scholarly journals N-BISHOP DARBOUX VECTOR OF A TIMELIKE CURVE IN MINKOWSKI 3-SPACE

2020 ◽  
Vol 20 (3) ◽  
pp. 519-528
Author(s):  
HATICE KUSAK SAMANCI
Keyword(s):  
Differential Geometry ◽  
Minkowski Space ◽  
Timelike Curve ◽  
Rotation Vector ◽  
Effective Alternative ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Alternative Approach ◽  
Darboux Frame ◽  
First Time

It is known that a Bishop frame of a curve is one of the effective alternative approach in the differential geometry. Recently, several important works have been done about the Bishop frames. The aim of our paper is to investigate the N-Bishop frame for timelike curves in Minkowski space. We define the N-Bishop frame for the timelike curve in Minkowski space. Then, we consider some properties of the frame. Moreover, we describe the N-Bishop Darboux frame for the first time. Additionally, we compute some geometrical characterizations for the N-Bishop Darboux axis and momentum rotation vector.

scholarly journals N-Bishop Darboux vector of the spacelike curve with spacelike binormal

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 353-360
Author(s):  
Hatice Kusak-Samanci ◽  
Huseyin Kocayigit
Keyword(s):  
Minkowski Space ◽  
Rotation Vector ◽  
Spacelike Curve ◽  
Geometrical Properties ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Darboux Frame ◽  
First Time

In this article, the N-Bishop frame in Minkowski space is investigated for spacelike curves with a spacelike binormial. Some features of the normal expansion are proven via for the spacelike curve. Then, a new Darboux frame called by the N-Bishop Darboux frame is introduced at first time. Furthermore, some geometrical properties of the N-Bishop Darboux frame are proven. As a result, the N-Bishop Darboux axis and momentum rotation vector are calculated.

scholarly journals Slant Helices of (k,m)-Type According to the ED-Frame in Minkowski 4-Space

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2185
Author(s):  
Fatma Bulut
Keyword(s):  
Differential Geometry ◽  
Minkowski Space ◽  
Symmetric Matrix ◽  
Space Curve ◽  
Frame Field ◽  
Dimensional Minkowski Space ◽  
Darboux Frame ◽  
Surface Curve ◽  
Area Of Study

In differential geometry, relations between curves are a large and important area of study for many researchers. Frame areas are an important tool when studying curves, specially the Frenet–Serret frame along a space curve and the Darboux frame along a surface curve in differential geometry. In this paper, we obtain slant helices of k-type according to the extended Darboux frame (or, for brevity, ED-frame) field by using the ED-frame field of the first kind (or, for brevity, EDFFK), which is formed with an anti-symmetric matrix for ε1=ε2=ε3=ε4∈{−1,1} and the ED-frame field of the second kind (or, for brevity, EDFSK), which is formed with an anti-symmetric matrix for ε1=ε2=ε3=ε4∈{−1,1} in four-dimensional Minkowski space E14. In addition, we present some characterizations of slant helices and determine (k,m)-type slant helices for the EDFFK and EDFSK in Minkowski 4-space.

scholarly journals On k-type spacelike slant helices lying on lightlike surfaces

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2781-2796
Author(s):  
Ufuk Öztürk ◽  
Emilija Nesovic ◽  
Öztürk Koç
Keyword(s):  
Minkowski Space ◽  
Sufficient Conditions ◽  
Geodesic Curvature ◽  
Normal Curvature ◽  
Spacelike Curve ◽  
Bishop Frame ◽  
Darboux Frame

In this paper, we define k-type spacelike slant helices lying on a lightlike surface in Minkowski space E31 according to their Darboux frame for k ? {0,1,2}. We obtain the necessary and the sufficient conditions for spacelike curves with non-null and null principal normal lying on lightlike surface to be the k-type spacelike slant helices in terms of their geodesic curvature, normal curvature and geodesic torsion. Additionally, we determine their axes and show that the Darboux frame of a spacelike curve lying on a lightlike surface coincides with its Bishop frame if and only if it has zero geodesic torsion. Finally, we give some examples.

Development of Students' Programming Abilities With the Means of Non-Programming Disciplines and Activities

2020 ◽  
pp. 89-97
Author(s):  
Sakibayev Spartak Razakhovich ◽  
Sakibayeva Bela Razakhovna
Keyword(s):  
Extracurricular Activities ◽  
Academic Disciplines ◽  
Effective Alternative ◽  
Educational Institutions ◽  
Professional Literature ◽  
Teaching Process ◽  
Alternative Approach ◽  
Development Of Students

The chapter contains the results of the research dedicated to the topic that has not been given much attention so far in the professional literature – discovering effective ways of developing students' programming abilities with the means of non-programming disciplines and activities. The authors argue that the process of forming capacities of students in programming becomes effective if students participate not only in programming lessons themselves but also dedicate a significant amount of time to other academic disciplines and extracurricular activities such as solving number-theoretic and chess endgame problems. The authors find that these disciplines and activities provide efficient means for developing programming capacities and therefore, their methods are the essential prerequisites for programming course. The significance of the obtained results is that they provide an effective alternative approach to organization of programming teaching process in those educational institutions where the traditional methodology does not bring the desired pedagogical effect.

Harmonic curvatures of the strip in Minkowski space

2018 ◽  
Vol 11 (04) ◽  
pp. 1850061
Author(s):  
Filiz Ertem Kaya ◽  
Ayşe Yavuz
Keyword(s):  
Euclidean Space ◽  
Minkowski Space ◽  
Strip Theory ◽  
First Time ◽  
Cylindrical Helix

This study aimed to give definitions and relations between strip theory and harmonic curvatures of the strip in Minkowski space. Previously, the same was done in Euclidean Space (see [F. Ertem Kaya, Y. Yayli and H. H. Hacısalihoglu, A characterization of cylindrical helix strip, Commun. Fac. Sci. Univ. Ank. Ser. A1 59(2) (2010) 37–51]). The present paper gives for the first time a generic characterization of the harmonic curvatures of the strip, helix strip and inclined strip in Minkowski space.

scholarly journals Gas–solid two-phase flow (GSF) mechanochemical synthesis of dual-metal–organic frameworks and research on electrochemical properties

2020 ◽  
Vol 2 (12) ◽  
pp. 5682-5687
Author(s):  
Jun Zhao ◽  
Bo Jin ◽  
Rufang Peng
Keyword(s):  
Electrochemical Properties ◽  
Mechanochemical Synthesis ◽  
Two Phase Flow ◽  
Metal Organic Frameworks ◽  
Phase Flow ◽  
Two Phase ◽  
Alternative Approach ◽  
Metal Organic ◽  
Dual Metal ◽  
First Time

As an alternative approach for conventional mechanochemical synthesis, a novel gas–solid two-phase flow (GSF) synthetic technique for the mechanochemical synthesis of dual metal–organic frameworks (DMOFs) was reported for the first time.

Relation between Darboux and type-2 Bishop frames in Euclidean space

2016 ◽  
Vol 13 (07) ◽  
pp. 1650101 ◽  
Author(s):  
Amine Yilmaz ◽  
Emin Özyilmaz
Keyword(s):  
Euclidean Space ◽  
Transition Matrix ◽  
Geodesic Curvature ◽  
Spherical Image ◽  
Darboux Vector ◽  
Bishop Frame ◽  
Spherical Images

In this work, we investigate relationships between Darboux and type-2 Bishop frames in Euclidean space. Then, we obtain the geodesic curvature of the spherical image curve of the Darboux vector of the type-2 Bishop frame. Also, we give transition matrix between the Darboux and type-2 Bishop frames of the type-2 Bishop frames of the spherical images of the edges [Formula: see text] and [Formula: see text]. Finally, we express some interesting relations and illustrate of the examples by the aid Maple programe.

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