An **N-monoid** is a concept in the field of algebra, specifically in the study of algebraic structures known as monoids. A monoid is a set equipped with an associative binary operation and an identity element. 1. **Basic Definition of a Monoid**: - A set \( M \) along with a binary operation \( \cdot: M \times M \to M \) (often written simply as juxtaposition, i.e.

The Herzog–Schönheim conjecture is a conjecture in the field of algebraic geometry and commutative algebra. It concerns the properties of ideals in polynomial rings or local rings. Specifically, it relates to the asymptotic behavior of the growth of the lengths of certain graded components of ideals.

Tressy is likely a reference to a fashion doll character that was popular in the 1960s and 1970s. The Tressy doll was notable for its unique feature: it had a mechanism that allowed her hair to be lengthened or shortened, giving the illusion of having different hairstyles. This was achieved by a pull-string mechanism, allowing children to style Tressy's hair in various ways.

The "17-animal inheritance puzzle" is a classic genetic puzzle that involves determining the inheritance patterns of certain traits in a group of animals, often used as an educational tool in genetics or introductory biology courses. The puzzle typically outlines a scenario where a certain trait is passed down through generations of animals, and participants must use information about the traits of the parents and offspring to deduce which animals carry specific traits.

Envy-free item allocation is a concept in resource allocation and fair division, particularly in economics and game theory, where the goal is to distribute a set of items (or resources) among a group of individuals in such a way that no individual prefers the items allocated to someone else over their own. In other words, each participant feels satisfied with what they received and does not desire what others have, leading to a perception of fairness.

Envy-free matching is a concept often discussed in the context of fair allocation and matching theory, particularly in economics and game theory. It describes a situation where a set of agents or participants is matched to a set of items (or other agents) in such a way that no agent prefers another agent's allocation over their own. To break it down: 1. **Agents**: These are the participants who have preferences for various items or other participants.

Equitability generally refers to the quality of being fair and impartial. In various contexts, it emphasizes the importance of justice, fairness, and equal treatment, often within social, economic, and legal frameworks. The concept can be applied in different fields, including economics, education, and social justice.

Proportional division is a method of dividing something, such as resources, assets, or benefits, among different parties in a way that reflects their respective shares or entitlements. This concept is often applied in various contexts, including finance, law, business, and even social or political settings.

Envy-freeness is a concept from the field of fair division and resource allocation, primarily used in economics and game theory. It refers to a condition in which each participant in a division of goods (e.g., resources, assets, or cake) prefers their own share over the shares allocated to others. In simpler terms, a division is envy-free if no individual envies another individual's portion.

Group envy-freeness is a concept that arises in the context of fair division, particularly in resource allocation among multiple agents or participants. It is an extension of the individual envy-freeness concept. **Individual Envy-freeness:** An allocation is said to be envy-free for an individual if no participant prefers another participant's share over their own. Simply put, each person believes they have received at least as good a share as anyone else in the group.

Population monotonicity is a concept in social choice theory and mechanism design that pertains to the allocation of resources or goods among a group of individuals as the population of individuals changes. Specifically, an allocation method is said to be population monotonic if the allocation to any existing individuals does not decrease when the population increases, assuming that the preferences and resources available remain constant.

There are several television series based on fashion dolls, but one of the most notable is "Barbie: Life in the Dreamhouse." This web series features Barbie and her friends in a comedic, animated format, showcasing their adventures and lifestyle within the Dreamhouse. Another example is "Bratz," which is based on the Bratz dolls created by MGA Entertainment. The animated series follows the lives of four teenage girls who are fashion-savvy and experience various high school adventures.

Resource monotonicity is a concept primarily used in the field of computational economics and mechanism design, particularly in the context of allocating resources efficiently among agents with varying preferences or types. The basic idea behind resource monotonicity is that if the total amount of resources available to be allocated increases, then the allocation to each agent should not decrease. In other words, if the total resources are augmented, the allocation strategy should ensure that no individual agent receives less than they would have with fewer resources.

Olivia Newton-John was an English-Australian singer, songwriter, and actress, renowned for her work in the music and film industries. Born on September 26, 1948, in Cambridge, England, she moved to Australia with her family in the 1950s.

Bleuette is a type of fashion doll that was first introduced in France in the early 1900s. Specifically, she was created in 1905 by the French company Petitcollin, which was known for producing high-quality dolls. Bleuette was designed to be a child's doll, but she also appealed to adult collectors. Bleuette is characterized by her distinctive features, including a lovely face, articulated limbs, and beautiful clothing, which reflect the fashion of the time.

Licca-chan is a popular Japanese fashion doll created by the company Takara in 1967. She is often considered Japan's answer to Barbie. Licca-chan has a distinctive appearance, characterized by her large, expressive eyes and a variety of hairstyles and outfits. Over the years, the doll has undergone various updates in design and fashion, keeping her relevant to changing trends and styles.

Gene Marshall is a fashion doll created by the American company Jamieshow Dolls. Introduced in the late 1990s, Gene Marshall is characterized by her glamorous 1940s and 1950s Hollywood look, often reminiscent of classic movie stars. The doll features a classic sculpt, intricate outfits, and a range of accessories that reflect the vintage film era.

The Alliance–Union universe is a science fiction universe created by author C.J. Cherryh. It is primarily explored in her novels and short stories, which delve into themes such as space exploration, interstellar politics, cultural conflict, and the complexities of human relationships. The universe is characterized by a civilization split between two major factions: the Alliance and the Union. The Alliance consists of a loose coalition of human-inhabited worlds, while the Union is a more centralized and authoritarian political entity.

"Beyond the Blue Event Horizon" is a concept that captures the fascination with black holes and the mysteries of the universe. However, it's important to note that the title may also refer to specific works, such as books, videos, or other media that delve into topics related to astrophysics, space exploration, or theoretical physics. In general, "event horizon" refers to a boundary surrounding a black hole, beyond which no information or matter can escape due to the extreme gravitational pull.

Momoko Doll is a line of fashion dolls created by the Japanese toy company PetWORKs. Launched in 2001, these dolls are known for their distinctive, stylized design that features a more realistic representation of human proportions compared to other popular dolls. Momoko Dolls typically have a retro or vintage aesthetic, often drawing inspiration from Japanese street fashion and pop culture. The dolls are characterized by their large heads, expressive faces, and a variety of hairstyles and outfits.