Dot-com companyA dot-com company, or simply a dot-com (alternatively rendered dot.com, dot com, dotcom or .com), is a company that does most of its business on the Internet, usually through a website on the World Wide Web that uses the popular top-level domain ".com". As of 2021, .com is by far the most used TLD, with almost half of all registrations. The suffix .com in a URL usually (but not always) refers to a commercial or for-profit entity, as opposed to a non-commercial entity or non-profit organization, which usually use .
Dot-com bubbleThe dot-com bubble (or dot-com boom) was a stock market bubble in the late 1990s. The period coincided with massive growth in Internet adoption, a proliferation of available venture capital, and the rapid growth of valuations in new dot-com startups. Between 1995 and its peak in March 2000, investments in the NASDAQ composite stock market index rose 800%, only to fall 740% from its peak by October 2002, giving up all its gains during the bubble. During the dot-com crash, many online shopping companies, notably Pets.
Einstein field equationsIn the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it. The equations were published by Albert Einstein in 1915 in the form of a tensor equation which related the local (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor).
SummationIn mathematics, summation is the addition of a sequence of any kind of numbers, called addends or summands; the result is their sum or total. Beside numbers, other types of values can be summed as well: functions, vectors, matrices, polynomials and, in general, elements of any type of mathematical objects on which an operation denoted "+" is defined. Summations of infinite sequences are called series. They involve the concept of limit, and are not considered in this article.
Leibniz's notationIn calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz, uses the symbols dx and dy to represent infinitely small (or infinitesimal) increments of x and y, respectively, just as Δx and Δy represent finite increments of x and y, respectively. Consider y as a function of a variable x, or y = f(x).
Equations of motionIn physics, equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. More specifically, the equations of motion describe the behavior of a physical system as a set of mathematical functions in terms of dynamic variables. These variables are usually spatial coordinates and time, but may include momentum components. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system.
Permutation matrixIn mathematics, particularly in matrix theory, a permutation matrix is a square binary matrix that has exactly one entry of 1 in each row and each column and 0s elsewhere. Each such matrix, say P, represents a permutation of m elements and, when used to multiply another matrix, say A, results in permuting the rows (when pre-multiplying, to form PA) or columns (when post-multiplying, to form AP) of the matrix A.
Iverson bracketIn mathematics, the Iverson bracket, named after Kenneth E. Iverson, is a notation that generalises the Kronecker delta, which is the Iverson bracket of the statement x = y. It maps any statement to a function of the free variables in that statement. This function is defined to take the value 1 for the values of the variables for which the statement is true, and takes the value 0 otherwise. It is generally denoted by putting the statement inside square brackets: In other words, the Iverson bracket of a statement is the indicator function of the set of values for which the statement is true.
Empty sumIn mathematics, an empty sum, or nullary sum, is a summation where the number of terms is zero. The natural way to extend non-empty sums is to let the empty sum be the additive identity. Let , , , ... be a sequence of numbers, and let be the sum of the first m terms of the sequence. This satisfies the recurrence provided that we use the following natural convention: . In other words, a "sum" with only one term evaluates to that one term, while a "sum" with no terms evaluates to 0.
Kronecker deltaIn mathematics, the Kronecker delta (named after Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: or with use of Iverson brackets: For example, because , whereas because . The Kronecker delta appears naturally in many areas of mathematics, physics, engineering and computer science, as a means of compactly expressing its definition above.
Mathematical notationMathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas. Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way. For example, Albert Einstein's equation is the quantitative representation in mathematical notation of the mass–energy equivalence.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
