Results 1 to 10 of about 1,489,079 (174)

Characteristic Scales, Scaling, and Geospatial Analysis [PDF]

Cartographica, 2021, 56(2): 91-105, 2020
Geographical phenomena fall into two categories: scaleful phenomena and scale-free phenomena. The former bears characteristic scales, and the latter has no characteristic scale. The conventional quantitative and mathematical methods can only be effectively applied to scaleful geographical phenomena rather than the scale-free geographical phenomena.
arxiv   +1 more source

Navier--Stokes regularity criteria in sum spaces [PDF]

Pure Appl. Analysis 3 (2021) 527-566, 2020
In this paper, we will consider regularity criteria for the Navier--Stokes equation in mixed Lebesgue sum spaces. In particular, we will prove regularity criteria that only require control of the velocity, vorticity, or the positive part of the second eigenvalue of the strain matrix, in the sum space of two scale critical spaces.
arxiv   +1 more source

Quantisation Scale-Spaces [PDF]

arXiv, 2021
Recently, sparsification scale-spaces have been obtained as a sequence of inpainted images by gradually removing known image data. Thus, these scale-spaces rely on spatial sparsity. In the present paper, we show that sparsification of the co-domain, the set of admissible grey values, also constitutes scale-spaces with induced hierarchical quantisation ...
arxiv  

Scale Equivariant Neural Networks with Morphological Scale-Spaces [PDF]

IAPR International Conference on Discrete Geometry and Mathematical Morphology (DGMM), 2021, May 2021, Uppsala, Sweden, 2021
The translation equivariance of convolutions can make convolutional neural networks translation equivariant or invariant. Equivariance to other transformations (e.g. rotations, affine transformations, scalings) may also be desirable as soon as we know a priori that transformed versions of the same objects appear in the data.
arxiv  

An extended Hilbert scale and its applications [PDF]

arXiv, 2021
We propose a new viewpoint on Hilbert scales extending them by means of all Hilbert spaces that are interpolation ones between spaces on the scale. We prove that this extension admits an explicit description with the help of $\mathrm{OR}$-varying functions of the operator generating the scale.
arxiv  

Geographical Analysis: from Distance-based Space to Dimension-based Space [PDF]

arXiv, 2020
The traditional concept of space in geography is based on the notion of distance. Where there is a spatial analysis, there is a distance measurement. However, the precondition for effective distance-based space is that the geographical systems have characteristic scales.
arxiv  

Bounded Scale Measure and Property A [PDF]

arXiv, 2020
We introduce a generalization for bounded geometry that we call bounded scale measure. We show that bounded scale measure is a coarse invariant unlike bounded geometry. We then show equivalent definitions for spaces with bounded scale measure and show other properties that spaces with bounded scale measure satisfy.
arxiv  

Scaled Enflo type is equivalent to Rademacher type [PDF]

Bull. London Math. Soc. 39(3):493-498, 2007, 2005
We introduce the notion of scaled Enflo type of a metric space, and show that for Banach spaces, scaled Enflo type p is equivalent to Rademacher type p.
arxiv   +1 more source

Temporal scale selection in time-causal scale space [PDF]

, 2017
When designing and developing scale selection mechanisms for generating hypotheses about characteristic scales in signals, it is essential that the selected scale levels reflect the extent of the underlying structures in the signal. This paper presents a theory and in-depth theoretical analysis about the scale selection properties of methods for ...
arxiv   +1 more source

Non-Abelian gauge field theory in scale relativity [PDF]

J.Math.Phys.47:032303,2006, 2006
Gauge field theory is developed in the framework of scale relativity. In this theory, space-time is described as a non-differentiable continuum, which implies it is fractal, i.e., explicitly dependent on internal scale variables. Owing to the principle of relativity that has been extended to scales, these scale variables can themselves become functions
arxiv   +1 more source