The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner produ...The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.展开更多
For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over ...For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d） （1≤ q ≤ ∞）, and obtain its weak asymptotic result.展开更多
In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some...In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some exact results.展开更多
This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the...This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.展开更多
AIM：To determine the Bruch＇s membrane opening-minimum rim width（BMO-MRW） tipping point where corresponding visual field（VF） damages become detectable.METHODS：A total of 85 normal subjects and 83 glaucoma patie...AIM：To determine the Bruch＇s membrane opening-minimum rim width（BMO-MRW） tipping point where corresponding visual field（VF） damages become detectable.METHODS：A total of 85 normal subjects and 83 glaucoma patients（one eye per participant） were recruited for the study.All of the patients had VF examinations and spectral-domain optical coherence tomography to measure the BMO-MRW.Total deviation values for 52 VF points were allocated to the corresponding sector according to the Garway-Heath distribution map.To evaluate the relationship between VF loss and BMOMRW measurements,a ＂broken-stick＂ statistical model was used.The tipping point where the VF values started to sharply decrease as a function of BMO-MRW measurements was estimated and the slopes above and below this tipping point were compared.RESULTS：A 25.9% global BMO-MRW loss from normative value was required for the VF loss to be detectable.Sectorally,substantial BMO-MRW thinning in inferotemporal sector（33.1%） and relatively less BMO-MRW thinning in the superotemporal sector（8.9%） were necessary for the detection of the VF loss.Beyond the tipping point,the slopes were close to zero throughout all of the sectors and the VF loss was unrelated to the BMO-MRW loss.The VF loss was related to the BMO-MRW loss below the tipping point.The difference between the two slopes was statistically significant（P≤0.002）.CONCLUSION：Substantial BMO-MRW loss appears to be necessary for VF loss to be detectable in patients with open angle glaucoma with standard achromatic perimetry.展开更多
Purpose: Swallowing function was in a patient with tongue cancer that was evaluated with video fluorography before and after subtotal glossectomy and reconstruction with a rectus abdominis muscuocutaneous flap. Materi...Purpose: Swallowing function was in a patient with tongue cancer that was evaluated with video fluorography before and after subtotal glossectomy and reconstruction with a rectus abdominis muscuocutaneous flap. Materials and Methods: A 41-year-old man underwent subtotal glossectomy and retained the unilateral posterior mylohyoid and unilateral stylohyoid muscles. The structure of the flap was evaluated postoperatively. To assess swallowing function, video fluorography was performed before surgery, 1 month after surgery and 1 year after surgery. Testing involved 1) ability to hold 10 mL of liquid in the oral cavity, 2) epiglottis turnover, 3) the presence of aspiration, 4) hyoid bone movement, and 5) maximum width of the esophageal entrance. Results: The flap was protuberant postoperatively. The patient was able to hold the test diet in the oral cavity before and after surgery. Epiglottis turnover was good before surgery but insufficient after surgery. Aspiration during swallowing was not observed before or after surgery. At rest, the hyoid bone sagged postoperatively, in comparison with preoperatively. Hyoid bone movement and width of the esophageal entrance decreased after surgery;however, they demonstrated gradual recovery. Conclusions: For good postoperative swallowing function after subtotal glossectomy, it is necessary to perform reconstruction with protuberant flap and to retain the suprahyoid muscles as much as possible.展开更多
An experimental setup successfuUy used for measuring the fluctuations in deep inelastic colli-sion(DIC)excitation functions is described.As the preliminary results of the experiment,the dependenceof the coherence ener...An experimental setup successfuUy used for measuring the fluctuations in deep inelastic colli-sion(DIC)excitation functions is described.As the preliminary results of the experiment,the dependenceof the coherence energy widths Γ on N/Z of the projectile-like fragments are presented.The oonstraintsfor this kind of measurement are discussed.展开更多
Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitab...Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitable internal uncertainties and external disturbances in practice, this inherent nonlinear character always hinders space vehicles autopilot from pursuing precise tracking performance. Compared to most of pre-existing methodologies that passively suppress the uncertainties and disturbances, a design based on predictive functional control(PFC) and generalized extended state observer(GESO) is firstly proposed for three-axis RCS control system to actively reject that with no requirement for additional fuel consumption. To obtain a high fidelity predictive model on which the performance of PFC greatly depends, the nonlinear coupling multiple-input multiple-output(MIMO) flight dynamics model is parameterized as a state-dependent coefficient form. And based on that, a MIMO PFC algorithm in state space domain for a plant of arbitrary orders is deduced in this paper.The internal uncertainties and external disturbances are lumped as a total disturbance, which is estimated and cancelled timely to further enhance the robustness. The continuous control command synthesised by above controller-rejector tandem is finally modulated by pulse width pulse frequency modulator(PWPF) to on-off signals to meet RCS requirement. The robustness and feasibility of the proposed design are validated by a series of performance comparison simulations with some prominent methods in the presence of significant perturbations and disturbances, as well as measurement noise.展开更多
基金supported by the National Natural Science Foundation of China(12071444,12201581)the Fundamental Research Program of Shanxi Province of China(202103021223191).
文摘The minimal widths of three bounded subsets of the unit sphere associated to a unit vector in a normed linear space are studied,and three related geometric constants are introduced.New characterizations of inner product spaces are also presented.From the perspective of minimal width,strongε-symmetry of Birkhoff orthogonality is introduced,and its relation toε-symmetry of Birkhoff orthogonality is shown.Unlike most of the existing parameters of the underlying space,these new constants are full dimensional in nature.
基金Supported partly by National Natural Science Foundation of China (10471010)partly by the project "Representation Theory and Related Topics" of the "985 Program" of Beijing Normal University
文摘For two subsets W and V of a Banach space X, let Kn（W, V, X） denote the relative Kolmogorov n-width of W relative to V defined by Kn（W,V,X）：=inf sup inf/Ln f∈W g∈V∩Ln‖f-g‖x, where the infimum is taken over all n-dimensional linear subspaces Ln of X. Let W2（△^τ） denote the class of 2π-periodic functions f with d-variables satisfying ∫[-π, π]^d｜△^τf（x）｜^2dx≤1, while △^τ is the r-iterate of Laplace operator △. This article discusses the relative Kolmogorov n-width of W2（△^τ） relative to W2（△^τ） in Lq（[-π, π]^d） （1≤ q ≤ ∞）, and obtain its weak asymptotic result.
基金The author was supported by the National Natural Science Found of China.
文摘In this paper. we study the average n-K width of the convolution class B_(pq)(G)(or B_(?)(G)), for which the kernel G(x) is a PF density, in the metric L_q(R)(or L_(qp)(R)) for the case 1≤q<p ≤∞, and obtain some exact results.
基金The project is supported partly by the NationalNatural Science Foundation of China(10071007)and partly by the Foundation for University Key Teachers bythe Ministry of Education of China and partly by the Scientific Research Foundation for Returned Ov
文摘This paper concerns the problem of the Kolmogorov n-width, the linear re-width, the Gel'fand n-width and the Bernstein re-width of Sobolev classes of the periodic multivariate functions in the space Lp(Td) and the average Bernstein o-width, average Kolmogorov o-widths, the average linear o-widths of Sobolev classes of the multivariate functions in the space LP(R ), where p = (p1,…,pd), 1 < Pj < ∞o, j = 1,2,…,d, or pj = ∞,j = 1,2,…, d. Their weak asymptotic behaviors are established for the corresponding quantities.
文摘AIM：To determine the Bruch＇s membrane opening-minimum rim width（BMO-MRW） tipping point where corresponding visual field（VF） damages become detectable.METHODS：A total of 85 normal subjects and 83 glaucoma patients（one eye per participant） were recruited for the study.All of the patients had VF examinations and spectral-domain optical coherence tomography to measure the BMO-MRW.Total deviation values for 52 VF points were allocated to the corresponding sector according to the Garway-Heath distribution map.To evaluate the relationship between VF loss and BMOMRW measurements,a ＂broken-stick＂ statistical model was used.The tipping point where the VF values started to sharply decrease as a function of BMO-MRW measurements was estimated and the slopes above and below this tipping point were compared.RESULTS：A 25.9% global BMO-MRW loss from normative value was required for the VF loss to be detectable.Sectorally,substantial BMO-MRW thinning in inferotemporal sector（33.1%） and relatively less BMO-MRW thinning in the superotemporal sector（8.9%） were necessary for the detection of the VF loss.Beyond the tipping point,the slopes were close to zero throughout all of the sectors and the VF loss was unrelated to the BMO-MRW loss.The VF loss was related to the BMO-MRW loss below the tipping point.The difference between the two slopes was statistically significant（P≤0.002）.CONCLUSION：Substantial BMO-MRW loss appears to be necessary for VF loss to be detectable in patients with open angle glaucoma with standard achromatic perimetry.
文摘Purpose: Swallowing function was in a patient with tongue cancer that was evaluated with video fluorography before and after subtotal glossectomy and reconstruction with a rectus abdominis muscuocutaneous flap. Materials and Methods: A 41-year-old man underwent subtotal glossectomy and retained the unilateral posterior mylohyoid and unilateral stylohyoid muscles. The structure of the flap was evaluated postoperatively. To assess swallowing function, video fluorography was performed before surgery, 1 month after surgery and 1 year after surgery. Testing involved 1) ability to hold 10 mL of liquid in the oral cavity, 2) epiglottis turnover, 3) the presence of aspiration, 4) hyoid bone movement, and 5) maximum width of the esophageal entrance. Results: The flap was protuberant postoperatively. The patient was able to hold the test diet in the oral cavity before and after surgery. Epiglottis turnover was good before surgery but insufficient after surgery. Aspiration during swallowing was not observed before or after surgery. At rest, the hyoid bone sagged postoperatively, in comparison with preoperatively. Hyoid bone movement and width of the esophageal entrance decreased after surgery;however, they demonstrated gradual recovery. Conclusions: For good postoperative swallowing function after subtotal glossectomy, it is necessary to perform reconstruction with protuberant flap and to retain the suprahyoid muscles as much as possible.
基金The project supported by the National Natural Science Foundation of China
文摘An experimental setup successfuUy used for measuring the fluctuations in deep inelastic colli-sion(DIC)excitation functions is described.As the preliminary results of the experiment,the dependenceof the coherence energy widths Γ on N/Z of the projectile-like fragments are presented.The oonstraintsfor this kind of measurement are discussed.
文摘Reaction control system(RCS) is a powerful and efficient actuator for space vehicles attitude control, which is typically characterized as a pulsed unilateral effector only with two states(off/on). Along with inevitable internal uncertainties and external disturbances in practice, this inherent nonlinear character always hinders space vehicles autopilot from pursuing precise tracking performance. Compared to most of pre-existing methodologies that passively suppress the uncertainties and disturbances, a design based on predictive functional control(PFC) and generalized extended state observer(GESO) is firstly proposed for three-axis RCS control system to actively reject that with no requirement for additional fuel consumption. To obtain a high fidelity predictive model on which the performance of PFC greatly depends, the nonlinear coupling multiple-input multiple-output(MIMO) flight dynamics model is parameterized as a state-dependent coefficient form. And based on that, a MIMO PFC algorithm in state space domain for a plant of arbitrary orders is deduced in this paper.The internal uncertainties and external disturbances are lumped as a total disturbance, which is estimated and cancelled timely to further enhance the robustness. The continuous control command synthesised by above controller-rejector tandem is finally modulated by pulse width pulse frequency modulator(PWPF) to on-off signals to meet RCS requirement. The robustness and feasibility of the proposed design are validated by a series of performance comparison simulations with some prominent methods in the presence of significant perturbations and disturbances, as well as measurement noise.
