It is noted that there has been little research to compare volume-based and number-based soil particle size distributions （PSDs）. Our objectives were to characterize the scaling properties and the possible connectio...It is noted that there has been little research to compare volume-based and number-based soil particle size distributions （PSDs）. Our objectives were to characterize the scaling properties and the possible connections between volume-based and number-based PSDs by applying single and joint multifractal analysis. Twelve soil samples were taken from selected sites in Northwest China and their PSDs were analyzed using laser diffractometry. The results indicated that the volume-based PSDs of all 12 samples and the number-based PSDs of 4 samples had multifractal scalings for moment order -6 〈 q 〈： 6. Some empirical relationships were identified between the extreme probability values, maximum probability （Pmax）, minimum probability （Pmin）, and Pmax/Pmin, and the multifractal indices, the difference and the ratio of generalized dimensions at q = 0 and 1 （Do - D1 and D1/Do）, maximum and minimum singularity strength （αmax and OZmin） and their difference （αmax - αmin, spectrum width）, and asymmetric index （RD）. An increase in Pmax generally resulted in corresponding increases of Do - D1, αmax, αmax - αmin, and RD, which indicated that a large Pmax increased the multifractality of a distribution. Joint multifractal analysis showed that there was significant correlation between the scaling indices of volume-based and number-based PSDs. The multifractality indices indicated that for a given soil, the volume-based PSD was more homogeneous than the number-based PSD, and more likely to display monofractal rather than multifractal scaling.展开更多
AIM：To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS：Fifty volunteers were enrolled in ...AIM：To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS：Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS：The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα=α_（max）-α_（min））and the spectrum arms＇ heights difference（│Δf│）of the normal images were expressed as mean±standard deviation（SD）：for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα）and the spectrum arms＇ heights difference（│Δf│）of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION：The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.展开更多
The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to pro...The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to provide high frequency pulse to a magnetic impedance（MI）element.The induced voltage on the pickup coil wound on the amorphous wire was sampled and held with a detect circuit using analog switch.A stable magnetic sensor was constructed.A three-dimension micro magnetic field detector was designed with a central controller MSP430F449.High stability and sensitivity were obtained in the MI sensor with the detect circuit.Experiment results showed that the resolution of the detector was 1nT in the full scale of±2 Oe and the detector worked stably from the room temperature to about 80℃.A small ferromagnetic target was detected by the three-dimension detector in laboratory environment without magnetic shielding.The target moving direction was ascertained with the wave shape of axis parallel in that direction.展开更多
The urban morphological system,developed over multiple phases,exhibits complex cross-scale characteristics,with significant scale disc repancies among morphological elements at the same hierarchical level,which sugges...The urban morphological system,developed over multiple phases,exhibits complex cross-scale characteristics,with significant scale disc repancies among morphological elements at the same hierarchical level,which suggests that the cross-scale sliding model holds the potential to reveal additional characteristics of urban morphology.This paper introduces a multifractal method that integrates Spacematrix morphological classification for the analysis of detailed urban building data within defined boundaries.Using the Nanjing Old City in China as a case study,the results reveal a dense yet balanced urban form,showing annular differentiation characterized by fragmented fringe belts at the macro level and a uniform mixture of diverse land use types and building types at the micro level.The typical scale invariance and multifractality are not consistently observed across single-type analyses.The study identifies height uniformization and spaciousness differentiation in the scaling of urban morphology,attributing the multifractal mechanism to the interweaving and transformation of multiple types across scales.This enhanced multifractal approach improves spatial mapping capabilities,aiding in the elucidation of the formation mechanisms of urban morphology.展开更多
By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of mani...By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.展开更多
Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,w...Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.展开更多
基金Supported by the National Natural Science Foundation of China (No. 50709028)the Basic Foundation for Scientific Researchof Northwest Agriculture and Forestry Sci-Tech University,China (No. QN2009087)
文摘It is noted that there has been little research to compare volume-based and number-based soil particle size distributions （PSDs）. Our objectives were to characterize the scaling properties and the possible connections between volume-based and number-based PSDs by applying single and joint multifractal analysis. Twelve soil samples were taken from selected sites in Northwest China and their PSDs were analyzed using laser diffractometry. The results indicated that the volume-based PSDs of all 12 samples and the number-based PSDs of 4 samples had multifractal scalings for moment order -6 〈 q 〈： 6. Some empirical relationships were identified between the extreme probability values, maximum probability （Pmax）, minimum probability （Pmin）, and Pmax/Pmin, and the multifractal indices, the difference and the ratio of generalized dimensions at q = 0 and 1 （Do - D1 and D1/Do）, maximum and minimum singularity strength （αmax and OZmin） and their difference （αmax - αmin, spectrum width）, and asymmetric index （RD）. An increase in Pmax generally resulted in corresponding increases of Do - D1, αmax, αmax - αmin, and RD, which indicated that a large Pmax increased the multifractality of a distribution. Joint multifractal analysis showed that there was significant correlation between the scaling indices of volume-based and number-based PSDs. The multifractality indices indicated that for a given soil, the volume-based PSD was more homogeneous than the number-based PSD, and more likely to display monofractal rather than multifractal scaling.
基金the Program"Partnerships in priority domains"with the support of the National Education Ministry,the Executive Agency for Higher Education,Research,Development and Innovation Funding (UEFISCDI),Romania (Project code:PN-II-PT-PCCA-2013-4-1232)
文摘AIM：To apply the multifractal analysis method as a quantitative approach to a comprehensive description of the microvascular network architecture of the normal human retina.METHODS：Fifty volunteers were enrolled in this study in the Ophthalmological Clinic of Cluj-Napoca,Romania,between January 2012 and January 2014. A set of 100 segmented and skeletonised human retinal images,corresponding to normal states of the retina were studied. An automatic unsupervised method for retinal vessel segmentation was applied before multifractal analysis. The multifractal analysis of digital retinal images was made with computer algorithms,applying the standard boxcounting method. Statistical analyses were performed using the Graph Pad In Stat software.RESULTS：The architecture of normal human retinal microvascular network was able to be described using the multifractal geometry. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα=α_（max）-α_（min））and the spectrum arms＇ heights difference（│Δf│）of the normal images were expressed as mean±standard deviation（SD）：for segmented versions,D_0=1.7014±0.0057; D_1=1.6507±0.0058; D_2=1.5772±0.0059; Δα=0.92441±0.0085; │Δf│= 0.1453±0.0051; for skeletonised versions,D_0=1.6303±0.0051; D_1=1.6012±0.0059; D_2=1.5531± 0.0058; Δα=0.65032±0.0162; │Δf│= 0.0238±0.0161. The average of generalized dimensions（D_q）for q=0,1,2,the width of the multifractal spectrum（Δα）and the spectrum arms＇ heights difference（│Δf│）of the segmented versions was slightly greater than the skeletonised versions.CONCLUSION：The multifractal analysis of fundus photographs may be used as a quantitative parameter for the evaluation of the complex three-dimensional structure of the retinal microvasculature as a potential marker for early detection of topological changes associated with retinal diseases.
基金Supported by the National Natural Science Foundation of China(60874100)
文摘The giant magneto-impedance（GMI）effect of amorphous wire was analyzed theoretically.The amorphous wire had strong GMI effect in the stimulation of sharp pulse of 680kHz and18 mV.A pulse generator was designed to provide high frequency pulse to a magnetic impedance（MI）element.The induced voltage on the pickup coil wound on the amorphous wire was sampled and held with a detect circuit using analog switch.A stable magnetic sensor was constructed.A three-dimension micro magnetic field detector was designed with a central controller MSP430F449.High stability and sensitivity were obtained in the MI sensor with the detect circuit.Experiment results showed that the resolution of the detector was 1nT in the full scale of±2 Oe and the detector worked stably from the room temperature to about 80℃.A small ferromagnetic target was detected by the three-dimension detector in laboratory environment without magnetic shielding.The target moving direction was ascertained with the wave shape of axis parallel in that direction.
基金supported by Jiangsu Provincial Department of Science and Technology(Grant No.BE2023799)the National Natural Science Foundation of China(Grant No.52308051)。
文摘The urban morphological system,developed over multiple phases,exhibits complex cross-scale characteristics,with significant scale disc repancies among morphological elements at the same hierarchical level,which suggests that the cross-scale sliding model holds the potential to reveal additional characteristics of urban morphology.This paper introduces a multifractal method that integrates Spacematrix morphological classification for the analysis of detailed urban building data within defined boundaries.Using the Nanjing Old City in China as a case study,the results reveal a dense yet balanced urban form,showing annular differentiation characterized by fragmented fringe belts at the macro level and a uniform mixture of diverse land use types and building types at the micro level.The typical scale invariance and multifractality are not consistently observed across single-type analyses.The study identifies height uniformization and spaciousness differentiation in the scaling of urban morphology,attributing the multifractal mechanism to the interweaving and transformation of multiple types across scales.This enhanced multifractal approach improves spatial mapping capabilities,aiding in the elucidation of the formation mechanisms of urban morphology.
基金Supported by NSFC(Grant Nos.11271062,NCET–13–0721)
文摘By studying modular invariance properties of some characteristic forms, we get some generalized anomaly cancellation formulas on(4 r-1)-dimensional manifolds with no assumption that the 3 rd de-Rham cohomology of manifolds vanishes. These anomaly cancellation formulas generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds. We also generalize our previous anomaly cancellation formulas on(4 r-1)-dimensional manifolds and the Han–Yu rigidity theorem to the(a, b) case.
基金Supported by the Ph. D. Program Foundation of Ministry of Education of China (Grant No.200803570003)
文摘Let R and S be a left coherent ring and a right coherent ring respectively,RωS be a faithfully balanced self-orthogonal bimodule.We give a sufficient condition to show that l.FP-idR（ω） ∞ implies G-dimω（M） ∞,where M ∈ modR.This result generalizes the result by Huang and Tang about the relationship between the FP-injective dimension and the generalized Gorenstein dimension in 2001.In addition,we get that the left orthogonal dimension is equal to the generalized Gorenstein dimension when G-dimω（M） is finite.
