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 us...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.展开更多
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...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.展开更多
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...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.展开更多
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...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.展开更多
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.
文摘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.
基金This work is supported by the Natural Science Foundation of Fujian Province of China(Grant No.2020J01783)the Project for High-Level Talent Innovation and Entrepreneurship of Quanzhou(Grant No.2018C087R)the Program for New Century Excellent Talents in Fujian Province University.
文摘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.
文摘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.
文摘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.
基金The NSF (10571040) of ChinaNSF (L2010Z02) of Hebei Normal University
文摘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.
