In linear algebra, a **minor** is a specific determinant that is associated with a square matrix. The minor of an element in a matrix is defined as the determinant of the submatrix formed by deleting the row and column in which that element is located.

In the context of abstract algebra, particularly in the study of modules over a ring, a **cyclic module** is a specific type of module that can be generated by a single element. More formally, let \( R \) be a ring and let \( M \) be a module over \( R \).

The Eilenberg–Mazur swindle is a technique in category theory and algebraic topology used to show that certain objects can be manipulated in a way that results in unexpected behaviors, particularly in the context of homological algebra. Specifically, it's often applied to demonstrate that certain abelian groups or modules can be considered "equivalent" by constructing a specific kind of isomorphism that leads to counterintuitive results.

The N! conjecture is a mathematical hypothesis related to combinatorial structures, particularly focusing on permutations and certain types of combinatorial objects. More specifically, the conjecture proposes that for any integer \( N \), there exists a link between the factorial of \( N \) (denoted as \( N! \)) and certain countable properties of permutations or combinations of \( N \) items. One of the well-known formulations of the N!

A multivector is an algebraic concept used primarily in the context of geometric algebra and vector calculus. It extends the idea of scalars (0D), vectors (1D), and bivectors (2D) to higher dimensions, providing a unified framework for various mathematical objects. In more detail: 1. **Definition**: A multivector is an element of a geometric algebra that can be expressed as a linear combination of scalars, vectors, bivectors, and higher-dimensional entities.

The linearity of differentiation refers to the property of the derivative operator that allows it to be distributed over addition and scalar multiplication.

In category theory, the term "lemma" is not a formal term with a specific definition, but rather refers to a proposition or statement that is proved and used as an aid in the proof of a larger theorem. In the context of mathematical writing, lemmas serve to break down complex arguments into smaller, more manageable parts.

Ralph Hiscox is not widely recognized, and there may not be specific widely known information about an individual by that name that is readily available. It's possible that he could be a private individual or a lesser-known figure.

Mark Bew is a prominent figure in the construction and engineering sectors, known for his contributions to digital transformation and the advancement of technology in infrastructure projects. He is associated with initiatives aimed at improving the efficiency and effectiveness of construction through the use of digital tools and methodologies. In particular, he has been involved with the development and promotion of BIM (Building Information Modeling) standards, advocating for their adoption to enhance collaboration and data sharing among stakeholders in the construction industry.

Product Structure Modeling refers to the process of defining and organizing the various components, subsystems, and relationships within a product. It is an integral part of product design and development, allowing teams to visualize, analyze, and manage the complex interactions and dependencies that exist within a product. Here are some key aspects of Product Structure Modeling: 1. **Hierarchical Representation**: The model often takes a hierarchical form, breaking down the product into its main components and subcomponents.

ROHR2 is a software tool used for the design and analysis of pressure vessels, piping, and other industrial equipment. It is often utilized in fields such as mechanical engineering, chemical engineering, and petrochemical industries. The software supports users in conducting stress analysis, preparing design calculations, and ensuring compliance with relevant standards and regulations, such as ASME (American Society of Mechanical Engineers) and other international codes.

SolveSpace is a parametric 2D and 3D CAD (computer-aided design) software that is primarily used for modeling, simulation, and design purposes. It is particularly notable for its parametric capabilities, allowing users to create models that can be easily adjusted by changing parameters, which is useful in design engineering and product development.

T-splines are a type of mathematical model used primarily in computer-aided design (CAD), computer graphics, and finite element analysis. They are an extension of NURBS (Non-Uniform Rational B-Splines) and offer benefits such as easier local control and the ability to represent complex geometries more efficiently.

XPIC, or Cross-Polarization Interference Cancelling, is a technology used in satellite communications to enhance the performance of communication links by reducing interference caused by cross-polarization. In satellite communications, signals intended for transmission can become mixed with signals of the opposite polarity, leading to degradation in signal quality and reliability. XPIC is particularly significant in systems utilizing polarization multiplexing, where two separate signals are transmitted simultaneously using different polarizations (horizontal and vertical, for instance).

Stephen Wiggins is a notable mathematician known for his work in the field of dynamical systems and differential equations. He has made significant contributions to understanding the behavior of dynamical systems, including aspects of chaos theory, bifurcation theory, and the mathematical modeling of physical systems. Wiggins is also known for his educational contributions, including textbooks that are widely used in graduate-level courses.

Securitization is a financial process that involves pooling various types of contractual debts, such as mortgages, car loans, or credit card debt, and then selling them as consolidated financial instruments, typically in the form of bonds, to investors. This process transforms illiquid assets into securities that can be traded in the financial markets.

In physics, "spin" is a fundamental property of particles, similar to charge or mass. It is an intrinsic form of angular momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei. Spin is a quantum mechanical phenomenon that does not have a direct classical analogue. Key aspects of spin include: 1. **Quantization**: Spin can take on only certain discrete values, characterized by quantum numbers.

Quantum configuration space is a concept used in quantum mechanics that extends the idea of classical configuration space, which refers to the set of all possible positions of a system of particles.

Qubit field theory is an emerging framework that combines concepts from quantum field theory (QFT) with the discrete nature of qubits, which are the fundamental units of quantum information. While traditional quantum field theory deals with continuous fields and is used to describe particle physics and interactions in a relativistic quantum context, qubit field theory explores how quantum fields can be discretized and treated in terms of qubits—essentially treating quantum states as combinations (superpositions) of binary values.