Matematik Öğretmenlerinin Kümeler Konusunda Temel Kavramlara İlişkin Uzmanlık Alan Bilgilerinin İncelenmesi

This research was carried out in order to examine the specialized content knowledge of mathematics teachers related to teaching basic concepts about sets within the MKT Model. In this study, a holistic single-case study design is used in qualitative research methods. The study group consists of 18 mathematics teachers at different educational background and professional experience in teaching sets selected through the sampling of criterion, which is working in different high schools in one province in the Mediterranean region in the academic year 2016-2017. Research data were obtained using semi-structured interview, observation and document analysis techniques. In the analysis of obtained data, descriptive analysis, content analysis, continuous comparison techniques and special data analysis methods were used together with each data collection tool. The findings of the research show that teachers gave correct answers to the questions asked about the basic concepts of "Why?" in the sets. However, it is clear that the teachers cannot write sufficient reason why the asked questions are "Why?". As a result of the research, it has been determined that the teachers have superficial knowledge about the concepts of "Set, Universal Set, Infinite Set" and "Equal Set". However, it was determined that teachers made explanations with a general mathematical knowledge based on the characteristics of the concept rather than providing persuasive mathematical explanations to the questions asked.Bu araştırmanın amacı kümelerde temel kavramların öğretimine ilişkin matematik öğretmenlerinin “Öğretim için Matematik Bilgisi” (ÖMB) modeli kapsamında uzmanlık alan bilgilerini incelemektir. Araştırmada nitel araştırma yöntemlerinden bütüncül tek durum çalışması deseni kullanılmıştır. Araştırmanın çalışma grubu, 2016-2017 eğitim öğretim yılında Akdeniz Bölgesi’nde bir ilimizdeki farklı liselerden ölçüt örnekleme yoluyla seçilen farklı öğrenim durumuna, mesleki deneyime ve kümeler konusunu öğretim tecrübesine sahip 18 matematik öğretmeninden oluşmaktadır. Araştırma verileri yarı-yapılandırılmış görüşme, gözlem ve doküman analizi teknikleri kullanılarak elde edilmiştir. Elde edilen verilerin çözümlenmesinde betimsel analiz, içerik analizi, sürekli karşılaştırma teknikleri ile her bir veri toplama aracına özel veri analiz yöntemleri birlikte kullanılmıştır. Araştırma bulgularında öğretmenlerin kendilerine yöneltilen sorulara yazdıkları gerekçelerin daha çok “kısmen doğru açıklama” ve “yanlış açıklama” şeklinde sınıflandırıldığı belirlenmiştir. Araştırma sonucunda öğretmenlerin “Küme, Evrensel Küme, Sonsuz Küme” ve “Eşit Küme” kavramlarına yönelik yüzeysel bilgilere sahip oldukları tespit edilmiştir. Bununla birlikte öğretmenlerin yöneltilen sorulara tatmin edici matematiksel açıklamalar getirmekten ziyade kavramın özelliklerinden hareketle genel bir matematik bilgisi ile açıklamalar yaptıkları da belirlenmiştir

A Solution Algorithm for Interval Transportation Problems via Time-Cost Tradeoff

In this paper, an algorithm for solving interval time-cost tradeoff transportation problemsis presented. In this problem, all the demands are defined as intervalto determine more realistic duration and cost. Mathematical methods can be used to convert the time-cost tradeoff problems to linear programming, integer programming, dynamic programming, goal programming or multi-objective linear programming problems for determining the optimum duration and cost. Using this approach, the algorithm is developed converting interval time-cost tradeoff transportation problem to the linear programming problem by taking into consideration of decision maker (DM)

(R1964) Solving Multi-Objective Linear Fractional Programming Problems via Zero-Sum Game

This study presents a hybrid algorithm consisting of game theory and the first order Taylor series approach to find compromise solutions to multi-objective linear fractional programming (MOLFP) problems. The proposed algorithm consists of three phases including different techniques: in the first phase, the optimal solution to each LFP problem is found using the simplex method; in the second phase, a zero-sum game is solved to determine the weights of the objective functions via the ratio matrix obtained from a payoff matrix; in the last phase, fractional objective functions of the MOLFP problem are linearized using the 1st order Taylor series. A compromise solution is found by solving the single-objective LP problem constructed in the third phase by using the weights. This algorithm can provide compromise solutions to the problem by constructing different ratio matrices in the second phase. The novelty of this study is that the decision-makers can choose the most suitable solution for their strategy among the compromise solutions. Numerical examples are provided to illustrate the efficiency of the algorithm

A New Successive Linearization Approach for Solving Nonlinear Programming Problems

In this paper, we focused on general nonlinear programming (NLP) problems having m nonlinear (or linear) algebraic inequality (or equality or mixed) constraints with a nonlinear (or linear) algebraic objective function in n variables. We proposed a new two-phase-successive linearization approach for solving NLP problems. Aim of this proposed approach is to find a solution of the NLP problem, based on optimal solution of linear programming (LP) problems, satisfying the nonlinear constraints oversensitively. This approach leads to novel methods. Numerical examples are given to illustrate the approach

COVID-19 and urology: A bibliometric analysis of the literature

Aim The aims of this research were to analyse the urological literature published during the COVID-19 pandemic and to guide future research. Material and methods Between 2019 and 2021, the Web of Science (WoS) All Databases collection was searched for publications related to COVID-19 and Urology. The keywords used during this search were coronavirus-19, COVID-19, SARS-CoV-2, novel coronavirus, 2019-nCoV, pandemic and/or urology. The top 50 cited (T50) publications were also identified and summarized. Exported Microsoft Excel files, Visualization of Similarities viewer (VOSviewer) software and descriptive assessment were used for bibliometric and statistical analyses of the publications. Results In total, 582 publications related to COVID-19 and urology were identified. In these publications, the most active author, journal, country and organisation were Francesco Porpiglia, European Urology, the United States of America (USA) and La Paz University Hospital, respectively. The most commonly used keywords were telemedicine-telehealth, SARS-CoV-2, coronavirus, pandemic, residency, testicle, semen, kidney transplantation, endourology and surgery. The most worrying issues in the articles are the negative impact of COVID-19 on resident training and permanent damage to urological organs. Conclusions We analysed all the articles related to COVID-19 and urology published to date in the WoS All Databases collection. The most commonly published articles were based on clinical and outpatient practice, telemedicine, residency training, transplantation, and testicles. The long-term adverse effects of the pandemic on urology practice and especially urological organs will need to be assessed further in future research

3-[(E)-(4-Ethyl­phen­yl)imino­meth­yl]benzene-1,2-diol

The title compound, C15H15NO2, adopts the enol–imine tautomeric form. The dihedral angle between the two benzene rings is 48.1 (1)°. Intra­molecular O—H⋯N and O—H⋯O hydrogen bonds generate S(6) and S(5) ring motifs, respectively. In the crystal, mol­ecules are linked into centrosymmetric R 2 2(10) dimers via pairs of O—H⋯O hydrogen bonds and the dimers may interact through very weak by π–π inter­actions [centroid–centroid distance = 4.150 (1) Å]. The ethyl group is disordered over two orientations, with occupancies of 0.587 (11) and 0.413 (11)

(E)-3-[(4-Butyl­phen­yl)imino­meth­yl]benzene-1,2-diol

The title compound, C17H19NO2, exists as an enol–imine tautomer. The dihedral angle between the two benzene rings is 4.6 (2)°. The mol­ecular structure is stabilized by intramol­ecular O—H⋯O and O—H⋯N hydrogen bonds which generate S(5) and S(6) ring motifs, respectively. In the crystal, mol­ecules are linked into centrosymmetric dimers by pairs of O—H⋯O hydrogen bonds. In addition, C—H⋯π inter­actions involving both benzene rings are observed

(E)-4-Meth­oxy-2-[3-(trifluoro­meth­yl)phenyl­imino­meth­yl]phenol

The title compound, C15H12F3NO2, adopts the phenol–imine tautomeric form, with the H atom attached to oxygen rather than to nitro­gen. There are two independent mol­ecules aligned nearly parallel in the asymmetric unit with their trifloramethyl groups pointing in opposite directions. The dihedral angles between the aromatic rings are 40.43 (1)° in the first mol­ecule and 36.12 (1)° in the second. Strong intra­molecular O—H⋯N hydrogen bonding generates S(6) ring motifs. Weak inter­molecular C—H⋯O hydrogen bonds link the independent mol­ecules separately into sheets normal to [010]. In addition, C—H⋯π inter­actions are also observed. The F atoms of the trifluoro­methyl groups are disordered over two sets of sites with refined site occupancies of 0.59 (2)/0.41 (2) and 0.62 (3)/0.38 (3), respectively

(E)-4-Meth­oxy-2-(o-tolyl­imino­meth­yl)phenol

In the mol­ecule of the title compound, C15H15NO2, the aromatic rings are oriented at a dihedral angle of 15.46 (6)°. An intra­molecular O—H⋯N hydrogen bond results in the formation of a nearly planar six-membered ring [maximum deviation of 0.035 (5) Å for the N atom] which is almost coplanar with the adjacent ring, making a dihedral angle of 0.8 (3)°. The title organic mol­ecule is a phenol–imine tautomer, as evidenced by the C—O, C—N and C—C bond lengths. Mol­ecules are linked by inter­molecular C—H⋯O hydrogen bonds that generate a C(5) chain. C—H⋯π and π–π inter­actions exist in the structure. The π–π inter­action occurs between the phenol ring and its symmetry equivalent at (1 − x, 1 − y, −z), with a centroid–centroid distance of 3.727 (7) Å and a plane-to-plane separation of 3.383 (5) Å, resulting in an offset angle of 24.82 (1)°