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In calculus and related areas of mathematics, a linear function from the real numbers to the real numbers is a function whose graph (in Cartesian coordinates) is a non-vertical line in the plane. [1] The characteristic property of linear functions is that when the input variable is changed, the change in the output is proportional to the change ...
LP-type problems include many important optimization problems that are not themselves linear programs, such as the problem of finding the smallest circle containing a given set of planar points. They may be solved by a combination of randomized algorithms in an amount of time that is linear in the number of elements defining the problem, and ...
CD-ROM drives are rated with a speed factor relative to music CDs. If a CD-ROM is read at the same rotational speed as an audio CD, the data transfer rate is 150 Kbyte/s, commonly called "1×" (with constant linear velocity, short "CLV"). At this data rate, the track moves along under the laser spot at about 1.2 m/s.
In three-dimensional Euclidean space, these three planes represent solutions to linear equations, and their intersection represents the set of common solutions: in this case, a unique point. The blue line is the common solution to two of these equations. Linear algebra is the branch of mathematics concerning linear equations such as:
However, some problems have distinct optimal solutions; for example, the problem of finding a feasible solution to a system of linear inequalities is a linear programming problem in which the objective function is the zero function (i.e., the constant function taking the value zero everywhere).
If the data density is the same everywhere on the disc, as is the case with CD and DVD and Blu-ray discs, the linear velocity directly correlates with the transfer rate (read speed or write speed), meaning an increase in linear velocity also increases the amount of data read from the disc in the same time, regardless of whether the laser is ...
If the problem is to solve a Dirichlet boundary value problem, the Green's function should be chosen such that G(x,x′) vanishes when either x or x′ is on the bounding surface. Thus only one of the two terms in the surface integral remains. If the problem is to solve a Neumann boundary value problem, it might seem logical to choose Green's ...
Early sound cards could include a CD-ROM drive interface. Initially, such interfaces were proprietary to each CD-ROM manufacturer. A sound card could often have two or three different interfaces which are able to communicate with the CD-ROM drive. A method for using the parallel port to use with external drives was developed at some point. This ...