The Central Limit Theorem (CLT) for directional statistics is an extension of the classical CLT that applies to circular or directional data, where directions are typically represented on a unit circle. This branch of statistics is particularly important in fields such as biology, geology, and meteorology, where data points may represent angles or orientations rather than linear quantities.

Faxén's law describes the force experienced by a spherical particle suspended in a fluid when it is subjected to an external oscillating field, such as a pressure gradient or a fluid flow. It is particularly relevant in the study of colloidal suspensions and the behavior of particles in non-Newtonian fluids.

Rayleigh's equation in fluid dynamics refers to a fundamental principle that describes the stability of a fluid flow. It is often associated with the stability analysis of boundary layers and the onset of turbulence and instabilities in various fluid flow situations. One common context in which Rayleigh's equation is discussed is in the study of stability of various flow regimes, particularly in relation to the growth of instabilities in a shear flow. The equation is typically derived from the Navier-Stokes equations under specific assumptions and conditions.

The Hazen–Williams equation is an empirical formula used to calculate the flow of water through pipes, specifically in civil engineering and hydraulics. It estimates the head loss (pressure loss due to friction) in a pipe based on the flow rate, pipe diameter, and the roughness of the pipe's interior surface. The equation is particularly applicable for water flow in pipes where the flow is turbulent. The general form of the Hazen–Williams equation is: \[ h_f = 0.

Kelvin's circulation theorem is a fundamental principle in fluid dynamics, particularly in the study of inviscid (non-viscous) and irrotational flows. It states that the circulation around a closed contour moving with the fluid is constant in time, provided the flow is conservative and the fluid is incompressible and inviscid.

The Milne-Thomson circle theorem is a concept in fluid dynamics and potential flow theory. It relates to the flow of an ideal fluid (inviscid and incompressible) around obstacles and is particularly useful for analyzing flow patterns around circular objects.

The Orr–Sommerfeld equation is a fundamental equation in fluid dynamics that describes the stability of an incompressible flow, particularly in the context of boundary layer theory. It is named after William Richard Orr and Arnold Sommerfeld, who contributed to its development. The equation arises when analyzing small disturbances or perturbations in a basic flow profile. It is particularly important in studying the stability of laminar flows and understanding transition to turbulence.

The Shallow Water Equations (SWE) are a set of hyperbolic partial differential equations that describe the flow of a thin layer of fluid, such as water in rivers, lakes, and coastal areas. These equations are particularly useful in hydraulic and environmental engineering for modeling phenomena like flooding, tsunami propagation, and sediment transport. The SWE are derived under the assumption that the horizontal length scale of the fluid flow is much larger than the vertical scale of the fluid depth.

Stokes' paradox refers to a phenomenon in fluid dynamics that highlights an apparent inconsistency in the flow of a viscous fluid around an object. The paradox is named after the British mathematician and physicist George Gabriel Stokes who analyzed the flow of a viscous (incompressible) fluid around a cylinder. The paradox arises when considering a two-dimensional flow of a viscous fluid past an infinitely long, solid cylinder.

A Kolmogorov automorphism is a specific concept from the theory of dynamical systems, particularly related to the study of certain types of stochastic processes. It is named after the Russian mathematician Andrey Kolmogorov, who made significant contributions to probability theory and dynamical systems. In the context of probability theory, an automorphism is a structure-preserving map from a set to itself.

Matti Vuorinen is a Finnish mathematician known for his contributions to complex analysis, particularly in the area of geometric function theory. He has published research on topics such as conformal mapping, analytic functions, and several complex variables. Vuorinen's work often explores the properties of various mathematical functions and their applications, influencing both pure and applied mathematics.