European emission standardsThe European emission standards are vehicle emission standards for pollution from the use of new land surface vehicles sold in the European Union and European Economic Area member states and the United Kingdom, and ships in EU waters. The standards are defined in a series of European Union directives staging the progressive introduction of increasingly stringent standards. the standards do not include non-exhaust emissions such as particulates from tyres and brakes.
Elliptic integralIn integral calculus, an elliptic integral is one of a number of related functions defined as the value of certain integrals, which were first studied by Giulio Fagnano and Leonhard Euler (1750). Their name originates from their originally arising in connection with the problem of finding the arc length of an ellipse. Modern mathematics defines an "elliptic integral" as any function f which can be expressed in the form where R is a rational function of its two arguments, P is a polynomial of degree 3 or 4 with no repeated roots, and c is a constant.
Four-dimensional spaceFour-dimensional space (4D) is the mathematical extension of the concept of three-dimensional space (3D). Three-dimensional space is the simplest possible abstraction of the observation that one needs only three numbers, called dimensions, to describe the sizes or locations of objects in the everyday world. For example, the volume of a rectangular box is found by measuring and multiplying its length, width, and height (often labeled x, y, and z).
Integral equationIn mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: where is an integral operator acting on u. Hence, integral equations may be viewed as the analog to differential equations where instead of the equation involving derivatives, the equation contains integrals.
Line integralIn mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms path integral, curve integral, and curvilinear integral are also used; contour integral is used as well, although that is typically reserved for line integrals in the complex plane. The function to be integrated may be a scalar field or a vector field. The value of the line integral is the sum of values of the field at all points on the curve, weighted by some scalar function on the curve (commonly arc length or, for a vector field, the scalar product of the vector field with a differential vector in the curve).
Improper integralIn mathematical analysis, an improper integral is an extension of the notion of a definite integral to cases that violate the usual assumptions for that kind of integral. In the context of Riemann integrals (or, equivalently, Darboux integrals), this typically involves unboundedness, either of the set over which the integral is taken or of the integrand (the function being integrated), or both. It may also involve bounded but not closed sets or bounded but not continuous functions.
Tangible user interfaceA tangible user interface (TUI) is a user interface in which a person interacts with digital information through the physical environment. The initial name was Graspable User Interface, which is no longer used. The purpose of TUI development is to empower collaboration, learning, and design by giving physical forms to digital information, thus taking advantage of the human ability to grasp and manipulate physical objects and materials.
AmplitudeThe amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of amplitude (see below), which are all functions of the magnitude of the differences between the variable's extreme values. In older texts, the phase of a periodic function is sometimes called the amplitude. For symmetric periodic waves, like sine waves, square waves or triangle waves peak amplitude and semi amplitude are the same.
Epidermal growth factor receptorThe epidermal growth factor receptor (EGFR; ErbB-1; HER1 in humans) is a transmembrane protein that is a receptor for members of the epidermal growth factor family (EGF family) of extracellular protein ligands. The epidermal growth factor receptor is a member of the ErbB family of receptors, a subfamily of four closely related receptor tyrosine kinases: EGFR (ErbB-1), HER2/neu (ErbB-2), Her 3 (ErbB-3) and Her 4 (ErbB-4). In many cancer types, mutations affecting EGFR expression or activity could result in cancer.
Hawaiian IslandsThe Hawaiian Islands (Hawaiian: Nā Moku o Hawai‘i) are an archipelago of eight major volcanic islands, several atolls, and numerous smaller islets in the North Pacific Ocean, extending some from the island of Hawaii in the south to northernmost Kure Atoll. Formerly the group was known to Europeans and Americans as the Sandwich Islands, a name that James Cook chose in honor of the 4th Earl of Sandwich, the then First Lord of the Admiralty.
