scheme for two fractional chaotic systems which is applied in image encryption. Based on Pecora and Carroll (PC) synchronization, fractional-order Lorenz-like system forms a master–slave configuration, and the sufficient conditions are derived to realize synchronization between these two systems via the Laplace transformation theory. An image encryption algorithm is introduced where the original image is encoded by a nonlinear function of a fractional chaotic state. Simulation results show that the original image is well masked in the cipher texts and recovered successfully through chaotic signals. Further, the cryptanalysis is conducted in detail through histogram, information entropy, key space and sensitivity to verify the high security. 相似文献
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Huixia Li ;Hongyong Zhao 《Discrete and continuous dynamical systems》2025,30(5):1617-1657
Alzheimer's disease (AD) is a fatal neurodegenerative disease characterized by the aggregation of $ beta $-amyloid ($ Abeta $). To explore the pathogenesis of AD, we propose a reaction-diffusion model that considers the dual regulatory effects and the chemotaxis of microglia on $ Abeta $, and conduct bifurcation research on it. When bifurcation occurs, the types of bifurcation and how to determine bifurcation parameters are worth discussing. However, the selection of bifurcation parameters remains a challenge. Of particular note, this problem can be effectively tackled by utilizing elasticity analysis. Subsequently, the rich bifurcation structure generated by non-spatial system is adequately uncovered, including saddle-node bifurcation, Hopf bifurcation, and Bogdanov-Takens bifurcation. This means that the evolution of $ Abeta $ is sensitive to parameters and initial values. For spatial system, some interesting phenomena can be obtained. Specifically, when the diffusion rate of $ Abeta $ is fast, the influence of chemotaxis can be negligible. In sharp contrast, for slow diffusion rate, our results indicate that the chemotaxis is a critical factor in determining the generation of Turing instability, spatially homogeneous and non-homogeneous Hopf bifurcation, as well as steady state bifurcation. Numerical simulations are conducted to validate the theoretical results and shed light on how these parameters influence the output of $ Abeta $. 相似文献