Slopes of smooth curves on Fano manifolds

Ross and Thomas introduced the concept of slope stability to study K-stability, which has conjectural relation with the existence of constant scalar curvature K\"ahler metric. This paper presents a study of slope stability of Fano manifolds of dimension $n\geq 3$ with respect to smooth curves. The question turns out to be easy for curves of genus $\geq 1$ and the interest lies in the case of smooth rational curves. Our main result classifies completely the cases when a polarized Fano manifold $(X, -K_X)$ is not slope stable with respect to a smooth curve. Our result also states that a Fano threefold $X$ with Picard number 1 is slope stable with respect to every smooth curve unless $X$ is the projective space.Comment: 13 pages, Theorems in the original version were modified. This paper will be published in the Bulletin of the London Mathematical Societ

Cost and Business Analysis Module (CABAM)

In the recent couple of decades, due to international competition, the US launchers lost a considerable amount of market share in the international space launch industry'. Increased international competition has continuously affected the US dominance to eventually place great pressure on future US space launch programs. To compete for future payload and passenger delivery markets, new launch vehicles must first be capable of reliably reaching a number of desired orbital destinations with customer-desired payload capacities. However, the ultimate success of a new launch vehicle program will depend on the launch price it is capable of offering it's customers. Extremely aggressive pricing strategies will be required for a new domestic launch service to compete with low-price international launchers. Low launch prices, then, naturally require a tight budget for the launch program economy. Therefore, budget constraints established by low-pricing requirements eventually place pressure on new launch vehicles to have unprecedentedly low Life Cycle Costs (LCC's)

Lagrangian fibration structure on the cotangent bundle of a del Pezzo surface of degree 4

In this paper, we show that there is a natural Lagrangian fibration structure on the map $\Phi$ from the cotangent bundle of a del Pezzo surface $X$ of degree 4 to $\mathbb C^2$. Moreover, we describe explicitly all level surfaces of the above natural map $\Phi$.Comment: 23 page

Ein Kommentar zum Kommentar der Authentizität. Zur koreanischen Übersetzung der Lebensläufe von Alexander Kluge

Verfolgt ein Übersetzer den Zweck, einen Originaltext seinen fremdkulturellen Lesern authentisch zu übermitteln, muss er diverse Inter- und Kontexte der Sätze, Zitate und Geschichten aufspüren. Dabei justiert er, wie weit der Zusammenhang dem Wissen, den Vorstellungen und den Forschungen der Leser überlassen werden soll. Der Übersetzer gerät in eine ähnliche Situation wie der Verfasser des Textes und die Übersetzung wird in dem Sinne zu einer Art politischer Fragestellung. Bei Alexander Kluge fließen oft die Stimmen von Autoren, Erzählern, und Figuren ineinander, was die Übersetzung besonders schwierig macht. Daraus erfolgen zwangsläufig die Veränderung des Textes und die Selbstteilung des Übersetzers in einen Transkribisten, Interpreten und Kommentator. Wenn man die kooperative Autorschaft Kluges auf die Übersetzung anwendet, kann man die Bildungsidee von A. Kluge, nämlich den „engagierten Pluralismus“, auch als die Aufgabe des Übersetzers verstehen.Quand un traducteur se donne pour but de faire parvenir un texte original d’une manière authentique à des lecteurs venant d’un horizon culturel différent, il doit identifier divers intertextes et contextes des phrases, citations et histoires. Il ajuste sa traduction pour permettre à la connaissance, à l’imagination et aux recherches des lecteurs d’établir les bonnes mises en rapport. Le traducteur se retrouve dans une situation comparable à celle de l’auteur du texte et, en ce sens, la traduction devient une sorte de question politique. Chez Alexander Kluge, les voix des auteurs, des narrateurs et des personnages se confondent souvent, ce qui rend la traduction particulièrement difficile. Cela mène inévitablement à une transformation du texte et à l’auto-division du traducteur en transcripteur, interprète et commentateur. En appliquant la coopération entre divers auteurs chère à Kluge à la traduction, on peut aussi comprendre l’idée de la « Bildung » propre à A. Kluge, c’est-à-dire le « pluralisme engagé », comme étant la tâche du traducteur.If a translator pursues the purpose to transfer an original text to the readers from an unfamiliar culture authentically, it is important to identify various intertexts and contexts of phrases, quotes and stories. He adjusts how far the interrelations should be entrusted to the knowledge, the imagination and the research of the readers. The translator finds himself in a situation similar to the one of the author of the text and to that extend translation becomes a kind of political question. Alexander Kluge often let the voices of authors, narrators and characters flow into each other, which makes the translation particularly difficult. This inevitably leads to the transformation of the text and the self-division of the translator himself into a transcribist, an interpreter and a commentator. Applying the cooperative authorship of Kluge to the translation, one can perceive the idea of “Bildung” of Alexander Kluge, namely the “engaged pluralism”, as the task of the translator

A Suboptimal Approach to Antenna Design Problem With Kernel Regression

This paper proposes a novel iterative algorithm based on a Kernel regression as a suboptimal approach to reliable and efficient antenna optimization. In our approach, the complex and non-linear cost surface calculated from antenna characteristics is fitted into a simple linear model using Kernels, and an argument that minimizes this Kernel regression model is used as a new input to calculate its cost using numerical simulations. This process is repeated by updating coefficients of the Kernel regression model with new entries until meeting the stopping criteria. At every iteration, existing inputs are partitioned into a limited number of clusters to reduce the computational time and resources and to prevent unexpected over-weighted situations. The proposed approach is validated for the Rastrigins function as well as a real engineering problem using an antipodal Vivaldi antenna in comparison with a genetic algorithm. Furthermore, we explore the most appropriate Kernel that minimizes the least-square error when fitting the antenna cost surface. The results demonstrate that the proposed process is suitable to be used in antenna design problems as a reliable approach with a fast convergence time