A **multigraph** is a type of graph in graph theory that allows for multiple edges between the same pair of vertices. This means that in a multigraph, it is possible to have two or more edges connecting the same vertices (like A and B) in addition to the regular edges that connect different pairs of vertices. In contrast, a simple graph does not allow multiple edges between the same pair of vertices or self-loops (edges that connect a vertex to itself).

Tetrathionate is a chemical compound that contains four sulfur atoms in its molecular structure. Its chemical formula is \( S_4O_6^{2-} \), and it is often encountered in the form of sodium tetrathionate (\( Na_2S_4O_6 \)) when it is in the salt form.

Thermal Integrity Profiling (TIP) is a method used primarily in civil engineering and construction to assess the integrity of concrete elements, particularly deep foundations like drilled shafts or bored piles. The technique leverages the heat generated during the hydration of concrete to create a temperature profile over time, which can provide insights into the quality and uniformity of the concrete placement.

The Beam Propagation Method (BPM) is a numerical technique used to simulate the propagation of electromagnetic waves, particularly in the context of optics and photonics. It is especially useful for analyzing waveguides and optical devices where light experiences significant changes in direction, such as in fiber optics, integrated optical circuits, and other photonic structures. ### Key Aspects of BPM: 1. **Wave Equation**: BPM is based on the solution of the scalar wave equation or the Helmholtz equation.

"Classical Electrodynamics" is a well-known textbook written by the physicist David J. Griffiths. It is widely used in graduate and advanced undergraduate courses in electromagnetism and is appreciated for its clarity, pedagogical approach, and thorough treatment of the subject. The book covers a range of topics in electromagnetism, including: 1. **Electrostatics**: The study of electric charges, electric fields, and potential energy in static situations.

Classical electromagnetism is a fundamental theory in physics that describes how electric charges interact with each other and with magnetic fields. It is based on the principles of classical physics, primarily articulated in the late 19th century through the formulation of Maxwell's equations, which unify electricity and magnetism into a single coherent framework. Here are some key components of classical electromagnetism: 1. **Electric Charge**: The basic property of matter that causes it to experience a force in an electric field.

The Larmor formula describes the power radiated by an accelerating charged particle, particularly in the context of classical electrodynamics. It is named after the British physicist Joseph Larmor, who derived the formula in the early 20th century.

A toposcope is a geographical tool or instrument used for visualizing and interpreting terrain features of a specific area. It typically consists of a horizontal disk marked with directional information, elevation data, and sometimes photographs or maps of the area that it represents. Toposcopes can be found in various settings, including scenic viewpoints, hiking trails, or historical landmarks, where they provide visitors with a way to identify and learn about the surrounding landscape and notable geographic features, such as mountains, rivers, and other landmarks.

"True north" refers to the direction along the earth's surface towards the North Pole, which is defined as the northernmost point on the globe where the Earth's axis of rotation meets its surface. In navigation and geography, true north is contrasted with magnetic north, which is the direction a compass points to and can vary due to magnetic declination. Understanding true north is essential for accurate navigation, cartography, and various outdoor activities like hiking and orienteering.

Jefimenko's equations are a set of equations in electrodynamics that describe the electric and magnetic fields produced by time-varying charge and current distributions. They are noteworthy because they provide an explicit expression for electromagnetic fields resulting from arbitrary distributions of charges and currents, without requiring the use of the more complex concepts of potentials. These equations are derived from Maxwell's equations and are especially important in the theory of electromagnetic radiation.

Materials with memory, often referred to as "shape memory materials," are a class of advanced materials that can undergo significant changes in shape or properties in response to external stimuli, such as temperature, stress, or electric/magnetic fields. The most well-known examples of shape memory materials include shape memory alloys (SMAs) and shape memory polymers (SMPs).

Band bending is a phenomenon that occurs in semiconductor physics and materials science, particularly at the interface between two different materials, such as a semiconductor and a metal or between two different semiconductors. It describes the change in energy band structure, specifically the bending of the energy bands (valence band and conduction band) in response to an electric field, charge distribution, or the presence of interfaces.

In mathematics, a locus (plural: loci) is a set of points that satisfy a particular condition or a set of conditions. It can be thought of as a geometric shape or figure that represents all possible locations in a given space that meet specified criteria. For example: 1. **Circle**: The locus of all points that are a fixed distance (radius) from a given point (the center) defines a circle.

Metal-induced gap states (MIGS) are electronic states that can form in the band gap of a semiconductor when a metal is in contact with it. These states emerge due to the interaction between the metal and the semiconductor's surface, which can modify the electronic structure. When a metal is deposited on a semiconductor, the Fermi level of the metal aligns with the energy levels in the semiconductor, creating an interface.

An algebraic fraction is a fraction in which the numerator and/or the denominator are algebraic expressions. An algebraic expression is an expression that can include numbers, variables (like \(x\) or \(y\)), and algebraic operations such as addition, subtraction, multiplication, and division. For example, the following are algebraic fractions: 1. \(\frac{x^2 + 2x + 1}{x - 1}\) 2.

Algebraic operations refer to mathematical processes that manipulate algebraic expressions and equations using rules of algebra. The primary algebraic operations include: 1. **Addition**: Combining two or more algebraic expressions. For example, \(a + b\) or \(2x + 3x = 5x\). 2. **Subtraction**: Removing one algebraic expression from another.

"Cancelling out," in a general context, refers to the process of nullifying or counteracting something so that it no longer has an effect or significance. This term can be applied in various fields, including mathematics, science, and everyday situations. Here are a few examples: 1. **Mathematics**: In algebra, cancelling out often refers to the process of simplifying fractions or equations.

In mathematics, the term "conjugate" can refer to different concepts depending on the context, particularly in complex numbers and algebraic expressions.

Equating coefficients is a mathematical technique often used to solve polynomial equations or to find relationships between different algebraic expressions. This method is particularly useful in situations where you have two polynomials that are set equal to each other, and you want to find values for their coefficients or variables. Here's how it generally works: 1. **Setup Equations**: Start with two polynomials that are equal to each other.

A worm's-eye view is a perspective used in photography, art, and visual storytelling that depicts a scene from a low angle, as if the viewer were at the level of a worm looking up. This perspective can emphasize the height of objects, such as buildings or trees, creating a sense of grandeur or immensity. It often conveys feelings of vulnerability or insignificance, as the viewer sees the world from a position that is usually not encountered in everyday life.