A capacitance probe is a type of sensor used to measure the level of liquids or solids by detecting changes in capacitance. It operates on the principle that the capacitance of a capacitor changes when the dielectric constant of the material between its plates changes, which occurs when the level of a substance (like liquid or solid) rises or falls.

Chemical polarity refers to the distribution of electrical charge over the atoms in a molecule. It describes how the bonding electrons are distributed between the atoms, which can lead to the formation of regions with partial positive and negative charges within the molecule. Polarity occurs due to differences in electronegativity between the atoms involved in a chemical bond. Electronegativity is the tendency of an atom to attract electrons towards itself.

"Gel" can refer to a few different things, depending on the context: 1. **Substance**: In a scientific or everyday context, a gel is a semi-solid, jelly-like substance that has properties between a liquid and a solid. Gels are often made by mixing a liquid with a gelling agent, which creates a network that traps the liquid, giving it a gel-like consistency. Common examples include gelatin, alginate, and agar.

Inner sphere electron transfer is a mechanism of electron transfer that involves a direct coordinate bond formation between the donor and acceptor species during the transfer process. This type of electron transfer is commonly discussed in the context of inorganic and organometallic chemistry, particularly in redox reactions involving metal complexes.

The Peter Debye Award in Physical Chemistry is an accolade presented by the American Chemical Society (ACS) to recognize outstanding contributions to the fields of physical chemistry. Established in honor of Peter Debye, a notable physical chemist and Nobel laureate, the award highlights achievements that significantly advance the understanding of physical chemistry, which includes studies on molecular structures, dynamics, thermodynamics, and other related areas.

In computer vision, "pose" refers to the position and orientation of an object in three-dimensional space. The term is often used in the context of human pose estimation, which involves determining the spatial arrangement of a person's body parts, typically represented as keypoints or joints. This can include the location of the head, shoulders, elbows, wrists, hips, knees, and ankles, among others.

The term "57-cell" can refer to a specific type of mathematical object in the field of geometry, particularly in the study of higher-dimensional polytopes. In this context, a "cell" refers to a higher-dimensional analogue of a polygon or polyhedron.

An icosahedral prism is a three-dimensional geometric shape that combines the properties of an icosahedron and a prism. An icosahedron is a polyhedron with 20 triangular faces, 12 vertices, and 30 edges. A prism, in general, is a solid shape with two parallel bases that are congruent polygons, and rectangular faces connecting the corresponding sides of the bases.

An icosahedral pyramid is a geometric structure that can be described as a pyramid whose base is an icosahedron—a polyhedron with 20 triangular faces. In this context, the term "pyramid" refers to a shape formed by connecting a point (the apex) to each vertex of the base, which in this case is the icosahedron.

A tetrahedral cupola is a type of geometric solid that features characteristics of both a tetrahedron and a cupola. It can be understood as a combination of two shapes: 1. **Tetrahedron**: A polyhedron with four triangular faces, six edges, and four vertices. 2. **Cupola**: A polyhedron formed by the combination of a polygonal base and two congruent polygonal faces on top, typically resulting in a shape that has an apex.

A truncated cubic prism is a geometric shape that can be described as a prism with its top and bottom faces being truncated (cut off) in such a way that the shape retains a polygonal top and a polygonal bottom, typically with the base being a rectangle or square.

An apeirogonal hosohedron is a type of polyhedron that is characterized by having an infinite number of faces, specifically, an infinite number of edges and vertices. The term "apeirogon" refers to a polygon with an infinite number of sides, and the term "hosohedron" refers to a polyhedron that is constructed by extending the concept of polygonal faces into three dimensions.

The term "atoroidal" generally refers to a shape or object that is not toroidal or donut-shaped. In a toroidal structure, there is a central void around which the material is distributed in a circular manner, resembling a donut. By contrast, an "atoroidal" shape would lack this characteristic of having a central void or hole, meaning it could refer to various forms such as spherical, cylindrical, or other geometrical shapes that do not incorporate the toroidal geometry.

A **spectrahedron** is a mathematical concept that arises in the context of convex geometry and optimization. More specifically, it refers to a type of convex set that can be defined using eigenvalues of certain matrices. The term is often associated with the study of semidefinite programming and various applications in optimization, control theory, and quantum physics.

In projective geometry, theorems and principles focus on properties of geometric figures that remain invariant under projective transformations. Projective geometry is primarily concerned with relationships and properties that are not dependent on measurements of distance or angles, but rather on incidence, collinearity, and concurrency.

ProSTEP iViP is a non-profit organization based in Germany that focuses on promoting and advancing the digitalization of product development and lifecycle management in the manufacturing and engineering sectors. The name "ProSTEP iViP" stands for "Project STEP - Innovative Virtual Product," and the organization plays a vital role in facilitating collaboration between industry and research institutions.

Liouville's theorem in the context of conformal mappings relates to the properties of holomorphic (or analytic) functions defined on the complex plane. Specifically, the theorem states that any entire (holomorphic everywhere in the complex plane) function that is bounded is constant.

The Non-Squeezing Theorem is a fundamental result in symplectic geometry, a branch of mathematics that studies structures and properties of spaces that are equipped with a symplectic form. Specifically, the theorem addresses the concept of symplectic embeddings, which are mappings between symplectic manifolds that preserve the symplectic structure. The Non-Squeezing Theorem asserts that there are limitations on how one can "squeeze" or transform symplectic spaces.