Jacobi elliptic functionsIn mathematics, the Jacobi elliptic functions are a set of basic elliptic functions. They are found in the description of the motion of a pendulum (see also pendulum (mathematics)), as well as in the design of electronic elliptic filters. While trigonometric functions are defined with reference to a circle, the Jacobi elliptic functions are a generalization which refer to other conic sections, the ellipse in particular. The relation to trigonometric functions is contained in the notation, for example, by the matching notation for .
Elliptic curveIn mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is defined over a field K and describes points in K^2, the Cartesian product of K with itself. If the field's characteristic is different from 2 and 3, then the curve can be described as a plane algebraic curve which consists of solutions (x, y) for: for some coefficients a and b in K. The curve is required to be non-singular, which means that the curve has no cusps or self-intersections.
Weierstrass elliptic functionIn mathematics, the Weierstrass elliptic functions are elliptic functions that take a particularly simple form. They are named for Karl Weierstrass. This class of functions are also referred to as ℘-functions and they are usually denoted by the symbol ℘, a uniquely fancy script p. They play an important role in the theory of elliptic functions. A ℘-function together with its derivative can be used to parameterize elliptic curves and they generate the field of elliptic functions with respect to a given period lattice.
Human backThe human back, also called the dorsum (: dorsa), is the large posterior area of the human body, rising from the top of the buttocks to the back of the neck. It is the surface of the body opposite from the chest and the abdomen. The vertebral column runs the length of the back and creates a central area of recession. The breadth of the back is created by the shoulders at the top and the pelvis at the bottom. Back pain is a common medical condition, generally benign in origin.
Back painBack pain is pain felt in the back. It may be classified as neck pain (cervical), middle back pain (thoracic), lower back pain (lumbar) or coccydynia (tailbone or sacral pain) based on the segment affected. The lumbar area is the most common area affected. An episode of back pain may be acute, subacute or chronic depending on the duration. The pain may be characterized as a dull ache, shooting or piercing pain or a burning sensation. Discomfort can radiate to the arms and hands as well as the legs or feet, and may include numbness or weakness in the legs and arms.
Srinivasa RamanujanSrinivasa Ramanujan (ˈsriːnᵻvɑːsə_rɑːˈmɑːnʊdʒən ; born Srinivasa Ramanujan Aiyangar, sriːniʋaːsa ɾaːmaːnud͡ʑan ajːaŋgar; 22 December 1887 26 April 1920) was an Indian mathematician. Though he had almost no formal training in pure mathematics, he made substantial contributions to mathematical analysis, number theory, infinite series, and continued fractions, including solutions to mathematical problems then considered unsolvable. Ramanujan initially developed his own mathematical research in isolation.
Low back painLow back pain (LBP) or lumbago is a common disorder involving the muscles, nerves, and bones of the back, in between the lower edge of the ribs and the lower fold of the buttocks. Pain can vary from a dull constant ache to a sudden sharp feeling. Low back pain may be classified by duration as acute (pain lasting less than 6 weeks), sub-chronic (6 to 12 weeks), or chronic (more than 12 weeks). The condition may be further classified by the underlying cause as either mechanical, non-mechanical, or referred pain.
Lp spaceDISPLAYTITLE:Lp space In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue , although according to the Bourbaki group they were first introduced by Frigyes Riesz . Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces.
Inequality (mathematics)In mathematics, an inequality is a relation which makes a non-equal comparison between two numbers or other mathematical expressions. It is used most often to compare two numbers on the number line by their size. There are several different notations used to represent different kinds of inequalities: The notation a < b means that a is less than b. The notation a > b means that a is greater than b. In either case, a is not equal to b. These relations are known as strict inequalities, meaning that a is strictly less than or strictly greater than b.
Set-builder notationIn set theory and its applications to logic, mathematics, and computer science, set-builder notation is a mathematical notation for describing a set by enumerating its elements, or stating the properties that its members must satisfy. Defining sets by properties is also known as set comprehension, set abstraction or as defining a set's intension. Set (mathematics)#Roster notation A set can be described directly by enumerating all of its elements between curly brackets, as in the following two examples: is the set containing the four numbers 3, 7, 15, and 31, and nothing else.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Monotonic functionIn mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of order theory. In calculus, a function defined on a subset of the real numbers with real values is called monotonic if and only if it is either entirely non-increasing, or entirely non-decreasing. That is, as per Fig. 1, a function that increases monotonically does not exclusively have to increase, it simply must not decrease.
