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Symmetry
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Mathematical Modeling and Computational Methods in Science and Engineering
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Mathematical Modeling and Computational Methods in Science and Engineering

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 January 2020) | Viewed by 73989

Special Issue Editor

Prof. Dr. Juan Luis García Guirao

E-Mail Website
Guest Editor
Department of Applied Mathematics and Statistics, Technical University of Cartagena, 30203 Cartagena, Spain
Interests: dynamical systems; celestial mechanics; Hamiltonian systems; low-dimensional dynamics; differential equations
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In recent years, computational mathematics, science, and engineering have turned into rapidly growing multidisciplinary areas with connections to business, economics, engineering, mathematics, and computer science through academia as well as industry to understand and solve complex problems. Applied Mathematics is currently playing an important role in scientific research. The success of mathematical modeling depends on the parallel development of efficient computational methods as well as more sophisticated mathematical models. To develop novel computational methods, an interdisciplinary approach is needed that involves a variety of methods, including aspects such as stochastics, statistics, numeric, and scientific computing. Please note that all submitted papers must be within the general scope of the Symmetry journal.

The topics of research areas covered for this Special Issue are:

  • Mathematical (biology, chemistry, economics, engineering, and physics);
  • Neural networks;
  • Optimal control problems;
  • Probability and statistics;
  • Scientific computing;
  • Soft computing;
  • System dynamics;
  • System engineering;
  • Artificial intelligence;
  • Automation;
  • Big data analytics;
  • Chaos theory, control, and robotics;
  • Circuits and networks;
  • Complexity theory;
  • Computational mechanics;
  • Information theory;
  • Symmetry.

All papers submitted to the Special Issue will be thoroughly reviewed by at least two or three independent experts. We hope that this Special Issue will bring some changes and some new useful tools and applications in different fields, and that it will enrich the scientific community for the researchers in the concerned fields.

Prof. Dr. Juan Luis Garc´ıa Guirao
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (30 papers)

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Research

36 pages, 20281 KiB  
Article
A Vertex-Aligned Model for Packing 4-Hexagonal Clusters in a Regular Hexagonal Container
by Marina Prvan, Arijana Burazin Mišura, Zoltan Gecse and Julije Ožegović
Symmetry 2020, 12(5), 700; https://doi.org/10.3390/sym12050700 - 01 May 2020
Viewed by 4610
Abstract
This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, [...] Read more.
This paper deals with a problem the packing polyhex clusters in a regular hexagonal container. It is a common problem in many applications with various cluster shapes used, but symmetric polyhex is the most useful in engineering due to its geometrical properties. Hence, we concentrate on mathematical modeling in such an application, where using the “bee” tetrahex is chosen for the new Compact Muon Solenoid (CMS) design upgrade, which is one of four detectors used in Large Hadron Collider (LHC) experiment at European Laboratory for Particle Physics (CERN). We start from the existing hexagonal containers with hexagonal cells packed inside, and uniform clustering applied. We compare the center-aligned (CA) and vertex-aligned (VA) models, analyzing cluster rotations providing the increased packing efficiency. We formally describe the geometrical properties of clustering approaches and show that cluster sharing is inevitable at the container border with uniform clustering. In addition, we propose a new vertex-aligned model decreasing the number of shared clusters in the uniform scenario, but with a smaller number of clusters contained inside the container. Also, we describe a non-uniform tetrahex cluster packing scheme in the proposed container model. With the proposed cluster packing solution, it is accomplished that all clusters are contained inside the container region. Since cluster-sharing is completely avoided at the container border, the maximal packing efficiency is obtained compared to the existing models. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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15 pages, 546 KiB  
Article
Numerical Study of Suspension Filtration Model in Porous Medium with Modified Deposition Kinetics
by Bekzodjon Fayziev, Gafurjan Ibragimov, Bakhtiyor Khuzhayorov and Idham Arif Alias
Symmetry 2020, 12(5), 696; https://doi.org/10.3390/sym12050696 - 01 May 2020
Cited by 15 | Viewed by 2074
Abstract
Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous [...] Read more.
Filtration is one of the most used technologies in chemical engineering. Development of computer technology and computational mathematics made it possible to explore such processes by mathematical modeling and computational methods. The article deals with the study of suspension filtration in a porous medium with modified deposition kinetics. It is suggested that deposition is formed in two types, reversible and irreversible. The model of suspension filtration in porous media consists of the mass balance equation and kinetic equations for each type of deposition. The model includes dynamic factors and multi-stage deposition kinetics. By using the symmetricity of porous media, the higher dimensional cases are reduced to the one-dimensional case. To solve the problem, a stable, effective and simple numerical algorithm is proposed based on the finite difference method. Sufficient conditions for stability of schemes are found. Based on numerical results, influences of dynamic factors on solid particle transport and deposition characteristics are analyzed. It is shown that the dynamic factors mainly affect the profiles of changes in the concentration of deposition of the active zone. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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14 pages, 1703 KiB  
Article
Dynamic Fuzzy Adjustment Algorithm for Web Information Acquisition and Data Transmission
by Hao Peng, Shun Yang, Qiong Liu, Qiong Peng and Qiao Li
Symmetry 2020, 12(4), 535; https://doi.org/10.3390/sym12040535 - 03 Apr 2020
Viewed by 1734
Abstract
In order to improve the transmission dynamic fuzzy adjustment ability of web information acquisition data, a dynamic fuzzy adjustment method of web information acquisition data transmission based on auto correlation feature matching is proposed. This paper constructs the key transfer protocol of the [...] Read more.
In order to improve the transmission dynamic fuzzy adjustment ability of web information acquisition data, a dynamic fuzzy adjustment method of web information acquisition data transmission based on auto correlation feature matching is proposed. This paper constructs the key transfer protocol of the dynamic fuzzy adjustment of web information acquisition data transmission, uses a chaotic sequence structure reconstruction design method to carry out vector quantization and coding processing in the process of the dynamic fuzzy adjustment of web information acquisition data transmission, extracts nonlinear associated feature quantities of web information acquisition data, adopts a statistical feature detection method to select features in dynamic fuzzy adjustment process of web information acquisition data transmission, constructs a feature selection model of the dynamic fuzzy adjustment of web information acquisition data transmission, dynamically adjusts the fuzzy data with a fuzzy information clustering analysis method, and dynamically adjusts the fuzzy data transmission through fuzzy design and fuzzy encryption. The simulation results show that the dynamic fuzzy adjustment of web information acquisition data transmission when using this method is better, and the accurate transmission ability is stronger. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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14 pages, 3128 KiB  
Article
Fuzzy Weighted Clustering Method for Numerical Attributes of Communication Big Data Based on Cloud Computing
by Haitao Ding, Chu Sun and Jianqiu Zeng
Symmetry 2020, 12(4), 530; https://doi.org/10.3390/sym12040530 - 03 Apr 2020
Cited by 8 | Viewed by 1857
Abstract
It is necessary to optimize clustering processing of communication big data numerical attribute feature information in order to improve the ability of numerical attribute mining of communication big data, and thus a big data clustering algorithm based on cloud computing was proposed. The [...] Read more.
It is necessary to optimize clustering processing of communication big data numerical attribute feature information in order to improve the ability of numerical attribute mining of communication big data, and thus a big data clustering algorithm based on cloud computing was proposed. The cloud extended distributed feature fitting method was used to process the numerical attribute linear programming of communication big data, and the mutual information feature quantity of communication big data numerical attribute was extracted. Combined with fuzzy C-means clustering and linear regression analysis, the statistical analysis of big data numerical attribute feature information was carried out, and the associated attribute sample set of communication big data numerical attribute cloud grid distribution was constructed. Cloud computing and adaptive quantitative recurrent classifiers were used for data classification, and block template matching and multi-sensor information fusion were combined to search the clustering center automatically to improve the convergence of clustering. The simulation results show that, after the application of this method, the information fusion performance of the clustering process was better, the automatic searching ability of the data clustering center was stronger, the frequency domain equalization control effect was good, the bit error rate was low, the energy consumption was small, and the ability of fuzzy weighted clustering retrieval of numerical attributes of communication big data was effectively improved. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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16 pages, 3734 KiB  
Article
A Multichannel Data Fusion Method Based on Multiple Deep Belief Networks for Intelligent Fault Diagnosis of Main Reducer
by Qing Ye and Changhua Liu
Symmetry 2020, 12(3), 483; https://doi.org/10.3390/sym12030483 - 23 Mar 2020
Cited by 8 | Viewed by 2941
Abstract
Aiming at the problems of poor efficiency of the intelligent fault diagnosis method of the main reducer and the poor effectiveness of multichannel data fusion, this paper proposes a multichannel data fusion method based on deep belief networks and random forest fusion for [...] Read more.
Aiming at the problems of poor efficiency of the intelligent fault diagnosis method of the main reducer and the poor effectiveness of multichannel data fusion, this paper proposes a multichannel data fusion method based on deep belief networks and random forest fusion for fault diagnosis. Multiple deep belief networks (MDBNs) are constructed to obtain deep representative features from multiple modalities of multichannel data. Random forest can fuse deep representative features achieved from MDBNs to construct the model of multiple deep belief networks fusion (MDBNF). The proposed method is applied to fault diagnosis of the main reducer and evaluation of the performance. Multiple deep belief network model fusions (MD BN F) are constructed to improve the multichannel data fusion effect. Single sensory data, multichannel data, and two intelligent models based on support vector machine and deep belief networks are used as comparison in the experiments. The results indicate that the classification accuracy of the test set collected by sensor 1 and sensor 2 is 88.35% and 88.73%, respectively. The comparison results show that the method has good convergence. The data fusion of the proposed diagnostic model can effectively improve the correlation between the collected vibration signals and the failure mode, thereby improving the diagnostic performance by nearly 8%, representing improved diagnostic accuracy. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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17 pages, 1803 KiB  
Article
A New Flexible Three-Parameter Model: Properties, Clayton Copula, and Modeling Real Data
by Abdulhakim A. Al-babtain, I. Elbatal and Haitham M. Yousof
Symmetry 2020, 12(3), 440; https://doi.org/10.3390/sym12030440 - 09 Mar 2020
Cited by 42 | Viewed by 2982
Abstract
In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the [...] Read more.
In this article, we introduced a new extension of the binomial-exponential 2 distribution. We discussed some of its structural mathematical properties. A simple type Copula-based construction is also presented to construct the bivariate- and multivariate-type distributions. We estimated the model parameters via the maximum likelihood method. Finally, we illustrated the importance of the new model by the study of two real data applications to show the flexibility and potentiality of the new model in modeling skewed and symmetric data sets. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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16 pages, 1176 KiB  
Article
Evaluation of the Mass Diffusion Coefficient and Mass Biot Number Using a Nondominated Sorting Genetic Algorithm
by Radosław Winiczenko, Krzysztof Górnicki and Agnieszka Kaleta
Symmetry 2020, 12(2), 260; https://doi.org/10.3390/sym12020260 - 08 Feb 2020
Cited by 1 | Viewed by 2092
Abstract
A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient [...] Read more.
A precise determination of the mass diffusion coefficient and the mass Biot number is indispensable for deeper mass transfer analysis that can enable finding optimum conditions for conducting a considered process. The aim of the article is to estimate the mass diffusion coefficient and the mass Biot number by applying nondominated sorting genetic algorithm (NSGA) II genetic algorithms. The method is used in drying. The maximization of coefficient of correlation (R) and simultaneous minimization of mean absolute error (MAE) and root mean square error (RMSE) between the model and experimental data were taken into account. The Biot number and moisture diffusion coefficient can be determined using the following equations: Bi = 0.7647141 + 10.1689977s − 0.003400086T + 948.715758s2 + 0.000024316T2 − 0.12478256sT, D = 1.27547936∙10−7 − 2.3808∙10−5s − 5.08365633∙10−9T + 0.0030005179s2 + 4.266495∙10−11T2 + 8.33633∙10−7sT or Bi = 0.764714 + 10.1689091s − 0.003400089T + 948.715738s2 + 0.000024316T2 − 0.12478252sT, D = 1.27547948∙10−7 − 2.3806∙10−5s − 5.08365753∙10−9T + 0.0030005175s2 + 4.266493∙10−11T2 + 8.336334∙10−7sT. The results of statistical analysis for the Biot number and moisture diffusion coefficient equations were as follows: R = 0.9905672, MAE = 0.0406375, RMSE = 0.050252 and R = 0.9905611, MAE = 0.0406403 and RMSE = 0.050273, respectively. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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15 pages, 1769 KiB  
Article
Detection Method of Data Integrity in Network Storage Based on Symmetrical Difference
by Xiaona Ding
Symmetry 2020, 12(2), 228; https://doi.org/10.3390/sym12020228 - 03 Feb 2020
Cited by 2 | Viewed by 1736
Abstract
In order to enhance the recall and the precision performance of data integrity detection, a method to detect the network storage data integrity based on symmetric difference was proposed. Through the complete automatic image annotation system, the crawler technology was used to capture [...] Read more.
In order to enhance the recall and the precision performance of data integrity detection, a method to detect the network storage data integrity based on symmetric difference was proposed. Through the complete automatic image annotation system, the crawler technology was used to capture the image and related text information. According to the automatic word segmentation, pos tagging and Chinese word segmentation, the feature analysis of text data was achieved. Based on the symmetrical difference algorithm and the background subtraction, the feature extraction of image data was realized. On the basis of data collection and feature extraction, the sentry data segment was introduced, and then the sentry data segment was randomly selected to detect the data integrity. Combined with the accountability scheme of data security of the trusted third party, the trusted third party was taken as the core. The online state judgment was made for each user operation. Meanwhile, credentials that cannot be denied by both parties were generated, and thus to prevent the verifier from providing false validation results. Experimental results prove that the proposed method has high precision rate, high recall rate, and strong reliability. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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14 pages, 6104 KiB  
Article
Single Image Rain Removal Based on Deep Learning and Symmetry Transform
by Qing Yang, Ming Yu, Yan Xu and Shixin Cen
Symmetry 2020, 12(2), 224; https://doi.org/10.3390/sym12020224 - 03 Feb 2020
Cited by 4 | Viewed by 2954
Abstract
Rainy, as an inevitable weather condition, will affect the acquired image. To solve this problem, a single image rain removal algorithm based on deep learning and symmetric transformation is proposed. Because of the important characteristics of wavelet transform, such as symmetry, orthogonality, flexibility [...] Read more.
Rainy, as an inevitable weather condition, will affect the acquired image. To solve this problem, a single image rain removal algorithm based on deep learning and symmetric transformation is proposed. Because of the important characteristics of wavelet transform, such as symmetry, orthogonality, flexibility and limited support, wavelet transform is used to remove rain from a single image. The image is denoised by using wavelet decomposition, threshold value and wavelet reconstruction in wavelet transform, and the rain drop image is transformed from RGB space to YUV (luma chroma) space by using deep learning to obtain the brightness component and color component of the image. the brightness component and residual component of the raindrop source image and the ideal recovered image without raindrop are extracted. The residual image and brightness component are overlapped again, the reconstructed image is restored to RGB space by YUV inverse transformation, and the final color raindrop free image is obtained. After training the network, the optimal parameters of the network are obtained, and finally the convolution neural network which can effectively remove the rain line is obtained. Experimental results show that compared with other algorithms, the proposed algorithm achieves the highest value in both peak signal-to-noise ratio (PSNR) and structural similarity, which shows that the image effect of the algorithm is better after rain removal. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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18 pages, 1420 KiB  
Article
Communication Fault Maintenance Decision of Information System Based on Inverse Symmetry Algorithm
by Qing Li, Chaoxuan Shang and Zhaorui Li
Symmetry 2020, 12(1), 126; https://doi.org/10.3390/sym12010126 - 08 Jan 2020
Cited by 3 | Viewed by 2065
Abstract
In view of the characteristics of various types of information system integrated hardware and software systems, complex network topology, complex causes of fault alarm and uncertainty, this paper studies the communication fault maintenance decision-making based on the inverse symmetry algorithm. Based on the [...] Read more.
In view of the characteristics of various types of information system integrated hardware and software systems, complex network topology, complex causes of fault alarm and uncertainty, this paper studies the communication fault maintenance decision-making based on the inverse symmetry algorithm. Based on the principle of the inverse symmetry algorithm, the modulation and demodulation process of information system is determined, the redundant system attributes in the information system are reduced by rough set, and the Bayesian network model with minimum diagnosis set is obtained by combining the prior knowledge in the operation process of the information system. The input and output of the network are the condition attributes and decision attributes of the decision table, respectively. Through the above process, the optimal fault diagnosis rules are established. After the communication fault is diagnosed, different communication fault maintenance decisions of the information system are used to eliminate the fault. The experimental results show that this method can effectively diagnose the communication fault of the information system and make effective maintenance decisions. The average accuracy of data transmission of the information system using this method is over 99.5% under different operating distances, which has better communication performance. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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10 pages, 1756 KiB  
Article
CARS Algorithm-Based Detection of Wheat Moisture Content before Harvest
by Hong Ji, Wanzhang Wang, Dongfeng Chong and Boyang Zhang
Symmetry 2020, 12(1), 115; https://doi.org/10.3390/sym12010115 - 07 Jan 2020
Cited by 4 | Viewed by 2060
Abstract
To rapidly detect the wheat moisture content (WMC) without harm to the wheat and before harvest, this paper measured wheat and panicle moisture content (PMC) and the corresponding spectral reflectance of panicle before harvest at the Beijing Tongzhou experimental station of China Agricultural [...] Read more.
To rapidly detect the wheat moisture content (WMC) without harm to the wheat and before harvest, this paper measured wheat and panicle moisture content (PMC) and the corresponding spectral reflectance of panicle before harvest at the Beijing Tongzhou experimental station of China Agricultural University. Firstly, we used correlation analysis to determine the optimal regression model of WMC and PMC. Secondly, we derived the spectral sensitive band of PMC before filtering the redundant variables competitive adaptive reweighted sampling (CARS) to select the variable subset with the least error. Finally, partial least squares regression (PLSR) was used to build and analyze the prediction model of PMC. At the early stage of wheat harvest, a high correlation existed between WMC and PMC. Among all regression models such as exponential, univariate linear, polynomial models, and the power function regression model, the logarithm regression model was the best. The determination coefficients of the modeling sample were: R2 = 0.9284, the significance F = 362.957, the determination coefficient of calibration sample R2v = 0.987, the root mean square error RMSEv = 3.859, and the relative error REv = 7.532. Within the range of 350–2500 nm, bands of 728–907 nm, 1407–1809 nm, and 1940–2459 nm had a correlation coefficient of PMC and wavelength reflectivity higher than 0.6. This paper used the CARS algorithm to optimize the variables and obtained the best variable subset, which included 30 wavelength variables. The PLSR model was established based on 30 variables optimized by the CARS algorithm. Compared with the all-sensitive band, which had 1103 variables, the PLSR model not only reduced the number of variables by 1073, but also had a higher accuracy in terms of prediction. The results showed that: RMSEC = 0.9301, R2c = 0.995, RMSEP = 2.676, R2p = 0.945, and RPD = 3.362, indicating that the CARS algorithm could effectively remove the variables of spectral redundant information. The CARS algorithm provided a new way of thinking for the non-destructive and rapid detection of WMC before harvest. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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15 pages, 2206 KiB  
Article
Recognition Algorithm of Transient Overvoltage Characteristic Based on Symmetrical Components Estimation
by Yanzan Han and Jimeng Zhang
Symmetry 2020, 12(1), 114; https://doi.org/10.3390/sym12010114 - 07 Jan 2020
Cited by 1 | Viewed by 2005
Abstract
The recognition of transient overvoltage characteristics is the premise of disturbance compensation of the transient overvoltage. Based on that, the recognition algorithm of transient overvoltage characteristics based on symmetrical components estimation was proposed. The generation mechanism of the transient overvoltage in gas insulated [...] Read more.
The recognition of transient overvoltage characteristics is the premise of disturbance compensation of the transient overvoltage. Based on that, the recognition algorithm of transient overvoltage characteristics based on symmetrical components estimation was proposed. The generation mechanism of the transient overvoltage in gas insulated switchgear (GIS) was analyzed. Then, the transient overvoltage was measured via the capacitive sensor method. The three-phase voltage of ultra-high voltage grid was asymmetrical when the transient overvoltage appeared. At present, the asymmetrical three-phase voltage was decomposed into the superposition of a symmetrical positive-sequence component, a negative-sequence component, and a zero-sequence component via the symmetrical components estimation to build the superposition model. The model was decomposed via the trigonometric identity and the modified neural network of the least mean square learning rule was used to estimate the parameter vector of the characteristic quantity of the transient overvoltage in real time. The feasibility of the proposed algorithm was verified via comparing the simulation of the proposed algorithm and the algorithm based on dp transformation. The experimental results show that the proposed algorithm has the advantages of a small operand, high detection precision, and fast action. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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13 pages, 2123 KiB  
Article
Autonomous Detection for Traffic Flow Parameters of a Vehicle-Mounted Sensing Device Based on Symmetrical Difference
by Jihai Huang and Jiansen Ye
Symmetry 2020, 12(1), 72; https://doi.org/10.3390/sym12010072 - 02 Jan 2020
Cited by 2 | Viewed by 1925
Abstract
Based on the research and analysis of traffic detectors, it is found that the existing vehicle detection equipment is generally vulnerable to environmental interference and the detection effect cannot meet the current traffic demand. Therefore, an automatic detection method of traffic flow parameters [...] Read more.
Based on the research and analysis of traffic detectors, it is found that the existing vehicle detection equipment is generally vulnerable to environmental interference and the detection effect cannot meet the current traffic demand. Therefore, an automatic detection method of traffic flow parameters based on symmetrical difference was put forward. This method collects the traffic flow parameters through wireless sensor nodes. Since the safety transmission protocol of VANET (Vehicular Ad Hoc Networks) can maximize the safety channel capacity, it transmits the traffic flow parameters to the data acquisition and control equipment of the upper computer through the cross layer pre-balanced safety transmission protocol of VANET in the wireless communication unit. The data acquisition and control equipment of the upper computer uses the traffic flow detection method based on the symmetrical difference to obtain the details of the moving objects in the traffic flow so as to realize the independent detection of the traffic flow parameters of the vehicle-borne sensor equipment. Experimental results show that the designed method has anti-interference abilities for the noise and light changes. Meanwhile, this method can completely extract moving objects from the traffic flow and can improve the detection effect of the moving objects in the traffic flow. Thus, the effectiveness of the proposed method can be fully verified. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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26 pages, 1623 KiB  
Article
Validation of the Topp-Leone-Lomax Model via a Modified Nikulin-Rao-Robson Goodness-of-Fit Test with Different Methods of Estimation
by Abhimanyu Singh Yadav, Hafida Goual, Refah Mohammed Alotaibi, Rezk H, M. Masoom Ali and Haitham M. Yousof
Symmetry 2020, 12(1), 57; https://doi.org/10.3390/sym12010057 - 26 Dec 2019
Cited by 62 | Viewed by 2790
Abstract
In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The [...] Read more.
In this paper, we introduce a new univariate version of the Lomax model as well as a simple type copula-based construction via Morgenstern family and via Clayton copula for introducing a new bivariate and a multivariate type extension of the new model. The new density has a strong physical interpretation and can be a symmetric function and unimodal with a heavy tail with positive skewness. The new failure rate function can be “upside-down”, “decreasing” with many different shapes and “decreasing-constant”. Some mathematical and statistical properties of the new model are derived. The model parameters are estimated using different estimation methods. For comparing the estimation methods, Markov Chain Monte Carlo (MCMC) simulations are performed. The applicability of the new model is illustrated via four real data applications, these data sets are symmetric and right skewed. We constructed a modified Chi-Square goodness-of-fit test based on Nikulin-Rao-Robson test in the case of complete and censored sample for the new model. Different simulation studies are performed along applications on real data for validation propose. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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15 pages, 1898 KiB  
Article
Research on the Detection Method of Implicit Self Symmetry in a High-Level Semantic Model
by Chao Wang
Symmetry 2020, 12(1), 28; https://doi.org/10.3390/sym12010028 - 21 Dec 2019
Cited by 3 | Viewed by 1844
Abstract
In order to improve the accuracy of semantic model intrinsic detection, a skeleton-based high-level semantic model intrinsic self-symmetry detection method is proposed. The semantic analysis of the model set is realized by the uniform segmentation of the model within the same style, the [...] Read more.
In order to improve the accuracy of semantic model intrinsic detection, a skeleton-based high-level semantic model intrinsic self-symmetry detection method is proposed. The semantic analysis of the model set is realized by the uniform segmentation of the model within the same style, the component correspondence of the model between different styles, and the shape content clustering. Based on the results of clustering analysis, for a given three-dimensional (3D) point cloud model, according to the curve skeleton, the skeleton point pairs reflecting the symmetry between the model surface points are obtained by the election method, and the symmetry is extended to the model surface vertices according to these skeleton point pairs. With the help of skeleton, the symmetry of the point cloud model is obtained, and then the symmetry region of point cloud model is obtained by the symmetric correspondence matrix and spectrum method, so as to realize the intrinsic symmetry detection of the model. The experimental results show that the proposed method has the advantages of less time, high accuracy, and high reliability. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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10 pages, 8819 KiB  
Article
Complex Patterns to the (3+1)-Dimensional B-type Kadomtsev-Petviashvili-Boussinesq Equation
by Juan Luis García Guirao, H. M. Baskonus, Ajay Kumar, M. S. Rawat and Gulnur Yel
Symmetry 2020, 12(1), 17; https://doi.org/10.3390/sym12010017 - 19 Dec 2019
Cited by 31 | Viewed by 2716
Abstract
This paper presents many new complex combined dark-bright soliton solutions obtained with the help of the accurate sine-Gordon expansion method to the B-type Kadomtsev-Petviashvili-Boussinesq equation with binary power order nonlinearity. With the use of some computational programs, we plot many new surfaces of [...] Read more.
This paper presents many new complex combined dark-bright soliton solutions obtained with the help of the accurate sine-Gordon expansion method to the B-type Kadomtsev-Petviashvili-Boussinesq equation with binary power order nonlinearity. With the use of some computational programs, we plot many new surfaces of the results obtained in this paper. In addition, we present the interactions between complex travelling wave patterns and their solitons. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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16 pages, 7731 KiB  
Article
Digital Watermarking Image Compression Method Based on Symmetric Encryption Algorithms
by Yanli Tan and Yongqiang Zhao
Symmetry 2019, 11(12), 1505; https://doi.org/10.3390/sym11121505 - 11 Dec 2019
Cited by 3 | Viewed by 2528
Abstract
A digital watermarking image compression method based on symmetrical encryption algorithm is proposed in this study. First, the original image and scrambled watermarking image are processed by wavelet transform, and then the watermarking image processed by the Arnold replacement method is transformed into [...] Read more.
A digital watermarking image compression method based on symmetrical encryption algorithm is proposed in this study. First, the original image and scrambled watermarking image are processed by wavelet transform, and then the watermarking image processed by the Arnold replacement method is transformed into a meaningless image in the time domain to achieve the effect of encryption. Watermarking is generated by embedding the watermarking image into the important coefficients of the wavelet transform. As an inverse process of watermarking embedding, watermarking extraction needs to be reconstructed by the wavelet transform. Finally, the watermarking is extracted from the inverse scrambled watermarking image, and a new symmetrically encrypted digital watermarking image is obtained. The compression method compresses the embedded digital watermarking image, so that the volume of the compressed watermarking image is greatly reduced when the visual difference is very small. The experimental results show that the watermarking image encrypted by this method not only has good transparency, but also has strong anti-brightness/contrast attack, anti-shearing, and anti-noise performance. When the volume of the compressed image is greatly reduced, the root mean square error and visual difference measurement of the watermarking image are very small. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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21 pages, 807 KiB  
Article
Type II Topp–Leone Inverted Kumaraswamy Distribution with Statistical Inference and Applications
by Ramadan A. ZeinEldin, Farrukh Jamal, Christophe Chesneau and Mohammed Elgarhy
Symmetry 2019, 11(12), 1459; https://doi.org/10.3390/sym11121459 - 28 Nov 2019
Cited by 8 | Viewed by 2400
Abstract
In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known [...] Read more.
In this paper, we present and study a new four-parameter lifetime distribution obtained by the combination of the so-called type II Topp–Leone-G and transmuted-G families and the inverted Kumaraswamy distribution. By construction, the new distribution enjoys nice flexible properties and covers some well-known distributions which have already proven themselves in statistical applications, including some extensions of the Bur XII distribution. We first present the main functions related to the new distribution, with discussions on their shapes. In particular, we show that the related probability density function is left, right skewed, near symmetrical and reverse J shaped, with a notable difference regarding the right tailed, illustrating the flexibility of the distribution. Then, the related model is displayed, with the estimation of the parameters by the maximum likelihood method and the consideration of two practical data sets. We show that the proposed model is the best one in terms of standard model selection criteria, including Akaike information and Bayesian information criteria, and goodness of fit tests against three well-established competitors. Then, for the new model, the theoretical background on the maximum likelihood method is given, with numerical guaranties of the efficiency of the estimates obtained via a simulation study. Finally, the main mathematical properties of the new distribution are discussed, including asymptotic results, quantile function, Bowley skewness and Moors kurtosis, mixture representations for the probability density and cumulative density functions, ordinary moments, incomplete moments, probability weighted moments, stress-strength reliability and order statistics. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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14 pages, 5658 KiB  
Article
Study of Indoor Ventilation Based on Large-Scale DNS by a Domain Decomposition Method
by Junyang Jiang, Zichao Jiang, Trevor Hocksun Kwan, Chun-Ho Liu and Qinghe Yao
Symmetry 2019, 11(11), 1416; https://doi.org/10.3390/sym11111416 - 15 Nov 2019
Cited by 3 | Viewed by 2436
Abstract
This paper presents a large-scale Domain Decomposition Method (DDM) based Direct Numerical Simulation (DNS) for predicting the behavior of indoor airflow, where the aim is to design a comfortable and efficient indoor air environment of modern buildings. An analogy of the single-phase convection [...] Read more.
This paper presents a large-scale Domain Decomposition Method (DDM) based Direct Numerical Simulation (DNS) for predicting the behavior of indoor airflow, where the aim is to design a comfortable and efficient indoor air environment of modern buildings. An analogy of the single-phase convection problems is applied, and the pressure stabilized domain decomposition method is used to symmetrize the linear systems of Navier-Stokes equations and the convection-diffusion equation. Furthermore, a balancing preconditioned conjugate gradient method is utilized to deal with the interface problem caused by domain decomposition. The entire simulation model is validated by comparing the numerical results with that of recognized experimental and numerical data from previous literature. The transient behavior of indoor airflow and its complexity in the ventilated room are discussed; the velocity and vortex distribution of airflow are investigated, and its possible influence on particle accumulation is classified. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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16 pages, 3043 KiB  
Article
Dynamic Soft Sensor Development for Time-Varying and Multirate Data Processes Based on Discount and Weighted ARMA Models
by Longhao Li and Yongshou Dai
Symmetry 2019, 11(11), 1414; https://doi.org/10.3390/sym11111414 - 15 Nov 2019
Cited by 3 | Viewed by 2164
Abstract
To solve the soft sensor modeling (SSMI) problem in a nonlinear chemical process with dynamic time variation and multi-rate data, this paper proposes a dynamic SSMI method based on an autoregressive moving average (ARMA) model of weighted process data with discount (DSSMI-AMWPDD) and [...] Read more.
To solve the soft sensor modeling (SSMI) problem in a nonlinear chemical process with dynamic time variation and multi-rate data, this paper proposes a dynamic SSMI method based on an autoregressive moving average (ARMA) model of weighted process data with discount (DSSMI-AMWPDD) and optimization methods. For the sustained influence of auxiliary variable data on the dominant variables, the ARMA model structure is adopted. To reduce the complexity of the model, the dynamic weighting model is combined with the ARMA model. To address the weights of auxiliary variable data with different sampling frequencies, a calculation method for AMWPDD is proposed using assumptions that are suitable for most sequential chemical processes. The proposed method can obtain a discount factor value (DFV) of auxiliary variable data, realizing the dynamic fusion of chemical process data. Particle swarm optimization (PSO) is employed to optimize the soft sensor model parameters. To address the poor convergence problem of PSO, ω-dynamic PSO (ωDPSO) is used to improve the PSO convergence via the dynamic fluctuation of the inertia weight. A continuous stirred tank reactor (CSTR) simulation experiment was performed. The results show that the proposed DSSMI-AMWPDD method can effectively improve the SSM prediction accuracy for a nonlinear time-varying chemical process. The AMWPDD proposed in this paper can reflect the dynamic change of chemical process and improve the accuracy of SSM data prediction. The ω dynamic PSO method proposed in this paper has faster convergence speed and higher convergence accuracy, thus, these models correlate with the concept of symmetry. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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15 pages, 1100 KiB  
Article
Optimization of Flocculation Settling Parameters of Whole Tailings Based on Spatial Difference Algorithm
by Yanlong Huang, Jianzhong Chen and Chuanzhen Wang
Symmetry 2019, 11(11), 1371; https://doi.org/10.3390/sym11111371 - 05 Nov 2019
Viewed by 1975
Abstract
In order to obtain the optimum parameters of total tailings flocculation settling, an optimization method of total tailings flocculation settling parameters based on the spatial difference algorithm was proposed. Firstly, the input and output factors of the whole tailings flocculation settling parameters are [...] Read more.
In order to obtain the optimum parameters of total tailings flocculation settling, an optimization method of total tailings flocculation settling parameters based on the spatial difference algorithm was proposed. Firstly, the input and output factors of the whole tailings flocculation settling parameters are effectively analyzed, and the relevant factors affecting the flocculation settling parameters are obtained. Secondly, the flocculation settling velocity of the whole tailings is optimized by combining the spatial difference algorithm with the mathematical symmetry algorithm, and the optimal value of the flocculation settling velocity of the whole tailings is obtained. The experimental results show that anionic flocculation has the best flocculation settling effect on the whole tailings. The optimal settlement velocity is close to the actual settlement velocity, and the error of settlement velocity is less than 3.5%. The results show that compared with the traditional method, this method is an effective method to optimize the flocculation and settlement parameters of the whole tailings. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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17 pages, 2933 KiB  
Article
Statistical Criteria of Nanofluid Flows over a Stretching Sheet with the Effects of Magnetic Field and Viscous Dissipation
by Alias Jedi, Noorhelyna Razali, Wan Mohd Faizal Wan Mahmood and Nor Ashikin Abu Bakar
Symmetry 2019, 11(11), 1367; https://doi.org/10.3390/sym11111367 - 04 Nov 2019
Cited by 2 | Viewed by 2060
Abstract
In this study, the heat and mass transfer characteristics of nanofluid flow over a nonlinearly stretching sheet are investigated. The important effects of axisymmetric of thermal conductivity and viscous dissipation have been included in the model of nanofluids. The Buongiorno model is considered [...] Read more.
In this study, the heat and mass transfer characteristics of nanofluid flow over a nonlinearly stretching sheet are investigated. The important effects of axisymmetric of thermal conductivity and viscous dissipation have been included in the model of nanofluids. The Buongiorno model is considered to solve the nanofluid boundary layer problem. The governing nonlinear partial differential equations have been transformed into a system of ordinary differential equations and are solved numerically via the shooting technique. The validity of this method was verified by comparison with previous work performed for nanofluids without the effects of the magnetic field and viscous dissipation. The analytical investigation is carried out for different governing parameters, namely, the Brownian motion parameter, thermophoresis parameter, magnetic parameter, Biot number, and Eckert number. The results indicate that the skin friction coefficient has a direct relationship with the Brownian motion number and thermophoresis number. Moreover, it can be seen that the Nusselt number decreases with the increase of the magnetic parameter and Eckert number. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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18 pages, 3361 KiB  
Article
An Improved Pigeon-Inspired Optimisation Algorithm and Its Application in Parameter Inversion
by Hanmin Liu, Xuesong Yan and Qinghua Wu
Symmetry 2019, 11(10), 1291; https://doi.org/10.3390/sym11101291 - 15 Oct 2019
Cited by 8 | Viewed by 3167
Abstract
Pre-stack amplitude variation with offset (AVO) elastic parameter inversion is a nonlinear, multi-solution optimisation problem. The techniques that combine intelligent optimisation algorithms and AVO inversion provide an effective identification method for oil and gas exploration. However, these techniques also have shortcomings in solving [...] Read more.
Pre-stack amplitude variation with offset (AVO) elastic parameter inversion is a nonlinear, multi-solution optimisation problem. The techniques that combine intelligent optimisation algorithms and AVO inversion provide an effective identification method for oil and gas exploration. However, these techniques also have shortcomings in solving nonlinear geophysical inversion problems. The evolutionary optimisation algorithms have recognised disadvantages, such as the tendency of convergence to a local optimum resulting in poor local optimisation performance when dealing with multimodal search problems, decreasing diversity and leading to the prematurity of the population as the number of evolutionary iterations increases. The pre-stack AVO elastic parameter inversion is nonlinear with slow convergence, while the pigeon-inspired optimisation (PIO) algorithm has the advantage of fast convergence and better optimisation characteristics. In this study, based on the characteristics of the pre-stack AVO elastic parameter inversion problem, an improved PIO algorithm (IPIO) is proposed by introducing the particle swarm optimisation (PSO) algorithm, an inverse factor, and a Gaussian factor into the PIO algorithm. The experimental comparisons indicate that the proposed IPIO algorithm can achieve better inversion results. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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14 pages, 256 KiB  
Article
On Energies of Charged Particles with Magnetic Field
by Muhammed Talat Sariaydin
Symmetry 2019, 11(10), 1204; https://doi.org/10.3390/sym11101204 - 26 Sep 2019
Cited by 2 | Viewed by 1582
Abstract
The present paper is about magnetic curves of spherical images in Euclidean 3-space. We obtain the Lorentz forces of the spherical images and then we determine if the spherical images have a magnetic curve or not. If a spherical image has a magnetic [...] Read more.
The present paper is about magnetic curves of spherical images in Euclidean 3-space. We obtain the Lorentz forces of the spherical images and then we determine if the spherical images have a magnetic curve or not. If a spherical image has a magnetic curve, then after presenting some basic concepts about the energy of a charged particle whose trajectory is that magnetic curve and the kinetic energy of a moving particle whose trajectory is the spherical indicatrix, we find the energy of the charged particle and the kinetic energy of the moving particle. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
16 pages, 7851 KiB  
Article
Kinematics Modeling and Analysis of Mid-Low Speed Maglev Vehicle with Screw and Product of Exponential Theory
by Peng Leng, Jie Li and Yuxin Jin
Symmetry 2019, 11(10), 1201; https://doi.org/10.3390/sym11101201 - 25 Sep 2019
Cited by 4 | Viewed by 2670
Abstract
Maglev transportation is a new type of rail transit, whose vehicle is different from the two-bogie structure of the wheel-rail train. Generally, it consists of four to five suspension frames supporting a car body in parallel. The moving mechanism of a vehicle often [...] Read more.
Maglev transportation is a new type of rail transit, whose vehicle is different from the two-bogie structure of the wheel-rail train. Generally, it consists of four to five suspension frames supporting a car body in parallel. The moving mechanism of a vehicle often consists of hundreds of moving parts, showing a multi-rigid body system in serial-parallel structure. At present, there is no theoretical framework for systematically and accurately describing the kinematics and dynamics of the Maglev train. The design work is at the level of simple equivalent estimation or measurement from the CAD drawing, which makes the system performance analysis and optimization work unable to be carried out scientifically. Based on the theoretical framework of screw theory and exponential mapping, the forward kinematics modeling, inverse kinematics solution, transition curve modeling and computational analysis methods for the Maglev train are proposed in this paper. A systematic and accurate theoretical framework is constructed for the modeling and analysis of the motion mechanism of the Maglev train, which makes the design and analysis of the Maglev train at the scientific level. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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13 pages, 368 KiB  
Article
The Circular Hill Problem Regarding Arbitrary Disturbing Forces: The Periodic Solutions that are Emerging from the Equilibria
by M. Teresa de Bustos, Miguel A. López and Raquel Martínez
Symmetry 2019, 11(10), 1196; https://doi.org/10.3390/sym11101196 - 24 Sep 2019
Viewed by 1654
Abstract
In this work, sufficient conditions for computing periodic solutions have been obtained in the circular Hill Problem with regard to arbitrary disturbing forces. This problem will be solved by means of using the averaging theory for dynamical systems as the main mathematical tool [...] Read more.
In this work, sufficient conditions for computing periodic solutions have been obtained in the circular Hill Problem with regard to arbitrary disturbing forces. This problem will be solved by means of using the averaging theory for dynamical systems as the main mathematical tool that has been applied in this work. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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16 pages, 1188 KiB  
Article
RGB Inter-Channel Measures for Morphological Color Texture Characterization
by Nelson Luis Durañona Sosa, José Luis Vázquez Noguera, Juan José Cáceres Silva, Miguel García Torres and Horacio Legal-Ayala
Symmetry 2019, 11(10), 1190; https://doi.org/10.3390/sym11101190 - 20 Sep 2019
Cited by 5 | Viewed by 3010
Abstract
The perception of textures is based on high-level features such as symmetry, brightness, color or direction. Texture characterization is a widely studied topic in the image processing community. The normalized volume of morphological series is used as a texture descriptor in RGB images. [...] Read more.
The perception of textures is based on high-level features such as symmetry, brightness, color or direction. Texture characterization is a widely studied topic in the image processing community. The normalized volume of morphological series is used as a texture descriptor in RGB images. However, the correlation between different color channels is not exploited with this descriptor. We propose the usage of inter-channel measures in addition to the volume, to enhance the descriptors potential to discriminate textures. The experiments show that standard texture classification techniques increase between 3%–10% in performance when using our descriptor instead of other state of the art descriptors that do not use inter-channel measures. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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13 pages, 782 KiB  
Article
Optimization of the Auxiliary-Beam System in Railway Bridge Vibration Mitigation Using FEM Simulation and Genetic Algorithms
by Jacobo Baldonedo, José A. López-Campos, Marcos López, Enrique Casarejos and José R. Fernández
Symmetry 2019, 11(9), 1089; https://doi.org/10.3390/sym11091089 - 31 Aug 2019
Cited by 3 | Viewed by 2169
Abstract
In this paper, we present the optimization of a vibration mitigation system for railway bridges. These structures are subjected to significant moving loads, whose dynamic characteristics may produce resonance effects, compromising the integrity of the bridge and the security of the passengers if [...] Read more.
In this paper, we present the optimization of a vibration mitigation system for railway bridges. These structures are subjected to significant moving loads, whose dynamic characteristics may produce resonance effects, compromising the integrity of the bridge and the security of the passengers if the speed or the load of the train is not controlled. The study focuses on the Auxiliary Beam system. It consists of a beam located under the bridge and connected to the slab by viscous dampers. The symmetry of the problem allowed for the use of a 2D Finite Element model of the system. This model was used together with a genetic algorithm in order to evaluate the behaviour of different candidates and to optimize the design parameters: the inertia of the beam and the damper coefficient. The goal of the optimization process is to minimize the acceleration of the bridge while adding the lightest mitigation system possible. The combination of a Finite Element Model and Genetic Algorithm helps to address the complex problem and to find an optimized set of structural parameters. The system finally shows good behaviour for optimal parameters. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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20 pages, 3324 KiB  
Article
Study on the Allocation of a Rescue Base in the Arctic
by Yulong Shan and Ren Zhang
Symmetry 2019, 11(9), 1073; https://doi.org/10.3390/sym11091073 - 24 Aug 2019
Cited by 12 | Viewed by 2629
Abstract
Risk assessment and emergency responses to ensure the safety of ships crossing the Arctic have gained tremendous attention in recent years. However, asymmetry in the probability that people will receive aid when navigating through the Arctic still exists because of the unsystematic allocation [...] Read more.
Risk assessment and emergency responses to ensure the safety of ships crossing the Arctic have gained tremendous attention in recent years. However, asymmetry in the probability that people will receive aid when navigating through the Arctic still exists because of the unsystematic allocation of rescue bases in the Arctic. At the same time, no study has proposed an overall solution to the problem of allocating rescue bases in the Arctic region to safeguard people’s interests. In this paper, we investigated the main natural factors affecting the safety of ship navigation in the Arctic based on the statistics of ship accidents in the Arctic from 1995 to 2004. The navigation risk of the Arctic was then assessed based on these natural factors, reflecting the need for rescue at all locations in the Arctic. Next, 37 cities with good infrastructure were selected among those along the Arctic as candidate locations for rescue bases. Finally, a new model was constructed based on the Set Covering Location Model, Double Covering Location Model, and P-Median Model to determine the optimal allocation of rescue bases in the Arctic. The rescue bases covered all the areas in the Arctic, and minimized cost in terms of distance and other economic factors. In addition, the constructed model ensured that two rescue bases were allocated to the areas with high navigation risk. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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17 pages, 6475 KiB  
Article
Image Enhancement Using Modified Histogram and Log-Exp Transformation
by Liyun Zhuang and Yepeng Guan
Symmetry 2019, 11(8), 1062; https://doi.org/10.3390/sym11081062 - 20 Aug 2019
Cited by 7 | Viewed by 4122
Abstract
An effective method to enhance the contrast of digital images is proposed in this paper. A histogram function is developed to make the histogram curve smoother, which can be used to avoid the loss of information in the processed image. Besides the histogram [...] Read more.
An effective method to enhance the contrast of digital images is proposed in this paper. A histogram function is developed to make the histogram curve smoother, which can be used to avoid the loss of information in the processed image. Besides the histogram function, an adaptive gamma correction for the histogram is proposed to stretch the brightness contrast. Moreover, the log-exp transformation strategy is presented to progressively increase the low intensity while suppressing the decrement of the high intensity. In order to further widen the dynamic range of the image, the nonlinear normalization transformation is put forward to make the output image more natural and clearer. In the experiment on non-uniform illumination images, the average contrast per pixel (CPP), root mean square (RMS), and discrete entropy (DE) metrics of the developed approach are shown to be superior to selected state-of-the-art methods. Full article
(This article belongs to the Special Issue Mathematical Modeling and Computational Methods in Science and Engineering)
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