Best Simultaneous LpL^p Approximation in the "Sum" Norm

In this paper we consider best simultaneous approximation byalgebraic polynomials respect to the norm $\sum_{j=1}^k\|f_j-P\|_p$, 1\le p<\infty. We prove an interpolation propertyof the best simultaneous approximations and we study the structureof the set of cluster points of the best simultaneousapproximations on the interval $[-\epsilon,\epsilon],$ as $\epsilon \to 0$

Teor´ıa general para flexi´on y corte (r´egimen el´astico)

En los cap´ıtulos 9.4 y 9.8 del libro Mec´anica de los Materiales de los autores (verap´endice en jpg) citados se aborda el problema general de la flexi´on y corte para el casoen que los ejes y y z no sean Principales de Inercia y por razones pr´acticas no se deseadeterminar los mismos y descomponer la flexi´on oblicua en dos flexiones normales comoes habitual

Fragilaria radians (Kützing) D.M.Williams et Round, the correct name for F. gracilis (Fragilariaceae, Bacillariophyta): a critical analysis of this species complex in Europe

Fragilaria gracilis is one of the most reported Fragilaria species in Europe, observed in a broad range of water bodies, ranging from (ultra)oligotrophic rivers to even eutrophic lakes. A revision of this im-portant taxon based on the analysis of the morphology of a large number of historic and recent populations was highly needed. In the present study, type material of Fragilaria gracilis and several related taxa such as Synedra radians, Fragilaria pseudolaevissima, S. utermoehlii, F. aquaplus, F. boreomongolica and F. tridentina together with more than 10 modern populations were investigated using LM and SEM observations. The results based on these comparisons show that Fragilaria (Synedra) radians is the name for the taxon formerly known as F. gracilis. Moreover, detailed analysis demonstrated that F. pseudolaevissima and Synedra utermoehlii are conspecific with F. radians and should be considered as heterotypic synonyms. The observations made in this study also resulted in the description of several new species, often with distinct ecologies and distribution ar-eas: Fragilaria huerlimannii Van de Vijver sp. nov., F. acerosa Van de Vijver, C.E.Wetzel, Jarlman et Ector sp. nov., F. neglecta Van de Vijver, C.E.Wetzel, Jarlman et Ector sp. nov., F. heudreana Van de Vijver, C.E.Wetzel et Ector sp. nov., F. eutraphenta Van de Vijver, Kusber et D.M.Williams sp. nov., and F. mertensiana Van de Vijver, C.E.Wetzel et Ector sp. nov. Using an analysis of the associated diatom flora, the ecological preferences of each taxon are briefly discussed

What is the level of evidence for combined cardiac resynchronization and defibrillation therapy in heart failure? reply

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3-D Respiratory Motion Compensation during EP Procedures by Image-Based 3-D Lasso Catheter Model Generation and Tracking

Abstract. Radio-frequency catheter ablation of the pulmonary veins attached to the left atrium is usually carried out under fluoroscopy guidance. Two-dimensional X-ray navigation may involve overlay im-ages derived from a static pre-operative 3-D volumetric data set to add anatomical details. However, respiratory motion may impair the utility of static overlay images for catheter navigation. We developed a system for image-based 3-D motion estimation and compensation as a solution to this problem for which no previous solution is yet known. It is based on 3-D catheter tracking involving 2-D/3-D registration. A biplane X-ray C-arm system is used to image a special circumferential (lasso) catheter from two directions. In the first step of the method, a 3-D model of the device is reconstructed. 3-D respiratory motion at the site of ablation is then estimated by tracking the reconstructed model in 3-D from bi-plane fluoroscopy. In our experiments, the circumferential catheter was tracked in 231 biplane fluoro frames (462 monoplane fluoro frames) with an average 2-D tracking error of 1.0 mm ± 0.5 mm.

Constrained 2-D/3-D Registration for Motion Compensation in AFib Ablation Procedures

Abstract. Fluoroscopic overlay images rendered from pre-operative vol-umetric data can provide additional guidance for physicians during catheter ablation procedures for treatment of atrial fibrillation (AFib). As these overlay images are compromised by cardiac and respiratory motion, mo-tion compensation methods have been proposed. The approaches so far either require simultaneous biplane imaging for 3-D motion compensa-tion or, in case of mono-plane X-ray imaging, provide only a limited 2-D functionality. To overcome the downsides of the previously suggested methods, we propose a new approach that facilitates full 3-D motion compensation even if only mono-plane X-ray views are available. To this end, we use constrained model-based 2-D/3-D registration to track a circumferential mapping catheter which is commonly used during AFib catheter ablation procedures. Our approach yields an average 2-D track-ing error of 0.6 mm and an average 3-D tracking error of 2.1 mm.