DirectXMicrosoft DirectX is a collection of application programming interfaces (APIs) for handling tasks related to multimedia, especially game programming and video, on Microsoft platforms. Originally, the names of these APIs all began with "Direct", such as Direct3D, DirectDraw, DirectMusic, DirectPlay, DirectSound, and so forth. The name DirectX was coined as a shorthand term for all of these APIs (the X standing in for the particular API names) and soon became the name of the collection.
PolyhedronIn geometry, a polyhedron (: polyhedra or polyhedrons; ) is a three-dimensional shape with flat polygonal faces, straight edges and sharp corners or vertices. A convex polyhedron is a polyhedron that bounds a convex set. Every convex polyhedron can be constructed as the convex hull of its vertices, and for every finite set of points, not all on the same plane, the convex hull is a convex polyhedron. Cubes and pyramids are examples of convex polyhedra. A polyhedron is a 3-dimensional example of a polytope, a more general concept in any number of dimensions.
Dual polyhedronIn geometry, every polyhedron is associated with a second dual structure, where the vertices of one correspond to the faces of the other, and the edges between pairs of vertices of one correspond to the edges between pairs of faces of the other. Such dual figures remain combinatorial or abstract polyhedra, but not all can also be constructed as geometric polyhedra. Starting with any given polyhedron, the dual of its dual is the original polyhedron. Duality preserves the symmetries of a polyhedron.
BASICBASIC (Beginners' All-purpose Symbolic Instruction Code) is a family of general-purpose, high-level programming languages designed for ease of use. The original version was created by John G. Kemeny and Thomas E. Kurtz at Dartmouth College in 1963. They wanted to enable students in non-scientific fields to use computers. At the time, nearly all computers required writing custom software, which only scientists and mathematicians tended to learn.
Flexible polyhedronIn geometry, a flexible polyhedron is a polyhedral surface without any boundary edges, whose shape can be continuously changed while keeping the shapes of all of its faces unchanged. The Cauchy rigidity theorem shows that in dimension 3 such a polyhedron cannot be convex (this is also true in higher dimensions). The first examples of flexible polyhedra, now called Bricard octahedra, were discovered by . They are self-intersecting surfaces isometric to an octahedron.
Schönhardt polyhedronIn geometry, the Schönhardt polyhedron is the simplest non-convex polyhedron that cannot be triangulated into tetrahedra without adding new vertices. It is named after German mathematician Erich Schönhardt, who described it in 1928. The same polyhedra have also been studied in connection with Cauchy's rigidity theorem as an example where polyhedra with two different shapes have faces of the same shapes. One way of constructing the Schönhardt polyhedron starts with a triangular prism, with two parallel equilateral triangles as its faces.
Császár polyhedronIn geometry, the Császár polyhedron (ˈt͡ʃaːsaːr) is a nonconvex toroidal polyhedron with 14 triangular faces. This polyhedron has no diagonals; every pair of vertices is connected by an edge. The seven vertices and 21 edges of the Császár polyhedron form an embedding of the complete graph K_7 onto a topological torus. Of the 35 possible triangles from vertices of the polyhedron, only 14 are faces.
Szilassi polyhedronIn geometry, the Szilassi polyhedron is a nonconvex polyhedron, topologically a torus, with seven hexagonal faces. The 14 vertices and 21 edges of the Szilassi polyhedron form an embedding of the Heawood graph onto the surface of a torus. Each face of this polyhedron shares an edge with each other face. As a result, it requires seven colours to colour all adjacent faces. This example shows that, on surfaces topologically equivalent to a torus, some subdivisions require seven colors, providing the lower bound for the seven colour theorem.
Net (polyhedron)In geometry, a net of a polyhedron is an arrangement of non-overlapping edge-joined polygons in the plane which can be folded (along edges) to become the faces of the polyhedron. Polyhedral nets are a useful aid to the study of polyhedra and solid geometry in general, as they allow for physical models of polyhedra to be constructed from material such as thin cardboard.
Microsoft BASICMicrosoft BASIC is the foundation software product of the Microsoft company and evolved into a line of BASIC interpreters and compiler(s) adapted for many different microcomputers. It first appeared in 1975 as Altair BASIC, which was the first version of BASIC published by Microsoft as well as the first high-level programming language available for the Altair 8800 microcomputer. During the home computer craze during the late-1970s and early-1980s, BASIC was ported to and supplied with many home computer designs.
Feasible regionIn mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.
Windows NT 4.0Windows NT 4.0 is a major release of the Windows NT operating system developed by Microsoft and oriented towards businesses. It is the direct successor to Windows NT 3.51, and was released to manufacturing on July 31, 1996, and then to retail in September 1996. It was Microsoft's primary business-oriented operating system until the introduction of Windows 2000. Workstation, server and embedded editions were sold, and all editions feature a graphical user interface similar to that of Windows 95, which was superseded by Windows 98 and could still be directly upgraded by either Windows 2000 Professional or Windows Me.
Direction findingDirection finding (DF), or radio direction finding (RDF), is - in accordance with International Telecommunication Union (ITU) - defined as radio location that uses the reception of radio waves to determine the direction in which a radio station or an object is located. This can refer to radio or other forms of wireless communication, including radar signals detection and monitoring (ELINT/ESM). By combining the direction information from two or more suitably spaced receivers (or a single mobile receiver), the source of a transmission may be located via triangulation.
High-frequency direction findingHigh-frequency direction finding, usually known by its abbreviation HF/DF or nickname huff-duff, is a type of radio direction finder (RDF) introduced in World War II. High frequency (HF) refers to a radio band that can effectively communicate over long distances; for example, between U-boats and their land-based headquarters. HF/DF was primarily used to catch enemy radios while they transmitted, although it was also used to locate friendly aircraft as a navigation aid.
Basis (linear algebra)In mathematics, a set B of vectors in a vector space V is called a basis (: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called . Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B.
Optimal controlOptimal control theory is a branch of mathematical optimization that deals with finding a control for a dynamical system over a period of time such that an objective function is optimized. It has numerous applications in science, engineering and operations research. For example, the dynamical system might be a spacecraft with controls corresponding to rocket thrusters, and the objective might be to reach the moon with minimum fuel expenditure.
Constraint (mathematics)In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy. There are several types of constraints—primarily equality constraints, inequality constraints, and integer constraints. The set of candidate solutions that satisfy all constraints is called the feasible set. The following is a simple optimization problem: subject to and where denotes the vector (x1, x2). In this example, the first line defines the function to be minimized (called the objective function, loss function, or cost function).
Linear programmingLinear programming (LP), also called linear optimization, is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (also known as mathematical optimization). More formally, linear programming is a technique for the optimization of a linear objective function, subject to linear equality and linear inequality constraints.
Athlon 64 X2The Athlon 64 X2 is the first native dual-core desktop central processing unit (CPU) designed by Advanced Micro Devices (AMD). It was designed from scratch as native dual-core by using an already multi-CPU enabled Athlon 64, joining it with another functional core on one die, and connecting both via a shared dual-channel memory controller/north bridge and additional control logic. The initial versions are based on the E stepping model of the Athlon 64 and, depending on the model, have either 512 or 1024 KB of L2 cache per core.
Standard basisIn mathematics, the standard basis (also called natural basis or canonical basis) of a coordinate vector space (such as or ) is the set of vectors, each of whose components are all zero, except one that equals 1. For example, in the case of the Euclidean plane formed by the pairs (x, y) of real numbers, the standard basis is formed by the vectors Similarly, the standard basis for the three-dimensional space is formed by vectors Here the vector ex points in the x direction, the vector ey points in the y direction, and the vector ez points in the z direction.
