14th Gordon Arthur Ransome Oration: continuity and change

According to the law of conservation of energy, any transition between kinetic and potential energy conserves the total energy of the system. Hence, the work done by a conservative force is completely reversible. It is path independent, which means that we can start and stop at any two points in the transition, and the total energy of the system (kinetic plus potential energy at these points) will remain conserved. This is characteristic of a conservative force. Some important examples of...

There are numerous types of normal and abnormal respiration. Based on ventilatory movements, breathing patterns are classified as regular, deep, or shallow. Examples include Biot's breathing, Cheyne-Stokes respiration, Kussmaul's breathing, hyperventilation, and hypoventilation. Each pattern is clinically significant and aids in evaluating patients.
In Biot's breathing, the respiratory rate and depth are irregular, alternating between periods of deep gasping and apnea. Common causes include...

The total amount of current flowing per unit cross-sectional area is called the current density. Hence, the current passing through a cross-sectional area can be written as the surface integral of the current density.

The continuity equation asserts that the mass flow rate must remain constant for a steady flow of an incompressible fluid within a confined system. This principle applies to systems where fluid passes through varying cross-sectional areas, such as nozzles, syringes, and pipes.
The mass flow rate is expressed as:

Gordon Allport, often regarded as the father of American personality psychology, developed a theory that emphasized the importance of understanding people in their present lives rather than focusing on their past, as psychoanalysis did. Allport believed that personality should be studied in healthy, well-adjusted individuals rather than those with psychological problems. He was particularly interested in defining traits, which he saw as fundamental mental structures that guide behavior across...

A function is continuous at a point a if three conditions are met: the function is defined at a, the limit of the function as x approaches a exists, and this limit equals the function’s value. Mathematically, this is written asThis definition ensures the graph of the function does not exhibit any breaks, holes, or jumps at that point. Discontinuities occur when any of these conditions fail. A removable discontinuity exists when the two-sided limit exists but the function is either undefined or...