scholarly journals Flat double rotational surfaces in Euclidean and Lorentz-Minkowski 4-space

2018 ◽  
Vol 103 (117) ◽  
pp. 61-68
Author(s):  
Wendy Goemans
Keyword(s):  
Minkowski Space ◽  
Side Product ◽  
Planar Curve ◽  
New Type ◽  
Rotational Surfaces

A new type of surfaces in 4-dimensional Euclidean and Lorentz-Minkowski space is constructed by performing two simultaneous rotations on a planar curve. In analogy with rotational surfaces, the resulting surfaces are called double rotational surfaces. Classification theorems of flat double rotational surfaces are proved. These classifications contain amongst other cones over 4-dimensional Clelia curves. As a side product these new kinds of curves in 4-space are defined.

scholarly journals Tiling Periodicity

2010 ◽  
Vol Vol. 12 no. 2 ◽  
Author(s):  
Juhani Karhumaki ◽  
Yury Lifshits ◽  
Wojciech Rytter
Keyword(s):  
Open Problem ◽  
Classical Case ◽  
Side Product ◽  
Compact Representation ◽  
Minimal Size ◽  
Partial Word ◽  
International Audience ◽  
New Type

International audience We contribute to combinatorics and algorithmics of words by introducing new types of periodicities in words. A tiling period of a word w is partial word u such that w can be decomposed into several disjoint parallel copies of u, e.g. a lozenge b is a tiling period of a a b b. We investigate properties of tiling periodicities and design an algorithm working in O(n log (n) log log (n)) time which finds a tiling period of minimal size, the number of such minimal periods and their compact representation. The combinatorics of tiling periods differs significantly from that for classical full periods, for example unlike the classical case the same word can have many different primitive tiling periods. We consider also a related new type of periods called in the paper multi-periods. As a side product of the paper we solve an open problem posted by T. Harju (2003).

Generalized Null Bertrand Curves In Minkowski Space-Time

2014 ◽  
Vol 60 (2) ◽  
pp. 489-502 ◽  
Author(s):  
Ferdag Kahraman Aksoyak ◽  
Ismail Gok ◽  
Kazim Ilarslan
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Nonzero Constant ◽  
Bertrand Curve ◽  
Zero Curvature ◽  
Null Curve ◽  
Minkowski Space Time ◽  
Similar Idea ◽  
New Type

Abstract Çöken and ÇIFTCI proved that a null Cartan curve in Minkowski space-time E41 is a null Bertrand curve if and only if k2 is nonzero constant and k3 is zero. That is, the null curve with non-zero curvature k2 is not a Bertrand curve in Minkowski space-time E41. So, in this paper we defined a new type of Bertrand curve in Minkowski space-time E41 for a null curve with non-zero curvature k3 by using the similar idea of generalized Bertrand curve given by Matsuda and Yorozu and we called it a null (1, 3)-Bertrand curve. Also, we proved that if a null curve with non-zero curvatures in Minkowski space-time E41 is a null (1, 3)-Bertrand curve then it is a null helix. We give an example of such curves.

scholarly journals Timelike rotational surfaces of elliptic, hyperbolic and parabolic types in Minkowski space E41 with pointwise 1-type Gauss map

Filomat ◽  
2015 ◽  
Vol 29 (3) ◽  
pp. 381-392 ◽  
Author(s):  
Burcu Bektaş ◽  
Uğur Dursun
Keyword(s):  
Minkowski Space ◽  
Parabolic Type ◽  
Gauss Map ◽  
Rotational Surface ◽  
Rotational Surfaces

In this work, we focus on a class of timelike rotational surfaces in Minkowski space E41 with 2-dimensional axis. There are three types of rotational surfaces with 2-dimensional axis, called rotational surfaces of elliptic, hyperbolic or parabolic type. We obtain all flat timelike rotational surface of elliptic and hyperbolic types with pointwise 1-type Gauss map of the first and second kind. We also prove that there exists no flat timelike rotational surface of parabolic type in E41 with pointwise 1-type Gauss map.

On parametrizations of loxodromes on time-like rotational surfaces in Minkowski space-time

2020 ◽  
pp. 2150080
Author(s):  
Murat Babaarslan ◽  
Murat Gümüş
Keyword(s):  
Minkowski Space ◽  
Space Time ◽  
Minkowski Space Time ◽  
Rotational Surfaces

We investigate the parametrizations of loxodromes on the time-like rotational surfaces by using suitable Lorentzian angles in Minkowski space-time. Also, some examples and corresponding graphs are given by using Mathematica.

scholarly journals A New Version of Spherical Magnetic Curves in the De-Sitter Space S 1 2

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 606 ◽  
Author(s):  
Selçuk Baş
Keyword(s):  
Charged Particle ◽  
Vector Field ◽  
Minkowski Space ◽  
Magnetic Force ◽  
De Sitter Space ◽  
Existence Condition ◽  
De Sitter ◽  
New Type ◽  
Physical Features

This paper presents a new type of spacelike magnetic curves associated with the Sabban vector field defined in the Minkowski space. In this approach, some geometrical and physical features of the moving charged particle corresponding to the spacelike magnetic curves are identified. An entire characterization is developed for spacelike spherical magnetic curves, denoting particularly the changes of their energy with respect to time, the influence of the magnetic force on them, and the existence condition for the uniformity of these curves.

scholarly journals General rotational surfaces in the 4-dimensional Minkowski space

2014 ◽  
Vol 38 ◽  
pp. 883-895 ◽  
Author(s):  
Georgi GANCHEV ◽  
Velichka MILOUSHEVA
Keyword(s):  
Minkowski Space ◽  
Dimensional Minkowski Space ◽  
Rotational Surfaces

The Microstructure of Shock-Synthesized Diamond

1967 ◽  
Vol 25 ◽  
pp. 324-325
Author(s):  
Lucien F. Trueb
Keyword(s):  
Single Crystals ◽  
Preferred Orientation ◽  
High Magnification ◽  
Texture Pattern ◽  
Shock Process ◽  
New Type ◽  
Diffraction Diagram

A new type of synthetic industrial diamond formed by an explosive shock process has been recently developed by the Du Pont Company. This material consists of a mixture of two basically different forms, as shown in Figure 1: relatively flat and compact aggregates of acicular crystallites, and single crystals in the form of irregular polyhedra with straight edges.Figure 2 is a high magnification micrograph typical for the fibrous aggregates; it shows that they are composed of bundles of crystallites 0.05-0.3 μ long and 0.02 μ. wide. The selected area diffraction diagram (insert in Figure 2) consists of a weak polycrystalline ring pattern and a strong texture pattern with arc reflections. The latter results from crystals having preferred orientation, which shows that in a given particle most fibrils have a similar orientation.

New type electron gun with electrostatic and electromagnetic lenses

1978 ◽  
Vol 36 (1) ◽  
pp. 62-63
Author(s):  
T. Ichinokawa ◽  
H. Maeda
Keyword(s):  
Electron Microscopy ◽  
Electron Beam ◽  
Optimum Condition ◽  
Bias Voltage ◽  
Electron Gun ◽  
Charge Effect ◽  
Micro Fabrication ◽  
Maximum Brightness ◽  
New Type ◽  
The Ideal

I. IntroductionThermionic electron gun with the Wehnelt grid is popularly used in the electron microscopy and electron beam micro-fabrication. It is well known that this gun could get the ideal brightness caluculated from the Lengumier and Richardson equations under the optimum condition. However, the design and ajustment to the optimum condition is not so easy. The gun has following properties with respect to the Wehnelt bias; (1) The maximum brightness is got only in the optimum bias. (2) In the larger bias than the optimum, the brightness decreases with increasing the bias voltage on account of the space charge effect. (3) In the smaller bias than the optimum, the brightness decreases with bias voltage on account of spreading of the cross over spot due to the aberrations of the electrostatic immersion lens.In the present experiment, a new type electron gun with the electrostatic and electromagnetic lens is designed, and its properties are examined experimentally.

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