In the present study, we give the conditions for a curve in the Minkowski space to be a Darboux helix. We show that is a Darboux helix if there exists a fixed direction d in 3 1 R such that the function d s W ), ( is constant. We give the relation between slant helice and Darboux helice. As a particular case, if we take constant, w the curves are constant precession. Some more particular cases of constant precession curves are studied. [Şenol A, Zıplar E, Yayli Y, Ghadami R. Darboux Helices in Minkowski space 3 1 R . Life Sci J 2012;9(4):5905-5910] (ISSN:1097-8135). http://www.lifesciencesite.com. 884
Tür çeşitliliği yüksek olan bir orman ekosistemi yangın, böcek, kirletici kaynaklar gibi her türlü tehlikeye karşı daha dayanıklı ve sağlıklı olmaktadır. Dolayısıyla orman ekosistemlerinin sürekliliğinde tür çeşitliği anahtar görevi görmektedir. Tür çeşitliliği alfa, beta ve gama düzeyinde belirlenmektedir. Bu çalışma, örnek alan içi çeşitlilik anlamına gelen alfa tür çeşitliliğinin pozitif gösterge türlerini tespit etmek amacıyla gerçekleştirilmiştir. Çalışmada Akdeniz Bölgesi'nin geçiş zonunda bulunan ve kuzey-güney doğrultusunda uzanan Kuyucak Dağı'ndan elde edilen veriler (bitki taksonlarına ait var-yok verileri) kullanılmıştır. Örnek alanlar için alfa çeşitliliğinin hesaplanmasında Simpson 1-λ, Shannon-Wiener, Brillouin, Menhinick, Margalef, Fisher α, Berger-Parker (1/d) ve Chao1 indisleri kullanılmıştır. Her örnek alan için hesaplanan alfa çeşitlilik indis değerleri ile alanda tespit edilen bitki taksonları arasındaki ilişkiyi belirlemek için Wilcoxon Sıra İstatistiği testi kullanılmıştır. Wilcoxon Sıra İstatistiği testi sonucunda ilişkinin gerçekliliğini test edebilmek için önemli ilişki tespit edilen bitki türleri sırayla çıkarılarak tekrar alfa çeşitlilik indisleri hesaplanmıştır. Elde edilen sonuçlara göre Fontanesia philliraeoides Labill., Phillyrea latifolia L. ve Pistacia terebinthus L. türlerinin odunsu ve yarı odunsu bitki türleri açısından daha zengin alanları temsil edebileceği belirlenmiştir.
Databases are very important sources for storing huge size of data. Today, yearly produced information is expressed as multiple size of the amount that produced before. Retrieving correct data is as important as storing it. At this point, querying becomes more important. Classical SQL queries return a record only if the database has a record which satisfies all search criteria. However, the user mostly wants to see similar records when there is no perfect match. For this reason, studies are focused on flexible SQL queries. In this sense, fuzzy logic can play an important role since it maintains the idea that there may be interval values between true and false, contrary to the logic of Aristotle. Genetic algorithm based database querying is another flexible querying approach to the mentioned problem. In this work, both approaches are applied on a sample real-estate database and the results are compared while discussing the efficiency of the two methods.
In this paper, we investigate special curves on a weak r-helix submanifold in Euclidean n-space E n . Also, we give the important relations between weak r-helix submanifolds and the special curves such as line of curvature, asymptotic curve and helix line. Recently, M. Ghomi worked out the shadow problem given by H.Wente. And, He mentioned the shadow boundary in [8]. Ruiz-Hernández investigated that shadow boundaries are related to helix submanifolds in [12].Helix hypersurfaces have been worked in nonflat ambient spaces in [6,7]. Cermelli and Di Scala have also studied helix hypersurfaces in liquid cristals in [2]. This paper is organized as follows. In section 2, we will give some basic properties in the general theory of weak r-helix, helix submanifolds and curves. And, in section 3, we will give the important relations between weak r-helix submanifolds and some special curves such as line of curvature, asymptotic curve and helix lines. Basic PropertiesDefinition 2.1. Given a submanifold M ⊂ R n and an unitary vector d in R n , we say that M is a helix with respect to d if for each q ∈ M the angle between d and T q M is constant.Let us recall that a unitary vector d can be decomposed in its tangent and orthogonal components along the submanifold M , i.e. d = cos(θ)T + sin(θ)ξ with T = ξ = 1, where T ∈ T M and ξ ∈ ϑ(M ).The angle between d and T q M is constant if and only if the tangential component of d has constant length cos(θ)T = cos(θ). We can assume that 0 < θ < π 2 and we can say that M is a helix of angle θ. We will call T and ξ the tangent and normal directions of the helix submanifold M . We can call d the helix direction of M and we will assume d always to be unitary [5].Definition 2.2. Let M ⊂ R n be a helix submanifold of angle θ = π 2 w.r. to the direction d ∈ R n . We will call the integral curves of the tangent direction T of the helix M , the helix lines of M w.r.to d. Moreover, we say that a helix submanifold M ⊂ R n is a ruled helix if all the helix lines of M are straight lines [5]. Proposition 2.1 The helix lines of a helix submanifold M ⊂ R n are geodesic in M [5]. Definition 2.3. A submanifold M ⊂ R n is a weak r-helix if there exist r linearly independent directions d 1 , ..., d r , such that M is a helix with respect to every d j [5].Remark 2.1 We say that ξ is parallel normal in the direction X ∈ T M if ∇ ⊥ X ξ = 0. Here, ∇ ⊥ denotes the normal connection of M induced by the standard covariant derivative of the Euclidean ambient. Let us denote by D the standard covariant derivative in R n and by ∇ the induced covariant derivative in M . Let A ξ and V be the shape operator and the second fundamental form of M ⊂ R n [5].
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.