A **reduced residue system** is a set of integers that are representatives of the distinct equivalence classes of integers modulo \( n \), where \( n \) is a positive integer, and each representative in the set is coprime to \( n \). In other words, a reduced residue system modulo \( n \) consists of integers that are both less than \( n \) and relatively prime to \( n \).

The Pisano period, denoted as \( \pi(m) \), is the period with which the sequence of Fibonacci numbers repeats modulo \( m \). In other words, if you take the Fibonacci sequence \( F_0, F_1, F_2, \ldots \), and reduce each number modulo \( m \), the resulting sequence will eventually start repeating. The length of this repeating sequence is known as the Pisano period for \( m \).

Supersymmetry (often abbreviated as SUSY) is a theoretical framework in particle physics that posits a relationship between two fundamental classes of particles: bosons and fermions. In the standard model of particle physics, bosons are force-carrying particles (e.g., photons, W and Z bosons, and gluons) that have integer spin, while fermions are matter particles (e.g., quarks and leptons) that have half-integer spin.

Pocklington's algorithm is a method used to test the primality of large integers. It was developed by the mathematician Henry Pocklington in 1914 and is particularly effective for numbers that can be represented in a specific form. The algorithm is based on the properties of prime numbers and relies on certain mathematical theorems related to divisibility and modular arithmetic.

The term "J-line" can refer to different concepts depending on the context in which it is used. Here are a few possibilities: 1. **Geometric or Mathematical Context**: In mathematics, especially in geometry and algebra, J-line may refer to curves or lines that follow a specified geometric property. However, this usage is not very common and could be specific to certain mathematical texts or studies.

In algebraic geometry, a **moduli scheme** is a geometric object that parameterizes a family of algebraic varieties (or schemes) with specific properties or structures. The idea is to study how these varieties vary and how they can be classified. Specifically, a moduli scheme provides a systematic way to understand families of objects of a given type, often incorporating varying geometric or algebraic structures.

A table of congruences is a systematic way to present the relationships between integers under modular arithmetic. It displays which numbers are congruent to each other modulo a particular base (or modulus). In modular arithmetic, two integers \( a \) and \( b \) are said to be congruent modulo \( n \) (written as \( a \equiv b \mod n \)) if they have the same remainder when divided by \( n \).

Vertex operator algebras (VOAs) are mathematical structures that arise in the study of two-dimensional conformal field theory, algebraic structures, and number theory. They play a significant role in various areas of mathematics and theoretical physics, particularly in the study of string theory, modular forms, and representation theory.

Thue's lemma, also known as Thue's theorem, is a result in the field of Diophantine approximation and number theory, named after the mathematician Axel Thue. The lemma addresses the approximation of real numbers by rationals and is particularly concerned with the properties of certain algebraic numbers.

The Tonelli–Shanks algorithm is a method used to compute square roots in finite fields, particularly useful for finding square roots of a number modulo a prime. This algorithm is significant in number theory and has applications in cryptography, especially in schemes dealing with quadratic residues.

Vantieghem's theorem is not a widely recognized theorem in mathematics or science, and it seems that there may be some confusion regarding the name. It's possible that it's a misspelling or miscommunication of a different theorem or concept. If you're referring to a specific area of mathematics or a particular field (such as graph theory, number theory, etc.

A **stable map** is a concept that arises in the context of algebraic geometry and topology, particularly when discussing the stability of certain mathematical objects under deformation. The term can refer to different specific definitions depending on the field of study, but one common context for stable maps is in relation to stable curves and their moduli.

APBS stands for Adaptive Poisson-Boltzmann Solver. It is a software package used primarily in computational biology and chemistry for solving the Poisson-Boltzmann equation, which is a mathematical representation of electrostatic interactions in systems like proteins, nucleic acids, and membranes in a solvent. APBS is particularly useful for calculating electrostatic potentials, which can help researchers understand how molecular structures interact with each other and their environment, especially in biological contexts.

The Critical Assessment of Prediction of Interactions (CAPRI) is a well-established initiative aimed at evaluating the accuracy of computational methods for predicting protein-protein and protein-ligand interactions. It serves as a platform for researchers to benchmark their computational algorithms against experimental results, thereby providing an assessment of the current state-of-the-art in the field of molecular modeling and docking simulations.

The Dewar reactivity number is a chemical concept used to assess the reactivity of a particular compound, particularly in the context of organic and inorganic chemistry. It is a numerical value assigned to the stability and reactivity of alkyl and aryl halides, aiding in the prediction of how these compounds will behave in various chemical reactions, such as nucleophilic substitutions and eliminations.

Sumio Iijima is a renowned Japanese physicist and nanotechnology pioneer, best known for his discoveries related to carbon nanotubes. He first reported the observation of carbon nanotubes in 1991 while working at NEC. His work has had a significant impact on materials science, nanotechnology, and electronics, leading to advancements in various applications, including electronics, materials engineering, and nanomedicine.

Cn3D (Coordinate Navigation 3D) is a software application developed by the National Center for Biotechnology Information (NCBI) that allows users to visualize 3D structures of biomolecules, primarily proteins and nucleic acids. It provides an interactive graphical interface where researchers can explore the spatial arrangements of atoms in a molecular structure, navigate through different zoom levels, and manipulate the view to understand molecular interactions, conformational changes, and other important features of the biomolecule.

Coulson-Fischer theory is a concept in computational chemistry that pertains to the electronic structure of molecules, particularly focusing on the description of electron correlation and electron density in molecular systems. It is mainly associated with the development and understanding of molecular orbital theory. The theory is named after the chemists Arthur Leslie Coulson and Walter Fischer, who contributed to the field of molecular orbital theory in the mid-20th century.