Convex and Two-Convex Hypersurfaces Along Exterior Flows

We study both convex and two-convex hypersurfaces embedded in Euclidean space. In 2009 Huisken and Sinestrari were able to classify surfaces undergoing two-convex mean curvature flow using the surgery algorithm Hamilton used for Ricci flow. Recently Head and Lauer were able to independently show that as we take our surgery parameter to infinity, that it will converge to the weak solution of level-set mean curvature flow as studied by Spruck-Evans as well as Chen, Giga and Goto. Ideally one would like to extend the surgery algorithm to the Riemannian setting, however, two-convexity is not preserved for mean curvature flow. Instead we look at Brendle-Huisken G-flow, which does preserve two-convexity. In their paper they were then able to use the Huisken-Sinestrari surgery algorithm for mean curvature flow for the Huisken-Brendle G-flow in both the Euclidean and Riemannian setting. We explicitly develop the details implied by Brendle and Huiskens paper, and address some adjustments which must be made to the arguments from the mean curvature case. In order to do so we make adjustments to the gradient estimate of Brendle and Huisken. We are then required to make some more adjustments to prove the Neck Detection Lemma and the Neck Continuation Theorem. To prove the latter theorem we also need a lower bound for the time needed between two consecutive surgeries which we provide. We then describe an interesting observation for the level-set equation of any extrinsic flow. We discover that the level-set PDE will always contain the infinity Laplacian which has well known unique viscosity solutions which have recently been shown by Evans and Smart to be everywhere differentiable. In the last section of the Appendix we prove a reconciliation result between the flow with surgeries and the viscosity solution, however this depends on explicitly obtaining a viscosity solution for G-flow

Combining Process Guidance and Industrial Feedback for Successfully Deploying Big Data Projects

Companies are faced with the challenge of handling increasing amounts of digital data to run or improve their business. Although a large set of technical solutions are available to manage such Big Data, many companies lack the maturity to manage that kind of projects, which results in a high failure rate. This paper aims at providing better process guidance for a successful deployment of Big Data projects. Our approach is based on the combination of a set of methodological bricks documented in the literature from early data mining projects to nowadays. It is complemented by learned lessons from pilots conducted in different areas (IT, health, space, food industry) with a focus on two pilots giving a concrete vision of how to drive the implementation with emphasis on the identification of values, the definition of a relevant strategy, the use of an Agile follow-up and a progressive rise in maturity

Polityka gospodarcza Trzeciej Rzeszy w poglądach Leopolda Caro

"Po I wojnie światowej - pomimo podpisania Traktatu Wersalskiego i konieczności zwrotu obcych terytoriów, w tym także tradycyjnie silnych ośrodków przemysłowych - Niemcy pozostały potęgą industrialną i handlową. Zajmowały trzecie miejsce na świecie w produkcji węgla kamiennego (1929 r.), a w produkcji energii elektrycznej, surówki żelaza oraz stali surowej - drugie. Przemysł zatrudniał 56% ogółu zatrudnionych (wg danych z 1925 r.), a na Niemcy przypadała blisko 1/10 światowego importu i eksportu (1929 r.). Jednak ta potęga industrialna nie przekładała się bezpośrednio na poziom życia obywateli. Porównując statystyki dotyczące przyrostu naturalnego, zgonów na gruźlicę, samobójstw, śmiertelności niemowląt i emigracji zamorskiej, widać, że Niemcy odstawały od czołówki, którą tworzyły Wielka Brytania, Szwajcaria i Holandia."(...

Trybunał kompetencyjny - geneza, struktura i zakres działalności

"Problematyka sądownictwa kompetencyjnego w Polsce od lat pozostaje poza zakresem zainteresowań badaczy. Co prawda - patrząc nań z perspektywy historycznej - odegrało ono relatywnie niewielką rolę w praktyce polskiego wymiaru sprawiedliwości, tym nie mniej dla badacza celowym wydaje się jej przybliżenie."(...

Phase transitions and local polarity above TC in a PbZr0.87Ti0.13O3 single crystal

Solid solutions of PbZr1_xTixO3 (PZT) are one of the most widely used piezoelectric materials with perovskite structure. Despite the decades of research, the phase diagram of PZT reported in 1971 has not been resolved yet. Recently, it turned out that single crystals of good quality of these solid solutions can be grown. By means of top-seeded solution growth (TSSG) technique, we succeeded to grow a single PbZr0.87Ti0.13O3 crystal. Hence, a partial verification of the diagram could be performed through investigations of the optical, dielectric, pyroelectric and elastic properties of this crystal, in a wide temperature range. The obtained results confirmed that the PbZr0.87Ti0.13O3 crystal undergoes a sequence of phase transitions, such as those observed in ceramics of similar chemical composition. However, additional anomalies of investigated physical properties were observed and discussed. Moreover, the influence of electric field on optical properties has been investigated for the first time and has proven the existence of local polar character of the phase above TC in a limited temperature range