For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, an...For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.展开更多
In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent im...In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.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
We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the ...We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the von Neumann-Jordan constant CNj（X） and the James constant J（X）. A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.展开更多
文摘For the step-weight function , we prove that the Holder spaces ∧a,p on the interval [-1,1], defined in terms of moduli of smoothness with the step-weight function ,are linearly isomorphic to some sequence spaces, and the isomorphism is given by the cofficients of function with respect to a system of orthonormal splines with knots uniformly distributed according to the measure with density . In case ∧a,p is contained in the space of continuous functions, we give a discrete characterization of this space, using only values of function at the appropriate knots. Application of these results to characterize the order of polynomial approximation is presented.
文摘In this paper, a class of smoothing modulus-based iterative method was presented for solving implicit complementarity problems. The main idea was to transform the implicit complementarity problem into an equivalent implicit fixed-point equation, then introduces a smoothing function to obtain its approximation solutions. The convergence analysis of the algorithm was given, and the efficiency of the algorithms was verified by numerical experiments.
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 partially by the NSF(61877039)the NSFC/RGC Joint Research Scheme of China(12061160462 and N_CityU102/20)the NSF of Zhejiang Province(LY19F020013)。
基金The second author is supported in part by Grant-in-Aid for Scientific Research,Japan Society for the Promotionof Science(Grant No.23540216)
文摘We shall introduce a new geometric constant A（X） of a Banach space X, which is closely related to the modulus of smoothness px （T）, and investigate it in relation with the constant As （X） by Baronti et al., the von Neumann-Jordan constant CNj（X） and the James constant J（X）. A sequence of recent results on these constants as well as some other geometric constants will be strengthened and improved.
基金Supported by Foundation of Key Item of Science and Technology of Education Ministry of China,Foundation of Higher School of Ningxia(No.JY2002107)Foundation of Science of Ningxia University (No.022101)
