The Casas-Alvero conjecture is a statement in algebraic geometry and commutative algebra concerning the properties of certain classes of varieties, and it addresses the relationship between numerical and geometric properties of projective varieties.
The class number problem is a central question in algebraic number theory that relates to the properties of the ideal class group of a number field, specifically its class number. The class number is an important invariant that measures the failure of unique factorization in the ring of integers of a number field.
"Weather by year" generally refers to the annual variations and trends in weather patterns for a specific location or globally. This can include average temperatures, precipitation, humidity, storm occurrences, and other relevant meteorological data over a certain time frame (typically year by year).
Weather lore refers to a collection of sayings, beliefs, and traditional knowledge about weather patterns and phenomena, often passed down through generations. These proverbs and observations are based on the experiences of farmers, fishermen, and local communities who have observed how weather changes can influence daily life, agriculture, and natural events. Weather lore often includes folk rhymes, sayings, and anecdotes that aim to predict future weather based on signs observed in nature.
"Works about weather" could refer to a variety of artistic, literary, and scientific works that focus on weather phenomena. Here are a few interpretations of this topic: 1. **Literature**: Many authors have written about weather in their novels, poetry, and essays, using it as a backdrop to explore themes such as change, mood, and human experience.
Django Girls is a nonprofit organization that aims to teach women and underrepresented groups how to build websites using the Django web framework and Python programming language. Founded in 2014, Django Girls organizes workshops around the world where participants can learn web development in a friendly and inclusive environment. These workshops typically include: 1. **Hands-on Coding:** Participants go through a tutorial that takes them step-by-step through the process of creating a blog web application using Django.
Jacques-Arsène d'Arsonval (1851–1940) was a French physicist and inventor known for his contributions to the field of electromagnetism and the development of instruments for measuring electrical parameters. He is notably recognized for his work on alternating current (AC) electricity and for inventing the d'Arsonval galvanometer, a sensitive device used for measuring small electric currents. His innovations laid the groundwork for various applications in physics and engineering.
Cramér's conjecture is a hypothesis in number theory related to the distribution of prime numbers. It was proposed by the Swedish mathematician Harald Cramér in 1936. The conjecture specifically addresses the gaps between consecutive prime numbers. Cramér's conjecture suggests that the gaps between successive primes \( p_n \) and \( p_{n+1} \) are relatively small compared to the size of the primes themselves.
The Feit-Thompson conjecture is a statement in group theory, which is a branch of mathematics that studies the algebraic structure known as groups. The conjecture was proposed by Walter Feit and John G. Thompson in their famous work in the 1960s on finite groups. The conjecture itself states that every finite group of odd order is solvable.
Firoozbakht's conjecture is a mathematical conjecture related to the properties of prime numbers, specifically concerning the gaps between consecutive prime numbers.
Gilbreath's conjecture is an observation in number theory regarding the differences between consecutive prime numbers. It asserts that if you take the sequence of prime numbers and repeatedly form new sequences by subtracting each prime from the next one, the resulting sequences will always contain primes. More formally, consider a list of prime numbers \( p_1, p_2, p_3, \ldots \).
Greenberg's conjecture is a statement in the field of number theory related to the study of Galois representations and p-adic fields. Specifically, it deals with the relation between the arithmetic of cyclotomic fields and the behavior of certain types of Galois representations.
Hall's conjecture is a concept in combinatorics and graph theory, specifically related to the properties of perfect matchings in bipartite graphs. The conjecture states that a certain condition involving the size of subsets of one partition of a bipartite graph must hold for the graph to contain a perfect matching.
Hermite's problem, named after the French mathematician Charles Hermite, refers to an important question in the theory of numbers that concerns the representation of numbers as sums of squares. Specifically, the problem seeks to establish conditions under which a natural number can be expressed as a sum of squares of integers. One of the notable results related to Hermite's problem is a theorem concerning the number of ways a given positive integer can be expressed as a sum of two squares.
Landau's problems refer to a list of open problems in physics and mathematics that were posed by the renowned Soviet physicist Lev Landau. These problems primarily focus on theoretical issues in condensed matter physics, statistical mechanics, and other areas where Landau made significant contributions. One of the most famous of these problems is related to the nature of phase transitions in materials and the theoretical understanding of critical phenomena.
Quantum Chromodynamics (QCD) is the theory that describes the strong interaction, one of the four fundamental forces in nature, responsible for holding quarks together to form protons, neutrons, and other hadrons. The QCD vacuum refers to the state of lowest energy in the QCD framework, which is fundamentally different from the classical concept of a vacuum. In classical physics, a vacuum is simply an emptiness devoid of matter and energy.
Ultra-high vacuum (UHV) refers to a type of vacuum that has an extremely low pressure, typically in the range of \(10^{-9}\) to \(10^{-12}\) torr (or equivalent pressures in pascals, around \(10^{-7}\) to \(10^{-10}\) pascals). This level of vacuum is significantly lower than high vacuum, which generally ranges from \(10^{-7}\) to \(10^{-3}\) torr.
Daniel Harlow is a theoretical physicist known for his work in areas such as black holes, quantum gravity, and quantum information. He has contributed to various discussions regarding the foundations of quantum mechanics and the nature of spacetime. Harlow's research often explores the connections between quantum mechanics and gravitational theories, particularly in the context of black hole thermodynamics and information paradoxes.
Jean-Louis Viovy is a French physicist known for his work in the fields of biophysics and physical chemistry. He has contributed to the study of complex systems and has been involved in research concerning the behavior and properties of biological macromolecules, such as DNA and proteins. His work often involves the use of advanced techniques in experimental and theoretical physics to understand the microscopic mechanisms that govern biological processes.