A supersingular isogeny graph is a mathematical structure used primarily in number theory and algebraic geometry, particularly in the study of elliptic curves and their isogenies (which are morphisms between elliptic curves that respect the group structure). These graphs have become increasingly important in the field of cryptography, especially in post-quantum cryptographic protocols.
The Guatemala City Choirbooks, also known as the "Guatemala City Polyphonic Choirbooks," are a collection of music manuscripts from the 17th century that are significant for their historical and cultural value. They were created in the context of colonial Central America, particularly in Guatemala, and they represent an important aspect of the musical heritage of the region. These choirbooks contain a variety of polyphonic choral music, primarily for liturgical use in churches.
The Gyffard partbooks are a collection of musical manuscripts compiled in the late 16th century, specifically around the 1580s, which contain vocal music, primarily polyphony, for four voices. They are named after their owner, the Englishman John Gyffard, who was a member of the nobility and had an interest in music.
The Lambeth Choirbook is a significant collection of English choral music from the late 16th century, specifically compiled around 1598. It is named after Lambeth Palace, the London residence of the Archbishop of Canterbury. The choirbook contains a variety of sacred music, primarily composed for the Anglican Church, including settings of the Mass, motets, anthems, and other liturgical works.
The term "Loire Valley chansonniers" typically refers to a group of musicians and singers who were active in the Loire Valley region of France, particularly during the Renaissance and early modern periods. The Loire Valley is known for its rich cultural heritage, including its historical châteaux, and it played a significant role in the development of French music and poetry. Chansonniers are collections of songs, often featuring a variety of lyrical themes such as love, nature, and daily life.
The Medici Codex, also known as the Medici Codex of Music, is a significant historical manuscript that pertains to Renaissance polyphony. It is a music book that has attracted interest for its collection of compositions from notable composers of the time, including those associated with the Florentine court. The codex is most famously associated with the family of the Medici, who were influential patrons of the arts and played a crucial role in the development of Renaissance culture, particularly in Florence.
"My Ladye Nevell's Booke" is a notable collection of music that dates from the late 16th century. Specifically, it is a manuscript compiled around 1591 and is attributed to the English composer William Byrd, among other composers. The book is named after Lady Mary Nevill, a notable figure of the time who was a patron of the arts and a member of the English nobility.
The Pepys Manuscript refers to a collection of musical compositions and writings that are preserved in a manuscript compiled by Samuel Pepys, a notable 17th-century English naval administrator and diarist. Pepys is particularly well-known for his detailed diary that provides insights into English life during the Restoration period. The manuscript itself contains a variety of music and lyrics, including pieces for instruments and songs, reflecting the musical tastes of the time.
The Ritson Manuscript is a collection of medieval English poetry, transcribed in the late 18th century by Joseph Ritson, an English antiquarian and scholar known for his work in the field of English literature and balladry. The manuscript includes a variety of texts, such as ballads, songs, and other forms of traditional English literature, showcasing the rich oral tradition of the time.
The Susanne van Soldt Manuscript is a significant collection of writings related to early modern art history, particularly pertaining to the art and culture of the Northern Renaissance. It may include discussions of artists, techniques, and cultural influences of the time. However, details about this specific manuscript, including its content and significance, may vary based on the context in which it is mentioned.
The Tutte graph is a specific, well-known example of a cubic graph (3-regular graph) that is often studied in the field of graph theory. It has several interesting properties and characteristics: 1. **Vertices and Edges**: The Tutte graph has 46 vertices and 69 edges. It is one of the smallest cubic graphs that is not 3-colorable, meaning it cannot be colored with three colors without two adjacent vertices sharing the same color.
The Tutte–Coxeter graph is a well-known graph in the study of graph theory and combinatorics. It is a bipartite graph with some interesting properties and significance. Here are some key features of the Tutte–Coxeter graph: 1. **Vertices and Edges**: The Tutte–Coxeter graph consists of 12 vertices and 18 edges.
The Reinforced Concrete Association (RCA) is a professional organization or group typically focused on the use, development, and promotion of reinforced concrete as a building material. Organizations like the RCA engage in various activities to advance knowledge and practices in the field of reinforced concrete, including: 1. **Research and Development**: Supporting studies and innovations in reinforced concrete materials and construction techniques.
Reinforced concrete columns are structural elements designed to support loads and transfer them to the foundations of buildings and other structures. They are made of concrete, which is strong in compression, and reinforced with steel bars (rebar) or steel mesh, which provides tensile strength. The combination of these materials allows reinforced concrete to effectively withstand both compressive and tensile forces.
Representation theory of Lie groups is a branch of mathematics that studies how Lie groups can be represented as groups of transformations on vector spaces. More formally, a representation of a Lie group \( G \) is a homomorphism from \( G \) to the general linear group GL(V) of invertible linear transformations on a vector space \( V \). This allows one to study properties of the group \( G \) through linear algebra and the geometry of vector spaces.
Unitary representation theory is a branch of mathematics and physics that studies how groups can be represented through unitary operators on Hilbert spaces. In this context, a **unitary representation** of a group \( G \) is a homomorphism from the group \( G \) into the group of unitary operators on a Hilbert space \( H \).
B-admissible representation is a concept in the realm of representation theory, particularly in the study of p-adic groups and their representations. The notion arises in the context of understanding how representations of a given group can be analyzed through the properties of certain subgroups. In more formal terms, let \( G \) be a p-adic group, and let \( B \) be a Borel subgroup of \( G \).
In mathematics and physics, particularly in the context of complex numbers and quantum mechanics, the term "complex conjugate representation" can have specific meanings depending on the context.
The concept of corepresentations of unitary and antiunitary groups arises primarily in the context of representation theory, which studies how groups act on vector spaces through linear transformations. In quantum mechanics and in many areas of physics, these groups often illustrate symmetries of systems, where unitary and antiunitary operators play significant roles. ### Unitary Groups Unitary operators are linear operators associated with a unitary group, which is a group of transformations that preserve inner products in complex vector spaces.