A subtractor is a digital circuit that performs subtraction on binary numbers. It is commonly used in arithmetic logic units (ALUs) and various computing applications. The simplest form of a subtractor is a **half subtractor**, which takes two input bits and produces a difference and a borrow output. A more complex version is the **full subtractor**, which handles borrowing from previous bits, allowing it to subtract multi-bit binary numbers.

Levi's lemma, also known as the Lebesgue’s dominated convergence theorem, is a result in the theory of integration, specifically concerning the conditions under which one can interchange limits and integrals.

ENO methods, or Essentially Non-Oscillatory methods, are a class of numerical techniques used primarily for the solution of hyperbolic partial differential equations (PDEs). They are particularly valuable for problems where shock waves or discontinuities are present, as they help prevent artificial oscillations that can occur in traditional numerical methods.

A simplicial sphere is a type of topological space that arises in the field of algebraic topology and combinatorial geometry. More specifically, it is a simplicial complex that is homeomorphic to a sphere. ### Definition A **simplicial complex** is a set of simplices that satisfies certain conditions, such as closure under taking faces and the intersection property.

Garnir relations refer to a specific set of algebraic identities that arise in the context of representation theory and the study of certain mathematical structures, particularly in relation to symmetric groups and permutation representations. Named after the mathematician Jean Garnir, these relations are particularly important in the study of the modular representation theory of symmetric groups and their related structures.

Partially solved games are games for which some knowledge about optimal strategies exists, but the game has not been completely solved. This means that while certain positions or states of the game may have been analyzed to the point of determining the best moves or strategies, not every possible position has been explored exhaustively.

Positional games are a type of combinatorial game that involve two players competing to control positions or resources on a board or in a structured environment. These games are often defined by specific rules regarding how players can make moves and how they can claim or occupy spaces. In a typical positional game, players take turns making moves that affect the game state, with the primary objective of achieving a particular configuration or control over the board.

"Col" is a minimalist strategy game designed by the company HyperCube, where players navigate a series of interconnected paths while trying to capture points on a grid-like board. The gameplay focuses on strategic movement and positioning while competing against other players or AI. The mechanics often involve simple rules that lead to complex strategies, making it accessible yet challenging. The game is known for its clean aesthetics and thoughtful design, appealing to fans of tactical board games and puzzle-solving.

The term "disjunctive sum" can refer to a few different concepts depending on context, but it is commonly associated with areas in mathematics and computer science, particularly in the field of logic and set theory. 1. **Mathematics/Set Theory**: In the context of set theory, a "disjunctive sum" might refer to the union of two or more sets, with the understanding that the sets are disjoint (i.e., they have no elements in common).

Claude Berge is a prominent French mathematician known for his contributions to several fields, particularly in combinatorics, graph theory, and topology. Born on February 29, 1926, and passing away on September 26, 2020, he made significant impacts through various theoretical advances and concepts. One of Berge’s notable contributions is the development of Berge's Lemma and Berge's Theorem in graph theory, which are fundamental in the study of matchings in bipartite graphs.

"Games, Puzzles, and Computation" typically refers to a field of study that intersects computer science, mathematics, and logic through the examination of games and puzzles. This field includes analyzing the computational complexity of various games and puzzles, as well as exploring algorithms that can solve them or determine optimal strategies for playing them. ### Key Aspects of the Field: 1. **Game Theory**: This involves the study of strategic interactions between rational decision-makers.

Benny Sudakov is a prominent mathematician known for his contributions to various fields, including combinatorics, graph theory, and discrete mathematics. He has published numerous papers and is recognized for his work in areas such as extremal graph theory and probabilistic methods in combinatorics. He has also held academic positions at various institutions and has been involved in the mathematical research community.

Doron Zeilberger is an influential mathematician known for his work in combinatorics, particularly in areas like enumeration and algebraic combinatorics. He is also recognized for his contributions to areas such as computer algebra and mathematical software. Zeilberger has developed several algorithms and tools for symbolic computation, particularly related to hypergeometric series and generating functions.

As of my last knowledge update in October 2021, Eric M. Rains could refer to various individuals, but there is not a widely recognized figure by that name in public discourse, literature, science, or other notable fields. If you could provide more context or specify who you are referring to, I may be able to assist you better. There might also be developments or new individuals named Eric M. Rains after my last update. Please check the latest sources for the most current information.

Belyi's theorem is a result in algebraic geometry concerning the characterization of certain algebraic curves. Specifically, it states that a smooth, projective, and geometrically irreducible algebraic curve defined over a number field can be defined over a finite field (in particular, over the algebraic closure of a finite field) if and only if it can be defined by a Belyi function.

Frank Ruskey is a mathematician known for his work in combinatorial and discrete mathematics. He is particularly recognized for his contributions to the fields of graph theory and topology, especially in relation to the study of knots and the enumeration of certain combinatorial structures. Ruskey has published numerous papers and has also been involved in developing mathematical software and algorithms.

George B. Purdy is known as a prominent figure in the field of education and academia, having made contributions to various subjects, particularly in the realms of mathematics and educational theory. However, specific context regarding his contributions or relevance may vary. If you are referring to something else or need more detailed information about a specific George B.

Heinrich August Rothe refers to a historical figure, particularly known for his contributions in the field of German philosophy and theology. However, information on specific individuals named Heinrich August Rothe can vary widely, and the context in which you are asking might yield different interpretations.

Igor Pak is a mathematician and professor known for his work in various fields, including combinatorics, mathematical biology, and mathematical education. He is associated with the University of California, Los Angeles (UCLA) and has made contributions to mathematical research and teaching. In addition to his academic work, Pak is known for creating engaging resources for mathematics education and promoting problem-solving skills among students.