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
The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn...The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.展开更多
In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied....In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied.For the case p=+∞,1≤q≤+∞,the case 1≤p <+∞,q=1,we get their exact values and identify their optimal subspaces.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
Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the...Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.展开更多
The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.
Objective: The aim of this study was to determine the average values of width of the upper central incisor (WUCI) in Congolese Bantu and compare them to those of Caucasians and Asiatic. Material and Methods: It was a ...Objective: The aim of this study was to determine the average values of width of the upper central incisor (WUCI) in Congolese Bantu and compare them to those of Caucasians and Asiatic. Material and Methods: It was a prospective cross-sectional study carried out at the Université de Kinshasa on the Congolese Bantu, Department of Dental Medicine, from March 2020 to March 2021. A maxillary imprint was taken by Jeltrate-type alginate. The measurement of two healthy upper central incisors (UCI) was carried out by the hard plaster casting type 4, with a brand caliper, carbon fiver composite mark. The study was approved by the Ethics Committee of the School of Public Health in the Université de Kinshasa and verbal consent was obtained from each participant. Results: The Average Width of the UCI was 8.74 mm ± 0.56. The average width of the right Upper Central incisor (RUCI) and the left UCI (LUCI) was 8.71 mm ± 0.57 and 8.77 mm ± 0.56, respectively. The average width of the RUCI and LUCI was not the same for men and women (p 0.001). A significant difference was observed between the average of the RUCI and the 18 - 28 and 40 - 50 age group (p = 0.056) as well as for the average LUCI (p = 0.085). The width average of UCI between the Congolese Bantu with those of Caucasians and Asians was significantly different (p = 0.000 and p = 0.009). Conclusion: The average width of the RUCI and LUCI was different among sex and age group. The average width of UCI of the Congolese Bantu is different from that of Caucasians and Asians.展开更多
In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear oper...In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.展开更多
Based on a simple classical model specifying that the primary electrons interact with the electrons of a lattice through the Coulomb force and a conclusion that the lattice scattering can be ignored, the formula for t...Based on a simple classical model specifying that the primary electrons interact with the electrons of a lattice through the Coulomb force and a conclusion that the lattice scattering can be ignored, the formula for the average energy required to produce a secondary electron （ε） is obtained. On the basis of the energy band of an insulator and the formula for e, the formula for the average energy required to produce a secondary electron in an insulator （εi） is deduced as a function of the width of the forbidden band （Eg） and electron affinity X. Experimental values and the εi values calculated with the formula are compared, and the results validate the theory that explains the relationships among Eg, X, and ei and suggest that the formula for εi is universal on the condition that the primary electrons at any energy hit the insulator.展开更多
The design of axial or radial swirlers typically governs a number of geometrical parameters that are determined by the desired flow field.In the meantime,the number of unknown parameters increases with the number of c...The design of axial or radial swirlers typically governs a number of geometrical parameters that are determined by the desired flow field.In the meantime,the number of unknown parameters increases with the number of concentrically mounted swirlers.The available literature is nonetheless limited,and designers are obligated to increase the number of initial assumptions.In this article,three kinds of triple swirlers are employed and simulations are performed to determine the effect of each parameter on the swirler performance.Based on the correlation provided,overlengthening the radial vane length could result in significant changes in the flow field from the jetlike pattern to a wide swirl-jet angle due to the Coanda effect.Passage width should also have the potential to alter the swirl-jet angle and velocity field at the exit of the swirler.展开更多
In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading level...In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading levels of serviceability state.The effects of the depth of normal section beams on the crack spacing and crack width were analyzed,and the modified model is proposed for calculating the average crack spacing by thinking about the depth of normal section,the reinforcement arrangement and the effective reinforcement ratio.The relationships of crack widths at any position in the tensile zone and at the reinforcement level on the side surface of beam were studied.By theoretical and statistical analysis,a method is proposed to calculate the ratios of crack widths between any position and the reinforcement level on the side surface of large depth reinforced concrete beams.展开更多
In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【...In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【q≤p【∞, and the weak asymptotical behavior of these quantities is obtained.展开更多
Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p&...Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes S r pθB(R d) in L p(R d) (1≤p≤∞).展开更多
Given a separable real Banach space F and a separable real Hilbert space X, we denote by S a bounded linear operator from F into X. Let μ be a Gaussian measure defined on the Borel field of F with mean element m_μ= ...Given a separable real Banach space F and a separable real Hilbert space X, we denote by S a bounded linear operator from F into X. Let μ be a Gaussian measure defined on the Borel field of F with mean element m_μ= 0 and correlation operator C_μ. By [1], C_μ is a bounded linear operator from F~*→F such展开更多
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.
文摘The average σ-K width of the Sobolev-Wiener class in Lq(Rn) is studied for and the asymptotic behaviour of this quantity is determined. The exact value of average σ-K width of some class of smooth functions in L2(Rn) is obtained.
文摘In this paper,a kind of generalized Sobolev-Wiener classes W_(pq)~y(R,h),h>0,defined on the whole real axis,is introduced,and the average σ-K width problem of these function classes in the metric L_q(R)is studied.For the case p=+∞,1≤q≤+∞,the case 1≤p <+∞,q=1,we get their exact values and identify their optimal subspaces.
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.
基金partially supported by National Nature Science Foundation of China(61372187)Sichuan Key Technology Research and Development Program(2012GZ0019,2013GXZ0155)the Fund of Lab of Security Insurance of Cyberspace,Sichuan Province(szjj2014-079)
文摘Probabilistic linear （N, δ）-widths and p-average linear N-widths of Sobolev space W2^r（T）, equipped with a Gaussian probability measure #, are studied in the metric of Sq （T） （1 ≤ Q ≤∞）, and determined the asymptotic equalities：λN,δ（W2^r（T）,μ,Sq（T））={（N^-1）^r＋p/2-1/q√1＋1/N·ln1/δ, 1≤q≤2, （N^-1）^r＋p/2-1/q（1＋N^-1/q√ln1/δ）,2〈q〈∞, （N^-1）^r＋p/2√lnN/δ, q=∞,and λN^（a）（W2^r（T）,μ,Sq（T））p={（N^-1）^r＋p/2-1/q, 1≤q〈∞, （N^-1）^r＋p/2-1/q√lnN, q=∞,where 0 〈 p 〈 ∞, δ∈ （0, 1/2], ρ 〉 1, and Sq（T） is a subspace of L1（T）, in which the Fourier series is absolutely convergent in lq sense.
基金Supported by the Foundation of Education Department of Yunnan Province (07Z10533)Supported partly by the National Natural Science Foundation of China (10471010)+1 种基金partly by the project "Representation Theory and Related Topics" of the "985 program" of Beijing Normal UniversitySupported by the Science Foundation of Yunnan University (2008YB027)
文摘The article concerns the average onesided widths of the Sobolev and Besov classes and the classes of functions with bounded moduli of smoothness. The weak asymptotic results are obtained for the corresponding quantities.
文摘Objective: The aim of this study was to determine the average values of width of the upper central incisor (WUCI) in Congolese Bantu and compare them to those of Caucasians and Asiatic. Material and Methods: It was a prospective cross-sectional study carried out at the Université de Kinshasa on the Congolese Bantu, Department of Dental Medicine, from March 2020 to March 2021. A maxillary imprint was taken by Jeltrate-type alginate. The measurement of two healthy upper central incisors (UCI) was carried out by the hard plaster casting type 4, with a brand caliper, carbon fiver composite mark. The study was approved by the Ethics Committee of the School of Public Health in the Université de Kinshasa and verbal consent was obtained from each participant. Results: The Average Width of the UCI was 8.74 mm ± 0.56. The average width of the right Upper Central incisor (RUCI) and the left UCI (LUCI) was 8.71 mm ± 0.57 and 8.77 mm ± 0.56, respectively. The average width of the RUCI and LUCI was not the same for men and women (p 0.001). A significant difference was observed between the average of the RUCI and the 18 - 28 and 40 - 50 age group (p = 0.056) as well as for the average LUCI (p = 0.085). The width average of UCI between the Congolese Bantu with those of Caucasians and Asians was significantly different (p = 0.000 and p = 0.009). Conclusion: The average width of the RUCI and LUCI was different among sex and age group. The average width of UCI of the Congolese Bantu is different from that of Caucasians and Asians.
文摘In this paper we study the average σ-K width and the average σ-linear width of the unit ball of l;（R） inl;（R）. The exact values of these widths are calculated and an optimal subspace with the optimal linear opera-tor （for the σ- linear width） are identified.
基金Project supported by the Special Funds of the National Natural Science Foundation of China (Grant No. 51245010)the Natural Science Foundation of Jiangsu Province, China (Grant No. 10KJB180004)
文摘Based on a simple classical model specifying that the primary electrons interact with the electrons of a lattice through the Coulomb force and a conclusion that the lattice scattering can be ignored, the formula for the average energy required to produce a secondary electron （ε） is obtained. On the basis of the energy band of an insulator and the formula for e, the formula for the average energy required to produce a secondary electron in an insulator （εi） is deduced as a function of the width of the forbidden band （Eg） and electron affinity X. Experimental values and the εi values calculated with the formula are compared, and the results validate the theory that explains the relationships among Eg, X, and ei and suggest that the formula for εi is universal on the condition that the primary electrons at any energy hit the insulator.
基金supported by Korea Electric Power Corporation through Korea Electrical Engineering and Science Research Institute(Grant 18B-022)
文摘The design of axial or radial swirlers typically governs a number of geometrical parameters that are determined by the desired flow field.In the meantime,the number of unknown parameters increases with the number of concentrically mounted swirlers.The available literature is nonetheless limited,and designers are obligated to increase the number of initial assumptions.In this article,three kinds of triple swirlers are employed and simulations are performed to determine the effect of each parameter on the swirler performance.Based on the correlation provided,overlengthening the radial vane length could result in significant changes in the flow field from the jetlike pattern to a wide swirl-jet angle due to the Coanda effect.Passage width should also have the potential to alter the swirl-jet angle and velocity field at the exit of the swirler.
基金Sponsored by the Outstanding Youth Scientific Fund of Henan Province(Grant No.04120002300)Program for Innovation in University of Henan Province(Grant No.[2004]294)
文摘In order to meet the requirement of structural inspection,the crack spacing and crack width at various heights in the tensile zone of six large depth reinforced concrete beams were measured under several loading levels of serviceability state.The effects of the depth of normal section beams on the crack spacing and crack width were analyzed,and the modified model is proposed for calculating the average crack spacing by thinking about the depth of normal section,the reinforcement arrangement and the effective reinforcement ratio.The relationships of crack widths at any position in the tensile zone and at the reinforcement level on the side surface of beam were studied.By theoretical and statistical analysis,a method is proposed to calculate the ratios of crack widths between any position and the reinforcement level on the side surface of large depth reinforced concrete beams.
基金Supported by Beijing Natural Science Foundation (Project No. 1982005)
文摘In this paper, the average σ-K width of Sobolev-Wiener classes S<sub>pq</sub><sup>r</sup> W with mixed smooth- ness in L<sub>q</sub>（R<sup>d</sup>） is studied for 1【q≤p【∞, and the weak asymptotical behavior of these quantities is obtained.
文摘Some weak asymptotic results for average σ-K width and average σ_L width of the isotropic Besov classes S r pθB(R d), S r pθb(R d) and the anisotropic Besov classes S r pθB(R d), S r pθb(R d) in L p(R d) (1≤p<∞) are obtained, and the corresponding weak asymptotic optimal subspaces are identified. Furthermore, the weak asymptotic behavior of optimal recovery is established for the isotropic Besov classes S r pθB(R d) in L p(R d) (1≤p≤∞).
基金Project supported by the National Natural Science Foundation of China.
文摘Given a separable real Banach space F and a separable real Hilbert space X, we denote by S a bounded linear operator from F into X. Let μ be a Gaussian measure defined on the Borel field of F with mean element m_μ= 0 and correlation operator C_μ. By [1], C_μ is a bounded linear operator from F~*→F such
