Diffraction is a phenomenon that occurs when a wave encounters an obstacle or a slit that is comparable in size to its wavelength. It results in the bending and spreading of waves as they pass around the edges of the obstacle or through the slit. This behavior is observed with various types of waves, including sound waves, light waves, and water waves.

Chromism refers to the ability of a substance to change color in response to changes in certain external conditions, such as temperature, light, or chemical environment. There are several types of chromism, including: 1. **Thermochromism** - Change of color with temperature. Substances exhibit different colors at different temperatures due to changes in molecular structure or interactions. 2. **Photochromism** - Change of color when exposed to light.

The Whipple formulae are a set of equations used in astronomy, specifically in the field of celestial mechanics. They are used to approximate the motion of a satellite or celestial body in the gravitational field of a primary body (such as the Earth or another planet). The formulas are named after the American astronomer Fred Whipple.

The Earle K. Plyler Prize for Molecular Spectroscopy is an award presented annually by the American Physical Society (APS) to recognize outstanding accomplishments in the field of molecular spectroscopy. Established in honor of Earle K. Plyler, a significant contributor to the field, the prize aims to acknowledge individuals who have made important contributions through innovative experimental techniques, theoretical work, or other significant achievements in molecular spectroscopy.

EUCMOS, or the European Consortium for the Molecular Orientation of Solvents, is a collaborative effort typically involving researchers and institutions across Europe. Its focus is on the study and application of molecular orientation in solvents, which is important for various fields, including chemistry, material science, and environmental science. The goals of EUCMOS may include advancing research on solvent properties, developing new experimental techniques, and promoting the exchange of knowledge and data among scientists in the field.

The Voigt profile is a mathematical function that describes the spectral line shape of light emitted or absorbed by atoms and molecules. It accounts for both Doppler broadening and pressure broadening (also known as collisional broadening). In more detail: - **Doppler Broadening** occurs due to the thermal motion of particles, which causes variations in the observed frequency of the spectral line based on the velocities of the emitting or absorbing species.

The term "triangular function" can refer to different concepts depending on the context in which it is used. Here are a couple of interpretations: 1. **Triangular Wave Function**: In signal processing and wave theory, a triangular function often refers to a triangular wave, which is a non-sinusoidal waveform resembling a triangular shape. It alternates linearly between a peak and a trough.

A transcendental function is a type of function that cannot be expressed as a solution of any algebraic equation with integer (or rational) coefficients. In other words, transcendental functions are not algebraic functions, which means they cannot be constructed from a finite number of additions, subtractions, multiplications, divisions, and taking roots of rational numbers.

The TANC function, commonly referred to in mathematical contexts, is related to trigonometry and represents the tangent of an angle in a right triangle. However, if you are referring to the specific function in programming, particularly in the context of spreadsheet software like Microsoft Excel or Google Sheets, the more appropriate reference would be the "TAN" function. The **TAN function** computes the tangent of an angle given in radians.

Student's t-distribution, commonly referred to as the t-distribution, is a probability distribution that is especially useful in statistics for estimating population parameters when the sample size is small and/or when the population standard deviation is unknown. It was first described by William Sealy Gosset under the pseudonym "Student" in the early 20th century.

A step function is a type of piecewise function that changes its value at specific intervals, resulting in a graph that looks like a series of steps. These intervals can be defined by any rules, leading to a function that stays constant over each interval before jumping to a new value at the boundaries. ### Key Characteristics of Step Functions: 1. **Piecewise Definition**: A step function can be defined using different constant values over different ranges of the input variable.

Diffusing-wave spectroscopy (DWS) is a technique used to study the dynamics of complex, opaque materials, such as colloids, biological tissues, and granular media. This method is based on the scattering of light from a sample that is not transparent, where the light is scattered multiple times due to the complex structure and dynamics of the sample.

Diffuse reflectance spectroscopy (DRS) is a technique used to analyze the optical properties of materials by measuring the light that is scattered from a sample. This method is particularly useful for studying opaque or semi-opaque samples, where traditional transmission spectroscopy would not be feasible due to light absorption or scattering. ### Key Concepts: 1. **Theory**: When light is incident on a sample, it can be absorbed, reflected, or transmitted.

Spence's function, often denoted as \( \text{Li}_2(x) \), is a special function in mathematics that is related to the dilogarithm. It is defined for real values of \( x \) typically in the range \( 0 < x < 1 \) and can be extended to complex values.

Scorer's function is a mathematical concept used primarily in the context of quantum mechanics and wave scattering. It is a tool used to analyze the behavior of wave functions and their interactions with potential barriers or wells. In particular, Scorer's function is often associated with the study of cylindrical waves and can provide solutions to certain types of differential equations. It plays a role in problems involving waves in cylindrical geometries, such as those encountered in acoustics or electromagnetism.

The term "Ruler function" can refer to different concepts depending on the context. Here are a couple of possible meanings: 1. **Mathematical Function**: In mathematics, specifically in the realm of measure theory, the "Ruler function" can refer to a specific kind of function related to measuring lengths. For example, it might be associated with the concept of a ruler that measures distances or lengths in certain contexts.

The rectangular function, often referred to as the "rect function," is a mathematical function that is commonly used in signal processing, communications, and other fields. It is defined as a piecewise function that takes the value 1 (or another constant value) over a specified interval and 0 elsewhere.

Prolate spheroidal wave functions (PSWFs) are a set of mathematical functions that arise in various fields such as physics and engineering, particularly in the context of solving certain types of differential equations and in wave propagation problems. They are particularly useful in problems that exhibit some form of spherical symmetry or where boundary conditions are imposed on elliptical domains.

The Pochhammer contour is a specific type of contour used in complex analysis, particularly in the context of integrals involving certain types of functions or singularities. The contour is named after the mathematician Leo Pochhammer. The Pochhammer contour consists of a path in the complex plane that typically encloses one or more branch points, where a function may be multi-valued, such as logarithms or fractional powers.

The parabolic cylinder functions, often denoted as \( U_n(x) \) and \( V_n(x) \), are special functions that arise in various applications, particularly in mathematical physics and solutions to certain differential equations. They are solutions to the parabolic cylinder differential equation, which is given by: \[ \frac{d^2 y}{dx^2} - \frac{1}{4} x^2 y = 0.