Holonomic functionIn mathematics, and more specifically in analysis, a holonomic function is a smooth function of several variables that is a solution of a system of linear homogeneous differential equations with polynomial coefficients and satisfies a suitable dimension condition in terms of D-modules theory. More precisely, a holonomic function is an element of a holonomic module of smooth functions. Holonomic functions can also be described as differentiably finite functions, also known as D-finite functions.
Special linear Lie algebraIn mathematics, the special linear Lie algebra of order n (denoted or ) is the Lie algebra of matrices with trace zero and with the Lie bracket . This algebra is well studied and understood, and is often used as a model for the study of other Lie algebras. The Lie group that it generates is the special linear group. The Lie algebra is central to the study of special relativity, general relativity and supersymmetry: its fundamental representation is the so-called spinor representation, while its adjoint representation generates the Lorentz group SO(3,1) of special relativity.
Linear algebraic groupIn mathematics, a linear algebraic group is a subgroup of the group of invertible matrices (under matrix multiplication) that is defined by polynomial equations. An example is the orthogonal group, defined by the relation where is the transpose of . Many Lie groups can be viewed as linear algebraic groups over the field of real or complex numbers. (For example, every compact Lie group can be regarded as a linear algebraic group over R (necessarily R-anisotropic and reductive), as can many noncompact groups such as the simple Lie group SL(n,R).
SQL injectionIn computing, SQL injection is a code injection technique used to attack data-driven applications, in which malicious SQL statements are inserted into an entry field for execution (e.g. to dump the database contents to the attacker). SQL injection must exploit a security vulnerability in an application's software, for example, when user input is either incorrectly filtered for string literal escape characters embedded in SQL statements or user input is not strongly typed and unexpectedly executed.
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.
Analytic functionIn mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions. Functions of each type are infinitely differentiable, but complex analytic functions exhibit properties that do not generally hold for real analytic functions. A function is analytic if and only if its Taylor series about converges to the function in some neighborhood for every in its domain.
Dirac delta functionIn mathematical physics, the Dirac delta distribution (δ distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. The current understanding of the unit impulse is as a linear functional that maps every continuous function (e.g., ) to its value at zero of its domain (), or as the weak limit of a sequence of bump functions (e.g.
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.
PhotographA photograph (also known as a photo, image, or picture) is an created by light falling on a photosensitive surface, usually photographic film or an electronic , such as a CCD or a CMOS chip. Most photographs are now created using a smartphone or camera, which uses a lens to focus the scene's visible wavelengths of light into a reproduction of what the human eye would see. The process and practice of creating such images is called photography.
Linear mapIn mathematics, and more specifically in linear algebra, a linear map (also called a linear mapping, linear transformation, vector space homomorphism, or in some contexts linear function) is a mapping between two vector spaces that preserves the operations of vector addition and scalar multiplication. The same names and the same definition are also used for the more general case of modules over a ring; see Module homomorphism. If a linear map is a bijection then it is called a .
Code injectionCode injection is the exploitation of a computer bug that is caused by processing invalid data. The injection is used by an attacker to introduce (or "inject") code into a vulnerable computer program and change the course of execution. The result of successful code injection can be disastrous, for example, by allowing computer viruses or computer worms to propagate. Code injection vulnerabilities occur when an application sends untrusted data to an interpreter.
