An Interplay between Commutative Rings and Graph Theory: A Review | Chapter 10 | Advancements in Science and Technology: Paving the Way to a Sustainable Future

The study of zero-divisor graphs has emerged as a key area of research in algebra, serving as a link between ring theory and graph theory. These graphs offer a valuable framework for exploring the structure of commutative rings. While many important findings have previously been established in the study of graphs associated with zero-divisors of a commutative ring, this chapter highlights some of the key findings that directly demonstrate the connection between algebra and graph theory.

 

Author (s) Details

Hem Lata
G.G.D.S.D. College, Hariana, Hoshiarpur, India.

 

Shelly Garg
DAV University, Jalandhar, India.

 

Please see the book here:-  https://doi.org/10.9734/bpi/mono/978-93-49473-39-3/CH10

An Introduction to Fulati-Suranjan Formulae in Calculating the Area and Perimeter of Any Circle Without Using Pi | Chapter 6 | Research and Applications Towards Mathematics and Computer Science Vol. 7

In this place chapter, an attempt was made to learn the Area and Perimeter or Perimeter of Circle, without utilizing Constant Pi, by the Fulati-Suranjan formulae (until two decimal places) in addition to a new constant, named Probir's Nonstop denoted by the Bengali message roshsho li-kar  ৢ . To fulfill these purposes attending, have been used few Theorems, Lemmas, Corollaries, the inner circle & the outer circle of the unchanging square, also the central square & the outer square of the same circle. Because without using pi, this division can calculate the field and perimeter of any circle nearly, which have been visualized in various models of this chapter so, demanding here the derived formulae are correct (until two decimal places). It bear be mentioned that a number of documents and online math sites have approximately discussed and explained some form of these theorems, lemma, and corollaries. We trust that readers interested in arithmetic, particularly those the one are students, will find the approach presented in this place chapter to be advantageous. Additionally, it appears that the troubled pupils are able to administer and memorize the formulae without the need for the usual constant pi.

Author(s) Details:

Probir Roy,
Department of Mathematics, Murarichand (M.C) College, Sylhet-3100, (Affiliated to Bangladesh National University), Bangladesh.

Please see the link here: https://stm.bookpi.org/RATMCS-V7/article/view/12841

Determination of Portal Vein Diameter and Velocity Using Ultrasound | Chapter 6 | New Frontiers in Medicine and Medical Research Vol. 1

 This study used ultrasound to establish standards for normal portal vein diameter and portal venous velocity, which can aid in the early detection of portal hypertension, as well as to develop an indigenous index for healthy Sudanese that correlates with body characteristics such as age, gender, weight, height, and abdominal circumference (AC). The study's importance lies in its ability to aid in the early detection of portal hypertension in order to avoid complications. In addition, to lower the cost and duration of the examination. The information was gathered and evaluated with the use of Statistical Package for Social Studies (SPSS). Duplex ultrasound exams were performed on 100 patients (49 male and 51 female) with normal abdominal scans in Khartoum Bahri Hospital, Khartoum State, between May and December 2015. (hypertension, DM and patient who has chronic liver disease are exclusion criteria). The results revealed that the most common age group was 20 to 29 years old, accounting for 33% of the sample volume, the most common body weight was 60 to 69 kg, accounting for 38%, the body height was 160 to 169% cm in 39%, and the abdominal circumference was 70-79 cm in 30% of the patients. As a result, we discovered that whereas portal vein diameter increases with age and weight, male and female values are similar. There was no discernible link between portal vein diameter, height, and belly circumference (AC). The patient's portal vein diameter and portal vein velocity were shown to have a highly significant correlation (increased velocity with decreasing diameter), which was expected and consistent with earlier research. The investigation also discovered a link between the Sudanese portal vain diameter and velocity and the international norm.

The researchers suggested that more research be done to determine the relationship between normal portal vein width and velocity and liver size.

Author (s) Details

Maram Mohammed Fathi Ahmed
Inaya Medical Colleges, Saudi Arabia.

View Book :- https://stm.bookpi.org/NFMMR-V1/article/view/2785

A Detailed Morphology and Histological Study of Placenta in Normal and Diabetic Pregnancies | Chapter 5 | Highlights on Medicine and Medical Science Vol. 17

 Introduction: Many physiological alterations that enhance insulin resistance are generated by pregnancy in a diabetogenic situation. The placenta is a vital organ for the developing foetus, as well as the human body's most accessible organ. Glucose tolerance has decreased by the third trimester of a typical pregnancy, although insulin levels in the blood have grown.

Aim: To determine the pregnancy's outcome, the placenta of a normal pregnancy is compared to the placenta of a diabetic pregnancy.

The current investigation used 50 placenta specimens with intact umbilical cords acquired from the Department of Obstetrics and Gynecology as part of a case-control study.

The shape and weight of the placenta varied slightly. The control group's mean placenta weight was 452.80 grammes, with a standard deviation of 140.93 grammes, while the case group's mean placenta weight was 406.00 grammes, with a standard deviation of 210.31 grammes. The mother's random blood sugar was substantially higher in the control group than in the cases (t=2.91, p0.01).

According to the current study, there was a tendency for placental weight and new-born weight to increase in complex pregnancies when compared to normal pregnancies. This showed an earlier diagnosis and adherence to the treatment strategy in diabetes pregnancies.

Author (S) Details

Durgesh Singh
Department of Anatomy, Shaikh-ul-Hind Maulana Mahmood Hasan (Government) Medical College, Saharanpur, Uttar Pradesh, India.

Shashi Prabha Singh
Department of Biochemistry, Shaikh-ul-Hind Maulana Mahmood Hasan (Government) Medical College, Saharanpur, Uttar Pradesh, India.

Priti Sinha
Department of Anatomy, Shaikh-ul-Hind Maulana Mahmood Hasan (Government) Medical College, Saharanpur, Uttar Pradesh, India.

Neha Gupta
Department of Anatomy, Shaikh-ul-Hind Maulana Mahmood Hasan (Government) Medical College, Saharanpur, Uttar Pradesh, India.

Rakesh Sharma
Department of Biochemistry, Shaikh-ul-Hind Maulana Mahmood Hasan (Government) Medical College, Saharanpur, Uttar Pradesh, India.

View Book :- https://stm.bookpi.org/HMMS-V17/article/view/2608

Can the Diameter of Longitudinal Bars of Extreme Edges of R/C Walls Halt Transverse Buckling? | Chapter 7 | Emerging Trends in Engineering Research and Technology Vol. 3

One important aspect of seismic design of buildings with a dual reinforced concrete structural system is the lateral stability of structural walls, when they face this danger mainly due to flexural overstrain. The deep excursion in the yield region of the boundary parts of bearing walls increases dramatically their flexibility and since at the same time they are liable, because of the earthquake vibration, to a reversing axial loading (tension – compression), their lateral stability is at stake. The possibility of failure because of lateral instability is limited significantly with the proper choice of an adequate thickness, which is specified by (most) modern seismic codes as a percentage of the height of the bottom storey. The current work investigates one parameter that may be affecting the stability of structural walls. This parameter is the diameter of the longitudinal reinforcement of the boundary edges of load-bearing walls. It contains an experimental research that tries to investigate the influence of the diameter of longitudinal reinforcement to the ultimate bearing capacity of test specimens. It has to be noted that in order to examine experimentally the influence of the diameter of longitudinal reinforcement, test specimens of scale 1:3 simulating the boundary edges of structural walls were used. These specimens were reinforced with the same or almost the same longitudinal reinforcement ratios (2.68% - 2.79%) but had a different number of reinforcement bars of varying diameter. The diameters of bars which were used were equal to 8 mm and 10 mm. The specimens which were compared to each other contained (apart from bars of different diameter) a different number of bars and consequently a different way of placement of these bars at the wall end sections. 

Author (s) Details

Theodoros Chrysanidis
 Laboratory of Reinforced Concrete and Masonry Structures, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece.

Ioannis Tegos
Laboratory of Reinforced Concrete and Masonry Structures, Aristotle University of Thessaloniki, Thessaloniki 54124, Greece

View Book :-  http://bp.bookpi.org/index.php/bpi/catalog/book/179