This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes $S_{pq\theta }^r b(\mathbb{R}{}^d) and S_{pq\theta }^r B(\mathbb{R}{}^d) in L_q (\mathbb{R}{}^d) (1...This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes $S_{pq\theta }^r b(\mathbb{R}{}^d) and S_{pq\theta }^r B(\mathbb{R}{}^d) in L_q (\mathbb{R}{}^d) (1 \leqslant q \leqslant p< \infty )$ . The weak asymptotic behavior is established for the corresponding quantities.展开更多
We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation....We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.展开更多
We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobole...We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R（Wpr（[0, 1]d）） （r R＋d）. Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R（H∞r（[0,1]d）） and Sobolev class R（W∞r（[0,1]d））. The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.展开更多
This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear wid...This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel’fand widths are obtained, respectively.展开更多
This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic So...This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.展开更多
We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding condition.To obtain the closed-form solution a suitable form of one of the gravitational potentials...We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding condition.To obtain the closed-form solution a suitable form of one of the gravitational potentials has been chosen to determine the other by analyzing the Karmarkar condition.The resulting solutions are found to be well-behaved and regular and could describe a compact stellar object.Considering the current estimated values of the mass and radius of the pulsar 4U1820-30 as input parameters,all the physically relevant parameters are shown to be well-behaved to a very good degree of accuracy.展开更多
Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for vari...Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for various stages and then compares the difference between CSCR before as well as after treatment using different application methods.Thefirst approach,which was focused on image quality,improves medical image accuracy.An enhancement algorithm was implemented to improve the OCT image contrast and denoise purpose called Boosted Anisotropic Diffusion with an Unsharp Masking Filter(BADWUMF).The classifier used here is tofigure out whether the OCT image is a CSCR case or not.150 images are checked for this research work(75 abnormal from Optical Coherence Tomography Image Retinal Database,in-house clinical database,and 75 normal images).This article explicitly decides that the approaches suggested aid the ophthalmologist with the precise retinal analysis and hence the risk factors to be minimized.The total precision is 90 percent obtained from the Two Class Support Vector Machine(TCSVM)classifier and 93.3 percent is obtained from Shallow Neural Network with the Powell-Beale(SNNWPB)classifier using the MATLAB 2019a program.展开更多
In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is construct...In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is constructed is chosen depending on the operator of the concrete equation (otherwise, nonadaptive direct method is then concerned), which would essentially let us increase the precision. For some classes of the second kind of Fredhlom integral equations with anisotropic smooth kernels we determine the exact order of the error of adaptive direct methods, and we also give an optimal algorithm.展开更多
文摘This paper concerns the problem of average σ-K width and average σ-L width of some anisotropic Besov-Wiener classes $S_{pq\theta }^r b(\mathbb{R}{}^d) and S_{pq\theta }^r B(\mathbb{R}{}^d) in L_q (\mathbb{R}{}^d) (1 \leqslant q \leqslant p< \infty )$ . The weak asymptotic behavior is established for the corresponding quantities.
基金Supported by the Natural Science Foundation of China(10501026,60675010,10971251)
文摘We study the approximation of functions from anisotropic Sobolev classes b（WpR（[0, 1]d）） and HSlder-Nikolskii classes B（HPr（[0, 1]d）） in the Lq （[0, 1]d） norm with q 〈 p in the quantum model of computation. We determine the quantum query complexity of this problem up to logarithmic factors. It shows that the quantum algorithms are significantly better than the classical deterministic or randomized algorithms.
基金Supported by National Natural Science Foundation of China (Grant Nos. 10501026 and 60675010)
文摘We study the approximation of the integration of multivariate functions in the quantum model of computation. Using a new reduction approach we obtain a lower bound of the n-th minimal query error on anisotropic Sobolev class R（Wpr（[0, 1]d）） （r R＋d）. Then combining this result with our previous one we determine the optimal bound of n-th minimal query error for anisotropic Hblder- Nikolskii class R（H∞r（[0,1]d）） and Sobolev class R（W∞r（[0,1]d））. The results show that for these two types of classes the quantum algorithms give significant speed up over classical deterministic and randomized algorithms.
文摘This paper concerns the problem of average σ-width of Sobolev–Wiener classes , and Besov-Wiener classes in the metric L q (R d ) for 1 ≤ q ≤ p ≤ ∞. The weak asymptotic results concerning the average linear widths, the average Bernstein widths and the infinite-dimensional Gel’fand widths are obtained, respectively.
基金Project supported by the Natural Science Foundation of China(10371009)Research Fund for the Doctoral Program Higher Education
文摘This paper determines the exact error order on optimization of adaptive direct methods of approximate solution of the class of Fredholm integral equations of the second kind with kernel belonging to the anisotropic Sobolev classes, and also gives an optimal algorithm.
文摘We obtained a new class of solutions for a relativistic anisotropic compact star by utilizing the Karmarkar embedding condition.To obtain the closed-form solution a suitable form of one of the gravitational potentials has been chosen to determine the other by analyzing the Karmarkar condition.The resulting solutions are found to be well-behaved and regular and could describe a compact stellar object.Considering the current estimated values of the mass and radius of the pulsar 4U1820-30 as input parameters,all the physically relevant parameters are shown to be well-behaved to a very good degree of accuracy.
文摘Nowadays in the medicalfield,imaging techniques such as Optical Coherence Tomography(OCT)are mainly used to identify retinal diseases.In this paper,the Central Serous Chorio Retinopathy(CSCR)image is analyzed for various stages and then compares the difference between CSCR before as well as after treatment using different application methods.Thefirst approach,which was focused on image quality,improves medical image accuracy.An enhancement algorithm was implemented to improve the OCT image contrast and denoise purpose called Boosted Anisotropic Diffusion with an Unsharp Masking Filter(BADWUMF).The classifier used here is tofigure out whether the OCT image is a CSCR case or not.150 images are checked for this research work(75 abnormal from Optical Coherence Tomography Image Retinal Database,in-house clinical database,and 75 normal images).This article explicitly decides that the approaches suggested aid the ophthalmologist with the precise retinal analysis and hence the risk factors to be minimized.The total precision is 90 percent obtained from the Two Class Support Vector Machine(TCSVM)classifier and 93.3 percent is obtained from Shallow Neural Network with the Powell-Beale(SNNWPB)classifier using the MATLAB 2019a program.
基金This work is supported by the Special Funds for Major State Basic Research Projects (Grant No. G19990328)the Zhejiang Provincial Natural Science Foundation (Grant No. 100002).
文摘In this paper, we consider the problem of optimization of adaptive direct methods of operator equations. Adaptivity of a direct method is understood in the sense that the subspace on the basis of which it is constructed is chosen depending on the operator of the concrete equation (otherwise, nonadaptive direct method is then concerned), which would essentially let us increase the precision. For some classes of the second kind of Fredhlom integral equations with anisotropic smooth kernels we determine the exact order of the error of adaptive direct methods, and we also give an optimal algorithm.
