The Singular Isothermal Sphere (SIS) profile is a mathematical model used in astrophysics and cosmology to describe the distribution of matter, particularly dark matter, in galaxy halos or clusters of galaxies. This model is particularly relevant in the context of gravitational lensing and the dynamics of galaxies. ### Key Features of the SIS Profile: 1. **Density Distribution**: The mass density \( \rho(r) \) of a singular isothermal sphere decreases with distance from the center.

Pauline Harrison may refer to various individuals, and without specific context, it's difficult to pinpoint exactly who you're referring to. There may be local figures, professionals in various fields, or other notable individuals with that name.

The Batchelor–Chandrasekhar equation is a fundamental equation in the field of fluid dynamics, specifically in the study of turbulence and the behavior of suspensions of small particles in a fluid. It describes the way that particles, such as bubbles or solid particles, interact with the surrounding fluid flow, particularly under conditions of sedimentation or dispersion.

Bernoulli's principle is a fundamental concept in fluid dynamics that describes the behavior of a fluid moving along a streamline. Formulated by the Swiss mathematician Daniel Bernoulli in the 18th century, the principle states that in a steady flow of an incompressible, non-viscous fluid, an increase in the fluid's speed occurs simultaneously with a decrease in pressure or potential energy in that flow.

The Boussinesq approximation is a mathematical simplification used in fluid dynamics, particularly in the study of weakly non-linear and dispersive wave phenomena, such as water waves. Named after the French physicist Joseph Boussinesq, this approximation is particularly useful for analyzing the behavior of surface waves in fluids where the amplitude of the waves is small compared to the wavelength.

The Darcy friction factor, often denoted as \( f \), is a key component in the Darcy-Weisbach equation, which is used to calculate pressure loss (or head loss) due to friction in a pipe or duct.

The Euler–Tricomi equation is a second-order partial differential equation (PDE) that arises in various fields, including fluid dynamics and mathematical physics. It is named after the mathematicians Leonhard Euler and Francesco Tricomi.

The Rankine–Hugoniot conditions are a set of mathematical conditions used in fluid dynamics and gas dynamics to describe the behavior of shock waves and discontinuities in a medium. These conditions relate the values of physical quantities (such as pressure, density, and velocity) on either side of a discontinuity, which can be a shock wave or a contact discontinuity.

Equivalent units are a concept used in cost accounting, particularly in process costing, to measure the work done during a period in terms of fully completed units. Since production processes often involve a mix of complete and incomplete units at the end of an accounting period, equivalent units allow businesses to assign costs more accurately.

The Kármán–Howarth equation is a fundamental relation in fluid dynamics, particularly in the study of turbulence. It describes the evolution of the second-order velocity correlation function in an incompressible flow. The equation provides insight into the relationships between different scales of motion in turbulent flows. In turbulent fluid mechanics, the velocity field can be characterized using correlation functions, which measure the statistical relationships between the velocities at different points in space.

The Oseen equations are a set of equations that describe the steady-state flow of a viscous fluid. They can be seen as a linearization of the Navier-Stokes equations, which govern the motion of fluid substances. The Oseen equations are particularly useful in the study of low Reynolds number flows, where inertial forces are negligible compared to viscous forces.

Annual Premium Equivalent (APE) is a financial metric commonly used in the insurance and financial services industry, particularly in the context of measuring and comparing the performance of life insurance products and sales. APE allows companies to evaluate the value of both regular premium and single premium life insurance policies on a standardized basis.

Ergodic flow is a concept from the field of dynamical systems, particularly in the study of dynamical systems that exhibit certain statistical properties over time. More specifically, it concerns how trajectories of a dynamical system explore the space in which they operate.

The Hopf decomposition is a concept in mathematics, particularly in the field of topology and algebraic topology. It is named after Heinz Hopf, who introduced it in the context of the study of spheres and bundles. The Hopf decomposition provides a way to analyze the structure of certain topological spaces by decomposing them into simpler components. In a more specific context, the Hopf decomposition is often discussed in relation to the Hopf fibration, which describes a particular type of mapping between spheres.

Kac's lemma, named after mathematician Mark Kac, is a result in probability theory concerning the expected value of a function of a random variable. It is particularly useful in the context of stochastic processes and the study of Brownian motion.

Matthew Wyatt Joseph Fry appears to be a relatively obscure individual, and there is limited publicly available information about him. It's possible that he may not be widely recognized or could belong to various contexts or fields, such as academia, the arts, or other professions. Could you provide more context or specify the area you're referring to? That would help in providing a more accurate answer.

Guergana Petrova is not widely known and doesn't refer to a well-documented public figure or entity as of my last knowledge update in October 2023. It may refer to a person, a business, or a fictional character that has not gained significant recognition in popular culture, literature, or news.

In mathematics, "mixing" generally refers to a concept in dynamical systems and, more specifically, in the study of chaotic systems and ergodic theory. It's a property that describes how a system evolves over time and the way its states become more uniformly distributed across the system's state space.

Ratner's theorems refer to a set of results in the field of ergodic theory and homogeneous dynamics, most notably established by the mathematician Marina Ratner in the 1980s. These theorems provide deep insights into the behavior of unipotent flows on homogeneous spaces, particularly in the context of algebraic groups and their actions.

The Sinai–Ruelle–Bowen (SRB) measure is a key concept in the study of dynamical systems, particularly in the context of chaotic systems and statistical mechanics. Named after Ya. G. Sinaï, David Ruelle, and Rufus Bowen, the SRB measure provides a way to describe the long-term statistical behavior of a system that exhibits chaotic dynamics.