scholarly journals Fractional Killing-Yano Tensors and Killing Vectors Using the Caputo Derivative in Some One- and Two-Dimensional Curved Space

2014 ◽  
Vol 2014 ◽  
pp. 1-4 ◽  
Author(s):  
Ehab Malkawi ◽  
D. Baleanu
Keyword(s):  
Fractional Calculus ◽  
Exact Solutions ◽  
Caputo Derivative ◽  
Dimensional Space ◽  
Two Dimensional ◽  
Curved Space ◽  
Killing Vectors ◽  
Constant Of Motion ◽  
Christoffel Symbols

The classical free Lagrangian admitting a constant of motion, in one- and two-dimensional space, is generalized using the Caputo derivative of fractional calculus. The corresponding metric is obtained and the fractional Christoffel symbols, Killing vectors, and Killing-Yano tensors are derived. Some exact solutions of these quantities are reported.

Properties of Spatial-Rotation Transformations of Fractional Derivatives

2020 ◽  
pp. 198-223
Author(s):  
Ehab Malkawi
Keyword(s):  
Fractional Calculus ◽  
Fractional Derivatives ◽  
Dimensional Space ◽  
Scalar Fields ◽  
Two Dimensional ◽  
Spatial Rotation ◽  
Essential Step ◽  
Derivatives Of

The transformation properties of the fractional derivatives under spatial rotation in two-dimensional space and for both the Riemann-Liouville and Caputo definitions are investigated and derived in their general form. In particular, the transformation properties of the fractional derivatives acting on scalar fields are studied and discussed. The study of the transformation properties of fractional derivatives is an essential step for the formulation of fractional calculus in multi-dimensional space. The inclusion of fractional calculus in the Lagrangian and Hamiltonian dynamical formulation relies on such transformation. Specific examples on the transformation of the fractional derivatives of scalar fields are discussed.

Quantum vacuum stress without regularization in two-dimensional space-time

1977 ◽  
Vol 354 (1679) ◽  
pp. 529-532 ◽  
Keyword(s):  
Stress Tensor ◽  
Dimensional Space ◽  
Space Time ◽  
Massless Scalar ◽  
Two Dimensional ◽  
Quantum Vacuum ◽  
Curved Space ◽  
Spinor Fields ◽  
Dimensional Space Time ◽  
Point Splitting

It is proved that there is a unique conserved stress tensor possessing a local trace, in the two-dimensional quantum theory of massless scalar and spinor fields propagating in curved space-time. No regularization is therefore required to obtain explicit expressions for the stress tensor. The results agree exactly with earlier expressions obtained from point-splitting regularization.

On the Classification of Fractal and Non-Fractal Objects in Two-Dimensional Space

2020 ◽  
Vol 14 (6) ◽  
pp. 1232-1239
Author(s):  
P. M. Pustovoit ◽  
E. G. Yashina ◽  
K. A. Pshenichnyi ◽  
S. V. Grigoriev
Keyword(s):  
Dimensional Space ◽  
Two Dimensional

Political Cleavages and Political Parties

2018 ◽  
Author(s):  
Russell J. Dalton
Keyword(s):  
Political Parties ◽  
Dimensional Space ◽  
New Left ◽  
Party Systems ◽  
European Parliament ◽  
Two Dimensional ◽  
Far Right ◽  
Policy Positions ◽  
Cultural Policies ◽  
Policy Choices

This chapter uses the cleavage positions of Candidates to the European Parliament (CEPs) to as representative of their parties’ political positions. Three surveys of CEPs track the evolution of party supply in European party systems. In 1979 parties were primarily aligned along a Left–Right economic cleavage. Gradually new left and Green parties began to compete in elections and crystallized and represented liberal cultural policies. In recent decades new far-right parties arose to represent culturally conservative positions. The cross-cutting cultural cleavage has also prompted many of the established parties to alter their policy positions. In most multiparty systems, political parties now compete in a fully populated two-dimensional space. This increases the supply of policy choices for the voters. The analyses are based on the Candidates to the European Parliament Studies in 1979, 1994, and 2009.

scholarly journals Three-Dimensional Thematic Map Imaging of the Yacht Port on the Example of the Polish National Sailing Centre Marina in Gdańsk

2021 ◽  
Vol 11 (15) ◽  
pp. 7016
Author(s):  
Pawel S. Dabrowski ◽  
Cezary Specht ◽  
Mariusz Specht ◽  
Artur Makar
Keyword(s):  
Spatial Data ◽  
Convex Surface ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Future Research ◽  
Two Dimensional ◽  
Thematic Maps ◽  
Research Directions ◽  
Future Research Directions ◽  
The Many

The theory of cartographic projections is a tool which can present the convex surface of the Earth on the plane. Of the many types of maps, thematic maps perform an important function due to the wide possibilities of adapting their content to current needs. The limitation of classic maps is their two-dimensional nature. In the era of rapidly growing methods of mass acquisition of spatial data, the use of flat images is often not enough to reveal the level of complexity of certain objects. In this case, it is necessary to use visualization in three-dimensional space. The motivation to conduct the study was the use of cartographic projections methods, spatial transformations, and the possibilities offered by thematic maps to create thematic three-dimensional map imaging (T3DMI). The authors presented a practical verification of the adopted methodology to create a T3DMI visualization of the marina of the National Sailing Centre of the Gdańsk University of Physical Education and Sport (Poland). The profiled characteristics of the object were used to emphasize the key elements of its function. The results confirmed the increase in the interpretative capabilities of the T3DMI method, relative to classic two-dimensional maps. Additionally, the study suggested future research directions of the presented solution.

scholarly journals Hyperbolic Center of Mass for a System of Particles in a Two-Dimensional Space with Constant Negative Curvature: An Application to the Curved 2-Body Problem

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 531
Author(s):  
Pedro Pablo Ortega Palencia ◽  
Ruben Dario Ortiz Ortiz ◽  
Ana Magnolia Marin Ramirez
Keyword(s):  
Negative Curvature ◽  
Dimensional Space ◽  
Center Of Mass ◽  
Simple Expression ◽  
Two Dimensional ◽  
Constant Negative Curvature ◽  
Euclidean Case ◽  
System Of Particles ◽  
Material Points ◽  
The One

In this article, a simple expression for the center of mass of a system of material points in a two-dimensional surface of Gaussian constant negative curvature is given. By using the basic techniques of geometry, we obtained an expression in intrinsic coordinates, and we showed how this extends the definition for the Euclidean case. The argument is constructive and serves to define the center of mass of a system of particles on the one-dimensional hyperbolic sphere LR1.

Sign in / Sign up

Export Citation Format

Share Document