Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Azimuthal equidistant projectionThe azimuthal equidistant projection is an azimuthal map projection. It has the useful properties that all points on the map are at proportionally correct distances from the center point, and that all points on the map are at the correct azimuth (direction) from the center point. A useful application for this type of projection is a polar projection which shows all meridians (lines of longitude) as straight, with distances from the pole represented correctly. The flag of the United Nations contains an example of a polar azimuthal equidistant projection.
Decade (log scale)One decade (symbol dec) is a unit for measuring ratios on a logarithmic scale, with one decade corresponding to a ratio of 10 between two numbers. Scientific notation When a real number like .007 is denoted alternatively by 7.0 × 10—3 then it is said that the number is represented in scientific notation. More generally, to write a number in the form a × 10b, where 1 < a < 10 and b is an integer, is to express it in scientific notation, and a is called the significand or the mantissa, and b is its exponent.
Open and closed mapsIn mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets. That is, a function is open if for any open set in the is open in Likewise, a closed map is a function that maps closed sets to closed sets. A map may be open, closed, both, or neither; in particular, an open map need not be closed and vice versa. Open and closed maps are not necessarily continuous.
Multi-pass compilerA multi-pass compiler is a type of compiler that processes the source code or abstract syntax tree of a program several times. This is in contrast to a one-pass compiler, which traverses the program only once. Each pass takes the result of the previous pass as the input, and creates an intermediate output. In this way, the (intermediate) code is improved pass by pass, until the final pass produces the final code. Multi-pass compilers are sometimes called wide compilers, referring to the greater scope of the passes: they can "see" the entire program being compiled, instead of just a small portion of it.
Hausdorff spaceIn topology and related branches of mathematics, a Hausdorff space (ˈhaʊsdɔːrf , ˈhaʊzdɔːrf ), separated space or T2 space is a topological space where, for any two distinct points, there exist neighbourhoods of each which are disjoint from each other. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters. Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology.
Convergence of Fourier seriesIn mathematics, the question of whether the Fourier series of a periodic function converges to a given function is researched by a field known as classical harmonic analysis, a branch of pure mathematics. Convergence is not necessarily given in the general case, and certain criteria must be met for convergence to occur. Determination of convergence requires the comprehension of pointwise convergence, uniform convergence, absolute convergence, Lp spaces, summability methods and the Cesàro mean.
One-pass compilerIn computer programming, a one-pass compiler is a compiler that passes through the parts of each compilation unit only once, immediately translating each part into its final machine code. This is in contrast to a multi-pass compiler which converts the program into one or more intermediate representations in steps between source code and machine code, and which reprocesses the entire compilation unit in each sequential pass. This refers to the logical functioning of the compiler, not to the actual reading of the source file once only.
Weierstrass M-testIn mathematics, the Weierstrass M-test is a test for determining whether an infinite series of functions converges uniformly and absolutely. It applies to series whose terms are bounded functions with real or complex values, and is analogous to the comparison test for determining the convergence of series of real or complex numbers. It is named after the German mathematician Karl Weierstrass (1815-1897). Weierstrass M-test.
