# American Institute of Mathematical Sciences

ISSN:
1937-1632

eISSN:
1937-1179

All Issues

## Discrete & Continuous Dynamical Systems - S

Open Access Articles

2019, 12(4&5): ⅲ-ⅳ doi: 10.3934/dcdss.2020320 +[Abstract](263) +[HTML](134) +[PDF](147.32KB)
Abstract:
2020, 13(1): 85-104 doi: 10.3934/dcdss.2020005 +[Abstract](3095) +[HTML](946) +[PDF](10539.3KB)
Abstract:

We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can be used to derive bounds on the persistent dynamics. The method is applicable to constant and variable delay problems, and we illustrate the method by applying it to the state-dependent delay differential equation known as the sawtooth equation, to find parameter regions for which the steady-state solution is globally asymptotically stable. We also establish bounds on the periodic orbits that arise when the steady-state is unstable. This technique can be readily extended to apply to other scalar delay differential equations with negative feedback.

2019, 12(7): 1841-1850 doi: 10.3934/dcdss.2019121 +[Abstract](2171) +[HTML](830) +[PDF](370.68KB)
Abstract:

We prove that second order Hamiltonian systems \begin{document}$-\ddot{u} = V_{u}(t,u)$\end{document} with a potential \begin{document}$V\colon \mathbb{R} \times \mathbb{R} ^N\to \mathbb{R}$\end{document} of class \begin{document}$C^1$\end{document}, periodic in time and superquadratic at infinity with respect to the space variable have subharmonic solutions. Our intention is to generalise a result on subharmonics for Hamiltonian systems with a potential satisfying the global Ambrosetti-Rabinowitz condition from [14]. Indeed, we weaken the latter condition in a neighbourhood of \begin{document}$0\in \mathbb{R} ^N$\end{document}. We will also discuss when subharmonics pass to a nontrivial homoclinic orbit.

2019, 12(4&5): 877-886 doi: 10.3934/dcdss.2019058 +[Abstract](2724) +[HTML](460) +[PDF](344.92KB)
Abstract:

Let \begin{document}$i≥2$ \end{document}, \begin{document}$Δ≥0$ \end{document}, \begin{document}$1≤ a≤ b-Δ$ \end{document}, \begin{document}$n>\frac{(a+b)(ib+2m-2)}{a}+n'$ \end{document} and \begin{document}$δ(G)≥\frac{b^{2}}{a}+n'+2m$ \end{document}, and let \begin{document}$g,f$ \end{document} be two integer-valued functions defined on \begin{document}$V(G)$ \end{document} such that \begin{document}$a≤ g(x)≤ f(x)-Δ≤ b-Δ$ \end{document} for each \begin{document}$x∈ V(G)$ \end{document}. In this article, it is determined that \begin{document}$G$ \end{document} is a fractional \begin{document}$(g,f,n',m)$ \end{document}-critical deleted graph if \begin{document}$\max\{d_{1},d_{2},···,d_{i}\}≥\frac{b(n+n')}{a+b}$ \end{document} for any independent subset \begin{document}$\{x_{1},x_{2},..., x_{i}\}\subseteq V(G)$ \end{document}. The result is tight on independent set degree condition.

2019, 12(4&5): 1471-1487 doi: 10.3934/dcdss.2019101 +[Abstract](2935) +[HTML](501) +[PDF](3424.44KB)
Abstract:

Rolling bearings are the most prone components to failure in urban rail trains, presenting potential danger to cities and their residents. This paper puts forward a rolling bearing fault diagnosis method by integrating empirical mode decomposition (EMD) and genetic neural network adaptive boosting (GNN-AdaBoost). EMD is an excellent tool for feature extraction and during which some intrinsic mode functions (IMFs) are obtained. GNN-AdaBoost fault identification algorithm, which uses genetic neural network (GNN) as sub-classifier of the boosting algorithm, is proposed in order to address the shortcomings in classification when only using a GNN. To demonstrate the excellent performance of the approach, experiments are performed to simulate different operating conditions of the rolling bearing, including high speed, low speed, heavy load and light load. For de-nosing signal, by EMD decomposition is applied to obtain IMFs, which is used for extracting the IMF energy feature parameters. The combination of IMF energy feature parameters and some time-domain feature parameters are selected as the input vectors of the classifiers. Finally, GNN-AdaBoost and GNN are applied to experimental examples and the identification results are compared. The results show that GNN-AdaBoost offers significant improvement in rolling bearing fault diagnosis for urban rail trains when compared to GNN alone.

2019, 12(4&5): 1101-1115 doi: 10.3934/dcdss.2019076 +[Abstract](2667) +[HTML](508) +[PDF](1335.88KB)
Abstract:

Stowage operations in container terminals are an important part of a port's operational system, as the quality of stowage operations will directly affect the efficiency of port loading and discharge operations, and the scheduling of container shipping liners. The intelligent stowage of containers in container ships was studied in this work. A multi-objective integer programming model was constructed with the minimization of container rehandling, yard crane movements, and the sum of weight differences between stacked container pairs as its objective functions, to address the need for intelligent optimization of single bay export container stowage on a ship's deck. This model also satisfies the stability requirements of preliminary stowage plans drawn by shipping companies, and the operational requirements of container terminals. Linear computational methods were then constructed to transform non-linear constraints into linear ones for better AIMMS solution. Through numerous case analyses and systematic tests, it was shown that our system is able to rapidly solve for stowage planning optimization problems with complex preliminary stowage data, thus proving the applicability and effectiveness of this model. In particular, the application of this model will simultaneously address the safety of ship voyages, the transportation quality of shipping containers and other forms of cargo, and the cost efficiency of ship operations. In addition, this model will also contribute to the optimization of loading and discharge processes in container terminals. Therefore, our model has immense practical value for improving port productivity, as it will contribute to the organization of port operations in a rational, orderly and effective manner.

2019, 12(4&5): 1297-1309 doi: 10.3934/dcdss.2019089 +[Abstract](2787) +[HTML](510) +[PDF](719.92KB)
Abstract:

The current global enhancement algorithm for medical X-ray image has problems of poor de-noising and enhancement effect and low reduction of the enhanced medical X-ray image. To address the problems, a global enhancement algorithm for X-ray image in medical image classification is proposed in this paper. The medical X-ray image is gray scaled, which provides the basis for the further processing of the image. The noise in medical X-ray image is removed by using multi-wavelet transform to improve the enhancement effect of the method. With the curve-let domain the medical X-ray image is enhanced, the reduction degree of medical X-ray image is improved and the global enhancement of the medical X-ray image is completed. Experimental results show that the de-noising effect of the proposed method is effective, the enhanced medical X ray image is better, and the reduction degree of medical X-ray image is high.

2019, 12(4&5): 1441-1455 doi: 10.3934/dcdss.2019099 +[Abstract](2514) +[HTML](400) +[PDF](495.83KB)
Abstract:

At present, in reversible information hiding algorithm of image, the difference expansion idea is used. After the carrier image encryption, in encrypted image, information bits are embedded in the low value, resulting in the fact that in the image embedded with watermarking information, a part of the boundary pixel value has flipped. After being extracted, the carrier image cannot be recovered completely that is not only a large quantity of calculation, and the image quality has also been some damage. A algorithm for reversible information hiding of encrypted the medical image in the homomorphic encryption domain is proposed. Combining wavelet and fast fuzzy algorithm, the image edge is extracted from the high frequency and low frequency parts of medical image, and the medical image is reconstructed in the compressed boundary part. Combined with the thought of block compressed sensing and block edge pixels, the reconstructed medical image is divided to multiple non-overlapping blocks. The pixel in the right lower edge of the block is made homomorphic encryption operation, the remaining pixels are made compressed sensing operation, and the two parts are combined to a ciphertext to be sent to the owner of the channel According to the information hiding key the secret information is embedded into the ciphertext by the channel owners. The receiver can extract the information and restore the original image based on the encryption key and the information hiding key. The experimental results show that the proposed algorithm has high embedding capacity, the image quality after recovery is high, and the computational complexity is low.

2019, 12(4&5): 1135-1145 doi: 10.3934/dcdss.2019078 +[Abstract](2086) +[HTML](407) +[PDF](356.69KB)
Abstract:

Multiplications in finite fields are playing a key role in areas of cryptography and mathematic. We present approaches to exploit systolic architecture for multiplications in composite fields, which are expected to reduce the time-area product substantially. We design a pipelined architecture for multiplications in composite fields \begin{document} $GF({({2^n})^2})$ \end{document}, where \begin{document} $n$ \end{document} is a positive integer. Besides, we design systolic architectures for multiplications and additions in finite fields \begin{document} $GF(2^n)$ \end{document}. By integrating main improvements and other minor optimizations for multiplications in \begin{document} $GF({({2^n})^2})$ \end{document}, the non-pipelined versions of our design takes \begin{document} $8n+4$ \end{document} AND gates and \begin{document} $8n$ \end{document} XOR gates to compute multiplications with the executing time of \begin{document} $nT_{AND}+4nT_{XOR}$ \end{document}, where \begin{document} $T_{AND}$ \end{document} and \begin{document} ${T_{XOR}}$ \end{document} are delays of AND and XOR gates respectively; with the aid of pipelining, the pipelined version of our design has a throughput rate of one result per \begin{document} $2nT_{XOR}$ \end{document}. Other words, the time complexity and area complexity of our design are \begin{document} $O(n)$ \end{document}. Thus, the complexity of time-area product of our design is \begin{document} $O(n^2)$ \end{document}. Experimental results and comparisons show that our design provides significant reductions in executing time and area of multiplications.

2019, 12(4&5): 849-875 doi: 10.3934/dcdss.2019057 +[Abstract](2669) +[HTML](559) +[PDF](4314.84KB)
Abstract:

In the framework of the perturbed photo-gravitational restricted three-body problem, the first order exterior resonant orbits and the first, third and fifth order interior resonant periodic orbits are analyzed. The location, eccentricity and period of the first order exterior and interior resonant orbits are investigated in the unperturbed and perturbed cases for a specified value of Jacobi constant C.

It is observed that as the number of loops increases successively from one loop to five loops, the period of infinitesimal body increases in such a way that the successive difference of periods is either 6 or 7 units. It is further observed that for the exterior resonance, as the number of loops increases, the location of the periodic orbit moves towards the Sun whereas for the interior resonance as the number of loops increases, location of the periodic orbit moves away from the Sun. Thereby we demonstrate that the location of resonant orbits of the given order moves away from the Sun when perturbation is included.

The evolution of interior first order resonant orbit with three loops is studied for different values of Jacobi constant C. It is observed that when the value of C increases, the size of the loop decreases and degenerates finally into a circle, the eccentricity of periodic orbit decreases and location of the periodic orbit moves towards the second primary body.

2019, 12(4&5): 957-968 doi: 10.3934/dcdss.2019064 +[Abstract](2642) +[HTML](433) +[PDF](538.49KB)
Abstract:

The issue of searching missing aircraft is valuable after the event of MH370. This paper provides a global optimal model to foster the efficiency of maritime search. Firstly, the limited scope, a circle whose center is the last known position of the aircraft, should be estimated based on the historical data recorded before the disappearance of the aircraft. And Bayes' theorem is applied to calculate the probability that the plane falling in the region can be found. Secondly, the drift of aircraft debris under the influence of wind and current is considered via Finite Volume Community Ocean Model(FVCOM) and Monte Carlo Method(MC), which make the theory more reasonable. Finally, a global optimal model about vessel and aircraft quantitative constraints is established, which fully considers factors including the area of sea region to be searched, the maximum speed, search capabilities, initial distance of the vessels by introducing 0-1 decision variables.

2019, 12(4&5): 783-793 doi: 10.3934/dcdss.2019052 +[Abstract](2187) +[HTML](441) +[PDF](1118.73KB)
Abstract:

This paper proposes a novel approach for full duplex using chaotic sequences which is known as the asynchronous code-division duplex (Async-CDD) system. The Async-CDD system can transmit and receive signals at the same time and in the same frequency channel without time slot synchronization. The data rate of the Async-CDD system is 8 times higher than the conventional CDD system and is the same as a non-spreading system. The property of low block cross-correlation of the chaotic sequence allows the Async-CDD system achieve duplex interference suppression at any duplex delay. And the huge number of available code words/blocks of the chaotic sequence allows the Async-CDD system increase the data rate by increasing the number of multiplexed sub-channels. When both of the code length of the orthogonal chaotic code and the number of multiplexed sub-channels are 128, the orthogonal chaotic code provides 30.40 dBc self-interference suppression in average, which is 6.99 dB better than the orthogonal Gold code.

2019, 12(4-5): 915-915 doi: 10.3934/dcdss.2019061 +[Abstract](3589) +[HTML](936) +[PDF](105.87KB)
Abstract:

Xiao-Qian Jiang and Lun-Chuan Zhang, Stock price fluctuation prediction method based on time series analysis

Discrete & Continuous Dynamical Systems - S, 12 (2019), 915-927

This paper is retracted by decision of the Editors in Chief of the journal Discrete &Continuous Dynamical Systems - S.

2019, 12(4&5): 771-782 doi: 10.3934/dcdss.2019051 +[Abstract](2412) +[HTML](475) +[PDF](354.06KB)
Abstract:

This study applied the combined methods of Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and Information Entropy Weights to evaluate the tourism destination competitiveness (TDC) of 13 cities in Sichuan Province. In the empirical study, IEW was used to determine the subjective weights of four aspects and 26 evaluation indexes, which have the influence on TDC. In addition, applying the essential ideas of TOPSIS, chosen alternative should have the shortest geometric from the positive ideal solution (PIS) and the longest geometric distance from the negative ideal solution (NIS), to conduct a comprehensive evaluation and sort-based analysis. In the end, the essay arranged the TDC of 13 cities in Sichuan Province from high to low, then produced policy recommendations. The results represent that IEW & TOPSIS were an efficient and effective way to evaluate TDC.

2019, 12(4&5): 1187-1198 doi: 10.3934/dcdss.2019082 +[Abstract](2539) +[HTML](414) +[PDF](384.57KB)
Abstract:

In real game problems not all players can cooperate directly, games with communication structures introduced by Myerson in 1977 can deal with these problems quite well. More recently, this concept has been introduced into fuzzy games. In this paper, games on (fuzzy) communication structures were studied. We proved that if a coalitional game has a nonempty core, then the game restricted on an n-person connected graph also has a nonempty core. Further, the fuzzy game restricted on the n-person connected graph also has a nonempty core. Moreover, we proved the above two cores are identical and the core of the coalitional game is included in them. In addition, optimal fuzzy communication structures of fuzzy games were studied. We showed that the optimal communication structures do exist and proposed three allocating methods. In the end, a full illustrating example was given.

2019, 12(4&5): 795-809 doi: 10.3934/dcdss.2019053 +[Abstract](2640) +[HTML](493) +[PDF](390.08KB)
Abstract:

The fast growing telecommunications industry in China has been experiencing dramatic technological change and substantial productivity growth. The actual productivity growth pattern in the sector, however, need to be empirically examined. In this paper, using input and output data at the provincial level, we employ DEA-based Malmquist productivity index to estimate productivity change, technological change and relative efficiency change in China's telecommunications industry for the period spanning the years from 2011 to 2015. The results show that based on our sample, the productivity improved by 22.9% per annum, which was exclusively due to an average of 25.5% technological progress in the industry production function, while the average efficiency change is slightly negative. Our results also indicate that regions with relatively low levels of telecommunications (and economic) development have a greater chance and ability of enhancing telecommunications productivity growth through technological catch-up. In addition, we find that the industry experienced significantly higher productivity growth and technological progress in the later sample period between 2013 and 2015 than in the early period between 2011 and 2013.

2019, 12(4&5): 1005-1013 doi: 10.3934/dcdss.2019068 +[Abstract](2424) +[HTML](432) +[PDF](376.5KB)
Abstract:

In this paper, we will study the uniform $L^1$ stability of the inelastic Boltzmann equation. More precisely, according to the existence result on the inelastic Boltzmann equation with external force near vacuum, we obtain the uniform $L^1$ stability estimates of mild solution for the hard potentials under the assumptions on the characteristic generated by force term which can be arbitrarily large. The proof is based on the exponentially decay estimate and Lu's trick in [10].

2019, 12(4&5): 747-759 doi: 10.3934/dcdss.2019049 +[Abstract](3034) +[HTML](589) +[PDF](6101.98KB)
Abstract:

This paper aims to solve the problem of Risk assessment for enterprise merger and acquisition (M&A), which is an important problem in modern company management. Firstly, we design an index system to assess risks of enterprise M&A behavior, and six risks are considered: 1) Systemic risk, 2) Law risk, 3) Financial risk, 4) Intermediary risk, 5) Integrated risk, and 6) Information risk. Furthermore, 18 indexes are chosen to cover these six aspects. Secondly, we illustrate how to utilize the proposed risk assessment in the decision system for enterprise M&A risk assessment. We separate the M&A risk assessment process to three steps, that is, 1) Before M&A, and 2) In M&A, and 3) After M&A. Particularly, after the risk assessment process, there are three decisions for enterprise managers, that is, 1) implement the original M&A plan, 2) modify the original M&A plan, and 3) refuse it. Thirdly, we propose the multiple classifier fusion based risk assessment algorithm, which aims to effectively combine the six support vector machines. To relax the limitation of the SVM classifier, we introduce the fuzzy theory in the multiple classifier fusion algorithm, and the category label assignment is determined by utilizing a maximum membership rule. Finally, we conduct an experiment to make performance evaluation by constructing a dataset which includes the M&A data of 200 enterprises, among which 185 enterprises are used as training dataset and others are regarded as testing dataset. Using ROC curve, MAE and MAPE as evaluation criterions, performance of the proposed method is compared with single SVM scheme. Experimental results demonstrate that combining multiple the SVM classifiers together, accuracy of M&A risk assessment is greatly enhanced.

2019, 12(4-5): 901-901 doi: 10.3934/dcdss.2019060 +[Abstract](3164) +[HTML](553) +[PDF](105.32KB)
Abstract:

Honggang Yu, An efficient face recognition algorithm using the improved convolutional neural network

Discrete & Continuous Dynamical Systems - S, 12 (2019), 901-914

This paper is retracted by decision of the Editors in Chief of the journal Discrete &Continuous Dynamical Systems - S.

2019, 12(4&5): 1091-1100 doi: 10.3934/dcdss.2019075 +[Abstract](2005) +[HTML](415) +[PDF](293.69KB)
Abstract:

Taking carbonation depth uncertainty into account is key to approach durability analysis of concrete girder bridges in a probabilistic way. The Normal distribution has been widely used to represent the probability distribution of carbonation depth. In this study, two new methods such as Least Squares method and Bayesian Quantile method, are used to estimate the parameters of the Normal distribution. These two considered methods are also compared with the commonly used Maximum Likelihood method via an extensive numerical simulation and three real carbonation depth data examples based on performance measures such as, K-S test, RMSE and \begin{document}${\text{R}}^{2}$\end{document}. The numerical study reveals that the Least Squares method is the best one for estimating the parameters of the Normal distribution. Statistical analysis of real carbonation depth data sets are presented to demonstrate the applicability and the conclusion of the simulation results.

2019  Impact Factor: 1.233