Isadore Perlman: April 12, 1915-August 3, 1991

When placed in an external electric field, a dielectric material gets polarized. The charge density in the dielectric material is given by the sum of the bound and free charge densities, while the total charge density can also be written in terms of the total electric field. The bound charge density can be measured in terms of polarization, leading to the relationship between electric displacement and polarization.

Spherical coordinate systems are preferred over Cartesian, polar, or cylindrical coordinates for systems with spherical symmetry. For example, to describe the surface of a sphere, Cartesian coordinates require all three coordinates. On the other hand, the spherical coordinate system requires only one parameter: the sphere's radius. As a result, the complicated mathematical calculations become simple. Spherical coordinates are used in science and engineering applications like electric and...

Adsorption isotherms are mathematical models that describe how molecules in a gas or liquid phase interact with surfaces. Two of the most common isotherm models are the Langmuir and Freundlich isotherms, which relate to Type I monolayer chemisorption. The Langmuir model is based on four key assumptions:• Adsorption cannot exceed monolayer coverage.• All surface sites are equivalent.• Molecules adsorb only at vacant sites.• There are no interactions between adsorbed molecules.Consider the...

Parseval's theorem is a fundamental concept in signal processing and harmonic analysis. It asserts that for a periodic function, the average power of the signal over one period equals the sum of the squared magnitudes of all its complex Fourier coefficients. This theorem, named after Marc-Antoine Parseval, provides a powerful tool for analyzing the energy distribution in signals.
Interestingly, Parseval's theorem also holds for the trigonometric form of the Fourier series, which expresses a...

Alfred Adler, a prominent figure in psychology, founded the school of individual psychology. In contrast to Freud's emphasis on sexual or aggressive motives, Adler suggested that individuals are primarily motivated by their purposes and goals. He believed that people strive for perfection rather than pleasure. Adler argued that individuals could creatively act upon their genetic inheritance and environmental experiences to shape their own lives, emphasizing conscious motivation over unconscious...

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...