Professor Atta-ur-Rahman: towering scientific achievements

Exponents provide a compact and efficient way of representing repeated multiplication. These tools are fundamental to algebra and broader areas of mathematics, including scientific computation, scaling laws, and dimensional analysis.Exponent Rules and PropertiesExponential notation expresses the repeated multiplication of a number by itself. For any nonzero real number a and integer n, an represent a multiplied by itself n times. Key properties include: These properties allow for the...

Scientists typically make repeated measurements of a quantity to ensure the quality of their findings and to evaluate both the precision and the accuracy of their results. Measurements are said to be precise if they yield very similar results when repeated in the same manner. A measurement is considered accurate if it yields a result that is very close to the true or the accepted value. Precise values agree with each other; accurate values agree with a true value.  Highly accurate measurements...

Abraham Maslow, a prominent figure in humanistic psychology, developed a theory centered on self-actualization, which he placed at the top of his hierarchy of needs. According to Maslow, self-actualization represents achieving one's full potential and is a rare accomplishment attained by approximately 2% of the population. Maslow identified notable historical figures such as Thomas Jefferson, Mahatma Gandhi, Helen Keller, and Martin Luther King Jr. as examples of self-actualized individuals.

A proteome is the entire set of proteins that a cell type produces. We can study proteomes using the knowledge of genomes because genes code for mRNAs, and the mRNAs encode proteins. Although mRNA analysis is a step in the right direction, not all mRNAs are translated into proteins.
Proteomics is the study of proteomes' function. It involves the large-scale systematic study of the proteome to denote the protein complement expressed by a genome. Scientist Mark Wilkins coined the term proteomics...

The perpendicular-axis theorem states that the moment of inertia of a planar object about an axis perpendicular to its plane is equal to the sum of the moments of inertia about two mutually perpendicular concurrent axes lying in the plane of the body.
Consider a circular disc of mass M and radius R lying along an x-y plane. The origin lies at the center of the disc, and the z-axis is perpendicular to the disc's plane. All three axes coincide at the disc's center. The moment of inertia of this...

Gravitation is one of the four fundamental forces in nature. The force between objects on Earth and Earth itself is called gravity.
Like other forces, gravity does work on an object if it displaces it toward the Earth's center. In this case, the work done by gravity is said to be positive. If an external force acts on the object against the pull of gravity and manages to lift it away from the Earth's center, work is done against gravity. In this case, the net work done is said to be negative.