scholarly journals The Geometrical Characterizations of the Bertrand Curves of the Null Curves in Semi-Euclidean 4-Space

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3294
Author(s):  
Jianguo Sun ◽  
Yanping Zhao
Keyword(s):  
Frenet Equations ◽  
Null Curves ◽  
Existence Conditions

According to the Frenet equations of the null curves in semi-Euclidean 4-space, the existence conditions and the geometrical characterizations of the Bertrand curves of the null curves are given in this paper. The examples and the graphs of the Bertrand pairs with two different conditions are also given in order to supplement the conclusion of this paper more intuitively.

Geometrical particles and Legendrian dualities related to null curves

2020 ◽  
Vol 35 (09) ◽  
pp. 2050051
Author(s):  
Chunxiao Wang ◽  
Qingxin Zhou ◽  
Zhigang Wang
Keyword(s):  
Topological Structure ◽  
Space Time ◽  
De Sitter ◽  
Contact Manifolds ◽  
Frenet Equations ◽  
Dual Relationship ◽  
Null Curves

In this paper, we investigate the special properties of geometrical particles with null paths in de Sitter 3-space–time, new Frenet equations and an important invariant associated with null paths are presented. By means of unfolding theory, the local topological structure of the lightlike dual surfaces is revealed. It is found that the lightlike dual surface has some singularities whose types can be determined by the invariant. Based on the theory of Legendrian dualities on pseudospheres and the theory of contact manifolds, it is shown that there exists the [Formula: see text]-dual relationship between the lightlike transversal trajectory of the particle and the lightlike dual surface. In addition, an interesting and important fact mentioned is that the contact of lightlike transversal trajectory with lightcone quadric and the contact of lightlike transversal trajectory with null hyperplane have the same order when they are related to the same type of singularities of the lightlike dual surface.

scholarly journals On Null Curves in Minkowski 3-Space and Its Fractal Folding

2020 ◽  
Vol 14 (4) ◽  
pp. 90
Author(s):  
A.E. El-Ahmady ◽  
Malak E. Raslan ◽  
A.T. M-Zidan
Keyword(s):  
Frenet Equations ◽  
Null Curves

In this paper, a form for Frenet equations of all null curves in Minkowski 3-space has been presented. New types of foldings of curves are obtained. The connection between folding, deformation and Frenet equations of curves are also deduced.

scholarly journals Personnel shift assignment: Existence conditions and network models

Networks ◽  
1994 ◽  
Vol 24 (7) ◽  
pp. 385-394 ◽  
Author(s):  
Yeroon van den Berg ◽  
David M. Panton
Keyword(s):  
Network Models ◽  
Existence Conditions ◽  
Shift Assignment

scholarly journals On the Existence of Positive Periodic Solutions for Second-Order Functional Differential Equations with Multiple Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Qiang Li ◽  
Yongxiang Li
Keyword(s):  
Periodic Solutions ◽  
Functional Differential Equations ◽  
Index Theory ◽  
Second Order ◽  
Multiple Delays ◽  
First Eigenvalue ◽  
Fixed Point Index Theory ◽  
Existence Conditions ◽  
Functional Differential ◽  
Periodic Boundary Problem

The existence results of positiveω-periodic solutions are obtained for the second-order functional differential equation with multiple delaysu″(t)+a(t)u(t)=f(t,u(t),u(t−τ1(t)),…,u(t−τn(t))), wherea(t)∈C(ℝ)is a positiveω-periodic function,f:ℝ×[0,+∞)n+1→[0,+∞)is a continuous function which isω-periodic int, andτ1(t),…,τn(t)∈C(ℝ,[0,+∞))areω-periodic functions. The existence conditions concern the first eigenvalue of the associated linear periodic boundary problem. Our discussion is based on the fixed-point index theory in cones.

scholarly journals Symmetry group analysis and invariant solutions of hydrodynamic-type systems

2004 ◽  
Vol 2004 (10) ◽  
pp. 487-534 ◽  
Author(s):  
M. B. Sheftel
Keyword(s):  
Group Analysis ◽  
Type Systems ◽  
Hydrodynamic Type ◽  
Recursion Operators ◽  
Higher Symmetries ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Component Systems ◽  
Two Component Systems ◽  
Existence Conditions

We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence ont,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail thann-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.

TESTING FOR WEAK SEPARABILITY USING STOCHASTIC SEMI-NONPARAMETRIC TESTS: AN EMPIRICAL STUDY ON US DATA

2017 ◽  
Vol 22 (6) ◽  
pp. 1510-1534
Author(s):  
Ryan S. Mattson ◽  
Philippe de Peretti
Keyword(s):  
Empirical Study ◽  
Financial Stability ◽  
Nonparametric Tests ◽  
Extended Version ◽  
Monthly Data ◽  
Monetary Aggregates ◽  
Separability Criterion ◽  
Weak Separability ◽  
Existence Conditions ◽  
Necessary Existence

In this paper, we use the weak separability criterion to check for the existence of six different monetary aggregates reported by the Center of Financial Stability (CFS). We implement an extended version of the semi-nonparametric tests introduced by Barnett and de Peretti on US monthly data from January 1967 to December 2012. The test, first, checks for the necessary existence conditions of an overall utility function and a monetary subutility function, and then tests for the separability of the latter. On different subsamples, our results suggest that only the DM1 aggregate meets the separability criterion. Implemented on macroeconomic data, we have tested a joint assumption about separability and the existence of a representative agent. Thus, the rejection of the null could also be due to the rejection of stringent Gorman's conditions. More advanced tests for weak separability are clearly required to confirm the results found in this paper.

scholarly journals Special Curves According to Bishop Frame in Minkowski 3-Space

2020 ◽  
Vol 5 (1) ◽  
pp. 237-248
Author(s):  
Muhammad Abubakar Isah ◽  
Mihriban Alyamaç Külahçı
Keyword(s):  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Bishop Frame ◽  
Null Curve ◽  
Minkowski Spaces ◽  
Slant Helix ◽  
Null Curves ◽  
Necessary And Sufficient

AbstractPseudo null curves were studied by some geometers in both Euclidean and Minkowski spaces, but some special characters of the curve are not considered. In this paper, we study weak AW (k) – type and AW (k) – type pseudo null curve in Minkowski 3-space [E_1^3 . We define helix and slant helix according to Bishop frame in [E_1^3 . Furthermore, the necessary and sufficient conditions for the slant helix and helix in Minkowski 3-space are obtained.

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