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
We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical ...We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.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
We prove a global estimate in the Sobolev spaces with variable exponents to the solution of a class of higher-order divergence parabolic equations with measurable coefficients over the non-smooth domains.Here,it is ma...We prove a global estimate in the Sobolev spaces with variable exponents to the solution of a class of higher-order divergence parabolic equations with measurable coefficients over the non-smooth domains.Here,it is mainly assumed that the coefficients are allowed to be merely measurable in one of the spatial variables and have a small BMO quasi-norm in the other variables at a sufficiently small scale,while the boundary of the underlying domain belongs to the so-called Reifenberg flatness.This is a natural outgrowth of Dong-Kim-Zhang’s papers[1,2]from the W^(m,p)-regularity to the W^(m,p(t,x))-regularity for such higher-order parabolic equations with merely measurable coefficients with Reifenberg flat domain which is beyond the Lipschitz domain with small Lipschitz constant.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
The high penetration of distributed generation(DG)has set up a challenge for energy management and consequently for the monitoring and assessment of power quality(PQ).Besides,there are new types of disturbances owing ...The high penetration of distributed generation(DG)has set up a challenge for energy management and consequently for the monitoring and assessment of power quality(PQ).Besides,there are new types of disturbances owing to the uncontrolled connections of non-linear loads.The stochastic behaviour triggers the need for new holistic indicators which also deal with big data of PQ in terms of compression and scalability so as to extract the useful information regarding different network states and the prevailing PQ disturbances for future risk assessment and energy management systems.Permanent and continuous monitoring would guarantee the report to claim for damages and to assess the risk of PQ distortions.In this context,we propose a measurement method that postulates the use of two-dimensional(2D)diagrams based on higher-order statistics(HOSs)and a previous voltage quality index that assesses the voltage supply waveform in a continous monitoring campaign.Being suitable for both PQ and reliability applications,the results conclude that the inclusion of HOS measurements in the industrial metrological reports helps characterize the deviations of the voltage supply waveform,extracting the individual customers’pattern fingerprint,and compressing the data from both time and spatial aspects.The method allows a continuous and robust performance needed in the SG framework.Consequently,the method can be used by an average consumer as a probabilistic method to assess the risk of PQ deviations in site characterization.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.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers of Zhejiang Agricultural and Forestry University, China (Grant No. 2009RC01)
文摘We reduce the variable-coefficient higher-order nonlinear Schrodinger equation （VCHNLSE） into the constantcoefficient （CC） one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.
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supported by the National Natural Science Foundation of China(Grant Nos.11901429 and 12071021).
文摘We prove a global estimate in the Sobolev spaces with variable exponents to the solution of a class of higher-order divergence parabolic equations with measurable coefficients over the non-smooth domains.Here,it is mainly assumed that the coefficients are allowed to be merely measurable in one of the spatial variables and have a small BMO quasi-norm in the other variables at a sufficiently small scale,while the boundary of the underlying domain belongs to the so-called Reifenberg flatness.This is a natural outgrowth of Dong-Kim-Zhang’s papers[1,2]from the W^(m,p)-regularity to the W^(m,p(t,x))-regularity for such higher-order parabolic equations with merely measurable coefficients with Reifenberg flat domain which is beyond the Lipschitz domain with small Lipschitz constant.
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.
基金This work was supported by the Spanish Ministry of Science and Innovation(Statal Agency for Research),the EU(AEI/FEDER/UE)via project PID2019-108953RB-C21 Strategies for Aggregated Generation of Photovoltaic Plants:Energy and Meteorological Operational Data(SAGPVEMOD),the precedent TEC2016-77632-C3-3-R.
文摘The high penetration of distributed generation(DG)has set up a challenge for energy management and consequently for the monitoring and assessment of power quality(PQ).Besides,there are new types of disturbances owing to the uncontrolled connections of non-linear loads.The stochastic behaviour triggers the need for new holistic indicators which also deal with big data of PQ in terms of compression and scalability so as to extract the useful information regarding different network states and the prevailing PQ disturbances for future risk assessment and energy management systems.Permanent and continuous monitoring would guarantee the report to claim for damages and to assess the risk of PQ distortions.In this context,we propose a measurement method that postulates the use of two-dimensional(2D)diagrams based on higher-order statistics(HOSs)and a previous voltage quality index that assesses the voltage supply waveform in a continous monitoring campaign.Being suitable for both PQ and reliability applications,the results conclude that the inclusion of HOS measurements in the industrial metrological reports helps characterize the deviations of the voltage supply waveform,extracting the individual customers’pattern fingerprint,and compressing the data from both time and spatial aspects.The method allows a continuous and robust performance needed in the SG framework.Consequently,the method can be used by an average consumer as a probabilistic method to assess the risk of PQ deviations in site characterization.
