In algebraic geometry and commutative algebra, a Weierstrass ring is a type of local ring that can be used to study singularities of algebraic varieties. More specifically, it is a particular kind of ring that arises in the context of the Weierstrass preparation theorem. A Weierstrass ring is defined as follows: 1. **Local Ring**: It is a local ring, which means it has a unique maximal ideal.

Win rate is a metric commonly used in various fields such as gaming, sports, finance, and business to quantify the percentage of wins relative to the total number of attempts or events.

Barga Jazz is an annual jazz festival that takes place in the town of Barga, located in the Tuscany region of Italy. This festival is known for its picturesque setting and its celebration of jazz music, attracting both local and international artists. It typically features a variety of performances, including concerts, jam sessions, and workshops, catering to jazz enthusiasts and musicians of all levels.

Game artificial intelligence (AI) refers to the techniques and methods used to create responsive, adaptive, and intelligent behavior in non-player characters (NPCs) or game elements within video games. The primary goal of game AI is to enhance the player experience by making the game world more immersive, challenging, and engaging. Here are some key aspects of game AI: 1. **Pathfinding:** - Game AI often involves pathfinding algorithms that help characters navigate the game world efficiently.

Organizations related to game theory typically focus on the study and application of strategic interactions among rational decision-makers. These organizations may be academic institutions, research centers, think tanks, or professional associations that emphasize the theoretical underpinnings and practical applications of game theory in various fields, such as economics, political science, biology, and computer science. Here are some examples: 1. **Academic Institutions**: Many universities have departments or programs in economics, mathematics, or political science that focus on game theory.

Fair division is a mathematical and economic concept that deals with dividing a set of resources or goods among individuals or parties in such a way that each participant believes they have received their fair share. This can involve tangible items, such as land or goods, as well as intangible resources, such as time or opportunities. The principles of fair division can be applied in various contexts, including: 1. **Dividing Chores or Tasks**: Splitting household responsibilities among family members or roommates.

Geometric objects are the fundamental entities studied in the field of geometry. They can be classified into various categories based on their dimensions and properties. Here are some common types of geometric objects: 1. **Points**: The most basic geometric object, a point has no dimensions (length, width, or height) and is defined by a specific location in space, usually represented by coordinates. 2. **Lines**: A line is an infinite collection of points extending in both directions.

Unsolved problems in geometry cover a wide range of topics and questions that have yet to be resolved. Here are a few notable examples: 1. **The Poincaré Conjecture**: While this conjecture was solved by Grigori Perelman in 2003, its implications and related questions about the topology of higher-dimensional manifolds are still active areas of research.

Space refers to the vast, seemingly infinite expanse that exists beyond the Earth's atmosphere, encompassing all celestial bodies, such as stars, planets, moons, asteroids, comets, and galaxies, as well as the vacuum between them. It is characterized by a near absence of matter, extremely low temperatures, and a lack of atmosphere, which results in many unique physical phenomena, including microgravity and cosmic radiation.

Bedtime Math is an initiative designed to make math fun and engaging for children by incorporating it into a daily routine, specifically around bedtime. Founded by Laura Overdeck, Bedtime Math aims to encourage families to spend time together through playful math challenges that can be easily integrated into a nightly ritual. The program offers a variety of math problems and activities that are designed for different age levels, making it accessible for a wide range of children, from preschoolers to middle schoolers.

Consumer demand tests are experimental methods used in animal research to assess animals' preferences and decisions regarding food choices and other consumable resources. These tests help researchers understand how animals allocate their time and energy towards accessing different food options or resources based on factors such as availability, palatability, and nutritional value.

"Begriffsschrift," which translates to "concept script" in English, is a formal language created by the German mathematician and philosopher Gottlob Frege. Introduced in his 1879 work of the same name, Begriffsschrift was one of the first attempts to provide a rigorous symbolic notation for logic and mathematics.

"Beggar-my-neighbour" is a traditional card game that is typically played by two players using a standard deck of playing cards. The goal of the game is to win all the cards from your opponent. The game is known for its simplicity and could be a fun way to pass the time. ### Rules of the Game: 1. **Setup**: The deck is shuffled, and the cards are divided equally between the two players, who keep their cards face down in a pile.

"Astrophysics for People in a Hurry" is a popular science book written by Neil deGrasse Tyson. Published in 2017, the book is intended to make complex concepts in astrophysics accessible to a general audience. It distills a vast amount of information about the universe, including topics like the Big Bang, black holes, dark matter, and the nature of time and space, into concise, easily digestible chapters.

An "outpost" in a military context refers to a fortified position or a military base that is established at a distance from the main forces or base of operations. Outposts serve several strategic purposes: 1. **Forward Operating Base**: They are often used as a base for operations that are conducted away from the main base, allowing for more flexibility and reach in military engagements.