The Hirsch conjecture is a famous statement in the field of computational geometry and polyhedral combinatorics. Proposed by the mathematician Warren Hirsch in 1957, the conjecture concerns the relationship between the dimensions of polyhedra and the lengths of their faces.
Linear programming relaxation is a technique used in optimization, particularly in the context of integer programming and combinatorial optimization problems. The primary goal of this technique is to simplify a complex integer programming problem into a linear programming one, which is generally easier to solve. Here's how it works: 1. **Original Problem**: Typically, an integer programming problem involves variables that are restricted to take only integer values (e.g., binary variables that can either be 0 or 1).
Polynomial functions are mathematical expressions that involve sums of powers of variables multiplied by coefficients. A polynomial function in one variable \( x \) can be expressed in the general form: \[ f(x) = a_n x^n + a_{n-1} x^{n-1} + \ldots + a_1 x + a_0 \] where: - \( n \) is a non-negative integer representing the degree of the polynomial.
Bell polynomials are a class of polynomials that are used in combinatorics to describe various structures, particularly partitions of sets. There are two main types of Bell polynomials: the exponential Bell polynomials and the incomplete Bell polynomials.
Bernoulli polynomials of the second kind, denoted by \( B_n^{(2)}(x) \), are a sequence of polynomials that are closely related to the traditional Bernoulli polynomials. They are defined through specific properties and relationships with other mathematical functions.
An **integer-valued polynomial** is a polynomial function that takes integer values for all integer inputs.
The Lebesgue constant is a concept from numerical analysis, specifically in the context of interpolation theory. It quantifies the worst-case scenario for how well a given set of interpolation nodes can approximate a continuous function. More formally, if we consider polynomial interpolation on a set of points (nodes), the Lebesgue constant provides a measure of the "instability" of the interpolation process.
Xiaoxing Xi is a Chinese-American physicist known for his contributions to condensed matter physics, particularly in areas related to superconductivity and topological materials. He gained significant attention in 2015 when he was wrongfully accused of espionage by the U.S. government, based on allegations that he had disclosed sensitive research information to China. The case raised important discussions about scientific collaboration, national security, and the treatment of researchers from minority backgrounds in the United States.
Judith Hillier does not appear to be a widely recognized public figure or subject based on the information available up until October 2021. It is possible that she could be a private individual or a name that is not commonly associated with notable events, achievements, or public discussions.
Kenneth Baldwin could refer to different individuals or contexts, depending on the specific area of interest. Without additional context, it’s challenging to pinpoint an exact definition. Here are a couple of possibilities: 1. **Academic Figure**: There are scholars and researchers named Kenneth Baldwin in various fields, including science or academia. 2. **Public Figure**: There may be public figures, artists, or personalities by that name in media or entertainment.
Lisa Jardine-Wright is a British physicist, science communicator, and educator known for her work in the field of physics and her efforts to promote science education. She has been involved in various outreach programs to engage the public, particularly young people, in the sciences and to foster a greater understanding of scientific concepts. Jardine-Wright is also recognized for her contributions to the development of curriculum resources and educational materials in physics.
Ben Green is a mathematician known for his work in number theory, particularly in the areas of additive combinatorics and the study of prime numbers. He is a professor at the University of Oxford and has made significant contributions to understanding the distribution of prime numbers and the structure of sets of integers. One of his notable achievements is his collaboration with Terence Tao, with whom he proved the Green-Tao theorem in 2004.
The degree of a polynomial is defined as the highest power of the variable (often denoted as \(x\)) that appears in the polynomial with a non-zero coefficient. In other words, it is the largest exponent in the polynomial expression.
An exponential polynomial is a type of mathematical expression that combines both polynomial terms and exponential terms.
The HOMFLY polynomial is a knot invariant, which means it is a mathematical object that can be used to distinguish different knots and links in three-dimensional space. It extends the concepts of the Alexander polynomial and the Jones polynomial, making it a more powerful tool in the study of knot theory. The HOMFLY polynomial was introduced by HOMFLY, which is an acronym for the initials of the authors: H. G. H. Kauffman, M. W. W. L.
A knot polynomial is a mathematical invariant associated with knots and links in the field of knot theory, which is a branch of topology. Knot polynomials are used to distinguish between different knots and to study their properties. Some of the most well-known knot polynomials include: 1. **Alexander Polynomial**: This is one of the earliest knot polynomials, defined for a knot or link as a polynomial in one variable. It provides insights into the topology of the knot and can help distinguish between different knots.
Young-Kee Kim is a prominent experimental particle physicist known for her contributions to the field of high-energy physics. She has been involved in important research at major particle physics experiments, including those at CERN. Kim is noted for her work on the properties of fundamental particles and has held various academic and administrative positions, including serving as a professor and department chair at institutions such as the University of Chicago. In addition to her research, she is recognized for her advocacy for diversity and inclusion in the sciences.
A multilinear polynomial is a polynomial that is linear in each of its variables when all other variables are held constant.