On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L_2 Space

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]) .

On n-K Width of Certain Function Classes Defined by Linear Differential Operators in L2 Space

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]) .

MNTZ RATIONAL APPROXIMATION FOR SPECIAL FUNCTION CLASSES IN Ba[0,1] SPACES

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.

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

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.

AVERAGE σ-K WIDTH OF CONVOLUTION FUNCTION CLASS OF L_(pq) (R) IN L_q(R)

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.

Correlation between the Six-Minute Walk Test and Subjective Functional Class in Patients with Heart Failure

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.

RELATIVE WIDTH OF SMOOTH CLASSES OF MULTIVARIATE PERIODIC FUNCTIONS WITH RESTRICTIONS ON ITERATED LAPLACE DERIVATIVES IN THE L_2-METRIC

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.

HAAR EXPANSIONS OF A CLASS OF FRACTAL INTERPOLATION FUNCTIONS AND THEIR LOGICAL DERIVATIVES

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.

CONVERGENCE OF A CLASS OF MEANS OF H^p FUNCTIONS(0

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.

APPROXIMATION BY FABER-LAURENT RATIONAL FUNCTIONS IN THE MEAN OF FUNCTIONS OF CLASS LP(T) WITH 1

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).

On the Symmetry Classes of Functions

Let R be an integral domain of characteristic zero such that the corresponding group rings have block decompositions. We first prove that the submodule consisting of all the R-valued ξi-symmetric functions of several variables is a symmetry class, where ξi is any block character. Then we present a relationship among certain operators introduced for block character. Then we present a relationship among certain operators introduced for block characters. As a consequence, we obtain a decomposition of an arbitrary R-valued function of several variables. Finally, we describe the symmetry property of such summands and determine all the symmetry classes.

Comparison of skeletal, dental and soft tissue changes in young adults with Class II malocclusion, treated either by camouflage, fixed functional appliance or orthognathic surgery—A prospective study on Indian subjects

Introduction: Borderline Class II malocclusion due to deficient mandible can be treated either by orthodontic camouflage, fixed functional appliances or by orthodontics followed by surgical mandibular advancement. Methodology: A prospective study was designed on young adults with Class II malocclusion on account of a deficient mandible. A total of 45 subjects were divided into three groups of 15 individuals each. The patients were treated either by camouflage, fixed functional appliances or by orthognathic surgery. Pre and post treatment cephalograms were used to assess the skeletal, dental and soft tissue changes. Pre and post treatment profile photographs were assessed on a Visual Analogue Scale (VAS) by orthodontists, oral surgeons and laypersons. Results: Each group achieved a reduction in facial convexity, but the results obtained from the surgical group were more pronounced than the camouflage and the fixed functional group. Conclusion: The reduction in convexity in the camouflage group was by retracting the upper anteriors, which increases the nasolabial angle. In the fixed functional appliance a combination of skeletal and dentoalveolar changes can be observed. However the most appropriate reduction in profile convexity can be obtained by combined orthodontic and surgical treatment of malocclusion.

Basic Functions for Computational Implementation of the Box-Cox Symmetric Class of Distributions

A class of distributions called Box-Cox symmetric was proposed for random variables with asymmetric distributions. This class allows through its structure an interpretation of the parameters in terms of quantiles (in particular, the median), relative dispersion and skewness. This study presents the initial results of the computational development of basic functions of each of the distributions that make up the Box-Cox symmetric class. Four functions have been developed to compose a routine in software R up to now. These functions are related to random numbers generation, probability density function, cumulative distribution function, and quantile function associated to a given probability. Examples of implemented functions were presented. The gamlss routine was used to check the performance of developed functions.

Polar Functions for Fractional Brownian Motion

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.

两类双单叶Bazilevic函数类的Fekete-Szegö不等式

在两类双单叶Bazilevic函数类的引入应用下,采用分析技巧研究Fekete-Szegö不等式.在完成f(x)∈M^(uλ)_(Σ)(ϕ)、f(x)∈H_(Σ)(u,λ,k)两类双单叶定义定理分析后探讨推论结果,所获取的第三项系数估计实现了对部分双单叶函数已有结果的改进.

面向类别不平衡语义分割的损失函数的研究

在图像语义分割的任务中,数据集的类别不平衡分布是一种普遍存在的现象;通过构造更加有效的损失函数来减轻其带来的不利影响是具有较大研究价值的。以损失函数为研究对象,利用训练样本像素的空间分布特性和相关性,改进了Focal损失函数的尺度度量方法,提出了一个基于迭代批次的权重自适应调整的Adapt-Focal损失函数。以类别不平衡的SAR图像数据集GDUT-Nansha为实验对象,采用三个经典的卷积神经网络DeepLabV3+、U-Net和RWL-ENet完成了定量实验。实验结果表明,所提出的Adapt-Focal损失函数相比于CE、FL、dfl、acw、lovász和softiou损失函数,有效提高了少样本地物类别裸地和道路的分割精度IoU和PA值;同时,整体分割精度指标mPA和mIoU均得到较大幅度的提高。验证了Adapt-Focal损失函数在类别不平衡图像语义分割中的有效性。

GENERALIZED FRACTIONAL CALCULUS OF THE ALEPH-FUNCTION INVOLVING A GENERAL CLASS OF POLYNOMIALS

The object of this article is to study and develop the generalized fractional calcu- lus operators given by Saigo and Maeda in 1996. We establish generalized fractional calculus formulas involving the product of R-function, Appell function F3 and a general class of poly- nomials. The results obtained provide unification and extension of the results given by Saxena et al. [13], Srivastava and Grag [17], Srivastava et al. [20], and etc. The results are obtained in compact form and are useful in preparing some tables of operators of fractional calculus. On account of the general nature of the Saigo-Maeda operators, R-function, and a general class of polynomials a large number of new and known results involving Saigo fractional calculus operators and several special functions notably H-function, /-function, Mittag-Leffier function, generalized Wright hypergeometric function, generalized Bessel-Maitland function follow as special cases of our main findings.

“双一流”视域下大学文化建设实践进路研究

“双一流”建设是新时代党中央、国务院为促进高等教育内涵式发展、提升高等教育质量、增强国家核心竞争力、建设教育强国做出的重大国家战略安排。传承创新优秀文化作为“双一流”建设五大建设任务之一,已经明确纳入“双一流”建设大格局,彰显大学所肩负的文化使命。文章以“双一流”建设所涵盖的重要维度为观察视角,在深刻把握大学文化建设发展规律的基础上,分析大学文化与大学功能之间的交互作用机理,进而从实践层面开展应用对策研究,旨在更好地推动中国特色大学文化创新发展,为深入推进新一轮“双一流”建设、加快建设教育强国、文化强国提供参考和建议。

Class Ⅲ过氧化物酶在植物中的作用及其研究进展

过氧化物酶广泛存在于各种有机体中,根据其结构和功能可分为不同的类型,其中ClassⅢ过氧化物酶是植物体内特有的一个多基因家族.ClassⅢ过氧化物酶的功能多样,能够参与生长素的代谢、细胞壁的延伸和加厚、活性氧和活性氮的代谢以及植物的抗病作用等各种生理活动.目前对ClassⅢ过氧化物酶的940个物种中的6 000条序列都已经进行了注释,包括其存在的物种、组织类型以及细胞中的定位等.该文对国内外近年来有关ClassⅢ过氧化物酶的结构特征及其在植物体内的功能等进行综述.

基于蓝墨云班课的功能性训练混合式“金课”教学模式设计研究

该文运用文献资料法、逻辑分析法,在“互联网+”赋能发展的时代背景下,积极探索“金课”课程教学模式。基于蓝墨云班课教学平台的优势,依托蓝墨云班课软件,结合教学环境、教师活动、学生活动三大板块,对课前、课中、课后3个阶段进行深入研究,以精心设计功能性训练混合式“金课”教学模式,旨在最大化改善课堂教学效果,从而全面提升课程教学质量水平。