Special issue in honor of professor Armen Galoyan. Preface

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.

The subclavian artery transitions into the axillary artery as it exits the chest and enters the axillary region. This artery is critical for supplying blood to the shoulder area, including the head of the humerus, through the humeral circumflex arteries. As the vessel continues into the upper arm or brachium, it becomes the brachial artery. This artery plays a key role in vascularizing the brachial region and bifurcates at the elbow into several branches. These branches include the deep...

Direct alkylation is not a suitable method for synthesizing amines because it produces polyalkylated products. Gabriel synthesis is the most preferred method to exclusively make primary amines. The method uses phthalimide, which contains a protected form of nitrogen that participates in alkylation only once to predominantly give primary amines.
Strong bases like NaOH or KOH deprotonate the phthalimide to form the corresponding anion, which acts as a nucleophile. Further, the anion attacks an...

The human body is a complex, well-organized machine, and at the heart of its operations lies the circulatory system. This network of blood vessels, which includes systemic arteries, plays a vital role in maintaining life by transporting nutrients, oxygen, and waste products to and from cells throughout the body.
Systemic circulation is the part of the cardiovascular system that carries oxygenated blood away from the heart to the body's tissues and returns deoxygenated blood back to the heart.

Myasthenia gravis is a neuromuscular transmission disorder characterized by weakness and increased fatigability of skeletal muscles. It is an autoimmune disease affecting approximately one in 2000 people, where antibodies against the α1 subunit of nicotinic acetylcholine receptors are produced.
These antibodies interfere with the function of the nicotinic receptors in three ways: by binding to the receptor and disrupting acetylcholine binding; by causing cross-linking of receptors which leads...