Lake GenevaLake Geneva (le Léman lə lemɑ̃, lac Léman lak lemɑ̃, rarely lac de Genève lak də ʒ(ə)nɛv; Lago Lemano; Genfersee ˈɡɛnfərˌzeː; Lai da Genevra) is a deep lake on the north side of the Alps, shared between Switzerland and France. It is one of the largest lakes in Western Europe and the largest on the course of the Rhône. Sixty per cent () of the lake belongs to Switzerland (the cantons of Vaud, Geneva and Valais) and forty per cent () to France (the department of Haute-Savoie).
Wind tunnelWind tunnels are machines where an object is held stationary inside a tube, and air is blown around it to study the interaction between the object and the moving air. They are used to test the aerodynamic effects of aircraft, rockets, cars, and buildings. Different wind tunnels range in size from less than a foot across, to over , and can have air that moves at speeds from a light breeze to hypersonic velocities. Usually, large fans move air through the wind tunnel, while the object being tested is held stationary.
RatioIn mathematics, a ratio (ˈreɪʃ(i)oʊ) shows how many times one number contains another. For example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six (that is, 8:6, which is equivalent to the ratio 4:3). Similarly, the ratio of lemons to oranges is 6:8 (or 3:4) and the ratio of oranges to the total amount of fruit is 8:14 (or 4:7). The numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Thermohaline circulationThermohaline circulation (THC) is a part of the large-scale ocean circulation that is driven by global density gradients created by surface heat and freshwater fluxes. The adjective thermohaline derives from thermo- referring to temperature and -haline referring to salt content, factors which together determine the density of sea water. Wind-driven surface currents (such as the Gulf Stream) travel polewards from the equatorial Atlantic Ocean, cooling en route, and eventually sinking at high latitudes (forming North Atlantic Deep Water).
Ideal (ring theory)In mathematics, and more specifically in ring theory, an ideal of a ring is a special subset of its elements. Ideals generalize certain subsets of the integers, such as the even numbers or the multiples of 3. Addition and subtraction of even numbers preserves evenness, and multiplying an even number by any integer (even or odd) results in an even number; these closure and absorption properties are the defining properties of an ideal.
Ideal class groupIn number theory, the ideal class group (or class group) of an algebraic number field K is the quotient group JK/PK where JK is the group of fractional ideals of the ring of integers of K, and PK is its subgroup of principal ideals. The class group is a measure of the extent to which unique factorization fails in the ring of integers of K. The order of the group, which is finite, is called the class number of K. The theory extends to Dedekind domains and their field of fractions, for which the multiplicative properties are intimately tied to the structure of the class group.
Fractional idealIn mathematics, in particular commutative algebra, the concept of fractional ideal is introduced in the context of integral domains and is particularly fruitful in the study of Dedekind domains. In some sense, fractional ideals of an integral domain are like ideals where denominators are allowed. In contexts where fractional ideals and ordinary ring ideals are both under discussion, the latter are sometimes termed integral ideals for clarity. Let be an integral domain, and let be its field of fractions.
Flow velocityIn continuum mechanics the flow velocity in fluid dynamics, also macroscopic velocity in statistical mechanics, or drift velocity in electromagnetism, is a vector field used to mathematically describe the motion of a continuum. The length of the flow velocity vector is the flow speed and is a scalar. It is also called velocity field; when evaluated along a line, it is called a velocity profile (as in, e.g., law of the wall).
Principal idealIn mathematics, specifically ring theory, a principal ideal is an ideal in a ring that is generated by a single element of through multiplication by every element of The term also has another, similar meaning in order theory, where it refers to an (order) ideal in a poset generated by a single element which is to say the set of all elements less than or equal to in The remainder of this article addresses the ring-theoretic concept.
