In this paper, we present a pioneering investigation on the fractional Hamiltonian amplitude equation involving the beta fractional derivative for the first time, addressing a research gap in the ...field of nonlinear fractional dynamics. Our primary objective is to develop effective analytical techniques capable of solving the fractional Hamiltonian amplitude equation and obtaining novel soliton solutions. To achieve this, we introduce two advanced methods: the extended fractional rational
sin
e
δ
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cos
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n
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δ
and the fractional rational
sinh
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cosh
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techniques. By employing these cutting-edge approaches, we successfully derive new types of soliton solutions, demonstrating the reliability and efficiency of the proposed methods. Furthermore, the applicability of these techniques extends to various fractional nonlinear evolution models, highlighting their versatility in the realm of fractional dynamics. Finally, we provide a comprehensive presentation of the results, which substantiate the effectiveness of the methods in solving the complex fractional Hamiltonian amplitude equation.
In this study, the modified fractal gas dynamics model (GDM) with variable coefficients is successfully represented using the fractal derivative. We obtain the fractal variational principle of the ...modified fractal GDM by employing the fractal semi‐inverse method. Based on the established fractal variational principle, a new and fascinating algorithm is presented to solve the fractal model, which is called fractal two‐scale variational method (FTSVM). Finally, two numerical examples are given to indicate the efficiency and accuracy of the proposed algorithm. The FTSVM sheds a new light on the fractal differential equations.
In this study, the modified fractal gas dynamics model (GDM) with variable coefficients is successfully represented using the fractal derivative. We obtain the fractal variational principle of the modified fractal GDM by employing the fractal semi‐inverse method. Based on the established fractal variational principle, a new and fascinating algorithm is presented to solve the fractal model, which is called fractal two‐scale variational method (FTSVM). Finally, two numerical examples are given to indicate the efficiency and accuracy of the proposed algorithm. The FTSVM sheds a new light on the fractal differential equations.
The primary objective of this study is to examine the behavior of the nonlinear Kaup-Newell equation. By employing the modified Kudryashov method and extended tanh function method, we have ...successfully derived novel solitary wave and periodic solutions. These new solutions are presented in trigonometric, hyperbolic and exponential function types. The proposed two approaches are efficient, direct and fascinating. These newly discovered solutions are illustrated using two-dimensional and three-dimensional graphs, incorporating suitable parameters values. These graphs are crucial for elucidating the dynamic properties of optical fibers.
In this study, we explore the fractional Zakharov system using the M-truncated derivative for the first time. Some new solitary wave and periodic solutions are derived for the fractional Zakharov ...equations through two advanced mathematical techniques: the fractional sine–Gordon expansion method and the fractional rational sine–cosine method. The obtained solutions are new to the fractional Zakharov equations that have not been reported in the previous literature. Visual representations of the solutions are provided using 3D and 2D graphical illustrations, offering insights relevant to associated physics and engineering disciplines. Notably, the proposed methodologies are streamlined, straightforward, and effective, holding promise for addressing various fractional evolution equations.
Phase change in locusts is an ideal model for studying the genetic architectures and regulatory mechanisms associated with phenotypic plasticity. The recent development of genomic and metabolomic ...tools and resources has furthered our understanding of the molecular basis of phase change in locusts. Thousands of phase-related genes and metabolites have been highlighted using large-scale expressed sequence tags, microarrays, high-throughput transcriptomic sequences, or metabolomic approaches. However, only several key factors, including genes, metabolites, and pathways, have a critical role in phase transition in locusts. For example, CSP (chemosensory protein) and takeout genes, the dopamine pathway, protein kinase A, and carnitines were found to be involved in the regulation of behavioral phase change and gram-negative bacteria-binding proteins in prophylaxical disease resistance of gregarious locusts. Epigenetic mechanisms including small noncoding RNAs and DNA methylation have been implicated. We review these new advances in the molecular basis of phase change in locusts and present some challenges that need to be addressed.
In this work, a fractal nonlinear oscillator is successfully established by fractal derivative in a fractal space, and its variational principle is obtained by semi-inverse transform method. The ...variational principle can provide conservation laws in an energy form. The approximate frequency of the fractal oscillator is found by a simple fractal frequency formula. An example shows the fractal frequency formula is a powerful and simple tool to fractal oscillators.
High-fat diets may promote growth, partly through their protein-sparing effects. However, high-fat diets often lead to excessive fat deposition, which may have a negative impact on fish such as poor ...growth and suppressive immune. Therefore, this study investigated the effects of a fat-rich diet on the mechanisms of fat deposition in the liver. Three-hundred blunt snout bream (Megalobrama amblycephala) juveniles (initial mass 18.00 ± 0.05 g) were fed with one of two diets (5% or 15% fat) for 8 weeks. β-Oxidation capacity and regulation of rate-limiting enzymes were assessed. Large fat droplets were present in hepatocytes of fish fed the high-fat diet. This observation is thought to be largely owing to the reduced capacity for mitochondrial and peroxisomal β-oxidation in the livers of fish fed the high-fat diet, as well as the decreased activities of carnitine palmitoyltransferase (CPT) I and acyl-CoA oxidase (ACO), which are enzymes involved in fatty-acid metabolism. Study of CPT I kinetics showed that CPT I had a low affinity for its substrates and a low catalytic efficiency in fish fed the high-fat diet. Expression of both CPT I and ACO was significantly down-regulated in fish fed the high-fat diet. Moreover, the fatty-acid composition of the mitochondrial membrane varied between the two groups. In conclusion, the attenuated β-oxidation capacity observed in fish fed a high-fat diet is proposed to be owing to decreased activity and/or catalytic efficiency of the rate-limiting enzymes CPT I and ACO, via both genetic and non-genetic mechanisms.
In this work we describe a Convolutional Neural Network (CNN) to accurately predict image quality without a reference image. Taking image patches as input, the CNN works in the spatial domain without ...using hand-crafted features that are employed by most previous methods. The network consists of one convolutional layer with max and min pooling, two fully connected layers and an output node. Within the network structure, feature learning and regression are integrated into one optimization process, which leads to a more effective model for estimating image quality. This approach achieves state of the art performance on the LIVE dataset and shows excellent generalization ability in cross dataset experiments. Further experiments on images with local distortions demonstrate the local quality estimation ability of our CNN, which is rarely reported in previous literature.
In this paper, the reduced differential transform method is modified and
successfully used to solve the fractional heat transfer equations. The
numerical examples show that the new method is ...efficient, simple, and
accurate.
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•Efficient HGA-LSTM method proposed for predicting life of energy storage devices.•Precise and robust lifetime estimation for Supercapacitors with error low to 1.61%•Low time cost of ...59 min for one remaining life predication, a 60% reduction.•Adaptability for predicting life of supercapacitor at real-time dynamic cycling.•High versatility of such method to deal with both online and offline untrained data.
Supercapacitor as a clean energy storage device has been widely adopted in powering electric motors of vehicles. Precise evaluation of aging state of supercapacitors, i.e., the remaining useful life provides a feedback to replace damaged cells to sustain the comfort and safety of electric vehicle. Currently reported evaluation methods for such aim are data or model-based predications, which are either time consuming or of low precision. To achieve efficient and robust evaluation of the remaining lifetime, this work proposes a general strategy based on the combination between a recurrent neutral network method, i.e., long short-term memory, and hybrid genetic algorithm. The sequential quadratic programming as a local search operator of the genetic algorithm, enhances its global search ability, which allows quickly search for the local optimal solution in the means of the dropout probability and the number of hidden layer units. Eventually we apply this predication method to supercapacitors charging at steady state mode and succeed in estimating their remaining useful life. Such life prediction approach also gains validity in supercapacitors with dynamic operative cycle. Indeed, high accuracy has been achieved at both the online trained supercapacitors with root mean square errors ranging from 0.0161 and 0.0214, and offline historical data with 0.0264 error. Moreover, the estimation time is shortened to 3550 s, which is shortened by 60%. This evaluation model may pave the way in predicting the remaining useful lifetime of supercapacitors as well as secondary ion batteries in a precise and robust fashion.
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