40 research outputs found
Ruled Surfaces According to Bishop Frame in the Euclidean 3-Space
No full textAttempts have been made to introduce ruled surfaces generated from any vector X, Bishop Darboux vector and Bishop vectors. Some properties with respect to developable and minimal and the relations between the integral invariants of these surfaces are discussed. Also the fundamental forms, geodesic curvatures, normal curvatures and geodesic torsions are calculated, and some results are obtained
Mannheim B-Curves in the Euclidean 3-Space E-3
No full textIn 1878, Mannheim defined the notion of a Mannheim pair of curves and in 2008 Liu and Wang gave the necessary and sufficient condition for the Mannheim curves using the Frenet frame as a key ingredient. In this article we consider Bishop frame and introduce Mannheim B-pair in the Euclidean 3-space E-3. Then a thorough examination of the relationships between curvatures of a Mannheim B-pair is given. As the results of this examination, the relations between the Bishop vectors and Frenet vectors of these curves are found. Besides the relation between the Bishop curvatures of the Mannheim B-curves is obtained as k(2)* = k(1)/1 + lambda k(1)
A Study on Dual Hyperbolic Fibonacci and Lucas Numbers
No full textIn this study, the dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers are introduced. Then, the fundamental identities are proven for these numbers. Additionally, we give the identities regarding negadual-hyperbolic Fibonacci and negadual-hyperbolic Lucas numbers. Finally, Binet formulas, D'Ocagne, Catalan and Cassini identities are obtained for dual-hyperbolic Fibonacci and dual-hyperbolic Lucas numbers
Frenet Apparatus of the Curves and Some Special Curves in the Euclidean 5-Space E-5
No full textIn this study, initially the geometric meanings of the curvatures of the curves parametrized with the arc length are given in E-5. This is followed by the calculation of the Frenet vectors and curvatures of any curve. After these, some results have been given for the state of evolute curve X being a W-curve and the Frenet vectors and curvatures of involute curve Y have been calculated in terms of Frenet vectors and curvatures of the curve X. At last, the differential equation of the spherical curves, the equation of the radius and the center of the osculating hyperspheres have been achieved in E-5
Türk Sinemasında İşçi Sınıfı ve Emek Görünümleri
No full textBu çalışma, Foucault ve Althusser'in özne, iktidar ve ideoloji kavramlarından yola çıkarak, Türk sinemasının tarihsel gelişimi boyunca üretilen filmlerde politik bir özne olarak işçi sınıfının ve emeğin görünümlerini çalışmayı amaçlamaktadır.This thesis aims to study the representations of labor and working class as a political subject in the films produced throughout the historical development of Turkish cinema, drawing upon the concepts of subject, power and ideology of Foucault and Althusser
Determination of University Students’ Self-efficacy and Attitudes towards Analytic Geometry Course
No full textAbstractThe purpose of this study to investigate self-efficacy and attitude of the pre-service elementary mathematics teachers and university students enrolling in mathematics department toward Analytic Geometry with respect to gender, department. There are 336 participants. The self efficacy and attitude toward analytic geometry scale (SAAG-S) developed by Ilgun, Azak ve Takunyaci (2012) was used. In order to analyze data, t-test and ANOVA were conducted and Pearson Correlation Coefficient was found. Results of this study showed that while there is a significant difference between the self-efficacy and attitudes of the pre-service elementary mathematics teachers and university students enrolling in mathematics department toward Analytic Geometry, there is no significant difference between the self-efficacy and attitudes of females and males
Pauli Gaussian Fibonacci and Pauli Gaussian Lucas Quaternions
No full textWe have investigated new Pauli Fibonacci and Pauli Lucas quaternions by taking the components of these quaternions as Gaussian Fibonacci and Gaussian Lucas numbers, respectively. We have calculated some basic identities for these quaternions. Later, the generating functions and Binet formulas are obtained for Pauli Gaussian Fibonacci and Pauli Gaussian Lucas quaternions. Furthermore, Honsberger’s identity, Catalan’s and Cassini’s identities have been given for Pauli Gaussian Fibonacci quaternions
Synthesis of acrylamide-based cryogels and investigation of their use in removal of textile dyes
No full textTekstil atık sularında bulunan boyar maddelerin giderimi, ekosistem dengesi, halk sağlığı ve sürdürülebilir su yönetimi açısından kritik bir öneme sahip olduğundan bu çalışmada, tekstil endüstrisi atık sularında bulunan boyar maddelerin giderimi için akrilamid tabanlı anyonik ve katyonik özellikte kriyojeller sentezlenmiş, model boyar maddeler olarak kullanılan katyonik özellikteki metilen mavisi ve anyonik özellikteki asit mavi 193 boyaları üzerindeki adsorpsiyon performanslarını karşılaştırmalı olarak değerlendirilmesi amaçlanmıştır. En etkin giderim yapan poli(akrilamid-vinilsülfonik asit) (poli(AAm-VSA)) anyonik ve poli(akrilamid-vinilimidazol)/kitosan (poli(AAm-VI)/CS) katyonik kriyojelleri kullanılarak adsorpsiyon prosesinde optimum koşullarının belirlenebilmesi için; kriyojel miktarı, başlangıç boya derişimi, çözeltinin pH'ı ve temas süresi gibi parametrelerin etkileri incelenmiştir. Kriyojellerin karakterizasyonu FT-IR ve SEM analizleri ile yapılmış, farklı pH ortamlarında şişme davranışları değerlendirilmiştir. Langmuir, Freundlich, Dubinin-Radushkevich adsorpsiyon izotermleri ve yalancı birinci derece, yalancı ikinci derece kinetik modelleri ile matematiksel modelleme yapılmıştır. Adsorpsiyon süreçlerinde; metilen mavisi giderimi için ise pH 7 başlangıç boya derişimi 100 ppm, temas süresi 60 dakika, 0.1 gram anyonik kriyojel miktarı; asit mavi 193 giderimi için ise pH 7, başlangıç boya derişimi 500 ppm, temas süresi 60 dakika, 0.1 gram katyonik kriyojel miktarı; optimum koşullar olarak belirlenmiştir. Her iki boyarmadde giderimi için Freundlich izotermi (metilen mavisi R2=0.9907; asit mavi 193 R2=0.9920) en iyi uyumu göstermiştir. Adsorpsiyon kinetiğinin ise her iki boyar madde giderimi için yalancı ikinci derece kinetiğe uyduğu belirlenmiştir. Sonuçlar, anyonik karakterli kriyojellerin katyonik metilen mavisi, katyonik karakterli kriyojellerin ise anyonik asit mavi 193 boyar maddelerini yüksek verimlilikle uzaklaştırabildiğini; dolayısıyla boyar madde türüne özgü seçicilik ve etkin bir adsorpsiyon mekanizmasına sergilediğini ortaya koymuştur. Bu bağlamda, yüksek adsorpsiyon kapasitesi, kolay uygulanabilirlik ve yeniden kullanılabilirlik gibi avantajlarıyla söz konusu kriyojellerin, sürdürülebilir ve çevre dostu adsorbanlar olarak tekstil atıksularının arıtımında güçlü bir alternatif oluşturabileceği sonucuna ulaşılmıştır.The removal of dyes present in textile wastewater is of critically important in terms of ecosystem balance, public health, and sustainable water management. In this study, acrylamide-based anionic and cationic cryogels were synthesized for the removal of dyes from textile industry wastewater, and their adsorption performances were comparatively evaluated using cationic methylene blue and anionic acid blue 193 as model dyes. The most effective cryogels, poly(acrylamide-vinylsulfonic acid) (poly(AAm-VSA)) with anionic character and poly(acrylamide-vinylimidazole)/chitosan (poly(AAm-VI)/CS) with cationic character, were employed to investigate the influence of process parameters such as cryogel dosage, initial dye concentration, solution pH, and contact time in order to determine the optimum conditions for adsorption. The structural characterization of the cryogels was performed using FT-IR and SEM analyses, while their swelling behavior in different pH environments was also evaluated. Mathematical modeling was carried out using Langmuir, Freundlich, and Dubinin–Radushkevich adsorption isotherms as well as pseudo-first-order and pseudo-second-order kinetic models. In adsorption processes, the optimum conditions were determined as follows: for methylene blue removal, pH 7, an initial dye concentration of 100 ppm, a contact time of 60 minutes, and 0.1 g of anionic cryogel; and for acid blue 193 removal, pH 7, an initial dye concentration of 500 ppm, a contact time of 60 minutes, and 0.1 g of cationic cryogel. In both dye removal processes, the Freundlich isotherm (R² = 0.9907 for methylene blue; R² = 0.9920 for acid blue 193) provided the best fit. Furthermore, adsorption kinetics were found to follow the pseudo-second-order model for both dyes. The results demonstrated that anionic cryogels can effectively remove cationic methylene blue, while cationic cryogels can efficiently remove anionic acid blue 193, thereby exhibiting dye-specific selectivity and an efficient adsorption mechanism. In this context, owing to their high adsorption capacity, ease of application, and reusability, these cryogels can be considered as sustainable and environmentally friendly adsorbents with strong potential for application in the treatment of textile wastewater
R13 3-boyutlu minkowski uzayında null paralel p-equidistant regle yüzeyler
No full text06.03.2018 tarihli ve 30352 sayılı Resmi Gazetede yayımlanan “Yükseköğretim Kanunu İle Bazı Kanun Ve Kanun Hükmünde Kararnamelerde Değişiklik Yapılması Hakkında Kanun” ile 18.06.2018 tarihli “Lisansüstü Tezlerin Elektronik Ortamda Toplanması, Düzenlenmesi ve Erişime Açılmasına İlişkin Yönerge” gereğince tam metin erişime açılmıştır.Bu çalışma, altı bölümden oluşmuştur. Birinci bölüm giriş kısmına ayrılmıştır. İkinci bölümde Öklid ve Minkowski uzayı ile ilgili bazı temel tanım ve teoremlere yer verilmiştir. Üçüncü bölümde 3-boyutlu Öklid ve Minkowski uzayında regle yüzey kavramı ve B-scrollar ifade edildi. Dördüncü bölümde , 3-boyutlu Öklid uzayında paralel p-equidistant regle yüzeyler ile , 3-boyutlu Minkowski uzayında spacelike ve timelike paralel p-equidistant regle yüzeyler ile ilgili tanım ve teoremlere yer verildi.Beşinci bölüm bu çalışmanın orijinal kısmını oluşturmaktadır ve dört alt bölüm olarak düzenlenmiştir. Beşinci bölümün birinci alt bölümünde null paralel p-equidistant B-scrollar tanıtıldı. İkinci alt bölümde null paralel p-equidistant B-scrolların şekil operatörlerine karşılık gelen matrisler hesaplanarak aralarındaki ilişki verildi. Üçüncü alt bölümde şekil operatörünün cebirsel değişmezleri ile ilgili bazı teorem ve sonuçlar elde edildi. Son olarak da null paralel p-equidistant B-scrolların dralleri, ikinci ortalama ve Gauss eğrilikleri arasındaki ilişkiler bulundu. Ayrıca null paralel p-equidistant B-scrolların dayanak eğrileri ile ilgili bazı karakteristik teorem ve sonuçlar ifade edildi.Altıncı bölümde tüm çalışmanın geniş bir özeti yapıldı ve bundan sonra null paralel p-equidistant B-scrollarla ile ilgili yapılacak araştırmalara yönelik öneride bulunuldu.This thesis consist of six chapters. The first chapter is devoted to the introduction. In the second chapter some basic definitions and theorems are given related to the Euclidean and Minkowski space. In the third chapter, the concept of ruled surface and B-scrolls are expressed in 3-dimensional Minkowski space and 3-dimensional Euclidean space . In the fourth chapter, definitions and theorems are given with related to parallel p-equidistant ruled surfaces in three dimensional Euclidean space and related to spacelike and timelike parallel p-equidistant ruled surfaces in three dimensional Minkowski space.The fifth chapter of this study constitutes the original part and settled as four sub-sections. In the first subsection null parallel p-equidistant B-scrolls are introduced. In the second subsection, the matrices of shape operators for null paralel p-equidistant B-scrolls are calculated and the relationships between the matrices of shape operators are given. In the third subsection, some theorems and conclutions are obtained about the algebraic invariants of the shape operators. Lastly, the relationships between dralls, second mean and second Gaussian curvatures of null p-parallel equidistant B-scrolls have been found. In addition, some characteristic theorems and conclutions have been expressed with related to base curves of null parallel p-equidistant B-scrolls.In the sixth chapter of this thesis, a brief summary of the study is given and a suggestion is proposed for investigations on the realm of null parallel p-equidistant B-scrolls
Spinor Equations of Smarandache Curves in E3
No full textThis study examines the spinor representations of TN (tangent and normal), NB (normal and binormal), TB (tangent and binormal) and TNB (tangent, normal and binormal)–Smarandache curves in three-dimensional Euclidean space E3. Spinors are complex column vectors and move on Pauli spin matrices. Isotropic vectors in the C3 complex vector space form a two-dimensional surface in the C2 complex space. Additionally, each isotropic vector in C3 space corresponds to two vectors in C2 space, called spinors. Based on this information, our goal is to establish a relationship between curve theory in differential geometry and spinor space by matching a spinor with an isotropic vector and a real vector generated from the vectors of the Frenet–Serret frame of a curve in three-dimensional Euclidean space. Accordingly, we initially assume two spinors corresponding to the Frenet–Serret frames of the main curve and its (TN, NB, TB and TNB)–Smarandache curves. Then, we utilize the relationships between the Frenet frames of these curves to examine the connections between the two spinors corresponding to these curves. Thus, we give the relationships between spinors corresponding to these Smarandache curves. For this reason, this study creates a bridge between mathematics and physics. This study can also serve as a reference for new studies in geometry and physics as a geometric interpretation of a physical expression
