Results 11 to 20 of about 3,791,283 (277)
The Second Generalization of the Hausdorff Dimension Theorem for Random Fractals
Mathematics, 2022 In this paper, we present a second partial solution for the problem of cardinality calculation of the set of fractals for its subcategory of the random virtual ones.
Mohsen Soltanifar
doaj +1 more source
On Hausdorff dimension of radial projections [PDF]
Revista matemática iberoamericana, 2019 For any $x\in\mathbb{R}^d$, $d\geq 2$, denote $\pi^x: \mathbb{R}^d\backslash\{x\}\rightarrow S^{d-1}$ as the radial projection $$\pi^x(y)=\frac{y-x}{|y-x|}.
Bochen Liu
semanticscholar +1 more source
GAN‐LSTM‐3D: An efficient method for lung tumour 3D reconstruction enhanced by attention‐based LSTM
CAAI Transactions on Intelligence Technology, EarlyView., 2023 Abstract Three‐dimensional (3D) image reconstruction of tumours can visualise their structures with precision and high resolution. In this article, GAN‐LSTM‐3D method is proposed for 3D reconstruction of lung cancer tumours from 2D CT images. Our method consists of three phases: lung segmentation, tumour segmentation, and tumour 3D reconstruction. Lung
Lu Hong +12 more
wiley +1 more source
Hausdorff dimension of an exceptional set in the theory of continued fractions
Nonlinearity, 2020 In this article we calculate the Hausdorff dimension of the setF(Φ)=x∈[0,1):an+1(x)an(x)⩾Φ(n)for infinitely many n∈Nandan+1(x)
Ayreena Bakhtawar +2 more
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Hausdorff dimension of Furstenberg-type sets associated to families of affine subspaces [PDF]
Annales Academiae Scientiarum Fennicae: Mathematica, 2018 We show that if $B \subset \mathbb{R}^n$ and $E \subset A(n,k)$ is a nonempty collection of $k$-dimensional affine subspaces of $\mathbb{R}^n$ such that every $P \in E$ intersects $B$ in a set of Hausdorff dimension at least $\alpha$ with $k-1 < \alpha ...
K. H'era
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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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On the Hausdorff Dimension of Bernoulli Convolutions [PDF]
International mathematics research notices, 2018 We give an expression for the Garsia entropy of Bernoulli convolutions in terms of products of matrices. This gives an explicit rate of convergence of the Garsia entropy and shows that one can calculate the Hausdorff dimension of the Bernoulli ...
S. Akiyama +3 more
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An improved bound on the Hausdorff dimension of Besicovitch sets in ℝ³ [PDF]
Journal of The American Mathematical Society, 2017 We prove that every Besicovitch set in R 3 \mathbb {R}^3 must have Hausdorff dimension at least 5 / 2 + ϵ 0 5/2 ...
N. Katz, Joshua Zahl
semanticscholar +1 more source
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
core +2 more sources