A Discussion on Some Topological and Algebraic Features of Symmetric Spaces | Chapter 3 | Mathematics and Computer Science: Contemporary Developments Vol. 10

Many scientific problems in various fields may have their own conditions that might not agree with the geometric structure and properties of some spaces familiar to mathematicians and geometers. Many properties of symmetric spaces can be studied through their Lie algebras and root systems, and especially the problem of classification of symmetric spaces.

This study introduced some approaches, geometrical and algebraic, which help to give a further understanding of symmetric spaces. Symmetric space is a very important field for understanding abstract and applied features of spaces. This study also introduced Riemannian Manifold, Lie groups and Lie algebras, and some of their topological and algebraic properties, with some concentration on Lie algebras and root systems, which help classification and many applications of symmetric spaces. The paper is an attempt to explain some algebraic features of symmetric spaces and how to get some of their properties using an algebraic approach, concluded with some results.

 

Author (s) Details

 

Umsalama Ahmed Abd Alla Elemam
Department of Mathematics, Jazan University Al- Dayer University College, Kingdom of Saudi Arabia.

 

Please see the book here:- https://doi.org/10.9734/bpi/mcscd/v10/3301

Study about Gini Coefficient and Discontinuity: Contribution to the Analysis of a Transformation | Chapter 12 | Research and Applications Towards Mathematics and Computer Science Vol. 4

 This phase reveals a stop in the mapping from a Lorenz curve to the associated accruing distribution function. The Gini co-effective is an important tool for resolving income or money distribution within a country or domain, but it should not make a mistake for an absolute measurement of gains or wealth. A productive country and a low-income country power have the same Gini co-effective, even with rather various income distributions. The issue is analytical in nature and is based on an test of how a limited random variable's allocation function gets converted into allure Lorenz curve. It will be proven that the renewal from a finite income classification to its Lorenz curve is a constant bijection with respect to the Lq ([0,1])-metric – for each q ≥ 1. The inverse revolution, however, is not continuous for some q ≥ 1. This implies a more painstaking attitude when interpreting the profit of a Gini coefficient.  Another issue is that you cannot trust the mixed distribution to be an correct representation of the fundamental income distribution if you computed a Lorenz curve utilizing empirical dossier. Generalisations in several directions are attainable when calculating the Gini cooperative using Lorenz curves. One that connects the Lorenz curve to difference is included present.

Author(s) Details:

Jens Peter Kristensen,
Teaching at Middelfart Gymnasium, 2005 – 2018, Denmark.

Please see the link here: https://stm.bookpi.org/RATMCS-V4/article/view/11820

Symmetric Contractions in Partially Ordered Metric Spaces and Coupled Coincidence Points| Chapter 9 | Research Highlights in Mathematics and Computer Science Vol. 3

 In this stage we present new symmetric contractions to produce the life of coupled agreement points in the setting of partially orderly metric spaces. The weighing are mixed monotone manipulators. The contraction deliberate in our work if of Geraghty type. The main feature of the present division is to highlight the experience that the requirements of commutativity or rapport of the pair of mappings, the monotony hypothesis of mappings complicated can be loose in coupled coincidence point results that is supported with appropriate illustrations.

Author(s) Details:

Manish Jain,
Department of Mathematics, Ahir College Rewari, 123401, India.

Please see the link here: https://stm.bookpi.org/RHMCS-V3/article/view/8881