Characterizations of special time-like curves in Lorentzian plane 𝕃2

2017 ◽  
Vol 14 (10) ◽  
pp. 1750140
Author(s):  
Abdullah Mağden ◽  
Süha Yılmaz ◽  
Yasin Ünlütürk
Keyword(s):  
Differential Equation ◽  
Position Vector ◽  
Constant Breadth ◽  
Lorentzian Plane ◽  
Special Time

In this paper, we first obtain the differential equation characterizing position vector of time-like curve in Lorentzian plane [Formula: see text] Then we study the special curves such as Smarandache curves, circular indicatrices, and curves of constant breadth in Lorentzian plane [Formula: see text] We give some characterizations of these special curves in [Formula: see text]

scholarly journals Spherical curves and quadratic relationships for special functions

1985 ◽  
Vol 27 (1) ◽  
pp. 111-124
Author(s):  
Even Mehlum ◽  
Jet Wimp
Keyword(s):  
Differential Equation ◽  
Hypergeometric Functions ◽  
Bessel Functions ◽  
Special Functions ◽  
Position Vector ◽  
Third Order ◽  
Generalized Hypergeometric Functions ◽  
Transcendental Functions ◽  
Horn Functions ◽  
Vector Differential Equation

AbstractWe show that the position vector of any 3-space curve lying on a sphere satisfies a third-order linear (vector) differential equation whose coefficients involve a single arbitrary function A(s). By making various identifications of A(s), we are led to nonlinear identities for a number of higher transcendental functions: Bessel functions, Horn functions, generalized hypergeometric functions, etc. These can be considered natural geometrical generalizations of sin2t + cos2t = 1. We conclude with some applications to the theory of splines.

scholarly journals Differential representation of the Lorentzian spherical timelike curves by using bishop frame

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 2037-2043
Author(s):  
Okullu Balki ◽  
Huseyin Kocayigit
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Timelike Curve ◽  
Position Vector ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Order Linear ◽  
Bishop Frame ◽  
Lorentzian Sphere ◽  
Linear Differential

In this study, we will give the differential representation of the Lorentzian spherical timelike curves according to Bishop frame and we obtain a third-order linear differential equation which represents the position vector of a timelike curve lying on a Lorentzian sphere.

scholarly journals Position Vectors of Curves Generalizing General Helices and Slant Helices in Euclidean 3-Space

2021 ◽  
Vol 52 ◽  
Author(s):  
Malika Izid ◽  
Abderrazak El Haimi ◽  
Amina Ouazzani Chahdi
Keyword(s):  
Differential Equation ◽  
Parametric Representation ◽  
Position Vector ◽  
Third Order ◽  
The Third ◽  
Slant Helix ◽  
Vector Differential Equation ◽  
Standard Frame

Inthispaper,wegiveanewcharacterizationofak-slanthelixwhichisageneral- ization of general helix and slant helix. Thereafter, we construct a vector differential equation of the third order to determine the parametric representation of a k-slant helix according to standard frame in Euclidean 3-space. Finally, we apply this method to find the position vector of some examples of 2-slant helix by means of intrinsic equations.

scholarly journals An explicit characterization of spherical curves according to bishop frame and an approximately solution

2019 ◽  
Vol 23 (Suppl. 1) ◽  
pp. 361-370
Author(s):  
Pınar Balki-Okullu ◽  
Huseyin Kocayigit ◽  
Tuba Agirman-Aydin
Keyword(s):  
Differential Equation ◽  
Linear Differential Equation ◽  
Series Solution ◽  
Solution Method ◽  
Position Vector ◽  
Order Linear Differential Equation ◽  
Third Order ◽  
Bishop Frame ◽  
Linear Differential

In this paper, spherical curves are studied by using Bishop frame. First, the differential equation characterizing the spherical curves is given. Then, we exhibit that the position vector of a curve which is lying on a sphere satisfies a third-order linear differential equation. Then we solve this linear differential equation by using Bernstein series solution method.

scholarly journals Forced motion of a charged particle in a magnetic field

1966 ◽  
Vol 6 (4) ◽  
pp. 385-398
Author(s):  
L. J. Gleeson
Keyword(s):  
Magnetic Field ◽  
Differential Equation ◽  
Charged Particle ◽  
Constant Magnetic Field ◽  
Unit Vector ◽  
Electrical Charge ◽  
Position Vector ◽  
Forced Motion ◽  
Image Position

We consider the motion of a particle of mass m and electrical charge e, moving in a constant magnetic field Bk, where k is a unit vector, and acted upon by a force mf(t). The position vector r(t) of this particle is governed by the differential equation where .

scholarly journals CURVES OF CONSTANT BREADTH ACCORDING TO DARBOUX FRAME IN GALILEAN SPACE G3>

2019 ◽  
pp. 837
Author(s):  
Hülya Gun Bozok
Keyword(s):  
Differential Equation ◽  
3 Dimensional ◽  
Special Cases ◽  
Darboux Frame ◽  
Constant Breadth ◽  
Galilean Space

In this work, the curves of constant breadth according to Darboux frame in the 3-dimensional Galilean Space are investigated. Firstly the curves of constant breadth according to Darboux frame are determined then the differential equation of the constant breadth curve with this frame is found. After that some special cases of this differential equation are researched.

The role of differential phase contrast in electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 176-177
Author(s):  
E.M. Waddell ◽  
J.N. Chapman ◽  
R.P. Ferrier
Keyword(s):  
Phase Contrast ◽  
Practical Method ◽  
Position Vector ◽  
Differential Phase ◽  
Pure Phase ◽  
Differential Phase Contrast ◽  
The Difference ◽  
Image Position ◽  
First Moment

Dekkers and de Lang (1977) have discussed a practical method of realising differential phase contrast in a STEM. The method involves taking the difference signal from two semi-circular detectors placed symmetrically about the optic axis and subtending the same angle (2α) at the specimen as that of the cone of illumination. Such a system, or an obvious generalisation of it, namely a quadrant detector, has the characteristic of responding to the gradient of the phase of the specimen transmittance. In this paper we shall compare the performance of this type of system with that of a first moment detector (Waddell et al.1977).For a first moment detector the response function R(k) is of the form R(k) = ck where c is a constant, k is a position vector in the detector plane and the vector nature of R(k)indicates that two signals are produced. This type of system would produce an image signal given bywhere the specimen transmittance is given by a (r) exp (iϕ (r), r is a position vector in object space, ro the position of the probe, ⊛ represents a convolution integral and it has been assumed that we have a coherent probe, with a complex disturbance of the form b(r-ro) exp (iζ (r-ro)). Thus the image signal for a pure phase object imaged in a STEM using a first moment detector is b2 ⊛ ▽ø. Note that this puts no restrictions on the magnitude of the variation of the phase function, but does assume an infinite detector.

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