Special Issue "Mathematics and Engineering"

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: 31 May 2019

Special Issue Editors

Guest Editor
Prof. Dr. Mingheng Li

Department of Chemical and Materials Engineering, California State Polytechnic University, Pomona, CA 91768, USA
Website | E-Mail
Interests: process systems engineering; coatings processing; energy and environmental systems
Guest Editor
Prof. Dr. Hui Sun

Department of Mathematics and Statistics, California State University, Long Beach, 1250 Bellflower Blvd, Long Beach, CA 90840, USA
E-Mail
Interests: mathematical modeling; scientific computations; dynamical systems

Special Issue Information

Dear Colleagues,

Engineering problems arising in energy, environment, materials and healthcare are featured by enormous scale and complexity, which have posed challenges and provided opportunities for the development of advanced mathematical tools to ensure sound decision making. For example, with the breakthrough of computational power over the last few decades, modeling and numerical linear algebra have been intensely utilized and developed to simulate various engineering processes. More recently, data sciences and machine learning emerge in a diverse collection of engineering fields.

The aim of this Special Issue is to bring together recent progresses in mathematics applied in complex engineering problems, which include, but are not limited to, modeling and simulation, computations, analysis, control, optimization, data science, and machine learning.

Prof. Dr. Mingheng Li
Prof. Dr. Hui Sun
Guest Editors

Manuscript Submission Information

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Keywords

  • mathematical models
  • systems of differential equations 
  • complex engineering systems 
  • scientific computation 
  • asymptotic analysis
  • control theory 
  • optimization 
  • data science 
  • machine learning

Published Papers (6 papers)

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Research

Open AccessArticle Weighted Block Golub-Kahan-Lanczos Algorithms for Linear Response Eigenvalue Problem
Mathematics 2019, 7(1), 53; https://doi.org/10.3390/math7010053
Received: 30 November 2018 / Revised: 25 December 2018 / Accepted: 29 December 2018 / Published: 7 January 2019
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Abstract
In order to solve all or some eigenvalues lied in a cluster, we propose a weighted block Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem. Error bounds of the approximations to an eigenvalue cluster, as well as their corresponding eigenspace, are established and [...] Read more.
In order to solve all or some eigenvalues lied in a cluster, we propose a weighted block Golub-Kahan-Lanczos algorithm for the linear response eigenvalue problem. Error bounds of the approximations to an eigenvalue cluster, as well as their corresponding eigenspace, are established and show the advantages. A practical thick-restart strategy is applied to the block algorithm to eliminate the increasing computational and memory costs, and the numerical instability. Numerical examples illustrate the effectiveness of our new algorithms. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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Open AccessArticle Target Fusion Detection of LiDAR and Camera Based on the Improved YOLO Algorithm
Mathematics 2018, 6(10), 213; https://doi.org/10.3390/math6100213
Received: 7 September 2018 / Revised: 16 October 2018 / Accepted: 17 October 2018 / Published: 19 October 2018
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Abstract
Target detection plays a key role in the safe driving of autonomous vehicles. At present, most studies use single sensor to collect obstacle information, but single sensor cannot deal with the complex urban road environment, and the rate of missed detection is high. [...] Read more.
Target detection plays a key role in the safe driving of autonomous vehicles. At present, most studies use single sensor to collect obstacle information, but single sensor cannot deal with the complex urban road environment, and the rate of missed detection is high. Therefore, this paper presents a detection fusion system with integrating LiDAR and color camera. Based on the original You Only Look Once (YOLO) algorithm, the second detection scheme is proposed to improve the YOLO algorithm for dim targets such as non-motorized vehicles and pedestrians. Many image samples are used to train the YOLO algorithm to obtain the relevant parameters and establish the target detection model. Then, the decision level fusion of sensors is introduced to fuse the color image and the depth image to improve the accuracy of the target detection. Finally, the test samples are used to verify the decision level fusion. The results show that the improved YOLO algorithm and decision level fusion have high accuracy of target detection, can meet the need of real-time, and can reduce the rate of missed detection of dim targets such as non-motor vehicles and pedestrians. Thus, the method in this paper, under the premise of considering accuracy and real-time, has better performance and larger application prospect. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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Open AccessArticle The Opening Capability for Security against Privacy Infringements in the Smart Grid Environment
Mathematics 2018, 6(10), 202; https://doi.org/10.3390/math6100202
Received: 10 September 2018 / Revised: 28 September 2018 / Accepted: 2 October 2018 / Published: 14 October 2018
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Abstract
It is now known that more information can be leaked into the smart grid environment than into the existing environment. In particular, specific information such as energy consumption data can be exposed via smart devices. Such a phenomenon can incur considerable risks due [...] Read more.
It is now known that more information can be leaked into the smart grid environment than into the existing environment. In particular, specific information such as energy consumption data can be exposed via smart devices. Such a phenomenon can incur considerable risks due to the fact that both the amount and the concreteness of information increase when more types of information are combined. As such, this study aimed to develop an anonymous signature technique along with a signature authentication technique to prevent infringements of privacy in the smart grid environment, and they were tested and verified at the testbed used in a previous study. To reinforce the security of the smart grid, a password and anonymous authentication algorithm which can be applied not only to extendable test sites but also to power plants, including nuclear power stations, was developed. The group signature scheme is an anonymous signature schemes where the authenticator verifies the group signature to determine whether the signer is a member of a certain group but he/she would not know which member actually signed in. However, in this scheme, the identity of the signer can be revealed through an “opener” in special circumstances involving accidents, incidents, or disputes. Since the opener can always identify the signer without his/her consent in such cases, the signer would be concerned about letting the opener find out his/her anonymous activities. Thus, an anonymous signature scheme where the signer issues a token when entering his/her signature to allow the opener to confirm his/her identity only from that token is proposed in this study. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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Graphical abstract

Open AccessArticle Green’s Classifications and Evolutions of Fixed-Order Networks
Mathematics 2018, 6(10), 174; https://doi.org/10.3390/math6100174
Received: 31 August 2018 / Revised: 20 September 2018 / Accepted: 20 September 2018 / Published: 25 September 2018
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Abstract
It is shown that the set of all networks of fixed order n form a semigroup that is isomorphic to the semigroup BX of binary relations on a set X of cardinality n. Consequently, BX provides for Green’s L, [...] Read more.
It is shown that the set of all networks of fixed order n form a semigroup that is isomorphic to the semigroup B X of binary relations on a set X of cardinality n . Consequently, B X provides for Green’s L , R , H , and D equivalence classifications of all networks of fixed order n . These classifications reveal that a fixed-order network which evolves within a Green’s equivalence class maintains certain structural invariants during its evolution. The “Green’s symmetry problem” is introduced and is defined as the determination of all symmetries (i.e., transformations) that produce an evolution between an initial and final network within an L or an R class such that each symmetry preserves the required structural invariants. Such symmetries are shown to be solutions to special Boolean equations specific to each class. The satisfiability and computational complexity of the “Green’s symmetry problem” are discussed and it is demonstrated that such symmetries encode information about which node neighborhoods in the initial network can be joined to form node neighborhoods in the final network such that the structural invariants required by the evolution are preserved, i.e., the internal dynamics of the evolution. The notion of “propensity” is also introduced. It is a measure of the tendency of node neighborhoods to join to form new neighborhoods during a network evolution and is used to define “energy”, which quantifies the complexity of the internal dynamics of a network evolution. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
Open AccessArticle Detecting and Handling Cyber-Attacks in Model Predictive Control of Chemical Processes
Mathematics 2018, 6(10), 173; https://doi.org/10.3390/math6100173
Received: 24 August 2018 / Revised: 20 September 2018 / Accepted: 21 September 2018 / Published: 25 September 2018
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Abstract
Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and [...] Read more.
Since industrial control systems are usually integrated with numerous physical devices, the security of control systems plays an important role in safe operation of industrial chemical processes. However, due to the use of a large number of control actuators and measurement sensors and the increasing use of wireless communication, control systems are becoming increasingly vulnerable to cyber-attacks, which may spread rapidly and may cause severe industrial incidents. To mitigate the impact of cyber-attacks in chemical processes, this work integrates a neural network (NN)-based detection method and a Lyapunov-based model predictive controller for a class of nonlinear systems. A chemical process example is used to illustrate the application of the proposed NN-based detection and LMPC methods to handle cyber-attacks. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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Open AccessArticle Kinematics in the Information Age
Mathematics 2018, 6(9), 148; https://doi.org/10.3390/math6090148
Received: 27 June 2018 / Revised: 20 August 2018 / Accepted: 21 August 2018 / Published: 27 August 2018
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Abstract
Modern kinematics derives directly from developments in the 1700s, and in their current instantiation, have been adopted as standard realizations…or templates that seem unquestionable. For example, so-called aerospace sequences of rotations are ubiquitously accepted as the norm for aerospace applications, owing from a [...] Read more.
Modern kinematics derives directly from developments in the 1700s, and in their current instantiation, have been adopted as standard realizations…or templates that seem unquestionable. For example, so-called aerospace sequences of rotations are ubiquitously accepted as the norm for aerospace applications, owing from a recent heritage in the space age of the late twentieth century. With the waning of the space-age as a driver for technology development, the information age has risen with the advent of digital computers, and this begs for re-evaluation of assumptions made in the former era. The new context of the digital computer defines the use of the term “information age” in the manuscript title and further highlights the novelty and originality of the research. The effects of selecting different Direction Cosine Matrices (DCM)-to-Euler Angle rotations on accuracy, step size, and computational time in modern digital computers will be simulated and analyzed. The experimental setup will include all twelve DCM rotations and also includes critical analysis of necessary computational step size. The results show that the rotations are classified into symmetric and non-symmetric rotations and that no one DCM rotation outperforms the others in all metrics used, yielding the potential for trade space analysis to select the best DCM for a specific instance. Novel illustrations include the fact that one of the ubiquitous sequences (the “313 sequence”) has degraded relative accuracy measured by mean and standard deviations of errors, but may be calculated faster than the other ubiquitous sequence (the “321 sequence”), while a lesser known “231 sequence” has comparable accuracy and calculation-time. Evaluation of the 231 sequence also illustrates the originality of the research. These novelties are applied to spacecraft attitude control in this manuscript, but equally apply to robotics, aircraft, and surface and subsurface vehicles. Full article
(This article belongs to the Special Issue Mathematics and Engineering)
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