A global solution for a reaction-diffusion equation on bounded domains

Khellat, Farhad; Khormizi, Mahmud Beyk

doi:10.21042/amns.2018.1.00002

Cited by 27 publications

(13 citation statements)

References 11 publications

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“…The four algorithms were independently run for 10 times. Table 4 summarizes the results of the four algorithms for the optimization of scheduling model [26- Figure 6 plots the convergence curves of four algorithms, indicating the proposed AFOA has better convergence speed and accuracy than BFO, PSO and standard FOA in solving the problem of urban rail transit scheduling [29][30][31].…”

Section: Resultsmentioning

confidence: 99%

Modeling and optimization of urban rail transit scheduling with adaptive fruit fly optimization algorithm

Wang

et al. 2019

Open Physics

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Despite the rapid development of urban rail transit in China, there are still some problems in train operation, such as low efficiency and poor punctuality. To realize a proper allocation of passenger flows and increase train frequency, this paper has proposed an improved urban rail transit scheduling model and solved the model with an adaptive fruit fly optimization algorithm (AFOA). For the benefits of both passengers and operators, the shortest average waiting time of passengers and the least train frequency are chosen as the optimization objective, and train headway is taken as the decision variable in the proposed model. To obtain higher computational efficiency and accuracy, an adaptive dynamic step size is built in the conventional FOA. Moreover, the data of urban rail transit in Zhengzhou was simulated for case study. The comparison results reveal that the proposed AFOA exhibits faster convergence speed and preferable accuracy than the conventional FOA, particle swarm optimization, and bacterial foraging optimization algorithms. Due to these superiorities, the proposed AFOA is feasible and effective for optimizing the scheduling of urban rail transit.

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Section: Resultsmentioning

confidence: 99%

Modeling and optimization of urban rail transit scheduling with adaptive fruit fly optimization algorithm

Wang

et al. 2019

Open Physics

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“…As it was stated in ([4], Subsection 3.1), many space-filling curves satisfy (1). On the other hand, despite F cannot be invertible, it can be still proved that F is a.e.…”

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confidence: 92%

“…Fractal dimension is a leading tool to explore fractal patterns on a wide range of scientific contexts (c.f., e.g., [1][2][3]). In the mathematical literature, there can be found (at least) a pair of theoretical results allowing the calculation of the box dimension of Euclidean objects in R d in terms of the box dimension of 1-dimensional Euclidean subsets.…”

Section: Introductionmentioning

confidence: 99%

“…, δ −nd − 1, and sub-cubes F ([k δ nd , (1 + k) δ nd ]) with lengths equal to δ n , where δ is a value depending on each space-filling curve. For instance, δ = 1 2 in both Hilbert's and Sierpiński's square-filling curves, and δ = 1 3 in the case of the Peano's filling curve. It is worth pointing out that space-filling curves satisfy the two following properties.…”

Section: Introductionmentioning

confidence: 99%

“…As such, suitable definitions of Ψ can be provided in these cases. It is worth noting that whether both properties (1) and (2) stand, then the quasi-inverse Ψ becomes Lebesgue measure preserving, i.e., µ d (Ψ −1 (A ∩ Ψ(I d ))) = µ 1 (A ∩ Ψ(I d )) for each Borel subset A of I 1 . Moreover, since the (Lebesgue) measure of Ψ(B) \ F −1 (B) is equal to zero, then we have µ 1 (Ψ(B)) = µ 1 (F −1 (B)) = µ d (B) for all Borel subsets B of I d .…”

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confidence: 99%

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Calculating Hausdorff Dimension in Higher Dimensional Spaces

2019

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In this paper, we prove the identity dim H(F) = d dim H(a?1(F)), where dim H denotesHausdorff dimension, F Rd, and a : [0, 1] ! [0, 1]d is a function whose constructive definition isaddressed from the viewpoint of the powerful concept of a fractal structure. Such a result standsparticularly from some other results stated in a more general setting. Thus, Hausdorff dimension ofhigher dimensional subsets can be calculated from Hausdorff dimension of 1-dimensional subsets of[0, 1]. As a consequence, Hausdorff dimension becomes available to deal with the effective calculationof the fractal dimension in applications by applying a procedure contributed by the authors inprevious works. It is also worth pointing out that our results generalize both Skubalska-Rafajłowiczand García-Mora-Redtwitz theorems.

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Preparation and electrochemical properties of nitrogen‐doped carbon electrode material

Zhang

Nasreen

2021

Asia-Pacific J Chem Eng

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In order to improve the lithium storage capacity of lithium-ion battery anode materials, three nitrogen-doped and nitrogen-doped hollow carbon materials (Cw-GO), nitrogen-doped carbon aerogels, and three-dimensional nitrogen-doped porous carbon materials (PCMs) were prepared, and their electrochemical properties were studied. Scanning electron microscopy (SEM), transmission electron microscopy (TEM), and nitrogen adsorption desorption instrument were used to detect the morphology and structure of the samples. The electrochemical properties of the samples were tested by cyclic voltammetry (CV), impedance spectroscopy (EIS), and cyclic charge discharge (GCD). The results show that the introduction of graphene oxide (GO) can improve the specific capacitance and electrochemical activity of the composites; nitrogen-doped carbon aerogel electrode material has better capacitance characteristics. PCM has a large specific surface area and a large capacitance response, which reaches 168.5 F g À1 at the current density of 1 A g À1 . When the current density is 10 A g À1 , 1000 cycles of constant current charge and discharge test is carried out. When the current density is 20 A g À1 , the specific capacitance of PCM keeps 88.3% of the original capacitance and has good electrochemical performance.

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A global solution for a reaction-diffusion equation on bounded domains

Cited by 27 publications

References 11 publications

Modeling and optimization of urban rail transit scheduling with adaptive fruit fly optimization algorithm

Modeling and optimization of urban rail transit scheduling with adaptive fruit fly optimization algorithm

Calculating Hausdorff Dimension in Higher Dimensional Spaces

Preparation and electrochemical properties of nitrogen‐doped carbon electrode material

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