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 \( y \).

Weber's theorem in the context of algebraic curves pertains to the genus of a plane algebraic curve. Specifically, the theorem provides a way to compute the genus of a smooth projective algebraic curve defined by a polynomial equation in two variables.

The Graham–Pollak theorem is a result in graph theory that pertains to the relationships between the edges of a complete graph and the configurations of points in Euclidean space. Specifically, it states that for a complete graph on \( n \) vertices, the number of edges that can be embedded in \( \mathbb{R}^d \) (real d-dimensional space) without any three edges crossing is limited.

An incidence matrix is a mathematical representation used primarily in graph theory and related fields to represent the relationship between two classes of objects. In the context of graph theory, an incidence matrix is used to describe the relationship between vertices (nodes) and edges in a graph.