Results 21 to 30 of about 66,461 (287)
A Generalization of the Hausdorff Dimension Theorem for Deterministic Fractals
Mathematics, 2021 How many fractals exist in nature or the virtual world? In this paper, we partially answer the second question using Mandelbrot’s fundamental definition of fractals and their quantities of the Hausdorff dimension and Lebesgue measure.
Mohsen Soltanifar
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Topological diagonalizations and Hausdorff dimension [PDF]
, 2002 The Hausdorff dimension of a product XxY can be strictly greater than that of Y, even when the Hausdorff dimension of X is zero. But when X is countable, the Hausdorff dimensions of Y and XxY are the same.
Tsaban, Boaz, Weiss, Tomasz
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Rigidity, Graphs and Hausdorff Dimension [PDF]
, 2021 For a compact set $E \subset \mathbb R^d$ and a connected graph $G$ on $k+1$ vertices, we define a $G$-framework to be a collection of $k+1$ points in $E$ such that the distance between a pair of points is specified if the corresponding vertices of $G$ are connected by an edge.
Chatzikonstantinou, N. +3 more
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Topics in Cognitive Science, EarlyView., 2023 Abstract Representational drift is a phenomenon of increasing interest in the cognitive and neural sciences. While investigations are ongoing for other sensory cortices, recent research has demonstrated the pervasiveness in which it occurs in the piriform cortex for olfaction.
Ann‐Sophie Barwich +1 more
wiley +1 more source
On the fractal structure of two-dimensional quantum gravity [PDF]
, 1995 We provide evidence that the Hausdorff dimension is 4 and the spectral dimension is 2 for two-dimensional quantum gravity coupled the matter with a central charge $c \leq 1$.
Ambjørn +29 more
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Lowness for effective Hausdorff dimension [PDF]
Journal of Mathematical Logic, 2014 We examine the sequences A that are low for dimension, i.e. those for which the effective (Hausdorff) dimension relative to A is the same as the unrelativized effective dimension. Lowness for dimension is a weakening of lowness for randomness, a central notion in effective randomness.
Turetsky, Daniel +4 more
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A deep-learning model for one-shot transcranial ultrasound simulation and phase aberration correction. [PDF]
Med PhysAbstract Background Transcranial ultrasound is a promising non‐invasive neuromodulation technique with applications, including neuronal activity modulation, blood–brain barrier opening, targeted drug delivery, and thermal ablation. Its ability to deliver focused ultrasound waves to precise brain regions has led to over 50 clinical trials targeting ...
Naftchi-Ardebili K +3 more
europepmc +2 more sources
Dimensions and singular traces for spectral triples, with applications to fractals [PDF]
, 1992 Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit.
Guido, Daniele, Isola, Tommaso
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International Journal of Mathematics and Mathematical Sciences, 1995 We define the coordinate d-dimension print to distinguish sets of same fractal dimension, and investigate its geometrical properties.
Hung Hwan Lee, In Soo Baek
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On the construction, properties and Hausdorff dimension of random Cantor one pth set
AIMS Mathematics, 2020 In 1883, German Mathematician George Cantor introduced Cantor ternary set which is a self-similar fractal. K. J. Falconer (1990) defined random Cantor set with statistical self-similarity.
Sudesh Kumari +3 more
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