Abu Said Gorgani, also known as Abu Sa'id al-Gurgani, was a Persian mathematician and astronomer who lived during the medieval period, around the 11th century. He is best known for his contributions to mathematics and science, particularly in the field of algebra. His works include an influential treatise on algebra that was notable for its clear exposition and innovative approach to solving equations.
The Predecessor Problem is a computational problem often encountered in the context of data structures, particularly in search and retrieval operations within ordered sets, such as ordered lists, balanced binary search trees, and other similar structures. The problem can be stated as follows: given a value \( x \) in a sorted data structure (for example, a sorted list or a binary search tree), find the predecessor of \( x \).
A **blind polytope** is a concept from combinatorial geometry, particularly related to the study of polytopes and their properties. In this context, a **polytope** is a geometric object with flat sides, which can be defined in any number of dimensions. The term "blind polytope" typically refers to a specific class of polytopes that share certain combinatorial properties, particularly in relation to visibility and edges.
A passing chord is a chord that connects two primary chords in a progression, helping to bridge the harmonic gap between them. It usually appears for a brief duration and serves to create smoother transitions, add tension, or embellish the music. Passing chords can be rooted in the diatonic scale (the scale based on the key of the piece) or can be chromatic (outside the main key). They often provide more harmonic interest and can enhance the overall movement of the progression.
Voice leading is a musical concept that refers to the way individual musical lines or voices (often referred to as "parts") move from one note to the next, particularly in the context of harmonic progressions. It is an essential aspect of counterpoint, composition, and arranging, as it deals with the horizontal aspect of music—how melodies interact with each other over time. Key principles of voice leading include: 1. **Smoothness**: The goal is often to create smooth transitions between notes.
In music, an accent refers to a specific way of emphasizing a note or chord, making it stand out from the surrounding notes. This can be achieved through various means, such as increasing the volume (loudness), altering the duration (length), or changing the articulation (the manner in which the note is played or sung).
Bonnesen's inequality is a result in geometry that relates to the area of a convex body and the distances between points in that body. More specifically, it often pertains to the geometry of convex bodies in Euclidean spaces, particularly those shapes that can be compared based on their geometric properties. One of the well-known forms of Bonnesen's inequality deals with convex sets and relates the volume (or area) and the diameter of convex bodies.
In music, articulation refers to the way in which notes are played or sung, particularly in terms of their attack, duration, and decay. It essentially describes how individual notes are expressed and connected to one another, affecting the overall phrasing and emotional impact of the performance. Different types of articulation include: 1. **Staccato**: Notes are played in a short, detached manner, creating a crisp, playful sound.
Martelé is a specific bowing technique used by string players, particularly violinists, violists, cellists, and double bassists. The term "martelé" comes from the French word for "hammered," and this bowing style is characterized by a sharp, accented start to the note followed by a quick release. To execute a martelé bow stroke, the player typically employs a heavy bow pressure at the beginning of the stroke, creating a strong, punchy sound.
"Meend" is a term primarily associated with Indian classical music, especially in contexts involving vocal and instrumental performances. It refers to a specific melodic ornamentation or glide that connects notes in a smooth, fluid manner. Meend involves bending or sliding between pitches, creating a continuous flow of sound instead of distinct, separate notes. This technique is essential in genres like Hindustani classical music and helps convey emotion and expression in a performance.
Pizzicato is a musical technique primarily used for stringed instruments, where the player plucks the strings with their fingers instead of using a bow. This technique can produce a distinct, sharp sound and is often used for artistic effect in various musical genres, including classical, jazz, and contemporary music. In written music, pizzicato is typically notated with the abbreviation "pizz." and is contrasted with "arco," which indicates that the musician should return to bowing.
Portamento is a musical technique that involves a smooth, continuous glide from one pitch to another. Unlike a standard note transition, where notes are played distinctly, portamento allows for a seamless shift, creating a fluid connection between two tones. This technique is commonly used in vocal performances and on instruments such as the slide trombone, string instruments, and synthesizers, where the performer can smoothly transition between notes. In the context of singing, portamento can enhance expressiveness and emotion.
Portato is a musical term that describes a style of playing that combines characteristics of both legato and staccato. In a portato performance, notes are played smoothly and connected (like legato), but with a slight separation or emphasis (similar to staccato). This technique typically involves a light, detached touch, where each note is slightly articulated, allowing for a sense of phrasing and nuance while still maintaining a cohesive melodic line.
The Butterfly curve is a well-known example of a transcendental curve in mathematics, characterized by its intricate, butterfly-like shape. It is defined using a set of parametric equations in the Cartesian coordinate system.
Duan Xuefu is a term that refers to a style of traditional Chinese poetry. More specifically, it is associated with poetry that emphasizes the expression of personal feelings, reflections, and experiences, often using rich imagery and emotional depth. This style is part of the broader category of classical Chinese poetry, which includes various forms such as shi, ci, and qu, each with its own rules and characteristics.
Farideh Firoozbakht is an Iranian poet, writer, and translator known for her contributions to Persian literature and her advocacy for women's rights. She has written extensively in various literary forms, including poetry and prose. Her work often explores themes of identity, culture, and social issues, particularly regarding the experiences of women in Iran. Firoozbakht is recognized for her unique voice and the emotional depth of her writing.
Gu Chaohao (顾朝豪) is a prominent figure in the field of mathematics, particularly known for his contributions to various branches including functional analysis, partial differential equations, and mathematical physics. He has made significant advances in both theoretical and applied mathematics, and his work often explores the connections between different mathematical disciplines.
As of my last update in October 2021, there is limited information available about someone named Kathy Vivas. It's possible that she could be a private individual, or it could refer to someone who has gained recognition after that time.