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In this paper, we obtain the solution of the two-body problem with variable masses by posing some assumptions on the classical equation and thereby reducing the solution of the problem to investigating the solutions of some Ricatti type differential equations. Along this process, we also give a simple proof of the well-known Mestscherskii Theorem and establish some related formal relations under these assumptions.

This article investigates the use of the history of mathematics as a pedagogical tool for the teaching and learning of mathematics, using the history of the cubic equation as a specific example.Cubic equations arise intrinsically in many applications in natural sciences and mathematics. For example, in physics, the solutions of the equations of state in thermodynamics, or the computation of the speed of seismic Rayleigh waves require the solutions of cubic equations. In mathematics, they are instrumental in solving the quartic equations, for in the process, these are reduced to cubic equations. The impossibility of trisecting an angle or doubling a cube using only a straightedge and compass is equivalent to solving some cubic equations. As the name implies, the cubic spline approximation, an important tool in numerical analysis, also entails working with cubic functions. Although cubic equations were explored by the ancient Babylonian, Greek, Chinese, Indian, and Egyptian scholars, it took the collective work of many well-known mathematicians such as Diophantus, Archimedes, Fibonacci, del Ferro, Khayyam, Tartaglia, Cardano, Viète, Descartes, and Lagrange to finally obtain a full solution. Our goal in this paper is to investigate one of the most formidable steps in this extensive and prolific history, namely the complete classification of the cubic equations by Omar Khayyam in eleventh century, who was the first scholar to classify cubic equation and hence facilitate a methodical and logical approach to obtaining a general solution.

In this paper, we will deal with the problem of calculating the average velocity of a celestial object revolving around another celestial object in an elliptical orbit. After proving our main theorem to this effect, we will give some alternate forms of the formula for the average velocity, and show that this average value is in fact, attained at certain points of the orbit. We will conclude the paper by providing an intuitively natural and straightforward amendment of this formula.

Of all the arguments directed against presenting mathematical topics within a cultural and historical context, the most serious ones are those that we will refer to as the time and the content arguments. In this paper, after briefly describing these stances, we will endeavor to evaluate and refute their rationales using a social constructivist line of reasoning. To this end, we will first discuss the basic tenets of radical and social constructivism and then, through some simple concrete examples, show how social constructivism organically heralds the pedagogical methodology that imparts mathematical concepts in conjunction with their historical and cultural contexts.

Bronchopulmonary dysplasia (BPD) is a condition of neonatal chronic lung disease due to disruption or dysregulation of pulmonary development. However, the pathophysiology of BPD in the larger conducting airways is not yet fully understood. The objective of our study was to determine if the area of the central airways are altered in patients with a history of BPD. We hypothesized that compared to age- and sex-matched controls, BPD patients would have decreased area of the central conducting airways. Twenty-two BPD patients (n = 10 male, n = 12 female; median age = 10 [range:1–49] yrs) and n = 22 matched controls (n = 10 male, n = 12 female; median age = 10 [range:1–48] yrs) who had undergone a chest computed tomography (CT) scan were retrospectively identified. Measurement and analysis was performed using software that reconstructs the airways into 3D. Measurements of airway area were conducted at three points based on anatomic bifurcations for each of the following structures: trachea, left main bronchus, left upper lobe, left lower lobe, right main bronchus, intermediate bronchus, and right upper lobe. The luminal area for each airway was calculated based on the averages of the three measures. Airway luminal area was not different between BPD patients and matched controls for any of the measured airways (p > 0.05). Total lung volume detected in the CT scans was not different between BPD patients and matched controls (median [range]; 2775 [522–6215] vs 2969 [851–5612] cm3, p > 0.05). Our results suggest the luminal areas of the large conducting airways in patients with BPD are not different from matched controls.

Yaklaşık kırk yıldır yeni ve farklı bir sosyal bilimler yöntemiymiş gibi karşımızda duran bellek çalışmaları, belli bir hatırlama nosyonundan hareketle yürütülmeye çalışılmaktadır. Bireyin ve/veya kurumun hafızasında taşıdığı her şey paralel bir bellek sorunu olarak ele alınmaktadır. Sosyal bilimlerde “bellek” kavramının oluşumuna zemin hazırlayan süreç belirsiz gibi görünmektedir; bunda muhakkak bellek alanını herkesin kendi beklentisine göre doldurması önemli bir rol oynamaktadır. Bir çalışma şekli olarak ele alınırsa bellek "türleri" (bireysel/kişisel ve kolektif bellek), esasen “hatırlama” biçimlerinden hareketle geliştirilmiştir. “Batı” düşünce geleneğinin hatırlama biçimlerini ele alışları, “geçmiş” düşüncesinin birçok farklı unsur ve bağlamın zaman anlayışına dayanmasından hareket eder. Edebiyat ile ilgili geçmiş, hatırlama ve bellek okumaları da Batı düşünce geleneğinin geldiği son noktadan hareketle yapılmaktadır. Bellek sorununda belleği bireysel bağlamda ele alan Bergson; kolektif bağlamda ele alan Halbwachs, sosyal bağlamda ele alan Burke, kültürel bağlamda ele alan Assmann’ın çalışmaları paralelinde sosyal bilimlerde geniş bir bakış açısının da kazanması gereken mekanizmalar alt metinde irdelenmiş olacaktır. Memory studies existing as if it was a new and different method of social sciences and literature since approximately forty years is tried to be undertaken by a certain notion of remembrance. All the storage of the individuals and/or institutions are considered as a parallel memory problem. In the social sciences the process to the formation of the conception “memory" seems to be uncertain. The past, history and memory readings about Turkic World moves also from the point of Western thought. In this article, in addition to the contents of notions of remembering, it will be discussed whether all forms of remembrance can be evaluated as a matter of memory. The differences of the view of past constituting the concept of memory from the knowledge and idea of individual past will be revealed. There will be an overall argument about different kinds of memory types that are developed individually-collectively and culturally. The term memory discussed in the light of two basic theories, both individual and collective; and discussed in the context of past. It has been found that the individual memory theory has an influence on the understanding of individual or personally perceived experiences over time, and the collective memory has an effect on the social perception of the experiments. On memory problem Bergson’s addressing individual context; Halbwachs’s addressing the collective context, Burke’s the social context, Assmann’s cultural context will be discussed. These mechanisms or contexts also will be elaborate in line the sub-text as the folkloric perspective.

The Pascal matrix and the Fibonacci matrix are among the most well-known and the most widely-used tools in elementary algebra. In this paper, after a brief introduction where we give the basic definitions and the historical backgrounds of these concepts, we propose an algorithm that will generate the elements of these matrices. In fact, we will show that the indicated algorithm can be used to construct the elements of any power series matrix generated by any polynomial (see Definition 1), and hence, it is a generalization of the specific algorithms that give us the Pascal and the Fibonacci matrices.

Introduction and Aims. Information on high-risk drug use in Turkey, particularly at the regional level, is lacking. The present analysis aims at estimating high-risk cannabis use (HRCU) and high-risk opiate use (HROU) in the cities of Ankara, Istanbul and Izmir. Design and Methods. Capture-recapture and multiplier methods were applied based on treatment and police data stratified by age and gender in the years 2009 and 2010. Case definitions refer to ICD-10 cannabis (F.12) and opiate (F.11) disorder diagnoses from outpatient and inpatient treatment records and illegal possession of these drugs as recorded by the police. Results. High-risk cannabis use was estimated at 28 500 (8.5 per 1000; 95% confidence interval 7.3-10.3) and 33 400 (11.9 per 1000; 95% confidence interval 10.7-13.5) in Ankara and Izmir, respectively. Using multipliers based on capture-recapture estimates for Izmir, HRCU in Istanbul was estimated up to 166 000 (18.0 per 1000; range: 2.8-18.0). Capture-recapture estimates of HROU resulted in 4800 (1.4 per 1000; 95% confidence interval 0.9-1.9) in Ankara and multipliers based on these gave estimates up to 20 000 (2.2 per 1000; range: 0.9-2.2) in Istanbul. HROU in Izmir was not estimated due to the low absolute numbers of opiate users. Discussion and Conclusions. While HRCU prevalence in both Ankara and Izmir was considerably lower in comparison to an estimate for Berlin, the rate for Istanbul was only slightly lower. Compared with the majority of European cities, HROU in these three Turkish cities may be considered rather low.

Bu makale 1970’lerde Diyarbakır’ın kültür ve tarihine duyduğum ilginin mahsulüdür. Diyarbakır şehri sadece surları ile değil, cami, mescid, han, hamam ve çeşmeleri ile açık bir müze olarak nitelendirilebilir. Diyarbakır’ın suyollarını ve çeşmelerini ele aldığım bu makalede konuya bir bütünlük sağlamak açısından Osmanlı suyollarının idaresi hakkında kısa bir girişe yer verdim. Makalenin sonuna eklenen çizelge, liste ve fotoğraflar kanımca terör sonrası Diyarbakır’ın mahalle ve sokaklarında tahribatın ne kadar vahim olduğunu kısmen de olsa gözler önüne serecektir. This article reflects my interest and attachment to the history and culture of Diyarbakır. Diyarbakır is an open museum not only with its five kilometres long walls that surround the city, but also with its mosques, hans, hamams and fountains mostly attached to the walls of houses and mosques. This article, therefore, is an outcome of this interest and attachments. This article is a study of the water conduits and the fountains of Diyarbakır based on my notes and photographs taken during my visits to the city in 1970s and 1990s. Detailed information on Diyarbakır’s water conduits and fountains as well as the table and list of the fountains and also the photographs in the appendices may reflect the damage caused to the city’s culture and monuments following the recent terror attacks.

URL: http://sutad.selcuk.edu.tr/sutad/article/view/989, Ahmet Hamdi Tanpınar, Osmanlı Devleti’nin son, Cumhuriyet’in ilk dönemi arasında, kültürel ve siyasi değişim dinamiklerinin ortasında yaşamış özel bir sanatçı ve düşünürdür. Sadece bir yazar ya da öğretim elemanı olarak adlandırılamayacak kadar özel biridir. Anlatısının derinliğini ve zenginliğini kültürel belleğin tüm mekanizmaları ve imkânları ile tesis etmiştir. Bunu hikâye kurgulamanın imkânlarından çok dilde aramış ve başarmıştır. Hatırlama mekanizmalarını halkbilimsel anlamdaki dil ve kültür varlığından (mitik düşünce, gelenek vb.) bir düş işçiliğine doğru yetkin bir şekilde evirmeyi başarmıştır. Bu çalışmanın birinci bölümünde hatırlamadan hayale doğru bir sürek içerisinde Tanpınar estetiğini oluşturan temel damarlardan bahsedilecektir. Bunun içinde romanlarını ve hikâyelerini hatta makalelerini bile inşa eden şiir düşüncesi üzerinde özellikle durulacaktır. Keza onun estetiğinde romanını, hikâyesini ve felsefesini kuşatan en temel bazen de yegâne unsur şiirdir. İkinci bölümde Ahmet Hamdi Tanpınar’ın estetik zihin dünyasının ve belleğinin temellerini oluşturan sözlü kültür kaynaklarının birkaçından bahsedilecektir. Bu sözlü kültür kaynaklarıyla Tanpınar’ın kurmuş olduğu ilişki üzerinde durulacaktır. Bu bağlamda özellikle büyükannesi ve ‚meşk hafızası‛nın önemine değinilecektir., Ahmet Hamdi Tanpınar is a special artist and an intellectual lived in changing cultural and political dynamics in the last period of Ottoman Empire, first period of Republic of Turkey. He cannot be named only as a writer or instructor. He has founded the profound and wealth of his narration with all the mechanisms and possibilities of cultural memory. He searched and achieved with the possibilities of language over fiction possibilities. He carried out to invert language and cultural existence (in folkloric definition as mythic thought, tradition etc.) to a dream workmanship. In the first part of this work, the core of Tanpınar’s aesthetics will be mentioned in duration from reminiscence to imagination. This core will be dwelling on his poetics that build his novels, stories even articles. Because poetry is most basic sometimes the only aesthetic core/sense of his novels, stories and philosophy. In the second part of this work Tanpınar’s world of aesthetic mind and the sources of his memory will be mentioned with a few of sources of orality. The relationship between this oral culture sources and Tanpınar’s founding will be emphasized. In this context, especially his grandmother and ‚affair memory‛ will be important.

In this paper our main objective is to interpret the major concepts in Wittgenstein’s philosophy of mathematics, in particular, language games and forms of life, from a social constructivist point of view in an attempt to show that this philosophy is still very relevant in the way mathematics is being taught and practiced today. We start out with a brief discussion of radical constructivism followed by a rudimentary analysis of the basic tenets of social constructivism, the final blow against absolutism – the soulless landmark of mathematics as often construed by the uninitiated. We observe that, the social constructivist epistemology of mathematics reinstates mathematics, and rightfully so, as “…a branch of knowledge which is indissolubly connected with other knowledge, through the web of language” (Ernest 1999), and portrays mathematical knowledge as a process that should be considered in conjunction with its historical origins and within a social context. Consequently, like any other form of knowledge based on human opinion or judgment, mathematical knowledge has the possibility of losing its truth or necessity, as well. In the third section we discuss the main points expounded in Wittgenstein’s two books, Tractatus Logico-Philosophicus and Philosophical Investigations, as well as in his “middle period” that is characterized by such works as Philosophical Remarks, Philosophical Grammar, and Remarks on the Foundations of Mathematics. We then briefly introduce the two main concepts in Wittgenstein’s philosophy that will be used in this paper: forms of life and language games. In the fifth and final section, we emphasize the connections between social constructivism and Wittgenstein’s philosophy of mathematics. Indeed, we argue that the apparent certainty and objectivity of mathematical knowledge, to paraphrase Ernest (Ernest 1998), rest on natural language. Moreover, mathematical symbolism is a refinement and extension of written language: the rules of logic which permeate the use of natural language afford the foundation upon which the objectivity of mathematics rests. Mathematical truths arise from the definitional truths of natural language, and are acquired by social interaction. Mathematical certainty rests on socially accepted rules of discourse embedded in our forms of life, a concept introduced by Wittgenstein (Wittgenstein, 1956).We argue that the social constructivist epistemology draws on Wittgenstein’s (1956) account of mathematical certainty as based on linguistic rules of use and forms of life, and Lakatos’ (1976) account of the social negotiation of mathematical concepts, results, and theories.

Digital roots of numbers have several interesting properties, most of which are well-known. In this paper, our goal is to prove some lesser known results concerning the digital roots of powers of numbers in an arithmetic progression. We will also state some theorems concerning the digital roots of Fermat numbers and star numbers. We will conclude our paper by an interesting application.

In this paper we will extend the well-known chain of inequalities involving the Pythagorean means, namely the harmonic, geometric, and arithmetic means to the more refined chain of inequalities by including the logarithmic and identric means using nothing more than basic calculus. Of course, these results are all well-known and several proofs of them and their generalizations have been given. See [1-6] for more information. Our goal here is to present a unified approach and give the proofs as corollaries of one basic theorem.

I would like to thank the following for the help they have extended to me in writing this. Zülfiye Çakıroğlu, one of my undergraduate students from Middle East Technical University, provided the photographs in the academic year 1999-2000. Her effort to get the information regarding the Jews of Akhisar locally was unfortunately fruitless. I am also grateful to several other scholars who made the translation of the inscriptions for me at the time; Dr. Faruk Toprak of Ankara University, Dr. David Grossman of Bar-Ilan University and Tal Fishman of Middle East Technical University. The latter two are also credited for their valuable suggestions. In the town of Akhisar, a Western Anatolian town, there lie some tombstones with inscriptions in Hebrew on them. It is clear that the place was once a Jewish cemetery. The place no longer looks like a cemetery for it is not only surrounded with buildings, but the land is ploughed for cultivation. Lately the cemetery had been taken into an enclosure and the tombstones have been aligned at certain intervals and the field has been patched with grass. The tombs can no longer be identified. There are twenty-six tombstones lying on the ground here and there. The number of tombstones is not enough so as to claim whether more than one person is buried in one tomb or to draw out family ties. In any case I observed that the field is big enough to encompass twenty-six tombstones. They all belong to the Ottoman period dating from 1884 to 1918. Today there is no longer a Jewish community in this town. The Jews in almost none of the Anatolian towns have been in majority and therefore it is difficult to say whether they ever had a lack of space for burial ground.

Objective: The aim was to investigate the prevalenceof hypertension in Van.Method: A total of 2010 subjects (586 male, mean age:44.8 ± 14.9; 1424 female, mean age: 39.1 ± 14.1) betweenthe ages of 20-74, were sampled from a targetpopulation of 315,866 according to systematicsampling technique. Blood pressure of each participantwas measured by using ErkaÆ sphygmomanometer fortwo times with a 3 minutes interval by a physician andan average was obtained.Results: Hypertension prevalence was 34.9 % (males:33.3 %, females: 35.5 %, p> 0.05) according to 140/90mmHg criterium and 19.1 % (males: 14.5 %, females:21.0 %, p < 0.001) according to 160/95 mmHg criterium.Mean systolic and diastolic blood pressures were129.97± 27.78 mmHg (95% CI:128.7, 131.2)(males:128.20 ± 24.30 (95 % CI: 126.2, 130.2), females:130.70 ± 29.10 (95 % CI: 129.2, 132.2), p = 0.013) and81.95 ± 14.24 mmHg (95 % CI: 81.3, 82.6) males: 81.10 ±13.0 (95 % CI: 80.0, 82.2), females: 82.30 ± 14.70 (95 %CI: 81.5, 83.1), p = 0.07), respectively.Conclusion: In Van, hypertension is a serious healthproblem and efficient public health measures andeducation programs are needed.Key words: Turkey, Van, hypertension, prevalence,epidemiology

the Archives that have survived intact to our day is a good indication that the Ottomans had an excellent system of administration established in almost all their government offices. It is well known that Mehmed II had established the Su Nezareti, the Department of Water, under the Director of Waterworks that was responsible for the administration of water issues. However, this does not mean that the Ottomans, who had inherited the Byzantine and Seljuqid lands along with their water conduits and aqueducts as well as some of their administration, did not have an administrative office to solve the water problems. In this article, based on the documents from Ottoman archives, I will concentrate on Ottoman system of administering and managing water conduits as well as the procedures followed in supplying water to the towns and cities. There is no doubt carrying water from springs and dams by way of water conduits and aqueducts into reservoirs and from there to the water tanks (maslak), chambers (maksem) and balances (su terazileri) from where the water is distributed to the mosques, medreses, hans, public baths, fountains and houses is a considerable task that can only be achieved through a well established administration. The Ottomans, as part of this system, built new water conduits and aqueducts as well as maintaining the old ones. The Department of Water, besides being responsible from inspecting and supervising such tasks as these, supplied men and material as well as found money, and insured that everything ran smoothly. It is a fact, based on the documents, that the Ottomans had the water conduits and aqueducts guarded, brought to justice those who were responsible for damage, made sure the water was distributed to the public equally, and had the waters analyzed regularly to ensure that it was hygienic and suitable for drinking, Osmanlı’nın modern bir devlete yakışır şekilde her konuda idari bir sistem geliştirdikleri günümüze kadar ulaşan son derece düzenli bir arşivin mevcudiyetinde kendini göstermektedir. Fatih Sultan Mehmed’in su yollarının sevk ve idaresi için Su Nezareti kurduğu bilinmektedir. Ancak Roma, Bizans ve Selçuklu döneminden kalma su yollarını ve şebekelerini kullanmaya devam eden ve yenilerini inşa eden Osmanlı’nın, Fatih Dönemi öncesinde de oturmuş bir yönetim sisteminden yoksun olduğu söylenemez. Bizans ve Selçuklu topraklarını devr alan Osmanlı’nın, devamlılık sürecinin kaçınılmaz bir gereği olarak, sabık yönetim sistemlerini de ne derece devr aldığı ve geliştirdiği çok geniş kapsamlı bir tartışmanın konusu olduğundan makalemizin dışında tutulmuştur. Arşiv kaynaklarına dayanan bu makalemizde bizim için önemli olan Osmanlı’nın su yolarını sevk ve idarede izledikleri yöntem, şehir ve kasabalarda halkın su ihtiyacını karşılamak için aldıkları önlemlerdir. Kilometrelerce uzaktaki suyun doğal kaynak ve barajlardan künkler ve su kemerleri yardımıyla havuzlara ve oradan sırasıyla maslak, maksem ve su terazilerine ulaştırılması ve akabinde şehir ve kasabalardaki sayısız cami, medrese, han, hamam, sebil, çeşme ve evlere tevzii şüphesiz oturmuş ve düzenli bir yönetim sistemi ile ancak gerçekleşebilirdi. Bu sistem çerçevesinde yeni su yollarının inşası veya eskilerinin tamiri için Su Nezareti’nce ve daha sonra ondokuzuncu yüzyılda oluşturulması üzerine Şehremaneti’nce bir keşif yapılır, gerekli insan gücü, para ve malzeme temin edilir ve işin bitiminde de varsa yolsuzlukları ve eksiklikleri ortaya çıkarmak için bir ikinci keşif daha yapılırdı. Osmanlı’nın su yollarını koruma altına aldığı, tahribata sebep olanları cezalandırdığı, suyun tevziinde adil davrandığı ve halkın sağlığını korumak için zaman zaman suyun tahlilini yaptırdığı Arşiv dokümanlarından anlaşılmaktadır