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CUBIC
Cubic may refer to: Science and mathematics * Cube (algebra), "cubic" measurement * Cube, a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex ** Cubic crystal system, a crystal system where the unit cell is in the shape of a cube * Cubic function, a polynomial function of degree three * Cubic equation, a polynomial equation (reducible to ''ax''3 + ''bx''2 + ''cx'' + ''d'' = 0) * Cubic form, a homogeneous polynomial of degree 3 * Cubic graph (mathematics - graph theory), a graph where all vertices have degree 3 * Cubic plane curve (mathematics), a plane algebraic curve ''C'' defined by a cubic equation * Cubic reciprocity (mathematics - number theory), a theorem analogous to quadratic reciprocity * Cubic surface, an algebraic surface in three-dimensional space * Cubic zirconia, in geology, a mineral that is widely synthesized for use as a diamond simulacra * CUBIC, a histology method Computing * Cubic IDE, a modular devel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Equation
In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d=0 in which is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of the coefficients , , , and of the cubic equation are real numbers, then it has at least one real root (this is true for all odd-degree polynomial functions). All of the roots of the cubic equation can be found by the following means: * algebraically: more precisely, they can be expressed by a ''cubic formula'' involving the four coefficients, the four basic arithmetic operations, square roots, and cube roots. (This is also true of quadratic (second-degree) and quartic (fourth-degree) equations, but not for higher-degree equations, by the Abel–Ruffini theorem.) * trigonometrically * numerical approximations of the roots can be found using root-finding algorithms such as Newton's method. The coefficients do not need to be real ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Plane Curve
In mathematics, a cubic plane curve is a plane algebraic curve defined by a cubic equation : applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation. Here is a non-zero linear combination of the third-degree monomials : These are ten in number; therefore the cubic curves form a projective space of dimension 9, over any given field . Each point imposes a single linear condition on , if we ask that pass through . Therefore, we can find some cubic curve through any nine given points, which may be degenerate, and may not be unique, but will be unique and non-degenerate if the points are in general position; compare to two points determining a line and how five points determine a conic. If two cubics pass through a given set of nine points, then in fact a pencil of cubics does, and the points satisfy additional properties; see Cayley–Bacharach theorem. A cubic curve may ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Surface
In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry. The theory is simplified by working in projective space rather than affine space, and so cubic surfaces are generally considered in projective 3-space \mathbf^3. The theory also becomes more uniform by focusing on surfaces over the complex numbers rather than the real numbers; note that a complex surface has real dimension 4. A simple example is the Fermat cubic surface :x^3+y^3+z^3+w^3=0 in \mathbf^3. Many properties of cubic surfaces hold more generally for del Pezzo surfaces. Rationality of cubic surfaces A central feature of smooth scheme, smooth cubic surfaces ''X'' over an algebraically closed field is that they are all rational variety, rational, as shown by Alfred Clebsch in 1866. That is, there is a one-to-one correspondence defined by rational functions between the projective plane \mathbf^2 min ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubicle
A cubicle is a partially enclosed office workspace that is separated from neighboring workspaces by partitions that are usually tall. Its purpose is to isolate office workers and managers from the sights and noises of an open workspace so that they may concentrate with fewer distractions. Cubicles are composed of modular elements such as walls, work surfaces, overhead bins, drawers, and shelving, which can be configured depending on the user's needs. Installation is generally performed by trained personnel, although some cubicles allow configuration changes to be performed by users without specific training. Cubicles in the 2010s and 2020s are usually equipped with a computer, monitor, keyboard and mouse on the work surface. Cubicles typically have a desk phone. Since many offices use overhead fluorescent lights to illuminate the office, cubicles may or may not have lamps or other additional lighting. Other furniture often found in cubicles includes office chairs and filing c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Graph
In the mathematical field of graph theory, a cubic graph is a graph in which all vertices have degree three. In other words, a cubic graph is a 3-regular graph. Cubic graphs are also called trivalent graphs. A bicubic graph is a cubic bipartite graph. Symmetry In 1932, Ronald M. Foster began collecting examples of cubic symmetric graphs, forming the start of the Foster census.. Many well-known individual graphs are cubic and symmetric, including the utility graph, the Petersen graph, the Heawood graph, the Möbius–Kantor graph, the Pappus graph, the Desargues graph, the Nauru graph, the Coxeter graph, the Tutte–Coxeter graph, the Dyck graph, the Foster graph and the Biggs–Smith graph. W. T. Tutte classified the symmetric cubic graphs by the smallest integer number ''s'' such that each two oriented paths of length ''s'' can be mapped to each other by exactly one symmetry of the graph. He showed that ''s'' is at most 5, and provided examples of graphs with ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Crystal System
In crystallography, the cubic (or isometric) crystal system is a crystal system where the unit cell is in the shape of a cube. This is one of the most common and simplest shapes found in crystals and minerals. There are three main varieties of these crystals: *Primitive cubic (abbreviated ''cP'' and alternatively called simple cubic) *Body-centered cubic (abbreviated ''cI'' or bcc) *Face-centered cubic (abbreviated ''cF'' or fcc) Note: the term fcc is often used in synonym for the ''cubic close-packed'' or ccp structure occurring in metals. However, fcc stands for a face-centered cubic Bravais lattice, which is not necessarily close-packed when a motif is set onto the lattice points. E.g. the diamond and the zincblende lattices are fcc but not close-packed. Each is subdivided into other variants listed below. Although the ''unit cells'' in these crystals are conventionally taken to be cubes, the primitive unit cells often are not. Bravais lattices The three Bravais latices ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Zirconia
Cubic zirconia (CZ) is the cubic crystalline form of zirconium dioxide (ZrO2). The synthesized material is hard and usually colorless, but may be made in a variety of different colors. It should not be confused with zircon, which is a zirconium silicate (ZrSiO4). It is sometimes erroneously called ''cubic zirconium''. Because of its low cost, durability, and close visual likeness to diamond, synthetic cubic zirconia has remained the most gemologically and economically important competitor for diamonds since commercial production began in 1976. Its main competitor as a synthetic gemstone is a more recently cultivated material, synthetic moissanite. Technical aspects Cubic zirconia is crystallographically isometric, an important attribute of a would-be diamond simulant. During synthesis zirconium oxide naturally forms monoclinic crystals, which are stable under normal atmospheric conditions. A stabilizer is required for cubic crystals (taking on the fluorite structure) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Corporation
Cubic Corporation is an American multinational defense and public transportation equipment manufacturer. It operates two business segments: Cubic Transportation Systems (CTS) and Cubic Mission and Performance Solutions (CMPS). History Cubic Corporation was founded in 1949 by Walter J. Zable as an electronics company in San Diego, California, and began operations in 1951. Zable devised the company name as he wanted the name to reflect both engineering and precision. Its first product was a calorimetric wattmeter, a device used for measuring microwave output. It became a publicly-traded company in 1959. In 1969, the company acquired United States Elevator Corporation, a maker of freight and passenger elevators. In early September 1984, Cubic moved its corporate domicile into Delaware General Corporation Law. The move was completed on June 11, 1985. Cubic employs 6,200 people globally. Stevan Slijepcevic was named president and chief executive officer of Cubic Corporation in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Function
In mathematics, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d, that is, a polynomial function of degree three. In many texts, the ''coefficients'' , , , and are supposed to be real numbers, and the function is considered as a real function that maps real numbers to real numbers or as a complex function that maps complex numbers to complex numbers. In other cases, the coefficients may be complex numbers, and the function is a complex function that has the set of the complex numbers as its codomain, even when the domain is restricted to the real numbers. Setting produces a cubic equation of the form :ax^3+bx^2+cx+d=0, whose solutions are called roots of the function. The derivative of a cubic function is a quadratic function. A cubic function with real coefficients has either one or three real roots ( which may not be distinct); all odd-degree polynomials with real coefficients have at least one real root. The graph of a cubic function always has a single ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Transportation Systems
Cubic Corporation is an American multinational defense and public transportation equipment manufacturer. It operates two business segments: Cubic Transportation Systems (CTS) and Cubic Mission and Performance Solutions (CMPS). History Cubic Corporation was founded in 1949 by Walter J. Zable as an electronics company in San Diego, California, and began operations in 1951. Zable devised the company name as he wanted the name to reflect both engineering and precision. Its first product was a calorimetric wattmeter, a device used for measuring microwave output. It became a publicly-traded company in 1959. In 1969, the company acquired United States Elevator Corporation, a maker of freight and passenger elevators. In early September 1984, Cubic moved its corporate domicile into Delaware General Corporation Law. The move was completed on June 11, 1985. Cubic employs 6,200 people globally. Stevan Slijepcevic was named president and chief executive officer of Cubic Corporation in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cubic Reciprocity
Cubic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence ''x''3 ≡ ''p'' (mod ''q'') is solvable; the word "reciprocity" comes from the form of the main theorem, which states that if ''p'' and ''q'' are primary numbers in the ring of Eisenstein integers, both coprime to 3, the congruence ''x''3 ≡ ''p'' (mod ''q'') is solvable if and only if ''x''3 ≡ ''q'' (mod ''p'') is solvable. History Sometime before 1748 Euler made the first conjectures about the cubic residuacity of small integers, but they were not published until 1849, 62 years after his death. Gauss's published works mention cubic residues and reciprocity three times: there is one result pertaining to cubic residues in the Disquisitiones Arithmeticae (1801). In the introduction to the fifth and sixth proofs of quadratic reciprocity (1818) he said that he was publishing these proofs because their techniques ( Gauss ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Quartic Function
In algebra, a quartic function is a function (mathematics), function of the form :f(x)=ax^4+bx^3+cx^2+dx+e, where ''a'' is nonzero, which is defined by a polynomial of Degree of a polynomial, degree four, called a quartic polynomial. A ''quartic equation'', or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form :ax^4+bx^3+cx^2+dx+e=0 , where . The derivative of a quartic function is a cubic function. Sometimes the term biquadratic is used instead of ''quartic'', but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form :f(x)=ax^4+cx^2+e. Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If ''a'' is positive, then the function increases to positive infinity at both ends; and thus the function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
