Dimension function information

(exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are...

mechanics is an infinite-dimensional function space. The concept of dimension is not restricted to physical objects. High-dimensional spaces frequently occur...

generalized to functions of several variables on Euclidean space, sending a function of 3-dimensional 'position space' to a function of 3-dimensional momentum...

the packing dimension is one of a number of concepts that can be used to define the dimension of a subset of a metric space. Packing dimension is in some...

typically only a one-dimensional, or sometimes a two-dimensional section is used, the three-dimensional optical transfer function can improve the understanding...

This is a complex-valued function of two real variables x and t. For one spinless particle in one dimension, if the wave function is interpreted as a probability...

Gaussian function," IEEE Sign. Proc. Mag. 28(9): 134-137 (2011). N. Hagen, M. Kupinski, and E. L. Dereniak, "Gaussian profile estimation in one dimension," Appl...

quantities named DimensionalCombations. Mathematica can also factor out certain dimension with UnitDimensions by specifying an argument to the function UnityDimensions...

Dimensionality reduction, or dimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the...

Neumann was motivated by his discovery of von Neumann algebras with a dimension function taking a continuous range of dimensions, and the first example of...

typical example of non-linear multimodal function. It was first proposed in 1974 by Rastrigin as a 2-dimensional function and has been generalized by Rudolph...

Appendix A in Dwork and Roth for a proof of this result). For high dimensional functions of the form f : D → R d {\displaystyle f:{\mathcal {D}}\to \mathbb...

convex function on an open set has no more than one minimum. Even in infinite-dimensional spaces, under suitable additional hypotheses, convex functions continue...

showed that the Hausdorff dimension of the set of non-differentiability of the Cantor function is the square of the dimension of the Cantor set, ( log...

In fluid dynamics, two types of stream function are defined: The two-dimensional (or Lagrange) stream function, introduced by Joseph Louis Lagrange in...

close, the function will not be monotone. The computation of the Hausdorff dimension D of the graph of the classical Weierstrass function was an open...

geometry, a synonym for dimension function; in control theory and dynamical systems, a synonym for Lyapunov candidate function; in gauge theory, a synonym...

region under the graph of its density function. Note that this property can be extended to N-dimension functions. To visualize the motivation behind rejection...

intrinsic dimension of the two-variable function f is neither zero or one, it is two. In the literature, functions which are of intrinsic dimension zero,...

The curse of dimensionality refers to various phenomena that arise when analyzing and organizing data in high-dimensional spaces that do not occur in low-dimensional...

In mathematics, Hausdorff dimension is a measure of roughness, or more specifically, fractal dimension, that was introduced in 1918 by mathematician Felix...

are countably infinite-dimensional vector spaces, and many function spaces have the cardinality of the continuum as a dimension. Many vector spaces that...

number called the scaling dimension of O {\displaystyle O} . This implies in particular that the two point correlation function ⟨ O ( x ) O ( 0 ) ⟩ {\displaystyle...