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In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives ...
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In this article, we develop the Yoccoz puzzle technique to study a family of rational maps termed McMullen maps. We show that the boundary of the immediate basin of infinity is always a Jordan curve if it is connected. This gives a positive answer to the question of Devaney. Higher regularity of this boundary is obtained in almost all cases. We show that the boundary is a quasi-circle if it contains neither a parabolic point nor a recurrent critical point. For the whole Julia set, we show that the McMullen maps have locally connected Julia sets except in some special cases.
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In this paper, we study the uniform asymptotics of the Meixner-Pollaczek polynomials Pn(λn)(z;φ{symbol}) with varying parameter λn=(n+12)A as n→∞, where A > 0 is a constant. Two asymptotic expansions are obtained, which hold ...
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In this paper, we study the uniform asymptotics of the Meixner-Pollaczek polynomials Pn(λn)(z;φ{symbol}) with varying parameter λn=(n+12)A as n→∞, where A > 0 is a constant. Two asymptotic expansions are obtained, which hold uniformly for z in two overlapping regions which together cover the whole complex plane. One involves parabolic cylinder functions, and the other is in terms of elementary functions only. Our approach is based on the steepest descent method for oscillatory Riemann-Hilbert problems first introduced by Deift and Zhou [1].
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We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed ...
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We present two new methods for linear elasticity that simultaneously yield stress and displacement approximations of optimal accuracy in both the mesh size h and polynomial degree p. This is achieved within the recently developed discontinuous Petrov-Galerkin (DPG) framework. In this framework, both the stress and the displacement approximations are discontinuous across element interfaces. We study locking-free convergence properties and the interrelationships between the two DPG methods.
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In this paper, we construct and analyze a Crank-Nicolson difference scheme for solving the semilinear Sobolev-type equation with the Riemann-Liouville fractional integral of order alpha is an element of (0, 1). The proposed scheme...
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In this paper, we construct and analyze a Crank-Nicolson difference scheme for solving the semilinear Sobolev-type equation with the Riemann-Liouville fractional integral of order alpha is an element of (0, 1). The proposed scheme consists of two main stages. First, to compensate for the singular behavior of the exact solution at the initial time t = 0, a Crank-Nicolson scheme and the product trapezoidal integration rule are proposed on graded meshes for time discretization. Second, a classical finite difference operator on uniform meshes is used for space discretization. Under suitable assumptions of the regularity condition, the stability and convergence analysis of this scheme in a new norm are given by the energy argument. It is shown that how the mesh grading exponent gamma affects the temporal convergence rate of the presented scheme in the final convergence result. This scheme can attain a second-order accuracy in both time and space by choosing an optimal grading parameter gamma. Numerical results confirm that the error analysis is sharp, and comparisons with results on uniform temporal meshes are included to indicate the effectiveness of our method. (c) 2023 Elsevier B.V. All rights reserved.
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The paper presents a generalization of Arnold-Falk-Winther elements for linear elasticity to meshes with elements of variable order. The generalization is straightforward but the stability analysis involves a nontrivial modificati...
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The paper presents a generalization of Arnold-Falk-Winther elements for linear elasticity to meshes with elements of variable order. The generalization is straightforward but the stability analysis involves a nontrivial modification of involved interpolation operators. The analysis addresses only the h-convergence. In addition, numerical experiments for two dimensional cases are provided.
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This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Cop...
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This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Copulas to model the extreme values, a strategy is proposed which allows to model continuous time series. As the concept of Copulas requires independent and identically distributed (iid) random variables, meteorological fields are transformed using an ARMA-GARCH time series model. In this paper, we focus on the positive pairs of observed and modelled (RCM) precipitation. According to the empirical copulas, significant upper and lower tail dependence between observed and modelled precipitation can be observed. These dependence structures are further conditioned on the prevailing large-scale weather situation. Based on the derived theoretical Copula models, stochastic rainfall simulations are performed, finally allowing for bias corrected and locally refined RCM simulations.
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This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Cop...
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This paper presents a new Copula-based method for further downscaling regional climate simulations. It is developed, applied and evaluated for selected stations in the alpine region of Germany. Apart from the common way to use Copulas to model the extreme values, a strategy is proposed which allows to model continuous time series. As the concept of Copulas requires independent and identically distributed (iid) random variables, meteorological fields are transformed using an ARMA-GARCH time series model. In this paper, we focus on the positive pairs of observed and modelled (RCM) precipitation. According to the empirical copulas, significant upper and lower tail dependence between observed and modelled precipitation can be observed. These dependence structures are further conditioned on the prevailing large-scale weather situation. Based on the derived theoretical Copula models, stochastic rainfall simulations are performed, finally allowing for bias corrected and locally refined RCM simulations.
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This study addresses the problem of combining radar information and gauge measurements. Gauge measurements are the best available source of absolute rainfall intensity albeit their spatial availability is limited. Precipitation in...
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This study addresses the problem of combining radar information and gauge measurements. Gauge measurements are the best available source of absolute rainfall intensity albeit their spatial availability is limited. Precipitation information obtained by radar mimics well the spatial patterns but is biased for their absolute values. In this study copula models are used to describe the dependence structure between gauge observations and rainfall derived from radar reflectivity at the corresponding grid cells. After appropriate time series transformation to generate "iid" variates, only the positive pairs (radar >0, gauge >0) of the residuals are considered. As not each grid cell can be assigned to one gauge, the integration of point information, i.e. gauge rainfall intensities, is achieved by considering the structure and the strength of dependence between the radar pixels and all the gauges within the radar image. Two different approaches, namely Maximum Theta and Multiple Theta, are presented. They finally allow for generating precipitation fields that mimic the spatial patterns of the radar fields and correct them for biases in their absolute rainfall intensities. The performance of the approach, which can be seen as a bias-correction for radar fields, is demonstrated for the Bavarian Alps. The bias-corrected rainfall fields are compared to a field of interpolated gauge values (ordinary kriging) and are validated with available gauge measurements. The simulated precipitation fields are compared to an operationally corrected radar precipitation field (RADOLAN). The copula-based approach performs similarly well as indicated by different validation measures and successfully corrects for errors in the radar precipitation.
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Characteristic patterns and changes in precipitation and temperature over the Greater Horn of Africa during the 20th and 21st century are analysed based on a sample of Coupled Model Intercomparison Project version 3 (CMIP3) models...
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Characteristic patterns and changes in precipitation and temperature over the Greater Horn of Africa during the 20th and 21st century are analysed based on a sample of Coupled Model Intercomparison Project version 3 (CMIP3) models output. Analysis of the 11 CMIP3 models indicates that the equatorial eastern Africa region (including the entire Greater Horn of Africa (GHA)) have been experiencing a significant increase in temperature beginning in the early 1980s, in both A1B and A2 scenarios. All the Atmosphere Ocean Global Circulation Models (AOGCMs) analysed represent the correct mean annual cycle of precipitation, but there is a fairly large spread among the models in capturing the dominant bimodal peaks. In particular, all the models tend to overestimate the peak of the October-November-December (OND) season, while at the same time the peak of the March-April-May (MAM) season tends to be centered on May in the models instead of April as observed. The projected changes and probability distribution of minimum (T_(min)) and maximum (T_(max)) temperatures over the GHA sub-region based on PDFs constructed from daily values showed very diverse distributions for the present (1981-2000) and future (2046-2065; 2081-2100) periods. Whereas in the reference (1981-2000) the probability distribution functions (PDFs) constructed for both T_(min) and T _(max), and during all the seasons had a near normal (but narrow) distribution, those of the future periods were quite diverse but generally very elongated, with significant shifts toward the positive tail. This generally implies that there is consensus among models and the ensemble mean about high likelihood of increase in extreme warmer T min and T max (more so T_(min)) in the future over the GHA region. Our results also show significant increase in the number of days with T_(min) and T_(max) greater the 2 °C (above 1981-2000 average) by the middle as well as the end of 21st century in both the A1B and A1 scenarios. This is especially so during the June, July, and August (JJA) season where all the 92 days of the season indicate projected minimum temperature to increase by more than 2 °C above the 1981-2000 average by the end of 21st century in both scenarios.
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In this paper, we propose a novel global optimization based 3-D multi-region segmentation algorithm for T1-weighted black-blood carotid magnetic resonance (MR) images. The proposed algorithm partitions a 3-D carotid MR image into ...
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In this paper, we propose a novel global optimization based 3-D multi-region segmentation algorithm for T1-weighted black-blood carotid magnetic resonance (MR) images. The proposed algorithm partitions a 3-D carotid MR image into three regions: wall, lumen, and background. The algorithm performs such partitioning by simultaneously evolving two coupled 3-D surfaces of carotid artery adventitia boundary (AB) and lumen-intima boundary (LIB) while preserving their anatomical inter-surface consistency such that the LIB is always located within the AB. In particular, we show that the proposed algorithm results in a fully time implicit scheme that propagates the two linearly ordered surfaces of the AB and LIB to their globally optimal positions during each discrete time frame by convex relaxation. In this regard, we introduce the continuous max-flow model and prove its duality/equivalence to the convex relaxed optimization problem with respect to each evolution step. We then propose a fully parallelized continuous max-flow-based algorithm, which can be readily implemented on a GPU to achieve high computational efficiency. Extensive experiments, with four users using 12 3T MR and 26 1.5T MR images, demonstrate that the proposed algorithm yields high accuracy and low operator variability in computing vessel wall volume. In addition, we show the algorithm outperforms previous methods in terms of high computational efficiency and robustness with fewer user interactions.
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