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In mathematical systems theory, a multidimensional system or m-D system is a system in which not only one independent variable exists (like time), but there are several independent variables. Important problems such as factorization and stability of m -D systems ( m > 1) have recently attracted the interest of many researchers and practitioners.
Multiple independent timeframes, in which time passes at different rates, have long been a feature of stories. [15] Fantasy writers such as J. R. R. Tolkien and C. S. Lewis have made use of these and other multiple time dimensions, such as those proposed by Dunne, in some of their most well-known stories. [15]
In mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety (and by extension that of a scheme).The need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most regular cases (see Dimension of an algebraic variety).
Processing in multi-dimension (m-D) requires more complex algorithms, compared to the 1-D case, to handle calculations such as the fast Fourier transform due to more degrees of freedom. [1] In some cases, m-D signals and systems can be simplified into single dimension signal processing methods, if the considered systems are separable.
This problem can be seen as a generalization of the linear assignment problem. [2] In words, the problem can be described as follows: An instance of the problem has a number of agents (i.e., cardinality parameter) and a number of job characteristics (i.e., dimensionality parameter) such as task, machine, time interval, etc. For example, an ...
There are infinite ways to approach a single point in higher dimensions, as opposed to two (from the positive and negative direction) in 1D; There are multiple extended objects associated with the dimension; for example, for a 1D function, it must be represented as a curve on the 2D Cartesian plane , but a function with two variables is a ...
In string theory, spacetime is ten-dimensional (nine spatial dimensions, and one time dimension), while in M-theory it is eleven-dimensional (ten spatial dimensions, and one time dimension). In order to describe real physical phenomena using these theories, one must therefore imagine scenarios in which these extra dimensions would not be ...
The same term in a large extra dimension model would give a mass to the neutrino in the MeV-GeV range, comparable to the mass of the other particles. In this view, models with large extra dimensions miscalculate the neutrino masses by inappropriately assuming that the mass is due to interactions with a hypothetical right-handed partner.