4 research outputs found
Galoisgruppen von Polynomen vierten Grades
No full textSoftcover, 17x24Die Galoistheorie genießt als Abschluss vieler Algebravorlesungen den Ruf, nur Experten zugänglich zu sein. Dieses Buch wendet sich an alle, die schon lange das Wesen der Galoistheorie begreifen wollten, aber vor der Komplexität in anderen Büchern zurückgeschreckt sind. Im Zentrum steht ein konkreter Satz über die Galoisgruppen von Polynomen vierten Grades und ein Korollar für biquadratische Polynome. Bei der Arbeit mit diesen Aussagen, deren Beweise ausführlich dargestellt und die mit Beispielen illustriert werden, lernt der/die Lesende viele Grundbegriffe und Methoden der Galoistheorie kennen. Auf sehr konkretem Niveau werden die nötigen Grundlagen zur Gruppentheorie sowie die benötigten Begriffe dieser eingeführt. Bewusst wird auf die volle Allgemeinheit zugunsten der Anschaulichkeit verzichtet. Abschließend werden die gefundenen Algorithmen realisiert, indem sie in Programmen implementiert und damit elementare Untersuchungen durchgeführt werden.The Galois Theory, the conclusion of many algebra lectures, has a reputation of only being under-stood by experts. This book is addressed to those who have been trying for years to understand the essence of the Galois Theory but were discouraged by its complexity in other books. The main focus of the book is a concrete theorem about the Galois groups of fourth-grade polynomials and a corollary for biquadratic polynomials. Working with these statements, for which detailed proof is presented and which are illustrated with examples, the reader learns many basis terms and methods for the Galois Theory. At a very practical level the necessary basics of the group theory and the required terms are introduced. A complete generality is intentionally dispensed with for the sake of clarity. In conclusion, the algorithms revealed are realised by implementing them in programmes and, thereby, elementary tests are carried out
Generation of short-pulse VUV and XUV radiation
No full textStarting from intense short-pulse KrF (248 nm, 25 mJ, 400 fs), ArF (193 nm, 10 mJ, sim1 ps), and Ti:sapphire (810 nm, 100 mJ, 150 fs) laser systems, schemes for the generation of fixed-frequency and tunable VUV and XUV radiation by nonlinear optical techniques are investigated. With the KrF system, a four-wave mixing process in xenon yields tunable radiation in the range of 130–200 nm with output energies of, so far, 100 mgrJ in less than 1 ps. For the XUV spectral range below 100 nm, nonperturbative high-order harmonic generation and frequency mixing processes in noble gas jets are considered. To achieve tunability, the intense fixed-frequency pump laser radiation is mixed with less intense but broadly tunable radiation from short-pulse dye lasers or optical parametric generator-amplifier systems. In this way, tunability down to wavelengths of less than 40 nm has been demonstrated
Detection of Truncated HER2 Forms in Formalin-Fixed, Paraffin-Embedded Breast Cancer Tissue Captures Heterogeneity and Is Not Affected by HER2-Targeted Therapy
No full textTruncated forms of HER2, previously identified in subsets of HER2-positive breast cancer, originate from proteolytic extracellular domain (ECD) cleavage or alternative translation initiation. They Lack ECD but may retain intracellular domain functionality, potentially associated with unfavorable prognosis, metastasis, and decreased sensitivity to antibody-based HER2-targeted therapy. To study the distribution of truncated HER2 in breast cancer, we detected loss of membrane-bound ECD independently of its molecular origin in paraffin sections, combining multispectral unmixing of chromogenic duplex IHC for HER2 ECD and intracellular domain with advanced image analysis. HER2 C-terminal fragment 611-transfected MCF7 and 4-aminophenylmercuric acetate-treated SKBR3 cell lines were used as controls. Applying a prototype work flow to whole sections, paired surgical resection/core needle biopsy samples, and paired samples from 69 patients of a phase 2 neoadjuvant clinical trial, we observed unexpected heterogeneity of ECD loss at the single-cell level, and in different areas of individual tumors, indicating that extent and Localization of HER2 ECD Loss add relevant information to averaging truncated HER2 across whole sections. We show acceptable run-to-run variation (coefficient of variation, <0.15), image analysis results in moderate agreement with conventional slide assessment (Cohen's kappa = 0.59), and no obvious interference with previous HER2-ECD-targeted therapy. We conclude that duplex IHC and digital image processing extend current approaches of truncated HER2 detection
