Don Caballero is a post-rock and math rock band from Pittsburgh, Pennsylvania, formed in 1991. They are known for their complex, instrumental compositions that often feature intricate guitar work, unconventional time signatures, and a mix of heavy and melodic elements. The band's sound is characterized by its focus on rhythm and dynamics rather than traditional song structures and lyrics.

June of 44, often stylized as "June of 44," is an American rock band formed in 1994 in Louisville, Kentucky. The band is known for its unique blend of post-rock, math rock, and indie rock styles. Their music often features intricate guitar work, dynamic shifts in tempo, and a range of emotional and atmospheric qualities.

Kimono was a Japanese rock band that gained recognition in the late 1990s and early 2000s. Known for their unique blend of rock and pop with various other musical influences, the band developed a distinctive sound that resonated with a diverse audience. Formed in 1996, Kimono released several albums and singles during their active years. Their innovative approach to music, coupled with engaging performances, helped them carve out a niche in the Japanese music scene.

Oucho Sparks is a fictional character created by the children's television show "Oucho Sparks," which is known for its engaging and entertaining content aimed at preschool-aged children. Oucho, often depicted as a puppet or animated figure, is characterized by its playful attitude and colorful appearance. The character is designed to teach children important lessons about friendships, problem-solving, and creativity through fun and interactive stories.

Piglet is an indie rock band formed in 2018, originating from the United States, specifically from Memphis, Tennessee. The band is known for its DIY ethos and blends various genres, including elements of pop, rock, and folk. Their music often incorporates introspective lyrics and emotive melodies, appealing to a diverse audience. Piglet has gained recognition for their energetic live performances and has released several singles and albums since their formation.

Ruby Falls is an American rock band formed in 2020. The band is known for its blend of alternative rock and pop elements, characterized by evocative lyrics and melodic instrumentation. They have garnered attention in the independent music scene and have been noted for their energetic performances and the emotional depth of their music. The band's name, "Ruby Falls," is derived from a well-known waterfall located in Tennessee, which reflects a sense of natural beauty and adventure.

"The Cast of Cheers" is a UK-based podcast that focuses on discussing the popular TV show "Cheers," which aired from 1982 to 1993. The podcast often features discussions on episodes, character developments, and the cultural impact of the show. Fans of the sitcom enjoy dissecting its humor, writing, and performances by the cast.

65daysofstatic is a British band known for their unique blend of post-rock, electronic, and math rock elements. They often incorporate intricate guitar work, dynamic rhythms, and atmospheric soundscapes in their music. Some notable albums and songs by 65daysofstatic include: 1. **"The Fall Of Math" (2004)** - This was one of their breakthrough albums and features tracks like "Radio Protector" and "Doubt.

A **force chain** is a concept primarily used in the fields of materials science, physics, and engineering to describe the way forces are transmitted through a granular material or a system of interconnected particles. In a force chain, the particles or grains that come into contact with each other transmit force from one to another, creating a network or "chain" of forces throughout the material. This concept is particularly relevant in the study of granular materials like sand, gravel, and other particulate substances.

Tricot is a Japanese math rock band formed in 2010 in Kyoto. The band consists of members Ikkyu (vocals and guitar), Motoko (guitar), Hiromi (bass), and drummer (who may vary in lineup). Known for their intricate rhythms, technical guitar work, and energetic performances, Tricot combines elements of rock, pop, and progressive styles.

Turing Machine is an American mathematical rock band formed in Washington, D.C., in 1997. The band is known for its unique blend of post-rock, math rock, and instrumental rock, often incorporating elements of progressive rock. They are characterized by complex time signatures, intricate guitar work, and a focus on rhythm and texture rather than traditional song structures.

Andy Hawkins is an American musician and composer, best known for his work in the genre of experimental music and for being a founding member of the influential band *The Stomach Books*. He has been involved in various musical projects and collaborations, showcasing his versatility as an artist. Hawkins is recognized for his contributions to the avant-garde and indie music scenes, often blending different styles and techniques in his compositions. Additionally, he has been noted for his work as a producer and in related artistic fields.

Damon Che is known as an influential figure in the music scene, particularly as the drummer and a founding member of the band **Dinosaur Jr.** He is recognized for his distinctive style and contributions to the alternative rock and indie music genres. Che's drumming is characterized by dynamic rhythms and an ability to blend various musical influences.

Doug Scharin is an American musician and composer known for his contributions to various music genres, particularly in rock, post-rock, and experimental music. He is associated with several bands and projects, including the influential post-rock band June of 44, which was active in the 1990s. Scharin is known for his work as a drummer and has collaborated with a variety of artists and bands throughout his career.

Ian Williams is a musician known for his work as a guitarist and keyboardist, particularly in the realm of post-rock and experimental music. He is a member of the band Don Caballero, which is known for its complex rhythms and innovative soundscapes. Williams has also been involved in other projects, notably the band Storm & Stress, which explores more avant-garde and improvisational styles. His playing style often features unconventional time signatures and intricate melodies.

Bernstein's theorem in the context of approximation theory, particularly in the field of polynomial approximation, refers to the result that relates to the uniform approximation of continuous functions on a closed interval using polynomial functions. The theorem states that if \( f \) is a continuous function defined on the interval \([a, b]\), then \( f \) can be uniformly approximated as closely as desired by a sequence of polynomials.

The Agranovich–Dynin formula is a mathematical result in the field of partial differential equations, particularly in the study of the spectral properties of self-adjoint operators. It provides a way to relate the spectral analysis of certain operators to the behavior of solutions of the differential equations associated with those operators. The formula is particularly relevant in the context of boundary value problems, where it can be used to analyze the distribution of eigenvalues and the properties of the eigenfunctions of the associated differential operators.

The Bishop–Phelps theorem is a result in functional analysis that addresses the relationship between the norm of a continuous linear functional on a Banach space and the structure of the space itself. More specifically, it deals with the existence of points at which the functional attains its norm.

The Cagniard–De Hoop method is a mathematical technique used in seismology and acoustics for solving wave propagation problems, particularly in the context of wave equations. It is especially useful for analyzing wavefields generated by a point source in a medium.

The Calogero–Degasperis–Fokas (CDF) equation is a nonlinear partial differential equation that arises in mathematical physics and integrable systems. It is named after mathematicians Francesco Calogero, Carlo Degasperis, and Vassilis Fokas.