Asymmetry refers to a lack of equality or equivalence between parts or aspects of something, resulting in an imbalance or disproportion. This concept can be applied in various contexts, including: 1. **Mathematics and Geometry**: In geometry, an asymmetrical shape does not have mirror symmetry or rotational symmetry. For example, a scalene triangle, where all sides and angles are different, is asymmetrical.

CPT symmetry is a fundamental principle in theoretical physics that combines three symmetries: Charge conjugation (C), Parity transformation (P), and Time reversal (T). 1. **Charge Conjugation (C)**: This symmetry relates particles to their antiparticles. For example, it transforms an electron into a positron and vice versa. 2. **Parity Transformation (P)**: This symmetry involves flipping the spatial coordinates, effectively reflecting a system through the origin.

Coxeter notation is a way of representing regular polytopes and their higher-dimensional analogs (such as regular polygons, polyhedra, and polychora) using a system based on pairs of numbers. It employs a compact notation that often consists of a string of integers, occasionally including letters or specific symbols to indicate certain geometric properties, relations, or symmetries.

A crystallographic point group is a mathematical classification of the symmetry of a crystal structure. These groups describe the symmetry operations that leave at least one point (typically the origin) invariant, meaning those operations do not alter the position of that point. The main symmetry operations included in crystallographic point groups are: 1. **Rotation**: Turning the crystal around an axis. 2. **Reflection**: Flipping the crystal across a plane.

Cymatics is the study of visible sound and vibration. The term is derived from the Greek word "kyma," meaning "wave." It refers to the phenomenon where sound waves create visible patterns in a medium, usually a viscous substance like water or a powder. In cymatics, sound frequencies are applied to a surface, causing it to resonate.

The FKG inequality, named after its contributors Fortuin, Kasteleyn, and Ginibre, is a result in probability theory that provides a relationship among joint distributions of certain random variables, particularly in the context of lattice structures, such as spins in statistical mechanics. It is most commonly applied in the study of lattice models in statistical physics, including the Ising model.

Inversion transformation typically refers to an operation used in various fields, including mathematics, computer science, statistics, and image processing. The specific meaning can vary based on the context, but here are a few common interpretations: 1. **Mathematics**: In mathematics, an inversion transformation often refers to a transformation that maps points in a space such that points are inverted relative to a particular point (the center of inversion) or a shape (like a circle or sphere).

A **non-Euclidean crystallographic group** refers to a symmetry group that arises in the study of lattices and patterns in geometries that are not based on Euclidean space. Crystallographic groups describe how a pattern can be repeated in space while maintaining certain symmetries, including rotations, translations, and reflections. In Euclidean geometry, the classifications of crystallographic groups are based on the 17 two-dimensional plane groups and the 230 three-dimensional space groups.

In geometry, symmetry refers to a property of a shape or object that remains unchanged under certain transformations, such as reflection, rotation, translation, or scaling. A geometric figure is said to be symmetric if there is a way to map it onto itself while preserving its overall structure and appearance.

Supersymmetry (SUSY) is a theoretical framework in particle physics that proposes a symmetry between two basic classes of particles: fermions (which make up matter, like electrons and quarks) and bosons (which mediate forces, like photons and gluons). In a fully realized supersymmetric model, each particle in the Standard Model of particle physics would have a superpartner with differing spin.

A "pancake sentence" is a type of sentence in which the structure allows for the stacking of phrases or clauses in a way that resembles the layering of pancakes. In this context, it typically refers to sentences that are structured with multiple elements, each building upon the previous one, often leading to a long, complex construction.

A **parse tree**, also known as a **syntax tree** or **derivation tree**, is a tree representation that illustrates the syntactic structure of a string according to a formal grammar. It is commonly used in the fields of computer science, particularly in programming language processing, natural language processing, and compiler design. ### Key Components of a Parse Tree: 1. **Root**: The top node of the tree, representing the starting symbol of the grammar.

Tessellation is a geometric concept that refers to the covering of a plane with one or more geometric shapes, called tiles, without any overlaps or gaps. These shapes can be regular polygons, irregular shapes, or even complex figures. The key characteristics of a tessellation are that it must fill the entire surface without leaving any spaces between the tiles and the tiles may be rotated and flipped as long as they fit together seamlessly.

Syntactic categories, also known as parts of speech, refer to the classifications of words based on their functions and roles in sentences. These categories help in understanding the structure of sentences and how different words interact with one another to convey meaning. Here are some common syntactic categories: 1. **Nouns**: Words that name people, places, things, or ideas (e.g., "dog," "city," "happiness").

Isoelastic utility, also known as constant relative risk aversion (CRRA) utility, is a type of utility function used in economics to model the preferences of individuals with respect to consumption over time and uncertainty. The key characteristics of isoelastic utility are that it represents a consistent level of relative risk aversion and exhibits constant elasticity of substitution between different levels of consumption.

In grammar, an antecedent is the word, phrase, or clause that a pronoun refers to or replaces. It typically appears earlier in the sentence or in a preceding sentence. Understanding the relationship between an antecedent and its pronoun is crucial for clarity and coherence in writing. For example, in the sentence: "The dog barked loudly, and it scared the neighbors." Here, "the dog" is the antecedent of the pronoun "it.

A clitic is a linguistic unit that has characteristics of both a word and a morpheme. It is a form that cannot stand alone as a separate word and must attach to another word (usually a host) to convey meaning. Clitics often serve grammatical functions, such as indicating possession, conjunction, or tense. Clitics can be classified into two main types: 1. **Proclitic**: A clitic that attaches to the beginning of a host word.

In linguistics, a "constituent" refers to a word or a group of words that function as a single unit within a hierarchical structure of a sentence. Constituents can be phrases or even individual words that can serve as subjects, objects, or complements in a sentence. The study of constituents is fundamental in syntax, which examines how words combine to create phrases and sentences.

In linguistics, coordination refers to the grammatical and syntactic process of linking two or more elements of equal status within a sentence. These elements can include words, phrases, or clauses. Coordination is typically achieved through coordinating conjunctions (also known as coordinators), the most common of which are "and," "but," and "or.

Basically a synonym of trope, but without the negative connotation.