How to teach the Pythagorean theorem: An analysis of lesson plans

This research was conducted among mathematics graduates who participated in a pedagogical formation certificate program. Participants were asked to prepare a lesson plan intended for use in teaching the Pythagorean theorem as part of a ninth grade mathematics course. Eighteen out of 43 participants included a proof of the Pythagorean theorem as a component of their lesson plan. These proofs were classified in three categories: visual proofs (two participants), algebraic proofs (nine participants), and proofs by using triangular similarities (seven participants). In addition, the solved examples, homework, and evaluation questions included in the lesson plans were classified according to TIMSS cognitive levels. Of the 233 questions prepared by 43 participants, 37% of the questions were at the knowledge level, 60% were at the application level, and the remaining 3% were at the reasoning level

Dynamic Vehicle Routing for Data Gathering in Wireless Networks

We consider a dynamic vehicle routing problem in wireless networks where messages arriving randomly in time and space are collected by a mobile receiver (vehicle or a collector). The collector is responsible for receiving these messages via wireless communication by dynamically adjusting its position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the delay performance in such networks. We show that the necessary and sufficient condition for the stability of such a system (in the bounded average number of messages sense) is given by {\rho}<1 where {\rho} is the average system load. We derive fundamental lower bounds for the delay in the system and develop policies that are stable for all loads {\rho}<1 and that have asymptotically optimal delay scaling. Furthermore, we extend our analysis to the case of multiple collectors in the network. We show that the combination of mobility and wireless transmission results in a delay scaling of {\Theta}(1/(1- {\rho})) with the system load {\rho} that is a factor of {\Theta}(1/(1- {\rho})) smaller than the delay scaling in the corresponding system where the collector visits each message location.Comment: 19 pages, 7 figure

Dynamic Server Allocation over Time Varying Channels with Switchover Delay

We consider a dynamic server allocation problem over parallel queues with randomly varying connectivity and server switchover delay between the queues. At each time slot the server decides either to stay with the current queue or switch to another queue based on the current connectivity and the queue length information. Switchover delay occurs in many telecommunications applications and is a new modeling component of this problem that has not been previously addressed. We show that the simultaneous presence of randomly varying connectivity and switchover delay changes the system stability region and the structure of optimal policies. In the first part of the paper, we consider a system of two parallel queues, and develop a novel approach to explicitly characterize the stability region of the system using state-action frequencies which are stationary solutions to a Markov Decision Process (MDP) formulation. We then develop a frame-based dynamic control (FBDC) policy, based on the state-action frequencies, and show that it is throughput-optimal asymptotically in the frame length. The FBDC policy is applicable to a broad class of network control systems and provides a new framework for developing throughput-optimal network control policies using state-action frequencies. Furthermore, we develop simple Myopic policies that provably achieve more than 90% of the stability region. In the second part of the paper, we extend our results to systems with an arbitrary but finite number of queues.Comment: 38 Pages, 18 figures. arXiv admin note: substantial text overlap with arXiv:1008.234

On the Quality of FFO Forecasts

This paper is the first attempt to provide an objective assessment of the quality of real estate funds from operations (FFO) forecasts. The work, which looks past the more primitive question concerning the appropriate measure for real estate earnings, quantifies and tests the quality of real estate investment trust (REIT) FFO forecasts relative to the net income forecasts of several comparison groups. The results show the high quality of REIT forecasts are remarkably robust and are not driven by the level of analyst attention. Investors in a post-Enron and Sarbanes-Oxley era may find the implications for high quality forecasts of real estate earning to be an appealing investment concept.

Topkapı Sarayı Müzesi ve ben

Taha Toros Arşivi, Dosya No: 120-Saraylarİstanbul Kalkınma Ajansı (TR10/14/YEN/0033) İstanbul Development Agency (TR10/14/YEN/0033

Financial Expertise of Directors

The composition and functioning of corporate boards is at the core of the academic and policy debate on optimal corporate governance. But does board composition matter for corporate decisions? In this paper, we analyze the role of financial experts on boards. In a novel panel data set on board composition, we find that financial experts significantly affect corporate decisions, though not necessarily in the interest of shareholders. First, when commercial bankers join boards, external funding increases and investment-cash flow sensitivity diminishes. But, the increased financing affects mostly firms with good credit and poor investment opportunities. Second, investment bankers on the board are associated with larger bond issues, but also worse acquisitions. Third, we find little evidence that financial expertise matters for compensation policy or for experts without affiliation to a financial institution. The results suggest a tradeoff between outside incentives (e.g. bank profits) and the incentive to maximize firm value. Requiring financial expertise on boards, as mandated by regulatory proposals, may not benefit shareholders if conflicting interests are neglected.

Emine Yılmaz, Narspi-Metin, Yazıçevrimi, Türkçe Çeviri, Sözlük-Dizin

[No Abstract Available

Reaction of central banks to federal reserve at zero lower bound

Bu çalışma; merkez bankalarının tepki fonksiyonlarında federal reserve e ne ağırlıkta yer verdiklerinin ve bu tepkinin 2008 finansal kriziyle ne ölçüde değiştiğini tespit etmeyi amaıyla 25 farklı ekonomi üzerinde yürütülmüştür.Federal funds rate in bağımsız değişken olarak eklendiği model 2000-2007 ve 2008-2014 dönemleri için ayrı ayrı sıradan en küçük karaler ekonometrik metoduyla test edilmiştir. Ampirik bulgulara göre ülkerin çoğu , dünyanın en büyük ekonomilerinin başında gelen ABD ekonomisine verilen tepki %5 anlamlılık düzeyinde istatistiki olarak anlamlı çıkmıştır. Ancak bu tepki kriz sonrası dönemde birçok ülke için devam etmekle beraber; ülke ülke incelediğinde her biri için önemli ölçüde değişikliğe uğramıştır. Ayrıca çalışmada; hem literatürden farklılaştırmak hem de sonuçları farklı bi yöntemle teyit etmek için zamanla değişen regression yöntemi de kullanılmıştır.Elde edilen sonuçlarla ilk bulgularla sağlamlaştırılmıştır. Anahtar Kelimeler: Para Politikası,Taylor Kuralı, Zamanla Değişen Regresyen, Sıfır Alt ÇizgisiThis study has been carried out on 25 different economies so as to determine how much central banks give place to federal reserve in reaction functions and to what extent this reaction changed with the effect of the financial crisis of 2008. The model to which federal funds rate was added as an independent variable was tested with OLS econometric method separately for 2000-2007 and 2008-2014 periods. According to the empirical evidence, the reaction of most of the countries to the US economy, which is the leading country of the world's biggest economies, turned out to be statistically 5% significant at the level of significance. However, together with this reaction's continuation for many countries after the crisis, it changed dramatically for each country when examined country-by-country. In addition, time varying regression method was used in this study so as to both differentiate it from literature and also to confirm the results with a different method. First findings were accordingly strengthened with the obtained results. Keywords: Monetary Policy, Taylor Rule, Time Varying Regression, Zero Lower Boun

The power of sharing knowledge

Electrical utilities all around the world face important challenges in asset management of rapidly ageing networks. Ageing power transformer fleets represent a particularly significant issue for network reliability. The COVID-19 pandemic reminded us again that having reliable condition assessment metrics and prioritisation models for lifecycle decisions are more important than ever