| 2 | ON THE UNIFORM CONVERGENCE OF THEGENERALIZED BIEBERBACH POLYNOMIALS INREGIONS WITH K-QUASICONFORMAL BOUNDARY显示文摘Let G be a finite domain in the complex plane with K-quasicon formal boundary,zo be an arbitrary fixed point in G and p>0. Let (z) be the conformal mapping from G onto the disk with radius r0>0 and centered at the origin 0, normalized by (z0)=0 and (z0)=1. Let us set (Z): = and let nn.p(Z) be the generalized Bieberbach polynomial ofdegree n for the pair (G,z0) that minimizes the integral (z) -- p1n(z)| dx in the class of all polynomials of <=n and satis f ying the conditions Pn(z0)=0 and Pn (z0) =1 . In this work we prove the uniform convergence of the generalized Bieberbach polynomials nn,p (z) to p(z) on G in case of P>(2-k2+1)/(2K4) | Abdullah Cavus (Karadeniz Technical University, Turkey) Fahreddin G. Abdullayev (Institute of Mathematics, & Mechanics Academy of Sciences of Azerbaijan Republic, Azerbaijan) | 2001 | Analysis in Theory and Applications2001，17，1： | 1 |
| 3 | Application of different clustering approaches to hydroclimatological catchment regionalization in mountainous regions, a case study in Utah State显示文摘With respect to the different hydrological responses of catchments, even the adjacent ones, in mountainous regions, there are a great number of motivations for classifying them into homogeneous clusters. These motivations include prediction in ungauged basins(PUB), model parameterization, understanding the potential impact of environmental changes, transferring information from gauged catchments to the ungauged ones. The present study investigated the similarity of catchments through the hydro-climatological pure time-series of a 14-year period from 2001 to 2015. Data sets encompass more than 13,000 month-station streamflow, rainfall, and temperature data obtained from 27 catchments in Utah State as one of the eight mountainous states of the USA. The identification, analysis, and interpretation of homogeneous catchments were investigated by applying the four approaches ofclustering, K-means, Ward, and SOM(Self-Organized Map) and a newly proposed Wavelet-Entropy-based(WE-SOM) clustering method. By using two clustering evaluation criteria, 3, 5, and 6 clusters were determined as the best numbers of clusters, depending on the method employed, where each cluster represents different hydro-climatological behaviors. Despite the absence of geographic characteristics in input data matrix, the results indicated a regionalization in agreement with topographic characteristics. Considering the dependency of the hydrological behavior of catchments on the physiographic field aspects and characteristics, WE-SOM method demonstrated a more acceptable performance, compared to the other three conventional clustering methods, by providing more clusters. WE-SOM appears to be a promising approach in catchment clustering. It preserves the topological structure of data which can, as a result, be proofed in a greater number of clusters by dividing data into higher numbers of distinct clusters withsimilar altitudes of catchments in each cluster. The results showed the aptitude of wavelets to quantify the time-based variability of temperature, rainfall and streamflow, in the way contributing to the regionalization of diverse catchments. | Elnaz SHARGHI Vahid NOURANI Saeed SOLEIMANI Fahreddin SADIKOGLU | 2018 | Journal of Mountain Science2018，15，3： | 1 |
| 4 | Uniform convergence of the p-Bieberbach polynomials in domains with zero angles显示文摘Let G C be a simply connected domain whose boundary L := αG is a Jordan curve and 0 ∈ G.Let w = ψ(z) be the conformal mapping of G onto the disk B(0, r0) := {w : |w| < r0}, satisfying ψ(0) = 0,ψ′(0) = 1. We consider the following extremal problem for p > 0:∫∫G|ψ′(z)- P ′n(z) pdσz→ min in the class of all polynomials Pn(z) of degree not exceeding n with Pn(0) = 0, P ′n(0) = 1. The solution to this extremal problem is called the p-Bieberbach polynomial of degree n for the pair(G, 0). We study the uniform convergence of the p-Bieberbach polynomials Bn,p(z) to the ψ(z) on G with interior and exterior zero angles determined depending on the properties of boundary arcs and the degree of their 'touch'. | ABDULLAYEV Fahreddin G ZKARTEPE Pelin N | 2015 | Science China Mathematics2015，58，5： | 0 |
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