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Abstract  

The present paper establishes a complete result on approximation by rational functions with prescribed numerator degree in L pspaces for 1 < p < ∞ and proves that if f(x)∈L p [-1,1] changes sign exactly l times in (-1,1), then there exists r(x)∈R n l such that

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\| {f(x) - r(x)} \right\|_{L^p } \leqq C_{p,l,b} \omega (f,n^{ - 1} )_{L^p } ,$$ \end{document}
where R n l indicates all rational functions whose denominators consist of polynomials of degree n and numerators polynomials of degree l, and C p , l,b is a positive constant depending only on p, l and b which relates to the distance among the sign change points of f(x) and will be given in 3.

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Abstract  

Let

\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$a = e^{ - 1/\sqrt n } ,p(x) = \Pi _{k = 1}^{n - 1} (a^k + x),r_n (x) = x\frac{{p(x) - p( - x)}} {{p(x) + p( - x)}}$$ \end{document}
. The present note gives the asymptotoc formula of max
\documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\mathop {\max }\limits_{|x| \leqq 1} \left| {|x| - r_n (x)} \right|$$ \end{document}
.

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Abstract

Let fL 2π be a real-valued even function with its Fourier series , and let S n(f,x) be the nth partial sum of the Fourier series, n≧1. The classical result says that if the nonnegative sequence {a n} is decreasing and , then if and only if . Later, the monotonicity condition set on {a n} is essentially generalized to MVBV (Mean Value Bounded Variation) condition. Very recently, Kórus further generalized the condition in the classical result to the so-called GM7 condition in real space. In this paper, we give a complete generalization to the complex space.

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Abstract  

Ultrahigh molecular mass polyethylene (UHMMPE) is filled with carbon nano-tubes (CNTs) by solution in the presence of maleic anhydride grafted styrene-(ethylene-co-butylene)-styrene copolymer (MA-SEBS) as a compatibilizer. The UHMMPE/CNT composites crystallized from melt were prepared at a cooling rate of 20C min-1. The melting and crystallization behaviors of UHMMPE/ CNT composites were investigated by differential scanning calorimetry. The results showed that onset melting temperature (T m) and degree of crystallinity (X c) of UHMMPE/CNT composites crystallized from solution are higher than those from melt due to the larger crystalline lamellar thickness. The onset crystallization temperature (T c) of UHMMPE/CNT composites tends to shift to higher temperature region with increasing CNT content in the composites. Tm and Tc of UHMMPE phase in UHMMPE/CNT composites decrease with the addition of MA-SEBS. Moreover, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is increased due to the introduction of CNTs. MA-SEBS acts as compatilizer, enhances the dispersion of CNTs in the UHMMPE matrix. Thereby, the crystallization rate of UHMMPE phase in UHMMPE/CNT composite is further increased with the addition of MA-SEBS.

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Abstract  

Polypropylene (PP) /ethylene-octene copolymer (POE) blends with different content of POE were prepared by mixing chamber of a Haake torque rheometer. The crystallization behaviors and crystal structure of PP/POE blends were systematically investigated by differential scanning calorimetry (DSC), wide angle X-ray diffraction (WAXD) and polarized optical microscopy (POM). The results showed that PP spherulites became defective and the crystallization behavior was influenced intensely with the introduction of POE. At the low content of POE, the addition of POE decreases the apparent incubation period (Δt i) and the apparent total crystallization period (Δt c) of PP in blends due to the heterogeneous nucleation of POE, and small amount of β-form PP crystals form because of the existence of POE. However, at high content of POE, the addition of POE decreases the mobility of PP segments due to their strong intermolecular interaction and chain entanglements, resulting in retarding the crystallization of PP, decreasing in the amount of β-form PP crystals, and increasing in Δt i and Δt c of PP in blends.

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The study site is the Honghe National Nature Reserve, a Ramsar designated site on the Sanjiang Plain in Northeast China. We present results regarding the spatial pattern and structure of plant communities in these most important natural but continually diminishing freshwater wetlands of China to help promote both protection and restoration. By investigating three ecological levels (landscape, ecosystem and community), this paper quantifies the characteristics of spatial pattern with the aim to identify specific ecological correlations with different hydrogeomorphic features. Specifically, the research involves hierarchical mapping of vegetation types by use of remote sensed data, and the coupling of landscape indices with fluvial topographic zones that have been deduced by GIS from DEM. Statistics from historical survey data are also used to measure the degradation of marshes as well as the historical change of the hydrological regime. We found that dominant is the Calamagrostis angustifolia — Carex spp. community type, a wet meadow and marsh complex within the prevailing landscape mosaic of shrubland and meadow. The results suggest that the sites’ hydro-geomorphic character has decisive influence on plant community structure and composition. There is only limited direct human interference in the sites and, as a consequence, the spatial pattern of vegetation distribution is natural. However, changes to the hydrological regime as the result of extensive irrigation activity in the surrounding area has led to rapid degradation of marsh wetlands within the sites, which threatens the ecological status in this storehouse of “Natural Genes” in the reserve.

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Abstract  

The processes of nucleation of Li2O-Al2O3-SiO2 glasses with TiO2 and TiO2+ZrO2 as nucleating agents were discussed. The DTA peak temperature and DTA peak height shown a strong dependence on the nucleation temperature in the glass with TiO2, while in the glass with TiO2+ZrO2 this tendency was small. The optimum nucleation temperatures were 745 and 760°C for two glasses. It suggested that with TiO2+ZrO2 as nucleating agents, the crystallization had lower sensitivity for nucleation temperature, and the glass had higher nucleation efficiency than with TiO2.

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This research was aimed to study the cell wall degradation and the dynamic changes of Ca2+ and related enzymes in developing aerenchyma of wheat root under waterlogging. An examination of morphological development by light and electron microscope revealed that the structure of cell wall in middle cortical cells remained intact after 12 h of waterlogging and turned thinner after waterlogging for 24 h. At 48 h, the aerenchyma has been formed. The cellulase activity gradually increased in middle cortical cells within 24 h of waterlogging, and decreased with the formation of aerenchyma. Fluorescence detection and subcellular localization of Ca2+ showed the dynamic changing of Ca2+ at the cellular and subcellular levels during the development of aerenchyma. The activity of Ca2+-ATPase enhanced markedly in intercellular space, plasma membrane and tonoplast of some middle cortical cells after 8 h of waterlogging and remained high after 24 h, but it decreased after 48 h of waterlogging. All these suggests that cellulase, Ca2+ and Ca2+-ATPase show a dynamic distribution during the aerenchyma development which associated with the cell wall degradation of middle cortical cells. Moreover, there is a feedback regulation between Ca2+ and Ca2+-ATPase.

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