Skip to main content

Homfly Polynomial of Knotted Trivalent Plane Graphs | Chapter 10 | Theory and Applications of Mathematical Science Vol. 1

We study the Homfly polynomial of periodic knotted trivalent plane graphs introduced in [1]. We show how periodicity of a knotted trivalent plane graphs is reflected in this polynomial. In particular, we derive congruences of periodic knotted trivalent plane graphs in terms of this polynomial invariant. These congruences yield criteria for periodicity of knotted trivalent plane graphs.

Author(s) Details

Ayman A. Aboufattoum
Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060, Kuwait.

K. Qazaqzeh
Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060,Kuwait.

E. A. Elsakhawy
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.

A. T. Diab
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.

View Books: http://bp.bookpi.org/index.php/bpi/catalog/book/117
Labels:

Comments

Post a Comment

Popular posts from this blog

Alkali Element Modification of Glucose Molecules as a Method to Dissolve Cancer Cells | Chapter 12 | New Visions in Medicine and Medical Science Vol. 4

  The present study highlights about alkali element modification of glucose molecules as a method to dissolve cancer cells. The central regulation of the mechanisms governing cell proliferation has little effect on cancer cells. Cancer cells are entirely independent of the central command and divide and proliferate on their own, making it challenging to activate their response mechanism. Precisely, this is the reason why they are at risk to the health of humans and/or any biological entities. Instead of trying to reconnect the central command of the growth control mechanism to cancer cells that are already out of the range, we present a method of using the cancer cell’s own irresponsive and uncontrolled growth mechanism to their disadvantage and destroy the cancer cells. We found that this is achievable in an atomic/molecular level study of the glucose molecule, which is the primary food source used for growth and energy generation by all cells in the body, including the cancer cells.
Post a Comment
Read more

Risk Factors for Postpartum Psychiatric Disorders. A Review of the Literature | Chapter 8 | New Visions in Medicine and Medical Science Vol. 4

  Objective: The aim of this study was to explore the risk factors for the development of postpartum psychiatric disorders through international literature. Materials and Methods: Throughout many articles in PubMed, Google scholar and PsycInfo, a great amount of recent data was gathered to identify the disorders that are most common as well as their risk factors. Results: After childbirth, most commonly women experience postpartum depression, anxiety disorders, post-traumatic stress disorder and postpartum psychosis. All the disorders have many similar risk-factors with the main one being preexisting psychiatric disorder and many similar symptoms too. Conclusions: Women after childbirth are at risk of experience many psychiatric disorders, such as postpartum distress, postpartum post traumatic stress disorder and even more rarely postpartum psychosis. It is important to provide comprehensive support to ensure the well-being of both the mother and the infant and this will be en
Post a Comment
Read more

Greening Regional Airports: A Vision for Carbon Neutral Infrastructure | Chapter 12 | Contemporary Perspective on Science, Technology and Research Vol. 3

 This study provides an overview of the energy demand of a regional airport, divided into individual time horizons. The electrification of aircraft systems raises the question of whether airports will be among the largest electricity consumers in our infrastructure in the future. Sustainability and especially emission reductions are significant challenges for airports that are currently being addressed. The Clean Sky 2 project GENESIS addresses the environmental sustainability of hybrid-electric 50-passenger aircraft systems in a life cycle perspective to support the development of a technology roadmap for the transition to sustainable and competitive electric aircraft systems. This article originates from the GENESIS research and describes various options for ground power supply at a regional airport. Potential solutions for airport infrastructure with a short (2030), medium (2040), and long (2050) time horizon are proposed. In addition to the environmental and conservation benefits,
Post a Comment
Read more