Brellochs reaction refers to a specific chemical reaction involving the conversion of an alkyl halide to an alkane using zinc in an acid medium, typically used in organic synthesis. This reaction is notable for its ability to remove halogen atoms and form carbon-carbon bonds. The general mechanism involves the formation of a zinc halide intermediate, which then undergoes reduction to produce the final alkane product.

Brian Schmidt is an American astrophysicist known for his work in the fields of cosmology and the study of the accelerating expansion of the universe. He was awarded the Nobel Prize in Physics in 2011, sharing the prize with Saul Perlmutter and Adam Riess, for their discovery of the acceleration of the universe's expansion through observations of distant supernovae.

Geometric morphometrics is a quantitative approach used in anthropology and other fields, primarily to study the shapes and forms of biological structures. It involves the statistical analysis of geometric data to understand biological variations in shape, which can be particularly useful for examining morphological changes over time, differences between populations, or adaptations to environmental pressures.

Bristol Perambulation refers to an historical tradition in Bristol, England, where officials and citizens would walk around the boundaries of the city. This practice was not just a ceremonial event but also served to reaffirm and maintain the city's legal boundaries. The event usually involved local dignitaries, such as the mayor and other officers, who would traverse specific routes, often accompanied by citizens, and occasionally include festivities along the way.

Proper acceleration is the acceleration that an object experiences as measured by an accelerometer carried with that object. It is the physical acceleration felt by an observer in a non-inertial reference frame, taking into account any forces acting on the object, such as gravitational and inertial forces. In contrast to coordinate acceleration, which can vary depending on the observer's frame of reference, proper acceleration is an absolute measure of how an object is accelerating in its own frame.

British crystallographers refer to scientists and researchers in the United Kingdom who specialize in crystallography, the study of the arrangement of atoms in crystalline solids. Crystallography is crucial in various fields, including chemistry, physics, biology, and materials science, as it helps determine the structure of molecules and solids, leading to insights in areas like drug development, materials engineering, and understanding biological structures.

The British National Corpus (BNC) is a large, structured collection of texts that represent a wide variety of written and spoken English from the late 20th century, specifically designed to provide a comprehensive overview of contemporary British English usage. Compiled between 1991 and 1994, the BNC includes about 100 million words and covers diverse genres, such as literature, newspapers, academic texts, spoken conversations, and more.

Brook Taylor (1685–1731) was an English mathematician best known for his contributions to calculus and for the Taylor series, which is named after him. The Taylor series is a method that expresses a function as an infinite sum of terms calculated from the values of its derivatives at a single point. This concept is fundamental in mathematical analysis, providing a way to approximate complex functions with polynomials.

The Brouwer–Heyting–Kolmogorov (BHK) interpretation is a key principle in intuitionistic logic and type theory that provides a constructive interpretation of mathematical statements. It is named after mathematicians L.E.J. Brouwer, Arend Heyting, and Andrey Kolmogorov. Unlike classical logic, which allows for non-constructive proofs (such as proof by contradiction), intuitionistic logic emphasizes the need for constructive evidence of existence.

Brown–Peterson cohomology is a homology theory in algebraic topology that is particularly focused on stable homotopy and complex cobordism. Introduced by Ronald Brown and F. P. Peterson in the context of stable homotopy theory, it serves as a tool for studying the cohomological properties of topological spaces, especially with respect to the stable homotopy category.

The Bruss–Duerinckx theorem is a result in the field of probability theory and mathematical finance, specifically related to the pricing and replication of contingent claims in incomplete markets. It presents conditions under which a contingent claim can be obtained as the limit of portfolios in a given financial market. The theorem states that if a financial market is incomplete, then under certain conditions, there exists an equivalent martingale measure (a probability measure that allows for the pricing of contingent claims).

Bulletproof hosting refers to a type of web hosting service that is designed to be resistant to legal action, often providing extremely high levels of privacy and anonymity. These hosting services typically cater to clients who engage in or promote illegal activities, such as cybercrime, malware distribution, phishing, and other illicit online ventures.

The Burr–Erdős conjecture is a statement in combinatorial mathematics related to graph theory. It was proposed by mathematicians Charles J. Burr and Paul Erdős in the early 1980s. The conjecture deals with the properties of graphs and specifically focuses on the existence of certain kinds of subgraphs within larger graphs.

Large deviations theory is a branch of probability theory that deals with the study of rare events—specifically, events that deviate significantly from expected behavior. It provides a mathematical framework for quantifying the probabilities of these rare deviations from the average or typical outcome of a stochastic process. The fundamental ideas in large deviations theory include: 1. **Rate Functions**: These are functions that describe the exponential decay rate of the probabilities of rare events.

The Method of Dominant Balance is a technique used in asymptotic analysis to approximate the solutions of differential equations and other mathematical problems, especially in the context of singular perturbation problems. This method is particularly useful when dealing with problems where the behavior of the solution changes dramatically in certain regions or under specific conditions. The key steps of the Method of Dominant Balance typically include: 1. **Identifying Scales**: First, identify the different terms in the equation and their respective scales.

Stokes phenomenon is a concept in the field of asymptotic analysis, particularly in the study of differential equations and complex analysis. It describes a behavior that occurs in the context of asymptotic expansions of solutions to differential equations when crossing certain "Stokes lines" in the complex plane.

Sequences and series are fundamental concepts in mathematics, particularly in the fields of algebra and calculus. ### Sequences A **sequence** is an ordered list of numbers, which are typically called terms. Each term in a sequence is identified by its position or index. Sequences can be finite (having a limited number of terms) or infinite (continuing indefinitely). **Examples of Sequences:** 1. **Arithmetic Sequence:** A sequence where the difference between consecutive terms is constant.