We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-function...We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.展开更多
Young′s Modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young′s modulus and dynamic Young′s modulus when dynamic...Young′s Modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young′s modulus and dynamic Young′s modulus when dynamic Poisson ratio μ d varies nearby 0.20.P wave velocity and elastic modulus have the same varying tendency as letter N. μ,μ d decrease with the increase of loading rate and μ d has a great effect on the parameters E d and E D.展开更多
Nonlinear elasticity of the earth medium produces a numerical difference between the dynamic and the static modulus of rock. The dynamic modulus is calculated with the ultrasonic velocity measurement, the small-cycle ...Nonlinear elasticity of the earth medium produces a numerical difference between the dynamic and the static modulus of rock. The dynamic modulus is calculated with the ultrasonic velocity measurement, the small-cycle modulus is calculated with small cycles in the load-unload experiment,the static modulus is calculated from the slope of the stress-strain curve in the large cycle, the Young’s modulus is obtained from the ratio of stress to strain in the measured point. The relationship between the modulus and the strain amplitudes is studied by changing the strain amplitude in the small cycles. The moduli obtained from different measuring methods are thus compared. The result shows that the dynamic modulus is the largest, the small-cycle modulus takes the second place, the static modulus of bigger-cycle is the third, and finally the Young’s modulus is the smallest. Nonlinear modulus of rock is a function of the strain level and strain amplitude. The modulus decreases exponentially with the ascending of the strain amplitude, while increases with the ascending of the strain level. Finally, the basic concept of the P-M model is briefly introduced and the relationship between the modulus and strain amplitude is explained by the rock having different distribution densities and the different open-and-close stresses of the micro-cracks.展开更多
In order to find out changes in the main fertility indicators of continuous cropping tobacco fields in Henan Province with years of continuous cropping,5 typical tobacco fields( Jia County,Shaoling District,Fangcheng ...In order to find out changes in the main fertility indicators of continuous cropping tobacco fields in Henan Province with years of continuous cropping,5 typical tobacco fields( Jia County,Shaoling District,Fangcheng County,Xiangcheng County,and Song County) were studied. Indicators in question included activity of main enzymes( sucrase,urease,catalase,and acid phosphatase),p H value,organic matters,total nitrogen,available phosphorus and available potassium. The results indicate that in most tobacco fields,the activity of sucrase and urease increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping; in some fields,it directly declined with increase in years of continuous cropping; the activity of catalase increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping,and it became stable after three years of continuous cropping;generally,the activity of acid phosphatase declined with increase in the years of continuous cropping within 3 years continuous cropping,later,it became stable. Except Fangcheng County,the soil p H value of other districts( counties) generally declined with increase in years of continuous cropping,and it was in the range of 5. 6-6. 8. With the increase in continuous cropping,the soil organic matters( SOM) in tobacco fields of Jia County and Song County declined,changes of SOM in tobacco fields of Fangcheng County and Xiangcheng County were not obvious,and SOM showed the trend of first decline then rise in Shaoling District. In most tobacco fields( Jia County,Xiangcheng County,and Song County),the total nitrogen showed a declining trend; in Shaoling District,it showed a trend of first decline then rise; in Fangcheng County,it showed a rising trend. The available phosphorus firstly slightly declined then rose in tobacco fields of Shaoling District and Song County; it showed a trend of first rise then decline in Jia County; there were no obvious changes in Fangcheng County and Xiangcheng County. Changes in the available potassium were different in tobacco fields. In sum,there are certain rules for changes in soil enzyme activity and nutrient content in tobacco fields in Henan Province,but changes are not completely the same. It is concluded that the site conditions and farming activities exert a certain influence on soil enzyme activity,p H value,organic matters,and nitrogen,phosphorus and potassium content. Therefore,to solve obstacles in continuous cropping of tobacco fields,different regions should take different measures.展开更多
Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcificat...Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.展开更多
In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg...In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.展开更多
文摘We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.
文摘Young′s Modulus of concrete is studied on the basis of triaxial compressive experiments. The authors proposed two empirical equations to calculate its static Young′s modulus and dynamic Young′s modulus when dynamic Poisson ratio μ d varies nearby 0.20.P wave velocity and elastic modulus have the same varying tendency as letter N. μ,μ d decrease with the increase of loading rate and μ d has a great effect on the parameters E d and E D.
基金Supported by the National Natural Science Foundation of China(11871452,12071052the Natural Science Foundation of Henan(202300410338)the Nanhu Scholar Program for Young Scholars of XYNU。
基金The project was funded by the National Natural ScienceFoundation,China (Item No.40274057) .
文摘Nonlinear elasticity of the earth medium produces a numerical difference between the dynamic and the static modulus of rock. The dynamic modulus is calculated with the ultrasonic velocity measurement, the small-cycle modulus is calculated with small cycles in the load-unload experiment,the static modulus is calculated from the slope of the stress-strain curve in the large cycle, the Young’s modulus is obtained from the ratio of stress to strain in the measured point. The relationship between the modulus and the strain amplitudes is studied by changing the strain amplitude in the small cycles. The moduli obtained from different measuring methods are thus compared. The result shows that the dynamic modulus is the largest, the small-cycle modulus takes the second place, the static modulus of bigger-cycle is the third, and finally the Young’s modulus is the smallest. Nonlinear modulus of rock is a function of the strain level and strain amplitude. The modulus decreases exponentially with the ascending of the strain amplitude, while increases with the ascending of the strain level. Finally, the basic concept of the P-M model is briefly introduced and the relationship between the modulus and strain amplitude is explained by the rock having different distribution densities and the different open-and-close stresses of the micro-cracks.
基金Supported by Key Scientific and Technological Plan Project of Henan Tobacco Company(HYKJM201304)
文摘In order to find out changes in the main fertility indicators of continuous cropping tobacco fields in Henan Province with years of continuous cropping,5 typical tobacco fields( Jia County,Shaoling District,Fangcheng County,Xiangcheng County,and Song County) were studied. Indicators in question included activity of main enzymes( sucrase,urease,catalase,and acid phosphatase),p H value,organic matters,total nitrogen,available phosphorus and available potassium. The results indicate that in most tobacco fields,the activity of sucrase and urease increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping; in some fields,it directly declined with increase in years of continuous cropping; the activity of catalase increased in two years of continuous cropping,later,it showed a declining trend with increase in years of continuous cropping,and it became stable after three years of continuous cropping;generally,the activity of acid phosphatase declined with increase in the years of continuous cropping within 3 years continuous cropping,later,it became stable. Except Fangcheng County,the soil p H value of other districts( counties) generally declined with increase in years of continuous cropping,and it was in the range of 5. 6-6. 8. With the increase in continuous cropping,the soil organic matters( SOM) in tobacco fields of Jia County and Song County declined,changes of SOM in tobacco fields of Fangcheng County and Xiangcheng County were not obvious,and SOM showed the trend of first decline then rise in Shaoling District. In most tobacco fields( Jia County,Xiangcheng County,and Song County),the total nitrogen showed a declining trend; in Shaoling District,it showed a trend of first decline then rise; in Fangcheng County,it showed a rising trend. The available phosphorus firstly slightly declined then rose in tobacco fields of Shaoling District and Song County; it showed a trend of first rise then decline in Jia County; there were no obvious changes in Fangcheng County and Xiangcheng County. Changes in the available potassium were different in tobacco fields. In sum,there are certain rules for changes in soil enzyme activity and nutrient content in tobacco fields in Henan Province,but changes are not completely the same. It is concluded that the site conditions and farming activities exert a certain influence on soil enzyme activity,p H value,organic matters,and nitrogen,phosphorus and potassium content. Therefore,to solve obstacles in continuous cropping of tobacco fields,different regions should take different measures.
文摘Continuous wavelet transform is employed to detect singularities in 2-D signals by tracking modulus maxima along maxima lines and particularly applied to microcalcification detection in mammograms. The microcalcifications are modeled as smoothed positive impulse functions. Other target property detection can be performed by adjusting its mathematical model. In this application, the general modulus maximum and its scale of each singular point are detected and statistically analyzed locally in its neighborhood. The diagnosed microcalcification cluster results are compared with health tissue results, showing that general modulus maxima can serve as a suspicious spot detection tool with the detection performance no significantly sensitive to the breast tissue background properties. Performed fractal analysis of selected singularities supports the statistical findings. It is important to select the suitable computation parameters-thresholds of magnitude, argument and frequency range-in accordance to mathematical description of the target property as well as spatial and numerical resolution of the analyzed signal. The tests are performed on a set of images with empirically selected parameters for 200 μm/pixel spatial and 8 bits/pixel numerical resolution, appropriate for detection of the suspicious spots in a mammogram. The results show that the magnitude of a singularity general maximum can play a significant role in the detection of microcalcification, while zooming into a cluster in image finer spatial resolution both magnitude of general maximum and the spatial distribution of the selected set of singularities may lead to the breast abnormality characterization.
基金Supported by the National Natural Science FundZhejiang Provincial Natural Science Foundation.
文摘In this paper, we gave a proof for the local continuity modulus theorem of the Wiener process, i. e., lim t→0 sup 0≤s≤t |W（s）|/（2s log log（1/s））<sup>1/2</sup>=1 a.s. This result was given by Csrg and Revesz （1981）, but the proof gets them nowhere. We also gave a similar local continuity modulus result for the infinite dimensional OU processes.
