Introduction: The Six-Minute Walk Test (6MWT) is an inexpensive method to objectively evaluate physical capacity or limitation and stratify prognosis in patients with Heart Failure (HF). Since the clinical p...Introduction: The Six-Minute Walk Test (6MWT) is an inexpensive method to objectively evaluate physical capacity or limitation and stratify prognosis in patients with Heart Failure (HF). Since the clinical perception of symptoms may be adapted or compromised, regular evaluation from medical interviews often fails to determine functional classification. This study aimed to assess the correlation between New York Heart Association Functional Class (NYHA-FC) and the distance walked in the 6MWT. Methods: We conducted a cross-sectional observational study that included patients with HF with reduced ejection fraction followed up at an outpatient service of a teaching hospital, from August 2018 to April 2019. Patients in NYHA-FC I, II, or III were included. We compared NYHA-FC subjectively obtained during the consultation with the 6MWT performed after medical consultation, and the correlation between these two parameters was assessed. Results: The study included 70 patients with HF, 41 (58.6%) of whom were female. The mean age was 61.2 ± 12.7 years. The most prevalent etiologies were dilated idiopathic cardiomyopathy (35.7%) followed by ischemic cardiomyopathy (25.7%). The mean ejection fraction was 34.1% ± 9.8%. The average distance walked in the 6MWT by NYHA-FC I patients was 437.8 ± 95.8 meters, NYHA-FC II 360.1 ± 96.4, and NYHA-FC III 248.4 ± 98.3. Functional class measured by the 6MWT was different than that estimated by NYHA-FC in 34 patients (48.6%), 23 (32.9%) for a higher functional class and 11 (15.7%) for a lower one (p = 0.07). Pearson’s correlation coefficient between NYHA-FC and the 6MWT was -0.55. Conclusion: There was a moderate correlation between the subjective NYHA-FC and the 6MWT. The 6MWT revealed a different classification from NYHA-FC in almost half of the patients. Among those who presented discrepancies between methods, 6MWT reclassification towards a higher functional class was more common.展开更多
In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) i...In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.展开更多
The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic sol...The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .展开更多
Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates...Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .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
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their...In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.展开更多
In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases....In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.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
In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabc...Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).展开更多
In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Ber...In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators.展开更多
Objectives To compare respiratory parameters of peripheral blood mononuclear cell mitochondria and iron metabolism indicators in patients with different NYHA functional classes of ischemic heart failure(HF).Methods Th...Objectives To compare respiratory parameters of peripheral blood mononuclear cell mitochondria and iron metabolism indicators in patients with different NYHA functional classes of ischemic heart failure(HF).Methods This single center, prospective, non-blinded study enrolled 20 patients with diagnosed chronic HF of ischemic genesis with reduced and mildly reduced left ventricle ejection fraction. The maximum oxygen consumption at the peak of the exercise test(VO2peak), iron metabolism parameters and respiratory activity of peripheral blood mononuclear cell mitochondria were assessed.Results Among the patients, a half of individuals were diagnosed with iron deficiency. Subgroups of patients with different HF severity did not significant differ in VO2peak(P=0.209), serum iron(P=0.468) and ferritin(P=0.235) levels. But there was a trend in increasing in these parameters with increasing NYHA HF functional class. Respiratory control coefficient(RC) in NADdependent and FAD-dependent mitochondrial oxidation were lower in patients with NYHA HF Ⅲ functional class compared to individuals with NYHA HF I functional class(P=0.028 and P=0.040, respectively). Serum iron(P=0.026), ferritin(P=0.045)levels, transferrin saturation(P=0.006) were negatively correlated with RC in NAD-dependent mitochondrial oxidation.Conclusions In aggravation of ischemic HF NYHA FC, there is a decrease in RC of PBMC mitochondria during the oxidation of NAD-dependent and FAD-dependent substrates. In the whole sample, patients with laboratory-confirmed iron deficiency accounted a half of the total number. Iron metabolism parameters had a paradoxical inverse relationship with the level of RC in PBMC mitochondria of patients with HF.展开更多
Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the cla...Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.展开更多
MitraClip therapy for mitral regurgitation （MR） in ad- vanced-end stage heart failure （HF）, could open a final bridge to improve symptoms and quality of life in ＂not transplant- able＂ patients. Functional MR is ...MitraClip therapy for mitral regurgitation （MR） in ad- vanced-end stage heart failure （HF）, could open a final bridge to improve symptoms and quality of life in ＂not transplant- able＂ patients. Functional MR is a complicating patho- physiological cofactor of dilated cardiomiopathy （DCM）, associated with poor HF survival.展开更多
In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term ...In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.展开更多
In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergen...In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.展开更多
Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a r...Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).展开更多
A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condit...A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.展开更多
文摘Introduction: The Six-Minute Walk Test (6MWT) is an inexpensive method to objectively evaluate physical capacity or limitation and stratify prognosis in patients with Heart Failure (HF). Since the clinical perception of symptoms may be adapted or compromised, regular evaluation from medical interviews often fails to determine functional classification. This study aimed to assess the correlation between New York Heart Association Functional Class (NYHA-FC) and the distance walked in the 6MWT. Methods: We conducted a cross-sectional observational study that included patients with HF with reduced ejection fraction followed up at an outpatient service of a teaching hospital, from August 2018 to April 2019. Patients in NYHA-FC I, II, or III were included. We compared NYHA-FC subjectively obtained during the consultation with the 6MWT performed after medical consultation, and the correlation between these two parameters was assessed. Results: The study included 70 patients with HF, 41 (58.6%) of whom were female. The mean age was 61.2 ± 12.7 years. The most prevalent etiologies were dilated idiopathic cardiomyopathy (35.7%) followed by ischemic cardiomyopathy (25.7%). The mean ejection fraction was 34.1% ± 9.8%. The average distance walked in the 6MWT by NYHA-FC I patients was 437.8 ± 95.8 meters, NYHA-FC II 360.1 ± 96.4, and NYHA-FC III 248.4 ± 98.3. Functional class measured by the 6MWT was different than that estimated by NYHA-FC in 34 patients (48.6%), 23 (32.9%) for a higher functional class and 11 (15.7%) for a lower one (p = 0.07). Pearson’s correlation coefficient between NYHA-FC and the 6MWT was -0.55. Conclusion: There was a moderate correlation between the subjective NYHA-FC and the 6MWT. The 6MWT revealed a different classification from NYHA-FC in almost half of the patients. Among those who presented discrepancies between methods, 6MWT reclassification towards a higher functional class was more common.
基金supported by the National Natural Science Foundation of China(12061035)the Research Foundation of Jiangxi Science and Technology Normal University of China(2021QNBJRC003)supported by the Graduate Innovation Fund of Jiangxi Science and Technology Normal University(YC2024-X10).
文摘In this paper,the class of starlike functions of complex order γ(γ∈ℂ−{0})is extended from the case on unit disk U=(z∈C:|z|<1)to the case on the unit ball B in a complex Banach space or the unit polydisk U^(n) in C^(n).Let g be a convex function in U. We mainly establish the sharp bounds of all terms of homogeneous polynomial expansions for a subclass of g-parametric starlike mappings of complex order γ on B (resp.U^(n))when the mappings f are k-fold symmetric, k ∈ N. Our results partly solve the Bieberbach conjecture in several complex variables and generalize some prior works.
基金Supported by National Natural Science Foundation of China(Grant No.11971015).
文摘The goal of this paper is to investigate the theory of Noether solvability for Volterra singular integral equations(VSIEs)with convolution and Cauchy kernels in a more general function class.To obtain the analytic solutions,we transform such equations into boundary value problems with discontinuous coefficients by the properties of Fourier analysis.In view of the analytical Riemann-Hilbert method,the generalized Liouville theorem and Sokhotski-Plemelj formula,we get the uniqueness and existence of solutions for such problems,and study the asymptotic property of solutions at nodes.Therefore,this paper improves the theory of singular integral equations and boundary value problems.
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
文摘Let M(u) be an N function, A=D r+∑r-1k=0a k(x)D k a linear differential operator and W M(A) the Sobolev Orlicz class defined by M(u) and A. In this paper we give the asymptotic estimates of the n K width d n(W M(A),L 2[0,1]) .
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supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
文摘In this paper,we study a special class of fractal interpolation functions,and give their Haar-wavelet expansions.On the basis of the expansions,we investigate the H(o|¨)lder smoothness of such functions and their logical derivatives of order α.
文摘In this paper we study the convergence nf a class of means on H^p(G)(0<p<1),the means take the Bochner-Riesz means in[1],the generalized Bochner-Riesz means in[2],and the operators T^(Φ_r)in[3]as special cases.We obtain weak-type estimates for the associated maximal operators and the maximal mean boundedness for the means.
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Supported by the National Natural Science Foundation of China(11161033)Inner Mongolia Natural Science Foundation (2009MS0105)
文摘In this paper, we research the Miintz rational approximation of two kinds of spe- cial function classes, and give the corresponding estimates of approximation rates of these classes.
文摘Let Γ be a regular curve and Lp (Γ), 1<p<+∞. be the class of all complex - valued functions f de-fined on Γ which are such that |f|p is mtegrabie in sense of Lebesgue. In this work, we define the k th p-Fabcrpolynomial F k,p (z),the kth p-Faber principle part F k.p (1/z) for Γ , and defined the nth p-Fcber- Laurent rational function Rn.p (f, z) and p- generalized modulus of continuity Ωp(f, t) of a function f of Lp(Γ) We inves-tigate some properties of Fk,p (z) and Fk.p (1/z). And then we prove a direct theorem characterizing the degree of approximation with respect to Ω (. , t) in the mean of functions of Lp(Γ) by the rational junctions Rn.p (. . z).
文摘In this paper we study the local measure of approximation of a class of special mathematical expectation operators to Lipschitz class of functions by probabilistic method. The some well known operators (e. g., the Bernstein, Bascakov and Szasz-Mirakjan operators etc) are special cases of a class of the mathematical expetation operators.
基金supported by Russian Science Foundation,RSF 23-75-00009(part of the study corresponding to finding 1)Part of the study corresponding to finding 2 was carried out within the state assignment,FSR No.:122020300045-5(03.02.2022).
文摘Objectives To compare respiratory parameters of peripheral blood mononuclear cell mitochondria and iron metabolism indicators in patients with different NYHA functional classes of ischemic heart failure(HF).Methods This single center, prospective, non-blinded study enrolled 20 patients with diagnosed chronic HF of ischemic genesis with reduced and mildly reduced left ventricle ejection fraction. The maximum oxygen consumption at the peak of the exercise test(VO2peak), iron metabolism parameters and respiratory activity of peripheral blood mononuclear cell mitochondria were assessed.Results Among the patients, a half of individuals were diagnosed with iron deficiency. Subgroups of patients with different HF severity did not significant differ in VO2peak(P=0.209), serum iron(P=0.468) and ferritin(P=0.235) levels. But there was a trend in increasing in these parameters with increasing NYHA HF functional class. Respiratory control coefficient(RC) in NADdependent and FAD-dependent mitochondrial oxidation were lower in patients with NYHA HF Ⅲ functional class compared to individuals with NYHA HF I functional class(P=0.028 and P=0.040, respectively). Serum iron(P=0.026), ferritin(P=0.045)levels, transferrin saturation(P=0.006) were negatively correlated with RC in NAD-dependent mitochondrial oxidation.Conclusions In aggravation of ischemic HF NYHA FC, there is a decrease in RC of PBMC mitochondria during the oxidation of NAD-dependent and FAD-dependent substrates. In the whole sample, patients with laboratory-confirmed iron deficiency accounted a half of the total number. Iron metabolism parameters had a paradoxical inverse relationship with the level of RC in PBMC mitochondria of patients with HF.
文摘Let X (t)(t∈R^N) be a d-dimensional fractional Brownian motion. A contiunous function f:R^N→R^d is called a polar function of X(t)(t∈R^N) if P{ t∈R^N\{0},X(t)=t(t)}=0. In this paper, the characteristies of the class of polar functions are studied. Our theorem 1 improves the previous results of Graversen and Legall. Theorem2 solves a problem of Legall (1987) on Brownian motion.
文摘MitraClip therapy for mitral regurgitation （MR） in ad- vanced-end stage heart failure （HF）, could open a final bridge to improve symptoms and quality of life in ＂not transplant- able＂ patients. Functional MR is a complicating patho- physiological cofactor of dilated cardiomiopathy （DCM）, associated with poor HF survival.
文摘In this paper, solutions of Riemann boundary value problems with nodes are extended to the case where they may have singularties of high order at the nodes. Moreover, further extension is discussed when the free term of the problem involved also possesses singularities at the nodes. As an application, certain singular integral equation is discussed.
文摘In this paper, we present a sufficient condition for uniform convergence of means to their expectations over the classes of real functions. Our proof is very simple via connecting this convergence to uniform convergence over the class of indicator functions. Furthermore, we obtain a convergent result concerning a non=VC class with an application to variable transformation for fitting regression model.
基金This project is supported by the National Natural Science Foundation of China
文摘Let B be a separable real Banach space and X(t) be a symmetric conservative diffusionprocess taking values in B. In this paper, we decompose the functional u(X(t),t) into a sumof a square integrable martingale and a regular 0-quadratic variation process. On this basis, weestablish the predictable representation theorem of X(t).
基金supported by the National Natural Science Foundation of China(No.11361064)
文摘A class Ф of 5-dimensional functions was introduced and an existence and uniqueness of common fixed points for a family of non-self mappings satisfying a Фi- quasi-contractive condition and a certain boundary condition was given on complete metrically convex metric spaces, and from which, more general unique common fixed point theorems were obtained. Our main results generalize and improve many same type common fixed point theorems in references.
