Metric Graph Approximations of Geodesic Spaces

A standard result in metric geometry is that every compact geodesic metric space can be approximated arbitrarily well by finite metric graphs in the Gromov-Hausdorff sense. It is well known that the first Betti number of the approximating graphs may blow up as the approximation gets finer. In our work, given a compact geodesic metric space $X$, we define a sequence $(\delta^X_n)_{n \geq 0}$ of non-negative real numbers by $$\delta^X_n:=\inf \{d_{\mathrm{GH}}(X,G): G \text{ a finite metric graph, } \beta_1(G)\leq n \} .$$ By construction, and the above result, this is a non-increasing sequence with limit $0$. We study this sequence and its rates of decay with $n$. We also identify a precise relationship between the sequence and the first Vietoris-Rips persistence barcode of $X$. Furthermore, we specifically analyze $\delta_0^X$ and find upper and lower bounds based on hyperbolicity and other metric invariants. As a consequence of the tools we develop, our work also provides a Gromov-Hausdorff stability result for the Reeb construction on geodesic metric spaces with respect to the function given by distance to a reference point

Fullerene as Spin Converter

It has now been more than 30 years since buckminsterfullerene became a real thing. An exclusive field of study called fullerene chemistry arises and is discovered to be unique in many respects. In a very short time, a great deal of effort has been devoted on the fullerene chemistry and properties of fullerene derivatives. The fields of fullerene and light-induced processes considerably overlapped, and now numerous wonderful examples are on exhibition. The large number of these systems has been designed to take advantage of the electron-accepting property of fullerene and broadcasts the fullerenes as universal spin converter advertising its perfect intersystem crossing (ISC) quantum yield where a spin converter can be identified as a chromophore that undergoes efficient ISC with a low first excited state (S1), but does not necessarily strongly harvest visible light. Thus, donor-acceptor systems in the field of light-induced processes within multicomponent fullerene arrays have been proposed as models for optical limiters, owing to the singlet oxygen production efficiency of C60 and the C60 derivatives in the field of medicinal chemistry

Does the Turkish Education System Have an Educational Philosophy?

There is a widespread belief as regards our educational system, which is also evaluated as the "Human Raising System", that it lacks an educational philosophy. It is obvious that as education system without an educational philosophy cannot raise people suitable for the information society. Considering the people raised by the system, it would not be a very unfair to label the education system as without philosophy. The objective of this study is to try to look for an answer to the question "if the education system has a philosophy or not" by examining the issue within the context of the objective and principles of the Turkish education system. To this end, objective and principles of the system were examined and discussed in terms of educational philosophies with an eye to achieve the cited objective. Given the fact that the human type that raised by the system in general “does not question things, believes that all the things said by the rulers is true, makes everything ordered without any objection (approach of “I Close My Eyes and Do My Duty”) and obeys the authority by all means”, the opinion that the system is "without philosophy" emerges by itself. However, although the system actually owns a philosophy, beliefs as to what this philosophy are different than each other. Keywords: philosophy, educational philosophy, philosophy of the Turkish education system DOI: 10.7176/JEP/12-17-10 Publication date:June 30th 202

Free actions on product of spheres at high dimensions

Ankara : The Department of Mathematics and the Graduate School of Engineering and Science of Bilkent University, 2012.Thesis (Master's) -- Bilkent University, 2012.Includes bibliographical references.Okutan, Osman BeratM.S

TK1951: an anatomy of crisis communication

This study focuses on how Turkish Airlines (THY) managed its communication strategy after the unfortunate accident of TK 1951 on February 25, 2009 near Amsterdam Schiphol Airport. Evaluating the efforts in a framework, authors set out to discuss THY’s performance in four important areas classified in eight headings: coordination of the messages, acknowledging uncertainty and taking responsibility, reaching the stakeholders and making use of online media tools. Hopefully, the results of this research will help THY and other airline companies to improve and develop their immediate crisis response strategies

Kademelendirilmiş Köpük Malzemelerin Sandviç Kirişin Darbe Davranışına Etkisi

Konferans Bildirisi -- Teorik ve Uygulamalı Mekanik Türk Milli Komitesi, 2013Conference Paper -- Theoretical and Applied Mechanical Turkish National Committee, 2013Bu çalışmanın amacı, kademelendirilmiş köpük malzemeye sahip sandviç kirişlerin, düşük hızlı darbe etkisi altındaki cevabını ortaya koymaktır. Araştırmada kullanılan sandviç kirişin kabuk malzemesi olarak karbon/epoksi kompozit ve çekirdek malzemesi olarak üç farklı yoğunluktaki Divinycell köpük seçilmiştir. Üç katmanlı çekirdeğe sahip sandviç kirişlerde, altı farklı çekirdek katmanı sıralanışı incelenmiştir. Kiriş boyutları ve çekirdek kalınlıkları tüm yapılandırmalar için sabit tutulmuştur. Kademeli sandviç kirişin darbe cevabı, sonlu elemanlar analizi (FEA) kullanılarak modellenmiştir. Kademeli köpük çekirdeğin, sandviç kompozitin darbe davranışına etkisi, aynı darbe enerjisi altındaki iki uçtan ankastre sandviç kirişlerin yer değişimleri, Von Mises gerilmeleri ve temas kuvvetleri analizleri ile değerlendirilmiştir. Sonuçlar, tek tip köpüğün kullanıldığı sandviçlerde, artan köpük yoğunluğunun yer değişim ve temas kuvvetlerini azaltmasına rağmen, Von Mises gerilmelerini artırdığını ortaya koymuştur. Benzer sonuç yoğunluğun adım adım arttığı ya da azaldığı kademeli köpük içeren sandviç kompozitlerde de bulunmuştur. Bunlarda, darbenin geldiği üst yüzeydeki köpük yoğunluğu sandviç özelliğini belirleyici olmaktadır. Üst yüzeydeki köpüğün artan yoğunluğuyla yer değişimi azaltmakta ve Von Mises gerilmeleri artmaktadır. Kademelendirmelerdeki yoğunluk artış ya da azalışının düzenli olmadığı sandviçlerde ise yer değişimi ve Von Mises gerilmelerine dair genelleme yapmak zor olup, özellikler kademelerin sıralanışına bağlı olarak değişmektedir. Anahtar kelimeler: Sandviç kompozit, kademelendirilmiş köpük çekirdek, darbeThe purpose of this study is to determine the low-velocity impact response of sandwich beams with graded core. In this study, carbon/epoxy composite was choosen as skin material, and three Divinycell foams with different densities were choosen as core material. Six different core arrays of sandwich beams with three layered core material were investigated. Beam dimensions and core thicknesses were constant in all six different arrays. Impact response of sandwich beams with graded core was modelled using the finite element analysis. The influence of graded foam core on the impact behaviour of sandwich composites was evaluated by the analysis of the displacement, Von Mises stresses and contact forces for both end fixed sandwich beams under the same impact energy. Results show that on sandwiches with uniform core, although the increasing foam density reduces displacement and contact forces, it increases Von Mises stresses. Similar results were observed on sandwich composites with foam cores that have gradually increasing or decreasing density. On these sandwiches, the foam density of the top surface, where impact hits, determines the sandwich features. It is difficult to generalize for displacements or Von Mises stresses of sandwiches with irregular foam core array. The properties of the sandwich beams change depending on the arrays of grades. Keywords: Sandwich composite, graded foam core, impac