Janet Brown Guernsey is an American artist known for her work as a painter, printmaker, and sculptor. Her art often combines various influences and mediums, exploring themes such as nature, identity, and the human experience. Specifically, she has gained recognition for her layered techniques and vibrant color palettes, which can be seen in her paintings and printmaking projects.

Bennett's inequality is a result in probability theory that provides a bound on the tail probabilities of sums of independent random variables, particularly in the context of bounded random variables. Specifically, Bennett's inequality is useful for establishing concentration results for random variables that are bounded and centered around their expected value.

Cantelli's inequality is a probabilistic inequality that provides a bound on the probability that a random variable deviates from its mean. Specifically, it is used to measure the tail probabilities of a probability distribution.

Doob's Martingale Inequality is a fundamental result in the theory of martingales, which are stochastic processes that model fair game scenarios. Specifically, Doob's inequality provides bounds on the probabilities related to the maximum of a martingale. There are a couple of versions of Doob's Martingale Inequality, but the most common one deals with a bounded integrable martingale.

The Janson inequality is a result in probability theory, particularly in the context of the study of random variables and dependent events. It provides a bound on the probability that a sum of random variables exceeds its expected value. Specifically, it is often used when dealing with random variables that exhibit some form of dependence.

An "appeal to probability" is a type of logical fallacy that occurs when someone assumes that because something is possible or likely, it must be true or will happen. This fallacy involves an unwarranted conclusion based on the probability of an event, rather than on solid evidence or deductive reasoning. For example, someone might argue, "It's likely that it will rain tomorrow, so it will rain.

The Law of Averages is a principle that suggests that over a large enough sample size, events will statistically tend to average out. In other words, it implies that if something happens with a certain probability, over time and numerous trials, the outcomes will reflect that probability.

The Yangian is an important algebraic structure in mathematical physics and representation theory, particularly related to integrable systems and quantum groups. It was first introduced by the physicist C.N. Yang in the context of two-dimensional integrable models. ### Key Aspects of Yangians: 1. **Quantum Groups**: The Yangian can be seen as a kind of quantum group deformation of classical symmetries.

Molecule mining is a term that typically refers to the process of identifying and extracting useful molecular compounds from a variety of sources, often with the goal of discovering new drugs or chemical substances. This process can involve several techniques and methodologies, depending on the context and the specific goals. Here are some key aspects: 1. **Natural Product Discovery**: Molecule mining can involve searching for bioactive compounds in natural sources like plants, fungi, and marine organisms.

Point-pair separation is a concept often used in various fields such as mathematics, computer science, and physics to describe the distance between a pair of points in a given space. It specifically focuses on measuring the minimum distance separating two distinct points, which can be important in applications such as spatial analysis, clustering, and geometric computations.

In the context of mathematics, particularly in topology and related fields, a "maximal arc" typically refers to a segment or a subset of a space that cannot be extended further while maintaining certain properties—often related to continuity or connectedness. The term is often associated with the study of curves or paths in metric spaces or topological spaces.

The Moufang plane is a specific type of finite projective plane that arises in the context of incidence geometry and group theory. It is named after the mathematician Ruth Moufang, who studied its properties. A key characteristic of the Moufang plane is that it is constructed using a projective geometry over a division ring (or skew field), which is a generalized field where multiplication may not be commutative.

"The Geometry of an Art" can refer to the intersection of mathematical concepts, particularly geometry, with artistic expression. This theme explores how geometric principles shape various art forms, encompassing topics like symmetry, proportion, perspective, and spatial relationships. Here are a few key areas where geometry plays a significant role in art: 1. **M.C. Escher**: The work of Dutch artist M.C.

Methods of proof are techniques used in mathematics and logic to demonstrate the validity of mathematical statements, theorems, or propositions. There are several fundamental methods of proof, each with its own approach. Here are some of the most common methods: 1. **Direct Proof**: This method involves directly showing that a statement is true by using definitions, axioms, and previously established theorems. You start from known truths and use logical reasoning to arrive at the statement you want to prove.

A focused proof is a type of logical reasoning and argumentation used primarily in formal settings, such as mathematics or computer science, to establish the validity of a statement or the correctness of a program. The concept emphasizes clarity and direct relevance, ensuring that each step of the proof contributes meaningfully to the conclusion without extraneous information.

"LowerUnits" is not a specific term or concept that is widely recognized or defined in general knowledge or popular culture as of my last update in October 2023. It could refer to one of several things depending on the context—such as a technical term in a specific industry, a component of a software application, or even a nickname for a product or service.

Peano–Russell notation, also known as the Peano-Russell system or Russell's notation, is a formal language developed in logic and mathematics, primarily associated with the work of Giuseppe Peano and Bertrand Russell. This notation is intended to express mathematical concepts, particularly in the context of set theory and the foundations of mathematics, using symbols and a structured format. ### General Features 1.

Resolution proof reduction via local context rewriting is a method used in automated theorem proving and logic reasoning that involves simplifying or reducing proofs in propositional logic or predicate logic. This approach typically aims to improve the efficiency of proof search or to generate more compact proofs by leveraging the concept of local context and rewriting rules. Here's a breakdown of the key components of this method: 1. **Resolution**: This is a rule of inference used in propositional and first-order logic.

Sequent calculus is a formal system that is used in mathematical logic and proof theory. Developed by Gerhard Gentzen in the 1930s, it provides a framework for representing and manipulating logical arguments through sequences, known as sequents.

An **orthocompact space** is a concept in topology that generalizes certain properties of compact spaces. A topological space \( X \) is defined to be orthocompact if every open cover of \( X \) has a certain "sufficient" refinement property.