The Experts below are selected from a list of 16623 Experts worldwide ranked by ideXlab platform
Xiaokang Yang - One of the best experts on this subject based on the ideXlab platform.
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single image super resolution with detail enhancement based on local Fractal analysis of gradient
IEEE Transactions on Circuits and Systems for Video Technology, 2013Co-Authors: Guangtao Zhai, Xiaokang YangAbstract:In this paper, we propose a single image super-resolution and enhancement algorithm using local Fractal analysis. If we treat the pixels of a natural image as a Fractal Set, the image gradient can then be regarded as a measure of the Fractal Set. According to the scale invariance (a special case of bi-Lipschitz invariance) feature of Fractal dimension, we will be able to estimate the gradient of a high-resolution image from that of a low-resolution one. Moreover, the high-resolution image can be further enhanced by preserving the local Fractal length of gradient during the up-sampling process. We show that a regularization term based on the scale invariance of Fractal dimension and length can be effective in recovering details of the high-resolution image. Analysis is provided on the relation and difference among the proposed approach and some other state of the art interpolation methods. Experimental results show that the proposed method has superior super-resolution and enhancement results as compared to other competitors.
Tim Palmer - One of the best experts on this subject based on the ideXlab platform.
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Discretization of the Bloch sphere, Fractal invariant Sets and Bell's theorem.
Proceedings. Mathematical physical and engineering sciences, 2020Co-Authors: Tim PalmerAbstract:An arbitrarily dense discretization of the Bloch sphere of complex Hilbert states is constructed, where points correspond to bit strings of fixed finite length. Number-theoretic properties of trigonometric functions (not part of the quantum-theoretic canon) are used to show that this constructive discretized representation incorporates many of the defining characteristics of quantum systems: completementarity, uncertainty relationships and (with a simple Cartesian product of discretized spheres) entanglement. Unlike Meyer's earlier discretization of the Bloch Sphere, there are no orthonormal triples, hence the Kocken-Specker theorem is not nullified. A physical interpretation of points on the discretized Bloch sphere is given in terms of ensembles of trajectories on a dynamically invariant Fractal Set in state space, where states of physical reality correspond to points on the invariant Set. This deterministic construction provides a new way to understand the violation of the Bell inequality without violating statistical independence or factorization, where these conditions are defined solely from states on the invariant Set. In this finite representation, there is an upper limit to the number of qubits that can be entangled, a property with potential experimental consequences.
Xin Sui - One of the best experts on this subject based on the ideXlab platform.
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hermite hadamard type inequalities for generalized s convex functions on real linear Fractal Set mathbb r alpha 0 alpha 1
mathematical sciences, 2017Co-Authors: Xin SuiAbstract:In this paper, we establish the Hermite–Hadamard-type inequalities for the generalized s-convex functions in the second sense on real linear Fractal Set \(\mathbb {R}^{\alpha }(0<\alpha <1).\)
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hermite hadamard type inequalities for generalized s convex functions on real linear Fractal Set mathbb r alpha 0 alpha 1
arXiv: Classical Analysis and ODEs, 2015Co-Authors: Xin SuiAbstract:In the paper, we establish the Hermite-Hadamard type inequalities for the generalized s-convex functions in the second sense on real linear Fractal Set $\mathbb{R}^{\alpha}(0<\alpha<1).$
Dhurjati Prasad Datta - One of the best experts on this subject based on the ideXlab platform.
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analysis on a Fractal Set
arXiv: General Mathematics, 2010Co-Authors: Santanu Raut, Dhurjati Prasad DattaAbstract:The formulation of a new analysis on a zero measure Cantor Set $C (\subSet I=[0,1])$ is presented. A non-archimedean absolute value is introduced in $C$ exploiting the concept of {\em relative} infinitesimals and a scale invariant ultrametric valuation of the form $\log_{\varepsilon^{-1}} (\varepsilon/x) $ for a given scale $\varepsilon>0$ and infinitesimals $0
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analysis on a Fractal Set
Fractals, 2009Co-Authors: Santanu Raut, Dhurjati Prasad DattaAbstract:The formulation of a new analysis on a zero measure Cantor Set C(⊂I = [0,1]) is presented. A non-Archimedean absolute value is introduced in C exploiting the concept of relative infinitesimals and a scale invariant ultrametric valuation of the form loge-1 (e/x) for a given scale e > 0 and infinitesimals 0 < x < e, x ∈ I\C. Using this new absolute value, a valued (metric) measure is defined on C and is shown to be equal to the finite Hausdorff measure of the Set, if it exists. The formulation of a scale invariant real analysis is also outlined, when the singleton {0} of the real line R is replaced by a zero measure Cantor Set. The Cantor function is realized as a locally constant function in this Setting. The ordinary derivative dx/dt in R is replaced by the scale invariant logarithmic derivative d log x/d log t on the Set of valued infinitesimals. As a result, the ordinary real valued functions are expected to enjoy some novel asymptotic properties, which might have important applications in number theory and in other areas of mathematics.
Francesco Morandin - One of the best experts on this subject based on the ideXlab platform.
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Structure Function and Fractal Dissipation for an Intermittent Inviscid Dyadic Model
Communications in Mathematical Physics, 2017Co-Authors: Luigi Amedeo Bianchi, Francesco MorandinAbstract:We study a generalization of the original tree-indexed dyadic model by Katz and Pavlović for the turbulent energy cascade of the three-dimensional Euler equation. We allow the coefficients to vary with some restrictions, thus giving the model a realistic spatial intermittency. By introducing a forcing term on the first component, the fixed point of the dynamics is well defined and some explicit computations allow us to prove the rich multiFractal structure of the solution. In particular the exponent of the structure function is concave in accordance with other theoretical and experimental models. Moreover, anomalous energy dissipation happens in a Fractal Set of dimension strictly less than 3.
