scholarly journals Conservation Laws for a Delayed Hamiltonian System in a Time Scales Version

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 668 ◽  
Author(s):  
Xiang-Hua Zhai ◽  
Yi Zhang
Keyword(s):  
Hamiltonian System ◽  
Conservation Laws ◽  
Time Scales ◽  
Scientific Research ◽  
Noether Theorem ◽  
Continuous Version ◽  
Difference Analysis ◽  
Delayed Arguments ◽  
New Perspective ◽  
Fowler Equation

The theory of time scales which unifies differential and difference analysis provides a new perspective for scientific research. In this paper, we derive the canonical equations of a delayed Hamiltonian system in a time scales version and prove the Noether theorem by using the method of reparameterization with time. The results extend not only the continuous version of the Noether theorem with delayed arguments but also the discrete one. As an application of the results, we find a Noether-type conserved quantity of a delayed Emden-Fowler equation on time scales.

scholarly journals Vartiational Optimal-Control Problems with Delayed Arguments on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Thabet Abdeljawad (Maraaba) ◽  
Fahd Jarad ◽  
Dumitru Baleanu
Keyword(s):  
Optimal Control ◽  
Time Scales ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Delayed Arguments

Beringia as an Ice Age genetic museum

2003 ◽  
Vol 60 (1) ◽  
pp. 94-100 ◽  
Author(s):  
Beth Shapiro ◽  
Alan Cooper
Keyword(s):  
Time Scales ◽  
Late Pleistocene ◽  
Ancient Dna ◽  
Human Impacts ◽  
Phylogenetic Analyses ◽  
Genetic Data ◽  
Ice Age ◽  
Ecological Change ◽  
Landscape Mosaics ◽  
New Perspective

AbstractThousands of Late Pleistocene remains are found in sites throughout Beringia. These specimens comprise an Ice Age genetic museum, and the DNA contained within them provide a means to observe evolutionary processes within populations over geologically significant time scales. Phylogenetic analyses can identify the taxonomic positions of extinct species and provide estimates of speciation dates. Geographic and temporal divisions apparent in the genetic data can be related to ecological change, human impacts, and possible landscape mosaics in Beringia. The application of ancient DNA techniques to traditional paleontological studies provides a new perspective to long-standing questions regarding the paleoenvironment and diversity of Late Pleistocene Beringia.

Noether theorem for Birkhoffian systems on time scales

2015 ◽  
Vol 56 (10) ◽  
pp. 102701 ◽  
Author(s):  
Chuan-Jing Song ◽  
Yi Zhang
Keyword(s):  
Time Scales ◽  
Noether Theorem

scholarly journals On certain new and exact solutions of the Emden-Fowler equation and Emden equation via invariant variational principles and group invariance

1991 ◽  
Vol 32 (4) ◽  
pp. 457-468 ◽  
Author(s):  
O. P. Bhutani ◽  
K. Vijayakumar
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Lie Group ◽  
Variational Principles ◽  
First Integrals ◽  
Noether Theorem ◽  
Repeated Application ◽  
Scale Invariant ◽  
Emden Equation ◽  
Fowler Equation

AbstractAfter formulating the alternate potential principle for the nonlinear differential equation corresponding to the generalised Emden-Fowler equation, the invariance identities of Rund [14] involving the Lagrangian and the generators of the infinitesimal Lie group are used for writing down the first integrals of the said equation via the Noether theorem. Further, for physical realisable forms of the parameters involved and through repeated application of invariance under the transformation obtained, a number of exact solutions are arrived at both for the Emden-Fowler equation and classical Emden equations. A comparative study with Bluman-Cole and scale-invariant techniques reveals quite a number of remarkable features of the techniques used here.

scholarly journals Using Relative Tie Strength to Identify Core Teams of Scientific Research

2019 ◽  
Vol 14 (23) ◽  
pp. 33
Author(s):  
Meishu Zhang ◽  
Yu Jia ◽  
Nianxin Wang ◽  
Shilun Ge
Keyword(s):  
Scientific Research ◽  
Absolute Threshold ◽  
Tie Strength ◽  
Threshold Method ◽  
Research Teams ◽  
Team Members ◽  
The Absolute ◽  
New Perspective ◽  
Cooperative Relationship ◽  
High Level

In China, it has long become imperative for the management of education and science and technology to build high-level scientific and technological innovation teams. Scientifically and accurately identifying core scientific research teams is an important condition for cultivating and building such teams. The absolute threshold method (e.g., c-level clique at, n- clique, k-core) is the prevailing means of identifying core teams and their core members. In fact, effects such as “the preference-dependent effect”, “the apostle effect” and “the star effect”, the cooperative relationship between the researchers is not even. This study, based on the co-authorship network, found that not choosing the absolute threshold properly can easily lead to poor identification of core members of some teams. Even worse, when the absolute threshold is too large, this “uniform” evaluation criterion of tie strength results in the elimination of some core teams in some disciplines. This paper uses relative tie strength to identify core scientific research teams from a new perspective, which can effectively avoid the situation of some core team members being ignored because of the mandatory requirements of the absolute tie strength among members, and can also solve the challenge of threshold selections for identifying different teams.

scholarly journals The Second Noether Theorem on Time Scales

2013 ◽  
Vol 2013 ◽  
pp. 1-14 ◽  
Author(s):  
Agnieszka B. Malinowska ◽  
Natália Martins
Keyword(s):  
Time Scales ◽  
Variational Problems ◽  
Noether Theorem

We extend the second Noether theorem to variational problems on time scales. As corollaries we obtain the classical second Noether theorem, the second Noether theorem for theh-calculus and the second Noether theorem for theq-calculus.

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