An **algebraic curve** is a curve defined by a polynomial equation in two variables with coefficients in a given field, often a field of real or complex numbers. More formally, an algebraic curve can be described as the set of points (x, y) in the plane that satisfy a polynomial equation of the form: \[ F(x, y) = 0 \] where \( F(x, y) \) is a polynomial in two variables.

N-ary associativity refers to a property of operations or functions that can be applied to multiple operands (or "n" operands) in a way that allows for flexible grouping without altering the result.

A **normed algebra** is a specific type of algebraic structure that combines features of both normed spaces and algebras. To qualify as a normed algebra, a mathematical object must meet the following criteria: 1. **Algebra over a field**: A normed algebra \( A \) is a vector space over a field \( F \) (typically the field of real or complex numbers) equipped with a multiplication operation that is associative and distributive with respect to vector addition.

The term "recurrent word" generally refers to a word that appears multiple times in a given text or context. In the study of language, literature, or data analysis, identifying recurrent words can be important for understanding themes, frequency of concepts, or the focus of a discussion. In computational contexts, such as natural language processing (NLP), recurrent words might also be analyzed to understand patterns in text, to build models for tasks like text classification, sentiment analysis, or topic modeling.

A system of bilinear equations involves equations that are bilinear in their variables. A bilinear equation is one where the product of two variables appears linearly.

A **topological semigroup** is a mathematical structure that combines elements of both semigroup theory and topology. Specifically, it is a set equipped with a binary operation that is associative and is also endowed with a topology that makes the operation continuous.

A Moody chart, also known as the Moody diagram, is a graphical representation used in fluid mechanics to determine the friction factor for flow in pipes. It provides a way to estimate the pressure loss due to friction in a duct or pipe system, which is critical for engineers and designers when designing fluid transport systems.

The Lyndon–Hochschild–Serre spectral sequence is a tool in algebraic topology and homological algebra that arises in the context of group cohomology and the study of group extensions. It provides a method for computing the cohomology of a group \( G \) by relating it to the cohomology of a normal subgroup \( N \) and the quotient group \( G/N \).

A bifolium is a term used in bookbinding and manuscript studies to refer to a single sheet of paper or parchment that is folded in half to create two leaves (or four pages). The word "bifolium" comes from Latin roots: "bi-" meaning two and "folium" meaning leaf.

A Cartesian oval is a type of mathematical curve that is defined as the locus of points that have a constant ratio of distances to two fixed points, known as foci.

The Hodge bundle is a significant object in the study of algebraic geometry and the theory of Hodge structures. Specifically, the term "Hodge bundle" often refers to a certain vector bundle associated with a smooth projective variety or a complex algebraic variety, particularly when considering its cohomology.

A Jacobian variety is a fundamental concept in algebraic geometry and is associated with algebraic curves. Specifically, it is the complex torus formed by the points of a smooth projective algebraic curve and is used to study the algebraic properties of the curve.

Bikiran Prasad Barua is likely a notable figure or a term that is associated with specific cultural, historical, or regional significance, particularly in the context of Assamese culture or history. If you are looking for detailed information about him, please provide more context or specify the area of interest, such as his contributions, background, or relevance in a particular field. This will help in giving a more accurate and informative response.

A quartic plane curve is a type of algebraic curve defined by a polynomial equation of degree four in two variables, typically \( x \) and \( y \).