Quadratic fieldIn algebraic number theory, a quadratic field is an algebraic number field of degree two over , the rational numbers. Every such quadratic field is some where is a (uniquely defined) square-free integer different from and . If , the corresponding quadratic field is called a real quadratic field, and, if , it is called an imaginary quadratic field or a complex quadratic field, corresponding to whether or not it is a subfield of the field of the real numbers.
Quadratic integerIn number theory, quadratic integers are a generalization of the usual integers to quadratic fields. Quadratic integers are algebraic integers of degree two, that is, solutions of equations of the form x2 + bx + c = 0 with b and c (usual) integers. When algebraic integers are considered, the usual integers are often called rational integers. Common examples of quadratic integers are the square roots of rational integers, such as , and the complex number i = , which generates the Gaussian integers.
Echo chamber (media)In news media and social media, an echo chamber is an environment or ecosystem in which participants encounter beliefs that amplify or reinforce their preexisting beliefs by communication and repetition inside a closed system and insulated from rebuttal. An echo chamber circulates existing views without encountering opposing views, potentially resulting in confirmation bias. Echo chambers may increase social and political polarization and extremism.
Quadratic reciprocityIn number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers. Due to its subtlety, it has many formulations, but the most standard statement is: Let p and q be distinct odd prime numbers, and define the Legendre symbol as: Then: This law, together with its supplements, allows the easy calculation of any Legendre symbol, making it possible to determine whether there is an integer solution for any quadratic equation of the form for an odd prime ; that is, to determine the "perfect squares" modulo .
Quadratic residueIn number theory, an integer q is called a quadratic residue modulo n if it is congruent to a perfect square modulo n; i.e., if there exists an integer x such that: Otherwise, q is called a quadratic nonresidue modulo n. Originally an abstract mathematical concept from the branch of number theory known as modular arithmetic, quadratic residues are now used in applications ranging from acoustical engineering to cryptography and the factoring of large numbers.
Quadratic formulaIn elementary algebra, the quadratic formula is a formula that provides the solution(s) to a quadratic equation. There are other ways of solving a quadratic equation instead of using the quadratic formula, such as factoring (direct factoring, grouping, AC method), completing the square, graphing and others. Given a general quadratic equation of the form whose discriminant is positive, with x representing an unknown, with a, b and c representing constants, and with a ≠ 0, the quadratic formula is: where the plus–minus symbol "±" indicates that the quadratic equation has two solutions.
Marketing communicationsMarketing Communications (MC, marcom(s), marcomm(s) or just simply communications) refers to the use of different marketing channels and tools in combination. Marketing communication channels focus on how businesses communicate a message to its desired market, or the market in general. It is also in charge of the internal communications of the organization. Marketing communication tools include advertising, personal selling, direct marketing, sponsorship, communication, public relations, social media, customer journey and promotion.
Binary quadratic formIn mathematics, a binary quadratic form is a quadratic homogeneous polynomial in two variables where a, b, c are the coefficients. When the coefficients can be arbitrary complex numbers, most results are not specific to the case of two variables, so they are described in quadratic form. A quadratic form with integer coefficients is called an integral binary quadratic form, often abbreviated to binary quadratic form. This article is entirely devoted to integral binary quadratic forms.
Donald TrumpDonald John Trump (born June 14, 1946) is an American politician, media personality, and businessman who served as the 45th president of the United States from 2017 to 2021. Trump graduated from the University of Pennsylvania with a bachelor's degree in economics in 1968. He became president of his father's real-estate business in 1971 and renamed it the Trump Organization. He expanded its operations to building and renovating skyscrapers, hotels, casinos, and golf courses and later started side ventures, mostly by licensing his name.
TwitterTwitter, currently rebranding to X, is an online social media and social networking service operated by the American company X Corp., the successor of Twitter, Inc. On Twitter, users can post texts, images and videos known as "tweets". Registered users can post, like, repost, comment and quote posts, and direct message other registered users. Users interact with Twitter through browser or mobile frontend software, or programmatically via its application programming interfaces (APIs).
Active usersActive users is a software performance metric that is commonly used to measure the level of engagement for a particular software product or object, by quantifying the number of active interactions from users or visitors within a relevant range of time (daily, weekly and monthly). The metric has many uses in software management such as in social networking services, online games, or mobile apps, in web analytics such as in web apps, in commerce such as in internet banking and in academia, such as in user behavior analytics and predictive analytics.
Meta PlatformsMeta Platforms, Inc., doing business as Meta, and formerly named Facebook, Inc., and TheFacebook, Inc., is an American multinational technology conglomerate based in Menlo Park, California. The company owns and operates Facebook, Instagram, Threads, and WhatsApp, among other products and services. Meta is one of the world's most valuable companies and among the ten largest publicly traded corporations in the United States. It is considered one of the Big Five American information technology companies, alongside Google's parent company Alphabet, Amazon, Apple, and Microsoft.
