Euclidean divisionIn arithmetic, Euclidean division – or division with remainder – is the process of dividing one integer (the dividend) by another (the divisor), in a way that produces an integer quotient and a natural number remainder strictly smaller than the absolute value of the divisor. A fundamental property is that the quotient and the remainder exist and are unique, under some conditions. Because of this uniqueness, Euclidean division is often considered without referring to any method of computation, and without explicitly computing the quotient and the remainder.
Natural logarithmThe natural logarithm of a number is its logarithm to the base of the mathematical constant e, which is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, loge x, or sometimes, if the base e is implicit, simply log x. Parentheses are sometimes added for clarity, giving ln(x), loge(x), or log(x). This is done particularly when the argument to the logarithm is not a single symbol, so as to prevent ambiguity.
Internet forumAn Internet forum, or message board, is an online discussion site where people can hold conversations in the form of posted messages. They differ from chat rooms in that messages are often longer than one line of text, and are at least temporarily archived. Also, depending on the access level of a user or the forum set-up, a posted message might need to be approved by a moderator before it becomes publicly visible. Forums have a specific set of jargon associated with them; for example, a single conversation is called a "thread", or topic.
Conversation threadingConversation threading is a feature used by many email clients, bulletin boards, newsgroups, and Internet forums in which the software aids the user by visually grouping messages with their replies. These groups are called a conversation, topic thread, or simply a thread. A discussion forum, e-mail client or news client is said to have a "conversation view", "threaded topics" or a "threaded mode" if messages can be grouped in this manner. An email thread is also sometimes called an email chain.
Atterberg limitsThe Atterberg limits are a basic measure of the critical water contents of a fine-grained soil: its shrinkage limit, plastic limit, and liquid limit. Depending on its water content, soil may appear in one of four states: solid, semi-solid, plastic and liquid. In each state, the consistency and behavior of soil are different, and consequently so are its engineering properties. Thus, the boundary between each state can be defined based on a change in the soil's behavior.
Power seriesIn mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant. Power series are useful in mathematical analysis, where they arise as Taylor series of infinitely differentiable functions. In fact, Borel's theorem implies that every power series is the Taylor series of some smooth function. In many situations, c (the center of the series) is equal to zero, for instance when considering a Maclaurin series.
Stop motionStop motion is an animated filmmaking technique in which objects are physically manipulated in small increments between individually photographed frames so that they will appear to exhibit independent motion or change when the series of frames is played back. Any kind of object can thus be animated, but puppets with movable joints (puppet animation) or plasticine figures (clay animation or claymation) are most commonly used. Puppets, models or clay figures built around an armature are used in model animation.
Full stopThe full stop (Commonwealth English), period (North American English), or full point is a punctuation mark. It is used for several purposes, most often to mark the end of a declarative sentence (as distinguished from a question or exclamation). This sentence-ending use, alone, defines the strictest sense of full stop. Although full stop technically applies only when the mark is used to end a sentence, the distinction – drawn since at least 1897 – is not maintained by all modern style guides and dictionaries.
Series (mathematics)In mathematics, a series is, roughly speaking, the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, mathematical analysis. Series are used in most areas of mathematics, even for studying finite structures (such as in combinatorics) through generating functions. In addition to their ubiquity in mathematics, infinite series are also widely used in other quantitative disciplines such as physics, computer science, statistics and finance.
Exponential functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers.
Convergence testsIn mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series . If the limit of the summand is undefined or nonzero, that is , then the series must diverge. In this sense, the partial sums are Cauchy only if this limit exists and is equal to zero. The test is inconclusive if the limit of the summand is zero. This is also known as the nth-term test, test for divergence, or the divergence test.
SmoothnessIn mathematical analysis, the smoothness of a function is a property measured by the number of continuous derivatives it has over some domain, called differentiability class. At the very minimum, a function could be considered smooth if it is differentiable everywhere (hence continuous). At the other end, it might also possess derivatives of all orders in its domain, in which case it is said to be infinitely differentiable and referred to as a C-infinity function (or function).
