The BSSN formalism is an advanced mathematical formulation used in the numerical simulation of Einstein's field equations in general relativity, particularly in the context of black hole simulations and gravitational wave research. BSSN stands for Baumgarte-Shapiro-Shibata-Nakamura, the names of the researchers who developed this approach.

Gaussian polar coordinates are a two-dimensional coordinate system that extends the concept of polar coordinates, typically used in the context of the standard Euclidean plane, to a Gaussian (or flat) geometry that can be useful for various applications, particularly in physics and engineering.

Higher gauge theory is a generalization of traditional gauge theory that incorporates higher-dimensional structures, often characterized by the presence of higher category theory. In typical gauge theories, such as those used in particle physics, one finds gauge fields associated with symmetries represented by groups. These gauge fields are typically connections on principal bundles. In higher gauge theories, the focus extends to fields that can be described not just by 0-cochains (i.e.

The term "respiratory pump" refers to the mechanism by which breathing aids in the movement of blood within the cardiovascular system, particularly the return of venous blood to the heart. This process is primarily facilitated by changes in pressure that occur in the thoracic cavity during inhalation and exhalation.

The Coefficient of Fractional Parentage (CFP) is a concept used in quantum mechanics and atomic physics, particularly in the context of many-particle systems, such as atoms or nuclei composed of multiple indistinguishable particles (e.g., electrons, protons, neutrons). When dealing with systems of identical particles, the overall wave function must be symmetric (for bosons) or antisymmetric (for fermions) under the exchange of particles.

D'Alembert's equation is a type of partial differential equation that describes wave propagation. It is named after the French mathematician Jean le Rond d'Alembert.

During the 17th century, many mathematicians made significant contributions to the field, and they came from various countries. Here’s a list of notable mathematicians from that period, categorized by nationality: ### Italian - **Bonaventura Cavalieri**: Known for his work on integral calculus and the method of indivisibles. - **Giorgio Vasari**: Contributed to geometry and arithmetic.

19th-century mathematicians came from various countries and made significant contributions to mathematics and related fields. Here’s a brief overview of some notable mathematicians categorized by their nationality: ### France - **Évariste Galois**: Known for his work on group theory and the unsolvability of polynomial equations. - **Henri Poincaré**: Made foundational contributions to topology and dynamical systems.

A hybrid bond graph is a modeling tool that combines elements from both bond graph theory and other modeling paradigms, such as discrete-event systems or system dynamics. The primary purpose of a bond graph is to represent the energy exchange between different components in a system, typically in the context of engineering systems, particularly in the fields of mechanical, electrical, and hydraulic systems.

The magnetic form factor is a concept in condensed matter physics and materials science that describes how the magnetic scattering amplitude of a particle, such as an electron or a neutron, depends on its momentum transfer during scattering experiments. It is a critical parameter for understanding the magnetic properties of materials at the atomic or subatomic level.

Matter collineation is a concept primarily associated with the field of general relativity and differential geometry. In this context, it refers to a special type of transformation that preserves the structure of matter fields in a spacetime manifold. Specifically, a matter collineation is a transformation that leads to an invariance of the energy-momentum tensor associated with matter.

The Newtonian gauge is a specific choice of gauge used in the study of cosmological perturbations in the context of General Relativity. It is particularly useful in cosmology for analyzing the evolution of perturbations in the spacetime geometry during the universe's expansion. In the Newtonian gauge, the perturbed metric is expressed in a way that simplifies the analysis of scalar perturbations, which are fluctuations in the energy density of the universe, such as those arising from gravitational waves or inflationary fluctuations.

Level-spacing distribution refers to a statistical analysis of the spacings between consecutive energy levels in a quantum system. In quantum mechanics, particularly in the study of quantum chaos and integrable systems, the properties of energy levels can provide significant insight into the system's underlying dynamics. **Key Concepts:** 1. **Energy Levels:** In quantum systems, particles occupy discrete energy states. The difference in energy between these states is called the "energy spacing.

Linear transport theory is a framework used to describe the transport of particles, energy, or other quantities through a medium in a manner that is linear with respect to the driving forces. It is commonly applied in fields like physics, engineering, and materials science to analyze diffusion, conduction, and convection processes.

Lovelock's theorem refers to a set of results in the field of geometric analysis and theoretical physics, named after the mathematician David Lovelock. The key results of Lovelock's theorem concern the existence of certain types of gravitational theories in higher-dimensional spacetimes and focus primarily on the properties of tensors and the equations of motion that can be derived from a Lagrangian formulation.

The 13th century was a period rich in mathematical development, and several notable mathematicians emerged from various regions. Here’s a breakdown of some prominent mathematicians from that era by nationality: 1. **Italy**: - **Fibonacci (Leonardo of Pisa)**: Known for introducing the Hindu-Arabic numeral system to Europe and for the Fibonacci sequence in his work "Liber Abaci" (1202), which had a lasting impact on mathematics.

Noether's second theorem is a result in theoretical physics and the mathematics of symmetries in field theory, which stems from the work of mathematician Emmy Noether. While Noether's first theorem links symmetries of the action of a physical system to conservation laws, her second theorem addresses a different aspect of symmetry, specifically related to gauge symmetries or more general symmetries of a system that might not lead to simple conservation laws.

The Plebanski action is a formulation of gravity in terms of a first-order action, which is particularly useful in the context of general relativity and its formulations in the language of higher-dimensional theories or in the study of topological properties of spacetime. Specifically, the Plebanski action describes a theory of gravity that is expressed in terms of a 2-form field and a metric structure.

The Pöschl–Teller potential is a mathematical potential used in quantum mechanics that is characterized by its solvable nature and analytical properties. It is particularly notable because it can describe a variety of physical systems, including certain types of quantum wells and barriers. The potential is named after the physicists Richard Pöschl and H. J. Teller, who investigated it in the context of one-dimensional quantum mechanics.

Relativistic chaos refers to chaotic behavior in dynamical systems that are governed by the principles of relativistic physics, particularly those described by Einstein's theory of relativity. In classical mechanics, chaos can occur in nonlinear dynamical systems where small changes in initial conditions can lead to dramatically different outcomes; this phenomenon is often characterized by a sensitive dependence on initial conditions.