In this paper, an extension of Besov classes of periodic functions on Td is given. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, and the Gel＇fand n-widths are obtained, respecti...In this paper, an extension of Besov classes of periodic functions on Td is given. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, and the Gel＇fand n-widths are obtained, respectively.展开更多
In this paper we will show that if an approximation process {Ln}n∈N is shape- preserving relative to the cone of all k-times differentiable functions with non-negative k-th derivative on [0,1], and the operators Ln a...In this paper we will show that if an approximation process {Ln}n∈N is shape- preserving relative to the cone of all k-times differentiable functions with non-negative k-th derivative on [0,1], and the operators Ln are assumed to be of finite rank n, then the order of convergence of D^kLnf to D^kf cannot be better than n-2 even for the functions x^k, x^k＋1, x^k＋2 on any subset of [0,1 ] with positive measure. Taking into account this fact, we will be able to find some asymptotic estimates of linear relative n-width of sets of differentiable functions in the space LP[0, 1], p ∈ N.展开更多
Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of ...Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of the approximation theory.We find the lower bound for Kolmogorov n-width d_n(F(Bl_p^m),l_q^m).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
In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of ...In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.展开更多
This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is ...This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov＇s widths, Gelfand＇s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.展开更多
In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q a...In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.展开更多
Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspac...Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspaces for d_(2n) and d^(2n) respectively, and construct an optimallinear operator of rank 2n for δ_(2n), from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W_(2n)={a +sum from i=0 to (2n-1) a_iG(x-iπ/n)a,a_i∈R,sum from i=0 to(2n-1) a_i=0} is an optimal subspace ford_(2n)(?_p,L_p) for p=q.展开更多
1 Introduction Let Q（x）be a polynomial with real coefficients and the Sobolev class W<sub>p</sub>（Q（D））be the set of continuous 2π-periodic functions f（x） for which f<sup>（degQ-1）</sup&...1 Introduction Let Q（x）be a polynomial with real coefficients and the Sobolev class W<sub>p</sub>（Q（D））be the set of continuous 2π-periodic functions f（x） for which f<sup>（degQ-1）</sup> is absolutely continuous and ‖Q（D）f‖<sub>p</sub>≤1, where degQ is the degree of Q, D=d/dt, and ‖·‖<sub>p</sub> is the usual L<sub>p</sub>[0, 2π]-展开更多
In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in ...In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.展开更多
目的通过对临床常规检验指标进行数据分析,筛选出对低癌胚抗原(carcinoembryonic antigen,CEA)结直肠癌具有潜在诊断价值的指标,构建列线图预测模型,并验证该模型的预测效能。方法选取2019年9月~2023年12月安徽医科大学附属巢湖医院收...目的通过对临床常规检验指标进行数据分析,筛选出对低癌胚抗原(carcinoembryonic antigen,CEA)结直肠癌具有潜在诊断价值的指标,构建列线图预测模型,并验证该模型的预测效能。方法选取2019年9月~2023年12月安徽医科大学附属巢湖医院收治的低CEA结直肠癌患者194例设为低CEA结直肠癌组,另外选取同期结直肠良性疾病患者184例作为非结直肠癌组。先对两组的临床常规检验指标包括血常规、生化常规、凝血功能及肿瘤标志物进行单因素分析,然后筛选出差异有统计学意义(P<0.05)的指标,进一步进行多因素Logistic分析,得出低CEA结直肠癌发生的独立影响因素;采用R 4.3.3软件建立列线图预测模型,运用Bootstrap法重复抽样1000次对列线图预测模型进行内部验证,绘制受试者工作特征(receiver operating characteristic,ROC)曲线、Calibration校准曲线、决策曲线分析(decision curve analysis,DCA)评价模型的区分度、校准度以及临床实用性。结果多因素Logistic回归分析结果显示,血红蛋白与红细胞分布宽度比值(hemoglobin-to-erythrocyte distribution width ratio,HRR)、血白蛋白(albumin,ALB)及CEA是低CEA结直肠癌的独立影响因素。ROC曲线分析结果显示,三者联合预测模型的曲线下面积(area under the curve,AUC)为0.822(95%CI:0.781~0.864),敏感度为71.10%,特异性为79.90%,运用Bootstrap法进行内部验证并绘制Calibration校准曲线及决策曲线分析提示该列线图模型区分度、一致性及临床效能较好。结论HRR、ALB及CEA对低CEA结直肠癌具有一定的诊断价值,三者联合的诊断效能较高,基于这3项血清学指标构建的风险预测列线图模型具有较好的临床应用前景。展开更多
文摘In this paper, an extension of Besov classes of periodic functions on Td is given. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, and the Gel＇fand n-widths are obtained, respectively.
基金Supported by RFBR(grant10-01-00270)the president of the Russian Federation(NS-4383.2010.1)
文摘In this paper we will show that if an approximation process {Ln}n∈N is shape- preserving relative to the cone of all k-times differentiable functions with non-negative k-th derivative on [0,1], and the operators Ln are assumed to be of finite rank n, then the order of convergence of D^kLnf to D^kf cannot be better than n-2 even for the functions x^k, x^k＋1, x^k＋2 on any subset of [0,1 ] with positive measure. Taking into account this fact, we will be able to find some asymptotic estimates of linear relative n-width of sets of differentiable functions in the space LP[0, 1], p ∈ N.
文摘Let F(x):R^m→R^m be an odd,continuously differentiable homogeneous map.The pa- per is devoted to the critical points of the generalized Rayleigh ratio||F(x)||_(l_q^m)/||x||_(l_p^m)and connected with some problems of the approximation theory.We find the lower bound for Kolmogorov n-width d_n(F(Bl_p^m),l_q^m).
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
基金supported by the Natural Science Foundation of China (Grant No. 10671019)Research Fund for the Doctoral Program Higher Education (No. 20050027007)Scientific Research Fund of Zhejiang Provincial Education Department (No. 20070509)
文摘In this paper, we consider some classes of 2π-periodic convolution functions Bp, and Kp with kernels having certain oscillation properties, which include the classical Sobolev class as special case. With the help of the spectral of nonlinear integral equations, we determine the exact values of Bernstein n-width of the classes Bp, Kp in the space Lp for 1 〈 p 〈 ∞.
基金Supported by National Natural Science Foundation of China(Grant No.11161033)
文摘This paper considers the problem of n-widths of a Sobolev function class Ωr∞ determined by Pr（D） = DσПlj=1 （D2 - tj2I） in Orlicz spaces. The relationship between the extreme value problem and width theory is revealed by using the methods of functional analysis. Particularly, as σ = 0 or σ = 1, the exact values of Kolmogorov＇s widths, Gelfand＇s widths, and linear widths are obtained respectively, and the related extremal subspaces and optimal linear operators are given.
基金supported by National Natural Science Foundation of China (Grant No.10771016)the "985" Programme of Beijing Normal University
文摘In this paper,we consider the relative n-widths of two kinds of periodic convolution classes,Kp(K) and Bp(G),whose convolution kernels are NCVD-kernel K and B-kernel G. The asymptotic estimations of Kn(Kp(K),Kp(K))q and Kn(Bp(G),Bp(G))q are obtained for p=1 and ∞,1≤ q≤∞.
基金Project supported by the National Natural Science Foundation of China.
文摘Let ? = {a +G*h|a∈R, h⊥1, ||h||_p≤1}, where G is a B--kernel. We obtain the exactvalues of the d_(2n)(B_p, L_p), d^(2n)(B_p,L_p) and δ_(2n)(B_p,L_p) for p∈(1,+∞)/{2}. Furthermore. weidentify some optimal subspaces for d_(2n) and d^(2n) respectively, and construct an optimallinear operator of rank 2n for δ_(2n), from which we answer affirmatively Pinkus Conjecture,i.e. ?p≥q≥1, W_(2n)={a +sum from i=0 to (2n-1) a_iG(x-iπ/n)a,a_i∈R,sum from i=0 to(2n-1) a_i=0} is an optimal subspace ford_(2n)(?_p,L_p) for p=q.
基金Project supported by the National Natural Science Foundation of China.
文摘1 Introduction Let Q（x）be a polynomial with real coefficients and the Sobolev class W<sub>p</sub>（Q（D））be the set of continuous 2π-periodic functions f（x） for which f<sup>（degQ-1）</sup> is absolutely continuous and ‖Q（D）f‖<sub>p</sub>≤1, where degQ is the degree of Q, D=d/dt, and ‖·‖<sub>p</sub> is the usual L<sub>p</sub>[0, 2π]-
基金Supported by Project(No.10471010)of National Natural Science Foundation of ChinaSupported by the Development Foundation of Science and Technology of Tianjin Universities(20040405)Supported by Project"Representation Theory and Related Topics"of the"985 Program"of Beijing Normal University
文摘In this paper, we consider the n-widths and average widths of Besov classes in the usual Sobolev spaces. The weak asymptotic results concerning the Kolmogorov n-widths, the linear n-widths, the Gel＇fand n-widths, in the Sobolev spaces on T^d, and the infinite-dimensional widths and the average widths in the Sobolev spaces on Ra are obtained, respectively.
文摘目的通过对临床常规检验指标进行数据分析,筛选出对低癌胚抗原(carcinoembryonic antigen,CEA)结直肠癌具有潜在诊断价值的指标,构建列线图预测模型,并验证该模型的预测效能。方法选取2019年9月~2023年12月安徽医科大学附属巢湖医院收治的低CEA结直肠癌患者194例设为低CEA结直肠癌组,另外选取同期结直肠良性疾病患者184例作为非结直肠癌组。先对两组的临床常规检验指标包括血常规、生化常规、凝血功能及肿瘤标志物进行单因素分析,然后筛选出差异有统计学意义(P<0.05)的指标,进一步进行多因素Logistic分析,得出低CEA结直肠癌发生的独立影响因素;采用R 4.3.3软件建立列线图预测模型,运用Bootstrap法重复抽样1000次对列线图预测模型进行内部验证,绘制受试者工作特征(receiver operating characteristic,ROC)曲线、Calibration校准曲线、决策曲线分析(decision curve analysis,DCA)评价模型的区分度、校准度以及临床实用性。结果多因素Logistic回归分析结果显示,血红蛋白与红细胞分布宽度比值(hemoglobin-to-erythrocyte distribution width ratio,HRR)、血白蛋白(albumin,ALB)及CEA是低CEA结直肠癌的独立影响因素。ROC曲线分析结果显示,三者联合预测模型的曲线下面积(area under the curve,AUC)为0.822(95%CI:0.781~0.864),敏感度为71.10%,特异性为79.90%,运用Bootstrap法进行内部验证并绘制Calibration校准曲线及决策曲线分析提示该列线图模型区分度、一致性及临床效能较好。结论HRR、ALB及CEA对低CEA结直肠癌具有一定的诊断价值,三者联合的诊断效能较高,基于这3项血清学指标构建的风险预测列线图模型具有较好的临床应用前景。
