In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existenc...In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.展开更多
vegetation continuous The scale-location specific control on distribution was investigated through wavelet transforms approaches in subtropical mountain-hill region, Fujian, China. The Normalized Difference Vegetatio...vegetation continuous The scale-location specific control on distribution was investigated through wavelet transforms approaches in subtropical mountain-hill region, Fujian, China. The Normalized Difference Vegetation Index （NDVI） was calculated as an indicator of vegetation greenness using Chinese Environmental Disaster Reduction Satellite images along latitudinal and longitudinal transects. Four scales of variations were identified from the local wavelet spectrum of NDVI, with much stronger wavelet variances observed at larger scales. The characteristic scale of vegetation distribution within mountainous and hilly regions in Southeast China was around 20 km. Significantly strong wavelet coherency was generally examined in regions with very diverse topography, typically characterized as small mountains and hills fractured by rivers and residents. The continuous wavelet based approaches provided valuable insight on the hierarchical structure and its corresponding characteristic scales of ecosystems, which might be applied in defining proper levels in multilevel models and optimal bandwidths in Geographically Weighted Regression.展开更多
Objective To establish early detection and diagnosis for bladder cancer.Methods In the current study,a metabolomics strategy was used to profile bladder cancer urine metabolites in mice and to further characterize the...Objective To establish early detection and diagnosis for bladder cancer.Methods In the current study,a metabolomics strategy was used to profile bladder cancer urine metabolites in mice and to further characterize the disease status at different stages.In addition,some chemometrics algorithms were adopted to analyze the metabolites fingerprints,including baseline removal and retention time shift,to overcome variations in the experimental process.After processing,metabolites were qualitatively and quantitatively analyzed in each sample at different stages.Finally,a random forest algorithm was used to discriminate the differences among different groups.Results Four potential biomarkers,including glyceric acid,(R*,R*)-2,3-Dihydroxybutanoic acid,N-(1-oxohexyl)-glycine and D-Turanose,were discovered by exploring the characteristics of different groups.Conclusion These results suggest that combining chemometrics with the metabolites profile is an effective approach to aid in clinical diagnosis.展开更多
Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We first...Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.展开更多
文摘In this paper, we consider the Cauchy problem of degenerate parabolic equation not in divergence form u, = uPAu ＋ uq, p 〉 1, q 〉 1, and give the blow-up conditions and the critical Fujita exponents for the existence of global and non-global solutions to the Cauchy problem.
基金supported by the National Natural Science Foundation of China(NSFC)(Grant No.41071267)Scientific Research Foundation for Returned Scholars,Ministry of Education of China(Grant No.[2012]940)the Science & Technology Department of Fujian Province,China(Grant Nos.2012I0005,2012J01167)
文摘vegetation continuous The scale-location specific control on distribution was investigated through wavelet transforms approaches in subtropical mountain-hill region, Fujian, China. The Normalized Difference Vegetation Index （NDVI） was calculated as an indicator of vegetation greenness using Chinese Environmental Disaster Reduction Satellite images along latitudinal and longitudinal transects. Four scales of variations were identified from the local wavelet spectrum of NDVI, with much stronger wavelet variances observed at larger scales. The characteristic scale of vegetation distribution within mountainous and hilly regions in Southeast China was around 20 km. Significantly strong wavelet coherency was generally examined in regions with very diverse topography, typically characterized as small mountains and hills fractured by rivers and residents. The continuous wavelet based approaches provided valuable insight on the hierarchical structure and its corresponding characteristic scales of ecosystems, which might be applied in defining proper levels in multilevel models and optimal bandwidths in Geographically Weighted Regression.
基金funding support from the Natural Science Foundation of China (No. 81673585 and No. 81603400)Hunan Provincial Key Laboratory of Diagnostics in Chinese Medicine Open Fund (No. 2015ZYZD13 and No. 2015ZYZD10)+2 种基金Key research and development project of Hunan Province Science and Technology (No. 2016SK2048)Innovative Project for Post-graduate of Hunan University of Chinese Medicine (No. 2017CX05)the National Standard Project of Chinese Medicine (No. ZYBZH-Y-HUN-21)
文摘Objective To establish early detection and diagnosis for bladder cancer.Methods In the current study,a metabolomics strategy was used to profile bladder cancer urine metabolites in mice and to further characterize the disease status at different stages.In addition,some chemometrics algorithms were adopted to analyze the metabolites fingerprints,including baseline removal and retention time shift,to overcome variations in the experimental process.After processing,metabolites were qualitatively and quantitatively analyzed in each sample at different stages.Finally,a random forest algorithm was used to discriminate the differences among different groups.Results Four potential biomarkers,including glyceric acid,(R*,R*)-2,3-Dihydroxybutanoic acid,N-(1-oxohexyl)-glycine and D-Turanose,were discovered by exploring the characteristics of different groups.Conclusion These results suggest that combining chemometrics with the metabolites profile is an effective approach to aid in clinical diagnosis.
基金supported by National Natural Science Foundation of China(Grant Nos.11421110002,11531005 and 11501102)National Science Foundation of Jiangsu Province(Grant No.BK20150594)
文摘Consider the reconstruction of the complex refraction index of an object, which is immersed in a known homogeneous background, from the knowledge of scattered waves of the point sources outside of the object. We firstly establish the uniqueness for this inverse problem, which provides the theoretical basis for the reconstruction scheme. Then based on the contrast source inversion(CSI) method, we propose an algorithm determining the refraction index and the artificial wave sources alternately by a dynamic iterative scheme. The algorithm defines the iterates by solving a series of minimization problems with uniformly convex penalty terms, which are allowed to be non-smooth to include L1 and total variation like functionals, ensuring the reconstruction quality when the unknown refraction index has the special features such as sparsity and discontinuity. By choosing the regularizing parameter automatically, the algorithm is terminated in terms of discrepancy principle. The convergence property of the iterative sequence is rigorously proven. Numerical implementations demonstrate the validity of the proposed algorithm.
