BESOV SPACES AND K-FUNCTIONALS IN L_p, 0

We investigate Besov spaces and their connection with trigonometric polynomial approximation in L_p[－π,π], algebraic polynomial approximation in L_p[-1,1], algebraic polynomial approximation in L_p(S), and entire function of exponential type approximation in Lp(R), and characterize K-functionals for certain pairs of function spaces including (Lp [-π,π], B_s~α (Lp[-π，π])), (L_p(R),B_s~α (Lp(R))), (Lp[-1,1],B_s~α (Lp[-1,1])), and (Lp(S),B_s~α (Lp(S))), where 0<s<, 0<p<1, S is a simple polytope and 0<α<r.

基于加权Ripley's K-function的多尺度景观格局分析——以江苏盐城滨海湿地为例

以1987,1992,1997,2002,2007年的遥感影像为例,首次尝试使用加权Ripley's K-function的多尺度格局分析方法,计算了20年来景观异质性在江苏盐城滨海湿地的时间变化和空间分布趋势。通过对研究区的样带划分以及景观类型的点状化处理,建立滨海湿地样带图层和1987—2007年间各类型景观的点格局数据库,从而分析滨海湿地不同类型景观的空间聚集特征变化。基于加权Ripley's K-function的计算表明,在各级空间尺度和时间变化上,各类型湿地的斑块都呈现出空间聚集分布状态,且1987年以来,不同湿地类型的聚集空间特征尺度和空间分布强度均出现了大幅的增减变化,除互花米草滩之外的自然湿地的聚集空间特征尺度和强度都有明显下降甚至少到无法被检测到,而人工湿地却呈现聚集特征尺度和强度的双增长,且该聚集程度有逐渐增强的趋势。分析表明,既考虑样点的空间位置信息又考虑样点分布范围的加权Ripley's K-function方法能很好地表征湿地景观在多尺度上的变异,且与传统空间景观指数等分析方法的结论在一定程度上保持一致。

A SPECIAL MODULUS OF CONTINUITY AND THE K-FUNCTIONAL

We consider the questions connected with the approximation of a real continuous 1-periodic functions and give a new proof of the equivalence of the special Boman-Shapiro modulus of continuity with Peetre’s K-functional. We also prove Jackson’s inequality for the approximation by trigonometric polynomials.

Equivalence between Modulus of Smoothness and K-Functional on Rotation Group SO(3)

In this paper we obtain the equivalence between modulus of smoothness and K-functional on rotation group SO(3).

Equivalence of <i>K</i>-Functionals and Modulus of Smoothness Generated by a Generalized Dunkl Operator on the Real Line

This paper is intended to establish the equivalence between K-functionals and modulus of smoothness tied to a Dunkl type operator on the real line.

Spatio-temporal point pattern analysis on Wenchuan strong earthquake

For exploring the aftershock occurrence process of the 2008 Wenchuan strong earthquake, the spatio-temporal point pattern analysis method is employed to study the sequences of aflershocks with magnitude M≥4.0, M≥4.5, and M≥5.0. It is found that these data exhibit the spatio-temporal clustering on a certain distance scale and on a certain time scale. In particular, the space-time interaction obviously strengthens when the distance is less than 60 km and the time is less than 260 h for the first two aftershock sequences; however, it becomes strong when the distance scale is less than 80 km and the time scale is less than 150 h for the last aftershock sequence. The completely spatial randomness analysis on the data regardless of time component shows that the spatial clustering of the aftershocks gradually strengthens on the condition that the distance is less than 60 km. The results are valuable for exploring the occurrence rules of the Wenchuan strong earthquake and for predicting the aftershocks.

Strong Converse Inequalities for Certain Mixed Szász-Beta Operators

In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.

The Convergence Rate of Ergodic Limits for Regularized Resolvent Families

This paper is concerned with the convergence rates of ergodic limits and approximation for regularized resolvent families for a linear Volterra integral equation. The results contain C 0-semigroups, cosine operator functions and α-times integrated resolvent family as special cases.

WEIGHTED L_p-APPROXIMATION OF DERIVATIVES BY THE METHOD OF BETA OPERATORS

The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness.

Note on a New Construction of Kantorovich Form q-Bernstein Operators Related to Shape Parameter λ

The main purpose of this paper is to introduce some approximation properties of a Kantorovich kind q-Bernstein operators related to B′ezier basis functions with shape parameterλ∈[−1,1].Firstly,we compute some basic results such as moments and central moments,and derive the Korovkin type approximation theorem for these operators.Next,we estimate the order of convergence in terms of the usual modulus of continuity,for the functions belong to Lipschitz-type class and Peetre’s K-functional,respectively.Lastly,with the aid of Maple software,we present the comparison of the convergence of these newly defined operators to the certain function with some graphical illustrations and error estimation table.

APPROXIMATION PROPERTIES OF rth ORDER GENERALIZED BERNSTEIN POLYNOMIALS BASED ON q-CALCULUS

In this paper we introduce a generalization of Bernstein polynomials based on q calculus. With the help of Bohman-Korovkin type theorem, we obtain A-statistical approximation properties of these operators. Also, by using the Modulus of continuity and Lipschitz class, the statistical rate of convergence is established. We also gives the rate of A-statistical convergence by means of Peetre＇s type K-functional. At last, approximation properties of a rth order generalization of these operators is discussed.

RECENT PROGRESS ON SPHERICAL HARMONIC APPROXIMATION MADE BY BNU RESEARCH GROUP -In memory of Professor Sun Yongsheng

As early as in 1990, Professor Sun Yongsheng, suggested his students at Beijing Normal University to consider research problems on the unit sphere. Under his guidance and encouragement his students started the research on spherical harmonic analysis and approximation. In this paper, we incompletely introduce the main achievements in this area obtained by our group and relative researchers during recent 5 years （2001-2005）. The main topics are： convergence of Cesaro summability, a.e. and strong summability of Fourier-Laplace series; smoothness and K-functionals; Kolmogorov and linear widths.

Strong Converse Inequality for the Meyer-Knig and Zeller-Durrmeyer Operators

In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.

Stechkin-Marchaud Type Inequalities in Lp for Linear Combination of Bernstein-Durrmeyer Operators

In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.

ArcGIS^TMProximity and Cluster Analysis of Electron Probe Micro-Maps of Round Top Critical Mineral Deposit

Critical and rare earth elements are in high demand for their increasing incorporation in modern technological devices for applications in the military, industrial, commercial, and consumer sectors. Round Top Mountain, a rhyolite laccolith in Sierra Blanca, west Texas, U.S.A. is a unique mineral deposit that offers opportunity for development of rare earth elements, especially the heavy rare earths, as well as associated critical elements. The main objective here is to evaluate the distances between accessory minerals of potential economic value (yttrofluorite, cryolite, uraninite, thorite, cassiterite, and columbite), and to major (potassium feldspar, albite, and quartz) and minor minerals (annite mi-ca, magnetite, and zircon). In this study we explore the proximity and clustering of these minor and accessory minerals, at the mi-cron-to-millimeter scale, from mineral maps constructed in a previous application of ArcGISTM tools to electron probe microanal-ysis (EPMA) element maps. Our goal is to determine whether specific minerals cluster spatially and, if so, at what distances. We noted that the high-value target yttrofluorite grains often neighbor potassium feldspar and quartz grains, but less commonly magnetite and mica grains. With regard to cluster analysis, most minor and accessory minerals were found to group together at small scales (low micrometer) and were dis-persed or random at larger (up to 1 mm) distances.

Small-Scale Spatial Patterns of <i>Copernicia alba</i>Morong near Bahia Negra, Paraguay

We assessed the spatial distribution of Copernicia alba Morong. In the study area, a lowland palm savanna floodplain, C. alba is the only overstory species. We hypothesized C. alba would be randomly distributed within natural stands. Palms were tallied in six randomly located 0.25 haplots and analyzed using a first-order, Ripley’s K function to assess the distribution of juvenile, adult, and total palm populations. While the total population had either aggregated or random distributions, when analyzing juvenile and adult population separately, we found juveniles were consistently more aggregated than the adults.

Spatio-Temporal Patterns of Wildlife Road Mortality in Golestan National Park-North East of Iran

Nowadays, wildlife road mortality is acknowledged as a main source of threatening long-term survival of wildlife. This paper as the first to analysis wild life vehicle collisions in Iran, aims to reconstruct and interpret the spatio-temporal patterns of WVCs on Asiaei highway in Golestan National Park (GNP). With the collaboration of environmental protection department of GNP, we identified about 1900 WVC Records involving 34 different species of mammals, birds, reptiles and amphibians between 2004 and 2013. Mammals were involved in more than 50% of overall WVCs, among which wild boar (Sus scrofa), Golden Jackal (Canis aureus), Red Fox (Vulpes vulpes), hedgehog (Erinaceus concolor), stone marten (Martes foina) and porcupine (Hystrix indica) were involved in more than 90% of mammals’ mortalities;So, we focused on analyzing spatio-temporal pattern of vehicle collisions of these six mammal species. During the study period, these species have undergone 95% increase in road mortalities, averagely. Detailed temporal analyses exhibited an increasing trend of road mortalities from spring to summer and then a reducing one to late winter. It was shown that a large number of collisions occurred in holiday periods when recreational trips considerably increased the traffic volume of Asiaei highway. Preliminary inspection of spatial patterns using Kernel density analysis revealed six collision hotspots, mostly located in the road bends with densely forested land cover on both sides;the promenades along the road seemed to play a significant role too. Scale dependency analyses of collision patterns, demonstrated clustering pattern at micro scales less than 10 km, randomness at meso scales 10 - 20 km and both regularity and clustering at macro scales more than 20 km. This paper suggests that road mortality of common species in GNP is a momentous issue, which needs to be considered by relevant governmental and public organizations. We also emphasize that the analyses of spatial and temporal patterns of WVCs are fundamentals to plan for mitigate wildlife road mortality.

K-Functional, Weighted Moduli of Smoothness, and Best Weighted Polynomial Approximation on a Simplex

An inverse theorem for the best weighted polynomial approximation of a function in Lwαp（S） is established. We also investigate Besov spaces generated by Freud weight and their connection with algebraic polynomial approximation in Lp（R）wλ, where wα is a Jacobi-type weight on S, 0【p≤∞, S is a simplex and Wλ is a Freud weight. For Ditzian-Totik K-functionals on LP（S）, 1≤P≤∞, we obtain a new equivalence expression.

Strong Approximation by Cesàro Means with Critical Index in the Hardy Spaces H^P(S^(d-1))(0

Let S^(d-1) = {x : |x| = 1} be a unit sphere of the d-dimensional Euclideanspace R^d and let H^p = H^p(S^(d-1)) (0 < p ≤ 1) denote the real Hardy space on S^(d-1). For 0 < p≤ 1 and f ∈ H^p(S^(d-1)), let E_j (f, H^p) (j =0,1,...) be the best approximation of f byspherical polynomials of degree less than or equal to j, in the space H^p(S^(d-1)). Given adistribution f on S^(d-1), its Cesaro mean of order δ > -1 is denoted by σ_k~δ(f). For 0 < p ≤1, it is known that δ(p) := (d-1)/p - d/2 is the critical index for the uniform summability ofσ_k~δ(f) in the metric H^p.

Historic distribution and driving factors of human-caused fires in the Chinese boreal forest between 1972 and 2005

Aims The pattern and driving factors of forest fires are of interest for fire occurrence prediction and forest fire management.The aims of the study were:(i)to describe the history of human-caused fires by season and size of burned area over time;(ii)to identify the spatial patterns of human-caused fires and test for the existence of‘hotspots’to determine their exact locations in the Daxing’an mountains;(iii)to determine the driving factors that determine the spatial distribution and the possibility of human-caused fire occurrence.Methods In this study,K-function and Kernel density estimation were used to analyze the spatial pattern of human-caused fires.The analysis was conducted in s-plus and arcgIs environments,respectively.The analysis of driving factors was performed in SPSS 19.0 based on a logistic regression model.The variables used to identify factors that influence fire occurrence included vegetation types,meteorological conditions,socioeconomic factors,topography and infrastructure factors,which were extracted and collected through the spatial analysis mode of arcgIs and from official statistics,respectively.Important Findings The annual number of human-caused fires and the area burnt have declined since 1987 due to the implementation of a forest fire protection act.There were significant spatial heterogeneity and seasonal variations in the distribution of human-caused fires in the Daxing’an mountains.The heterogeneity was caused by elevation,distance to the nearest railway,forest type and temperature.a logistic regression model was developed to predict the likelihood of human-caused fire occurrence in the Daxing’an mountains;its global accuracy attained 64.8%.The model was thus comparable to other relevant studies.