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
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
Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<...Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.展开更多
The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
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
In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of...In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson＇s ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly, and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C-S-H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.展开更多
This paper discusses pointwise error estimates for the approximation by bounded linear operators of coatinuous functions defined on compact meric spaces (X, d). The authors introduce a new majorant of the modulus of t...This paper discusses pointwise error estimates for the approximation by bounded linear operators of coatinuous functions defined on compact meric spaces (X, d). The authors introduce a new majorant of the modulus of the coutinuity which is the smallest among those g(ξ)’s which have the following peoperties ω(f, ξ)≤g(f,ε) and g(f, λε)≤ (1 + λ)g(f,ε) and by tthe majorant a new quatitative Korovkin type theorem on any compact metric space is proved.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 NNSFC (10071072) and Science Foundation of Hangzhou Teacher's College.
文摘Let {W(t),t > 0} be a standard Wiener process and S be the set of Strassen's functions. In this paper we investigate the exact rates of convergence to zero of the variables supp<t<1-h inff∈s sup0<x<1 |(W(t + hx) - W(t))(2hlogh-1)-1/2 - f(x)| and inf0<t<1-h sup0<x<1|(W(t + hx) -W(t))(2hlogh-1)-1/2 - f(x)| for any f ∈ S. As a consequence, a relation between the modulus of non-differentiability and the functional modulus of continuity for a Wiener process is established.
文摘The author establishes a large deviation for k-dimensional Brownian motion B in stronger topology, by which the functional modulus of continuity for B in Holder norm can be obtained.
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.
基金the financial support by the National Natural Science Foundation of China (NSFC#11772164,#11272165,#11572163)the National Basic Research Program of China (973 Program,2009CB623203)+2 种基金the Key Research Program of Society Development of Ningbo (2013C51007)the K.C.Wong Magna Fund in Ningbo Universitysupported by the Research Project Foundation of Zhejiang Educational Department (Y201636745)
文摘In this paper, new models of the density and modulus development of concrete under continued hydration were studied. Experimental study was performed for different mixes of concrete. To avoid considering the effect of variation of Poisson＇s ratio, the one-dimensional ultrasonic technique was adopted to detect the modulus development of concrete under continued hydration. The experimental results indicate the nonlinear characteristics of density and modulus evolution. At the initial stage of continued hydration, the density and modulus increase quickly, and then the increases slow down and finally tend to be constant. The mechanism of modulus enhancement is that the newly produced C-S-H gel in the continued hydration process not only leads to the decrease in porosity, but also repairs the initial defects of concrete. Based on this mechanism, simple differential equations for the density and modulus development of concrete were established by considering the chemical reactions of continued hydration, and new simple models for density and modulus development were proposed.
文摘This paper discusses pointwise error estimates for the approximation by bounded linear operators of coatinuous functions defined on compact meric spaces (X, d). The authors introduce a new majorant of the modulus of the coutinuity which is the smallest among those g(ξ)’s which have the following peoperties ω(f, ξ)≤g(f,ε) and g(f, λε)≤ (1 + λ)g(f,ε) and by tthe majorant a new quatitative Korovkin type theorem on any compact metric space is proved.
