Cube rootIn mathematics, a cube root of a number x is a number y such that y3 = x. All nonzero real numbers, have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots. For example, the real cube root of 8, denoted , is 2, because 23 = 8, while the other cube roots of 8 are and .
Voltage-gated potassium channelVoltage-gated potassium channels (VGKCs) are transmembrane channels specific for potassium and sensitive to voltage changes in the cell's membrane potential. During action potentials, they play a crucial role in returning the depolarized cell to a resting state. Alpha subunits form the actual conductance pore. Based on sequence homology of the hydrophobic transmembrane cores, the alpha subunits of voltage-gated potassium channels are grouped into 12 classes. These are labeled Kvα1-12.
Nth rootIn mathematics, taking the nth root is an operation involving two numbers, the radicand and the index or degree. Taking the nth root is written as , where x is the radicand and n is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an nth root of a number x is a number r (the root) which, when raised to the power of the positive integer n, yields x: A root of degree 2 is called a square root (usually written without the n as just ) and a root of degree 3, a cube root (written ).
Nowhere continuous functionIn mathematics, a nowhere continuous function, also called an everywhere discontinuous function, is a function that is not continuous at any point of its domain. If is a function from real numbers to real numbers, then is nowhere continuous if for each point there is some such that for every we can find a point such that and . Therefore, no matter how close we get to any fixed point, there are even closer points at which the function takes not-nearby values.
Vector calculus identitiesThe following are important identities involving derivatives and integrals in vector calculus. Gradient For a function in three-dimensional Cartesian coordinate variables, the gradient is the vector field: where i, j, k are the standard unit vectors for the x, y, z-axes. More generally, for a function of n variables , also called a scalar field, the gradient is the vector field: where are orthogonal unit vectors in arbitrary directions. As the name implies, the gradient is proportional to and points in the direction of the function's most rapid (positive) change.
Halley's methodIn numerical analysis, Halley's method is a root-finding algorithm used for functions of one real variable with a continuous second derivative. It is named after its inventor Edmond Halley. The algorithm is second in the class of Householder's methods, after Newton's method. Like the latter, it iteratively produces a sequence of approximations to the root; their rate of convergence to the root is cubic. Multidimensional versions of this method exist.
Differentiable functionIn mathematics, a differentiable function of one real variable is a function whose derivative exists at each point in its domain. In other words, the graph of a differentiable function has a non-vertical tangent line at each interior point in its domain. A differentiable function is smooth (the function is locally well approximated as a linear function at each interior point) and does not contain any break, angle, or cusp. If x0 is an interior point in the domain of a function f, then f is said to be differentiable at x0 if the derivative exists.
Uniform continuityIn mathematics, a real function of real numbers is said to be uniformly continuous if there is a positive real number such that function values over any function domain interval of the size are as close to each other as we want. In other words, for a uniformly continuous real function of real numbers, if we want function value differences to be less than any positive real number , then there is a positive real number such that at any and in any function interval of the size .
Continuous linear operatorIn functional analysis and related areas of mathematics, a continuous linear operator or continuous linear mapping is a continuous linear transformation between topological vector spaces. An operator between two normed spaces is a bounded linear operator if and only if it is a continuous linear operator. Continuous function (topology) and Discontinuous linear map Bounded operator Suppose that is a linear operator between two topological vector spaces (TVSs). The following are equivalent: is continuous.
Fox Broadcasting CompanyThe Fox Broadcasting Company, commonly known simply as Fox and stylized in all caps, is an American commercial broadcast television network owned by Fox Corporation and headquartered in New York City, with master control operations and additional offices at the Fox Network Center in Los Angeles and the Fox Media Center in Tempe. Launched as a competitor to the Big Three television networks (ABC, CBS, and NBC) on October 9, 1986, Fox went on to become the most successful attempt at a fourth television network.
Fox NewsThe Fox News Channel (FNC), commonly known as Fox News, is an American multinational conservative news and political commentary television channel and website based in New York City. It is owned by Fox News Media, which itself is owned by the Fox Corporation. It is the most-watched cable network in the U.S., and as of 2023 generates approximately 70% of its parent company's pre-tax profit. The channel broadcasts primarily from studios at 1211 Avenue of the Americas in Midtown Manhattan.
FoxFoxes are small to medium-sized, omnivorous mammals belonging to several genera of the family Canidae. They have a flattened skull, upright, triangular ears, a pointed, slightly upturned snout, and a long bushy tail ("brush"). Twelve species belong to the monophyletic "true fox" group of genus Vulpes. Approximately another 25 current or extinct species are always or sometimes called foxes; these foxes are either part of the paraphyletic group of the South American foxes, or of the outlying group, which consists of the bat-eared fox, gray fox, and island fox.
