Search results
Results From The WOW.Com Content Network
Itzhak Bars has proposed models of a two-time physics, noting in 2001 that "The 2T-physics approach in d + 2 dimensions offers a highly symmetric and unified version of the phenomena described by 1T-physics in d dimensions." [4] [5] F-theory, a branch of modern string theory, describes a 12-dimensional spacetime having two dimensions of time ...
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.
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 surface in 3D, while curves can also live in 3D space.
Similar to the one-dimensional case, an asterisk is used to represent the convolution operation. The number of dimensions in the given operation is reflected in the number of asterisks. For example, an M-dimensional convolution would be written with M asterisks. The following represents a M-dimensional convolution of discrete signals:
As with the Nyquist–Shannon sampling theorem, this theorem also assumes an idealization of any real-world situation, as it only applies to functions that are sampled over an infinitude of points. Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-world functions and sampling techniques ...
The theory of Riemann surfaces can be applied to G\H ∗ to obtain further information about modular forms and functions. For example, the spaces M k (G) and S k (G) are finite-dimensional, and their dimensions can be computed thanks to the Riemann–Roch theorem in terms of the geometry of the G-action on H. [8] For example,
Laplace transforms are used to solve partial differential equations. The general theory for obtaining solutions in this technique is developed by theorems on Laplace transform in n dimensions. [3] The multidimensional Z transform can also be used to solve partial differential equations. [11]
Typically, a prototype filter is designed in a single dimension and that filter is extrapolated to m-D using a mapping function. [3] One of the original mapping functions from 1-D to 2-D was the McClellan Transform. [4] Both FIR and IIR filters can be transformed to m-D, depending on the application and the mapping function.