"Numbers," also styled as "Numb3rs," is an American crime drama television series that aired on CBS from January 2005 to March 2010. The show was created by Nicolas Falacci and Cheryl Heuton. The premise revolves around FBI agent Don Eppes, played by Rob Morrow, who recruits his brother Charlie Eppes, portrayed by David Krumholtz, a mathematical genius, to help solve crimes.
A partial differential equation (PDE) is a type of mathematical equation that involves partial derivatives of an unknown function with respect to two or more independent variables. Unlike ordinary differential equations (ODEs), which deal with functions of a single variable, PDEs allow for the modeling of phenomena where multiple variables are involved, such as time and space.
Perturbation theory is a mathematical technique used in various fields, including physics, chemistry, and engineering, to find an approximate solution to a problem that cannot be solved exactly. It is particularly useful in quantum mechanics, where systems can often be analyzed in terms of small changes (or "perturbations") to a known solvable system.
Perturbation theory in quantum mechanics is a mathematical method used to find an approximate solution to a problem that cannot be solved exactly. It is particularly useful when the Hamiltonian (the total energy operator) of a quantum system can be expressed as the sum of a solvable part and a "perturbing" part that represents a small deviation from that solvable system. ### Key Concepts 1.
Potential theory is a branch of mathematical analysis that deals with potentials and potential functions, typically in relation to fields such as electrostatics, gravitation, fluid dynamics, and various areas of applied mathematics. The theory is largely concerned with the behavior of harmonic functions and their properties. At its core, potential theory examines the concept of a potential function, which describes gravitational or electrostatic potentials in physics.
Pregeometry is a concept in theoretical physics that seeks to describe the fundamental structure of spacetime and matter in a way that is more primitive than the traditional notions of geometry used in classical and quantum physics. The idea is that the familiar geometric structure of spacetime, as described by general relativity, emerges from a more basic underlying framework that does not rely on pre-existing notions of points, lines, and surfaces.
A crystallographic database is a specialized repository that stores and organizes crystallographic data, which includes information about the arrangement of atoms within crystalline materials. These databases are crucial for researchers in fields like chemistry, materials science, and solid-state physics, as they provide essential data for the analysis and understanding of crystal structures.
A **propagator** is a concept used in various fields, particularly in physics and mathematics, with specific meanings depending on the context: 1. **Quantum Field Theory (QFT)**: In the context of quantum field theory, a propagator is a mathematical function that describes the behavior of particles as they propagate from one point to another in spacetime. It essentially provides a mechanism to account for the interactions and effects of fields and particles.
Spin structure is a concept from topology and theoretical physics that arises in the context of manifold theory, particularly in relation to spin manifolds. In mathematics, a spin structure is typically defined on a manifold that enables the definition of spinors, which are mathematical objects that generalize the notion of complex numbers and vectors.
The "stability of matter" refers to the concept that matter, in various forms, tends to maintain its structure and properties under certain conditions. This stability is a fundamental aspect of physics and chemistry, encompassing both atomic and molecular stability, as well as material stability on larger scales. Key aspects of the stability of matter include: 1. **Atomic Structure**: Atoms are composed of protons, neutrons, and electrons.
A **supermanifold** is a mathematical structure that generalizes the concept of a manifold by incorporating both commuting and anti-commuting coordinates. These structures arise in the context of **supersymmetry** in theoretical physics, particularly in string theory and the study of supersymmetric quantum field theories. In a standard manifold, coordinates are typically real numbers that commute with each other. In contrast, supermanifolds introduce additional "Grassmann" coordinates, which are anti-commuting variables.
Supersymmetry (SUSY) algebras are extensions of the Poincaré algebra that include fermionic generators, which act on bosonic and fermionic states. In 1+1 dimensions, the structure of supersymmetry algebras is somewhat simplified compared to higher dimensions.
Symmetry-protected topological order (SPT order) is a concept in condensed matter physics and quantum many-body systems that describes certain phases of matter. These phases are characterized by long-range quantum entanglement and unusual global properties, and they exist in a manner that is robust against local perturbations, as long as certain symmetries are preserved.
The theory of sonics generally refers to the study of sound, its properties, and its behavior in various environments. It encompasses several fields, including physics, engineering, music, and acoustics. Here are some key components involved in the theory of sonics: 1. **Sound Waves**: Sonics examines how sound waves travel through different mediums—such as air, water, and solids. It looks at properties like frequency, wavelength, amplitude, and speed.
The three-body problem is a classic problem in physics and mathematics that involves predicting the motion of three celestial bodies as they interact with one another through gravitational forces. The challenge of the three-body problem arises from the fact that while the gravitational interactions between two bodies can be described by simple equations (the two-body problem), adding a third body leads to a complex and chaotic system that generally cannot be solved analytically.
The Toda oscillator is a type of nonlinear dynamical system that serves as a model for studying certain physical phenomena, particularly in the context of lattice dynamics and integrable systems in statistical mechanics. It was introduced by the Japanese physicist M. Toda in the 1960s. The Toda oscillator consists of a chain of particles that interact with nearest neighbors through a nonlinear potential. Specifically, the potential energy between two adjacent particles is typically described by an exponential form, which leads to rich dynamical behavior.
Topological recursion is a mathematical technique developed primarily in the context of algebraic geometry, combinatorics, and mathematical physics. It is particularly employed in the study of topological properties of certain kinds of mathematical objects, such as algebraic curves, and it has connections to areas like gauge theory, string theory, and random matrix theory. The concept was introduced by Mirzayan and others in the context of enumerative geometry and has found numerous applications since then.
Darken's equations are a set of thermodynamic relations in physical chemistry, specifically related to the diffusion of species in multicomponent systems. They provide a way to relate the fluxes of components in a mixture to their concentrations, and are particularly useful in describing transport phenomena in liquid mixtures and solid solutions. The key components of Darken's equations include: 1. **Diffusion Flux**: The flux of a component \( i \) is represented by \( J_i \).