An irreducible fraction is a fraction in which the numerator and denominator are integers that have no other common divisors than 1. In other words, a fraction a⁄b is irreducible if and only if a and b are coprime, that is, if a and b have a greatest common divisor of 1. In higher mathematics, "irreducible fraction" may also refer to rational fractions such that the numerator and the denominator are coprime polynomials. Every positive rational number can be represented as an irreducible fraction in exactly one way.
Radiation therapy or radiotherapy, often abbreviated RT, RTx, or XRT, is a therapy using ionizing radiation, generally as part of cancer treatment to control or kill malignant cells and normally delivered by a linear accelerator. Radiation therapy may be curative in a number of types of cancer if they are localized to one area of the body. It may also be used as part of adjuvant therapy, to prevent tumor recurrence after surgery to remove a primary malignant tumor. Radiation therapy is synergistic with chemotherapy, and has been used before, during, and after chemotherapy in susceptible cancers. The subspecialty of oncology concerned with radiotherapy is called radiation oncologist.
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. The division sign ÷, a symbol consisting of a short horizontal line with a dot above and another dot below, is often used to indicate mathematical division. This usage, though widespread in anglophone countries, is neither universal nor recommended: the ISO 80000-2 standard for mathematical notation recommends only the solidus / or fraction bar for division, or the colon for ratios; it says that this symbol "should not be used" for division.
Double-precision floating-point format is a computer number format, usually occupying 64 bits in computer memory; it represents a wide dynamic range of numeric values by using a floating radix point.
A computer algebra system (CAS) or symbolic algebra system (SAS) is any mathematical software with the ability to manipulate mathematical expressions in a way similar to the traditional manual computations of mathematicians and scientists. The development of the computer algebra systems in the second half of the 20th century is part of the discipline of "computer algebra" or "symbolic computation", which has spurred work in algorithms over mathematical objects such as polynomials.
Factor, a Latin word meaning "who/which acts", may refer to:
In mathematics, division by zero is division where the divisor (denominator) is zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, when multiplied by 0, gives a, and so division by zero is undefined. Since any number multiplied by zero is zero, the expression 0/0 is also undefined; when it is the form of a limit, it is an indeterminate form. Historically, one of the earliest recorded references to the mathematical impossibility of assigning a value to a/0 is contained in George Berkeley's criticism of infinitesimal calculus in 1734 in The Analyst.
The sheaf of rational functionsKX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. In the case of varieties, such a sheaf associates to each open set U the ring of all rational functions on that open set; in other words, KX(U) is the set of fractions of regular functions on U. Despite its name, KX does not always give a field for a general scheme X.
Third or 3rd may refer to:
In mathematics, the remainder is the amount "left over" after performing some computation. In arithmetic, the remainder is the integer "left over" after dividing one integer by another to produce an integer quotient. In algebra of polynomials, the remainder is the polynomial "left over" after dividing one polynomial by another. The modulo operation is the operation that produces such a remainder when given a dividend and divisor.
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers, an algebraic surface has complex dimension two and so of dimension four as a smooth manifold.
This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Much of the theory is in the form of proposed conjectures, which can be related at various levels of generality.
Dose fractionation effects are utilised in the treatment of cancer with radiation therapy. When the total dose of radiation is divided into several, smaller doses over a period of several days, there are fewer toxic effects on healthy cells. This maximizes the effect of radiation on cancer and minimizes the negative side effects. A typical fractionation scheme divides the dose into 30 units delivered every weekday over six weeks. Hypofractionation is a treatment regimen that delivers higher doses of radiation in fewer visits, which tends to lower the effects of accelerated tumor growth that typically occurs during the later stages of radiotherapy. Hyperfractionation is dividing the same total dose into more deliveries, so that treatments are given more than once a day. Hyperfractionated radiation therapy is given over the same period of time as standard radiation therapy. Accelerated fractionation has also been investigated.
Mathematics is a field of study that investigates topics such as number, space, structure, and change. More on the relationship between mathematics and science can be found at Mathematics and science.
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