The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation ...The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
In this paper,a novel hybrid texture feature set and fractional derivative filter-based breast cancer detection model is introduced.This paper also introduces the application of a histogram of linear bipolar pattern f...In this paper,a novel hybrid texture feature set and fractional derivative filter-based breast cancer detection model is introduced.This paper also introduces the application of a histogram of linear bipolar pattern features(HLBP)for breast thermogram classification.Initially,breast tissues are separated by masking operation and filtered by Gr¨umwald–Letnikov fractional derivative-based Sobel mask to enhance the texture and rectify the noise.A novel hybrid feature set usingHLBP and other statistical feature sets is derived and reduced by principal component analysis.Radial basis function kernel-based support vector machine is employed for detecting the abnormality in the thermogram.The performance parameters are calculated using five-fold cross-validation scheme using MATLAB 2015a simulation software.The proposedmodel achieves the classification accuracy,sensitivity,specificity,and area under the curve of 94.44%,95.55%,92.22%,96.11%,respectively.A comparative investigation of different texture features with respect to fractional orderαto classify the breast malignancy is also presented.The proposed model is also compared with a few existing state-of-art schemes which verifies the efficacy of the model.Fractional orderαoffers extra adaptability in overcoming the limitations of thermal imaging techniques and assists radiologists in prior breast cancer detection.The proposed model is more generalized which can be used with different thermal image acquisition protocols and IoT based applications.展开更多
<div style="text-align:justify;"> <span style="font-family:Verdana;">Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addr...<div style="text-align:justify;"> <span style="font-family:Verdana;">Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addressing the criticisms of their black-box behaviour. Such analysis of RBFNs for hydrological modelling has previously been limited to exploring perturbations to both inputs and connecting weights. In this paper, the backward chaining rule that has been used for sensitivity analysis of MLPs, is applied to RBFNs and it is shown how such analysis can provide insight into physical relationships. A trigonometric example is first presented to show the effectiveness and accuracy of this approach for first order derivatives alongside a comparison of the results with an equivalent MLP. The paper presents a real-world application in the modelling of river stage shows the importance of such approaches helping to justify and select such models.</span> </div>展开更多
文摘The first through ninth radial derivatives of a harmonic function and gravity anomaly are derived in this paper. These derivatives can be used in the analytical continuation application. For the downward continuation of gravity anomaly, the Taylor series approach developed in the paper is equivalent theoretically to but more efficient and storage-saving computationally than the well-known gradient operator approach. Numerical simulation shows that Taylor series expansion constructed by the derived formulas for the radial derivatives of gravity disturbance is still convergent for height up to 4 km.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
基金The research is supported by NNSF of China(19771082)
文摘In this paper, The integral characterizations of alpha-Bloch (little alpha-Bloch) axe given in terms of higher radial derivative, and their characterizations of Caxleson type measure are obtained.
基金Praveen Agarwal,thanks to the SERB(Project TAR/2018/000001)DST(Projects DST/INT/DAAD/P-21/2019 and INT/RUS/RFBR/308)NBHM(DAE)(Project 02011/12/2020 NBHM(R.P)/RD II/7867).
文摘In this paper,a novel hybrid texture feature set and fractional derivative filter-based breast cancer detection model is introduced.This paper also introduces the application of a histogram of linear bipolar pattern features(HLBP)for breast thermogram classification.Initially,breast tissues are separated by masking operation and filtered by Gr¨umwald–Letnikov fractional derivative-based Sobel mask to enhance the texture and rectify the noise.A novel hybrid feature set usingHLBP and other statistical feature sets is derived and reduced by principal component analysis.Radial basis function kernel-based support vector machine is employed for detecting the abnormality in the thermogram.The performance parameters are calculated using five-fold cross-validation scheme using MATLAB 2015a simulation software.The proposedmodel achieves the classification accuracy,sensitivity,specificity,and area under the curve of 94.44%,95.55%,92.22%,96.11%,respectively.A comparative investigation of different texture features with respect to fractional orderαto classify the breast malignancy is also presented.The proposed model is also compared with a few existing state-of-art schemes which verifies the efficacy of the model.Fractional orderαoffers extra adaptability in overcoming the limitations of thermal imaging techniques and assists radiologists in prior breast cancer detection.The proposed model is more generalized which can be used with different thermal image acquisition protocols and IoT based applications.
文摘<div style="text-align:justify;"> <span style="font-family:Verdana;">Sensitivity analysis of neural networks to input variation is an important research area as it goes some way to addressing the criticisms of their black-box behaviour. Such analysis of RBFNs for hydrological modelling has previously been limited to exploring perturbations to both inputs and connecting weights. In this paper, the backward chaining rule that has been used for sensitivity analysis of MLPs, is applied to RBFNs and it is shown how such analysis can provide insight into physical relationships. A trigonometric example is first presented to show the effectiveness and accuracy of this approach for first order derivatives alongside a comparison of the results with an equivalent MLP. The paper presents a real-world application in the modelling of river stage shows the importance of such approaches helping to justify and select such models.</span> </div>
