Singular integrals are a class of integrals that arise in various fields, such as mathematics, physics, and engineering. They often involve integrands that have singularities—points at which they become infinite or undefined. The study of singular integrals is particularly important in the analysis of boundary value problems, harmonic functions, and potential theory. ### Characteristics: 1. **Singularities**: The integrands typically exhibit singular behavior at certain points.

Orlicz spaces are a type of functional space that generalizes classical \( L^p \) spaces, where the integrability condition is governed by a function known as a 'Young function'. An Orlicz space is often denoted as \( L(\Phi) \), where \( \Phi \) is a given Young function.

Krull's theorem is a result in commutative algebra that pertains to the structure of integral domains, specifically regarding the heights of prime ideals in a Noetherian ring. The theorem states: In a Noetherian ring (or integral domain), the height of a prime ideal \( P \) is less than or equal to the number of elements in any generating set of the ideal \( P \).

Deck-building card games are a genre of tabletop games in which players start with a small, predetermined set of cards and gradually build a larger deck throughout the game. The primary mechanic involves acquiring new cards to add to one's deck, which enhances gameplay options and strategies as the game progresses. ### Key Features of Deck-Building Games: 1. **Starting Deck**: All players begin with the same or a similar set of basic cards that dictate their initial capabilities.

Digital collectible card games (CCGs) are a genre of digital games that combine elements of traditional collectible card games with digital gameplay mechanics. In these games, players build their decks by acquiring cards, which can represent characters, abilities, items, or spells, and use these decks to compete against other players or challenges in the game.

"Heaven & Earth" is a video game released in the late 1990s by the development studio DTI and published by GameTek. It is an educational title that combines elements of adventure and exploration, with an emphasis on learning about different cultures and philosophies. The game is notable for its unique narrative style, allowing players to explore various cultures, philosophical concepts, and historical events. Players engage in a series of puzzles and quests that encourage critical thinking and problem-solving.

"Hoyle's Official Book of Games" is a compilation of rules and strategies for a variety of card games, board games, and other types of games. It is associated with the Hoyle brand, named after Edmond Hoyle, an 18th-century writer and authority on the rules of card games. The book serves as a comprehensive reference for both casual and serious gamers, providing detailed explanations of game rules, variations, and sometimes strategies to improve play.

"Star Wars: Force Collection" is a mobile trading card game that was released in 2014. Developed by Konami, it allows players to assemble a collection of cards featuring characters, vehicles, and creatures from the Star Wars universe. Players can engage in battles, complete missions, and participate in events using their collected cards. The gameplay involves strategic deck building, where players create decks with different characters that have unique abilities.

Ariel D. Procaccia is a prominent researcher in the fields of computer science and artificial intelligence, particularly known for his work on algorithmic game theory, computational social choice, and auction design. He has made significant contributions to understanding how algorithms can be used to solve complex problems in social settings, such as voting and resource allocation. Procaccia has published extensively on topics such as fairness in algorithms, the mechanisms of decision-making processes, and the mathematical foundations of social choice theory.

"Games by designer" typically refers to a categorization of games based on their individual creators or designers. This approach allows players and enthusiasts to explore the works of specific game designers, showcasing their unique styles, themes, and gameplay mechanics.

Puzzle designers are creators who conceptualize, design, and develop puzzles for various formats, including games, escape rooms, online platforms, and printed materials. Their work involves crafting engaging and challenging puzzles that often require logical reasoning, problem-solving skills, and creativity to solve. Puzzle designers may work in various fields, including: 1. **Board Games and Video Games**: They create puzzles that are integral to gameplay and narrative progression.

Video game designers are professionals who create the concepts, mechanics, and overall vision for video games. Their role encompasses a variety of tasks, and they work collaboratively within a team that may include programmers, artists, sound designers, and writers. Here are some key aspects of what video game designers do: 1. **Game Concept Development**: Designers brainstorm and develop ideas for games, including themes, genres, and target audiences. They may create initial game prototypes or concepts that outline the gameplay experience.

A list of game designers typically includes individuals known for their significant contributions to the video game industry. Here are some notable game designers: 1. **Shigeru Miyamoto** - Creator of iconic series such as Mario, The Legend of Zelda, and Donkey Kong. 2. **Hideo Kojima** - Known for the Metal Gear series, particularly Metal Gear Solid, and Death Stranding.

Visibility Graph Analysis (VGA) is a method used primarily in the fields of spatial analysis, urban planning, landscape architecture, and other areas to assess spatial relationships and visibility within a given environment. It transforms physical spaces into a mathematical representation to analyze how different locations can be "seen" from one another, thus helping to understand visibility, accessibility, and spatial integration.

The Assouad dimension is a concept from geometric measure theory and fractal geometry that provides a way to measure the "size" or "complexity" of a set in terms of its dimensionality. It is particularly useful in analyzing the structure of sets that may exhibit fractal behavior.

Classical Wiener space, often referred to in the context of stochastic analysis and probability theory, is a mathematical construct used to represent the space of continuous functions that describe paths of Brownian motion. It provides a rigorous framework for the analysis of stochastic processes, particularly in the study of Gaussian processes.

A Delone set, also known as a uniformly discrete or relatively dense set, is a concept from mathematics, particularly in the study of point sets in Euclidean spaces and in the area of mathematical physics, crystallography, and non-periodic structures.

Doubling space is a concept often used in various fields, including mathematics, computer science, and physics, and it can refer to different ideas depending on the context. 1. **Mathematics and Geometry**: In the context of mathematical spaces, doubling often refers to the property of metric spaces where ball sizes can be controlled by the number of smaller balls that can cover the larger ones.

Flat convergence generally refers to a concept in optimization and machine learning, particularly in the context of training neural networks. It describes a situation where the loss landscape of a model has regions where the loss does not change much, even with significant changes in the model parameters. In other words, a "flat" region in the loss landscape indicates that there are many parameter configurations that yield similar performance (loss values), as opposed to "sharp" regions where small changes in parameters lead to large changes in loss.

The Hopf-Rinow theorem is a fundamental result in differential geometry and the study of Riemannian manifolds. It connects concepts of completeness, compactness, and geodesics in the context of Riemannian geometry. The theorem states the following: 1. **For a complete Riemannian manifold**: If \( M \) is a complete Riemannian manifold, then it is compact if and only if it is geodesically complete.