Mathematics

11 pages, 252 KiB

Open AccessArticle

Uniform Dichotomy Concepts for Discrete-Time Skew Evolution Cocycles in Banach Spaces

by Ariana Găină, Mihail Megan and Carmen Florinela Popa

Mathematics 2021, 9(17), 2177; https://doi.org/10.3390/math9172177 - 6 Sep 2021

Cited by 5 | Viewed by 1798

In the present paper, we consider the problem of dichotomic behaviors of dynamical systems described by discrete-time skew evolution cocycles in Banach spaces. We study two concepts of uniform dichotomy: uniform exponential dichotomy and uniform polynomial dichotomy. Some characterizations of these notions and [...] Read more.

In the present paper, we consider the problem of dichotomic behaviors of dynamical systems described by discrete-time skew evolution cocycles in Banach spaces. We study two concepts of uniform dichotomy: uniform exponential dichotomy and uniform polynomial dichotomy. Some characterizations of these notions and connections between these concepts are given. Full article

17 pages, 11882 KiB

Open AccessArticle

Adaptive Levenberg–Marquardt Algorithm: A New Optimization Strategy for Levenberg–Marquardt Neural Networks

by Zhiqi Yan, Shisheng Zhong, Lin Lin and Zhiquan Cui

Mathematics 2021, 9(17), 2176; https://doi.org/10.3390/math9172176 - 6 Sep 2021

Cited by 23 | Viewed by 3975

Abstract

Engineering data are often highly nonlinear and contain high-frequency noise, so the Levenberg–Marquardt (LM) algorithm may not converge when a neural network optimized by the algorithm is trained with engineering data. In this work, we analyzed the reasons for the LM neural network’s [...] Read more.

Engineering data are often highly nonlinear and contain high-frequency noise, so the Levenberg–Marquardt (LM) algorithm may not converge when a neural network optimized by the algorithm is trained with engineering data. In this work, we analyzed the reasons for the LM neural network’s poor convergence commonly associated with the LM algorithm. Specifically, the effects of different activation functions such as Sigmoid, Tanh, Rectified Linear Unit (RELU) and Parametric Rectified Linear Unit (PRLU) were evaluated on the general performance of LM neural networks, and special values of LM neural network parameters were found that could make the LM algorithm converge poorly. We proposed an adaptive LM (AdaLM) algorithm to solve the problem of the LM algorithm. The algorithm coordinates the descent direction and the descent step by the iteration number, which can prevent falling into the local minimum value and avoid the influence of the parameter state of LM neural networks. We compared the AdaLM algorithm with the traditional LM algorithm and its variants in terms of accuracy and speed in the context of testing common datasets and aero-engine data, and the results verified the effectiveness of the AdaLM algorithm. Full article

(This article belongs to the Special Issue Applied Mathematics to Mechanisms and Machines)

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35 pages, 1427 KiB

Open AccessArticle

On the Reachability of a Feedback Controlled Leontief-Type Singular Model Involving Scheduled Production, Recycling and Non-Renewable Resources

by Manuel De la Sen, Asier Ibeas and Santiago Alonso-Quesada

Mathematics 2021, 9(17), 2175; https://doi.org/10.3390/math9172175 - 6 Sep 2021

Cited by 3 | Viewed by 1709

Abstract

This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject [...] Read more.

This paper proposes and studies the reachability of a singular regular dynamic discrete Leontief-type economic model which includes production industries, recycling industries, and non-renewable products in an integrated way. The designed prefixed final state to be reached, under discussed reachability conditions, is subject to necessary additional positivity-type constraints which depend on the initial conditions and the final time for the solution to match such a final prescribed state. It is assumed that the model may be driven by both the demand and an additional correcting control in order to achieve the final targeted state in finite time. Formal sufficiency-type conditions are established for the proposed singular Leontief model to be reachable under positive feedback, correcting controls designed for appropriate demand/supply regulation. Basically, the proposed regulation scheme allows fixing a prescribed final state of economic goods stock in finite time if the model is reachable. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Economic - Related Data)

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12 pages, 4863 KiB

Open AccessFeature PaperArticle

A Framework for Economically Optimal Operation of Explosive Waste Incineration Process to Reduce NOx Emission Concentration

by Sunghyun Cho, Dongwoo Kang, Joseph Sang-Il Kwon, Minsu Kim, Hyungtae Cho, Il Moon and Junghwan Kim

Mathematics 2021, 9(17), 2174; https://doi.org/10.3390/math9172174 - 6 Sep 2021

Cited by 4 | Viewed by 2979

Abstract

Explosives, especially those used for military weapons, have a short lifespan and their performance noticeably deteriorates over time. These old explosives need to be disposed of safely. Fluidized bed incinerators (FBIs) are safe for disposal of explosive waste (such as TNT) and produce [...] Read more.

Explosives, especially those used for military weapons, have a short lifespan and their performance noticeably deteriorates over time. These old explosives need to be disposed of safely. Fluidized bed incinerators (FBIs) are safe for disposal of explosive waste (such as TNT) and produce fewer gas emissions compared to conventional methods, such as the rotary kiln. However, previous studies on this FBI process have only focused on minimizing the amount of NOx emissions without considering the operating and unitality costs (i.e., total cost) associated with the process. It is important to note that, in general, a number of different operating conditions are available to achieve a target NOx emission concentration and, thus, it requires a significant computational requirement to compare the total costs among those candidate operating conditions using a computational fluid dynamics simulation. To this end, a novel framework is proposed to quickly determine the most economically viable FBI process operating condition for a target NOx concentration. First, a surrogate model was developed to replace the high-fidelity model of an FBI process, and utilized to determine a set of possible operating conditions that may lead to a target NOx emission concentration. Second, the candidate operating conditions were fed to the Aspen Plus™ process simulation program to determine the most economically competitive option with respect to its total cost. The developed framework can provide operational guidelines for a clean and economical incineration process of explosive waste. Full article

(This article belongs to the Special Issue Mathematics and Engineering II)

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17 pages, 305 KiB

Open AccessArticle

Positive Solutions for a Singular Elliptic Equation Arising in a Theory of Thermal Explosion

by Song-Yue Yu and Baoqiang Yan

Mathematics 2021, 9(17), 2173; https://doi.org/10.3390/math9172173 - 6 Sep 2021

Cited by 2 | Viewed by 1435

Abstract

In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case [...] Read more.

In this paper, the thermal explosion model described by a nonlinear boundary value problem is studied. Firstly, we prove the comparison principle under nonlinear boundary conditions. Secondly, using the sub-super solution theorem, we prove the existence of a positive solution for the case

K (x) > 0

, as well as the monotonicity of the maximal solution on parameter

λ

. Thirdly, the uniqueness of the solution for

K (x) < 0

is proved, as well as the monotonicity of the solutions on parameter

λ

. Finally, we obtain some new results for the existence of solutions, and the dependence on the

λ

for the case

K (x)

is sign-changing. Full article

(This article belongs to the Special Issue Nonlinear Boundary Value Problems and Their Applications)

12 pages, 415 KiB

Open AccessArticle

A Novel Method for Solving Second Kind Volterra Integral Equations with Discontinuous Kernel

by Samad Noeiaghdam and Sanda Micula

Mathematics 2021, 9(17), 2172; https://doi.org/10.3390/math9172172 - 5 Sep 2021

Cited by 9 | Viewed by 2168

Abstract

Load leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision of the method. To control [...] Read more.

Load leveling problems and energy storage systems can be modeled in the form of Volterra integral equations (VIE) with a discontinuous kernel. The Lagrange–collocation method is applied for solving the problem. Proving a theorem, we discuss the precision of the method. To control the accuracy, we apply the CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method and the CADNA (Control of Accuracy and Debugging for Numerical Applications) library. For this aim, we apply discrete stochastic mathematics (DSA). Using this method, we can control the number of iterations, errors and accuracy. Additionally, some numerical instabilities can be identified. With the aid of this theorem, a novel condition is used instead of the traditional conditions. Full article

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13 pages, 1790 KiB

Open AccessArticle

Mathematical Modeling, Analysis and Evaluation of the Complexity of Flight Paths of Groups of Unmanned Aerial Vehicles in Aviation and Transport Systems

by Andrey Kositzyn, Denis Serdechnyy, Sergey Korchagin, Ekaterina Pleshakova, Petr Nikitin and Natalia Kurileva

Mathematics 2021, 9(17), 2171; https://doi.org/10.3390/math9172171 - 5 Sep 2021

Cited by 8 | Viewed by 3263

Abstract

Recently, we have seen the rapidly growing popularity of unmanned aerial vehicles. This is due to some advantages, namely portability, the ability to fly over hard-to-reach areas without human intervention. They are also widely used for commercial purposes, agriculture, delivery, automation in warehouses. [...] Read more.

Recently, we have seen the rapidly growing popularity of unmanned aerial vehicles. This is due to some advantages, namely portability, the ability to fly over hard-to-reach areas without human intervention. They are also widely used for commercial purposes, agriculture, delivery, automation in warehouses. The potential of unmanned aerial vehicles is vast and demonstrates promising opportunities. However, when using these devices, the issue of safety is acute. This article presents a developed software application that is used to improve the efficiency of flight research of groups of unmanned aerial vehicles, based on a new method for assessing flight safety by comparing the complexity of specified air routes. A practical approach to modeling and evaluating the search for a safe way is proposed. A suitable method of research is computer and simulation modeling. It is suggested to use the spectrum of dynamic characteristics of the sequence as a formal attribute for analyzing routes. The method is illustrated by an example of comparing air trajectories according to the flight safety criterion. The software application is intended for use in the educational process when training specialists in transport security, robotics, and system analysis. Full article

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19 pages, 577 KiB

Open AccessArticle

Analysis of the Tax Compliance in the EU: VECM and SEM

by Marius-Răzvan Surugiu, Cristina-Raluca Mazilescu and Camelia Surugiu

Mathematics 2021, 9(17), 2170; https://doi.org/10.3390/math9172170 - 5 Sep 2021

Cited by 3 | Viewed by 3121

Abstract

Tax compliance is an important indicator for the proper functioning of the tax authority, influencing the budget revenue level. In this study, a Vector Error Correction Model (VECM) analysis was developed to identify the long-term relationships between the compliance in individual income taxation [...] Read more.

Tax compliance is an important indicator for the proper functioning of the tax authority, influencing the budget revenue level. In this study, a Vector Error Correction Model (VECM) analysis was developed to identify the long-term relationships between the compliance in individual income taxation (taxpayer’s behavior), public trust in politicians (trust in authorities), and rule of law (power of the authorities), using unbalanced panel data for the European Union (EU28) during the 2007–2017 period. The results underline the causality of the long-run relationships between the variables. The results of the VECM analysis underline the need for various support measures for voluntary tax compliance, with the trust variable having an important impact on tax compliance. In addition, a Structural Equation Modeling (SEM) analysis was employed using an improved data set with variables such as the compliance in corporation taxation (taxpayer’s behavior), wastefulness of government spending, and quality of the education system. The results of the SEM analysis underline the positive and significant influences of the variables on tax compliance. Full article

(This article belongs to the Special Issue Analysis and Mathematical Modeling of Economic - Related Data)

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15 pages, 309 KiB

Open AccessArticle

Dynamics of Stage-Structured Predator–Prey Model with Beddington–DeAngelis Functional Response and Harvesting

by Haiyin Li and Xuhua Cheng

Mathematics 2021, 9(17), 2169; https://doi.org/10.3390/math9172169 - 5 Sep 2021

Cited by 3 | Viewed by 2009

Abstract

In this paper, we investigate the stability of equilibrium in the stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking the sign of the real part for eigenvalue, local stability of origin equilibrium and boundary equilibrium are studied. Second, we [...] Read more.

In this paper, we investigate the stability of equilibrium in the stage-structured and density-dependent predator–prey system with Beddington–DeAngelis functional response. First, by checking the sign of the real part for eigenvalue, local stability of origin equilibrium and boundary equilibrium are studied. Second, we explore the local stability of the positive equilibrium for

τ = 0

and

τ \neq 0

(time delay

τ

is the time taken from immaturity to maturity predator), which shows that local stability of the positive equilibrium is dependent on parameter

τ

. Third, we qualitatively analyze global asymptotical stability of the positive equilibrium. Based on stability theory of periodic solutions, global asymptotical stability of the positive equilibrium is obtained when

τ = 0

; by constructing Lyapunov functions, we conclude that the positive equilibrium is also globally asymptotically stable when

τ \neq 0

. Finally, examples with numerical simulations are given to illustrate the obtained results. Full article

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23 pages, 13298 KiB

Open AccessArticle

Application of a Fuzzy Inference System for Optimization of an Amplifier Design

by M. Isabel Dieste-Velasco

Mathematics 2021, 9(17), 2168; https://doi.org/10.3390/math9172168 - 5 Sep 2021

Cited by 4 | Viewed by 2060

Abstract

Simulation programs are widely used in the design of analog electronic circuits to analyze their behavior and to predict the response of a circuit to variations in the circuit components. A fuzzy inference system (FIS) in combination with these simulation tools can be [...] Read more.

Simulation programs are widely used in the design of analog electronic circuits to analyze their behavior and to predict the response of a circuit to variations in the circuit components. A fuzzy inference system (FIS) in combination with these simulation tools can be applied to identify both the main and interaction effects of circuit parameters on the response variables, which can help to optimize them. This paper describes an application of fuzzy inference systems to modeling the behavior of analog electronic circuits for further optimization. First, a Monte Carlo analysis, generated from the tolerances of the circuit components, is performed. Once the Monte Carlo results are obtained for each of the response variables, the fuzzy inference systems are generated and then optimized using a particle swarm optimization (PSO) algorithm. These fuzzy inference systems are used to determine the influence of the circuit components on the response variables and to select them to optimize the amplifier design. The methodology proposed in this study can be used as the basis for optimizing the design of similar analog electronic circuits. Full article

(This article belongs to the Special Issue Advanced Analytical and Numerical Techniques for Technological Processes and Applications)

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19 pages, 6145 KiB

Open AccessArticle

Optimization of Microjet Location Using Surrogate Model Coupled with Particle Swarm Optimization Algorithm

by Mohammad Owais Qidwai, Irfan Anjum Badruddin, Noor Zaman Khan, Mohammad Anas Khan and Saad Alshahrani

Mathematics 2021, 9(17), 2167; https://doi.org/10.3390/math9172167 - 5 Sep 2021

Cited by 7 | Viewed by 2677

Abstract

This study aimed to present the design methodology of microjet heat sinks with unequal jet spacing, using a machine learning technique which alleviates hot spots in heat sinks with non-uniform heat flux conditions. Latin hypercube sampling was used to obtain 30 design sample [...] Read more.

This study aimed to present the design methodology of microjet heat sinks with unequal jet spacing, using a machine learning technique which alleviates hot spots in heat sinks with non-uniform heat flux conditions. Latin hypercube sampling was used to obtain 30 design sample points on which three-dimensional Computational Fluid Dynamics (CFD) solutions were calculated, which were used to train the machine learning model. Radial Basis Neural Network (RBNN) was used as a surrogate model coupled with Particle Swarm Optimization (PSO) to obtain the optimized location of jets. The RBNN provides continuous space for searching the optimum values. At the predicted optimum values from the coupled model, the CFD solution was calculated for comparison. The percentage error for the target function was 0.56%, whereas for the accompanied function it was 1.3%. The coupled algorithm has variable inputs at user discretion, including gaussian spread, number of search particles, and number of iterations. The sensitivity of each variable was obtained. Analysis of Variance (ANOVA) was performed to investigate the effect of the input variable on thermal resistance. ANOVA results revealed that gaussian spread is the dominant variable affecting the thermal resistance. Full article

(This article belongs to the Special Issue Mathematical Problems in Mechanical Engineering)

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Figure 1
(a) Physical model of microjet heat sink. (b) A non-uniform power map adopted from Sharma et al. [<a href="#B17-mathematics-09-02167" class="html-bibr">17</a>]. Full article ">Figure 2
The results of grid independence test based on thermal resistance and mean substrate temperature. Full article ">Figure 3
Comparison of the current numerical simulation result with the experimental results of Wang et al. [<a href="#B51-mathematics-09-02167" class="html-bibr">51</a>] for a flow rate of 8 mL/min. Full article ">Figure 4
Schematic diagram of inlet holes on the top plate with position constraints in sections A, B, A’, and B’. Full article ">Figure 5
Radial Basis Neural Network mechanism. Full article ">Figure 6
Optimization procedure. Full article ">Figure 7
Global range of substrate temperature contour of the optimal solution obtained from the CFD solution. Full article ">Figure 8
Best cost of Objective functions with γ = 0.9, ñ = 100, ɨ = 150, P = 120. Full article ">

15 pages, 4102 KiB

Open AccessArticle

High-Capacity Reversible Data Hiding in Encrypted Images Based on Adaptive Predictor and Compression of Prediction Errors

by Bin Huang, Chun Wan and Kaimeng Chen

Mathematics 2021, 9(17), 2166; https://doi.org/10.3390/math9172166 - 5 Sep 2021

Cited by 1 | Viewed by 2058

Abstract

Reversible data hiding in encrypted images (RDHEI) is a technology which embeds secret data into encrypted images in a reversible way. In this paper, we proposed a novel high-capacity RDHEI method which is based on the compression of prediction errors. Before image encryption, [...] Read more.

Reversible data hiding in encrypted images (RDHEI) is a technology which embeds secret data into encrypted images in a reversible way. In this paper, we proposed a novel high-capacity RDHEI method which is based on the compression of prediction errors. Before image encryption, an adaptive linear regression predictor is trained from the original image. Then, the predictor is used to obtain the prediction errors of the pixels in the original image, and the prediction errors are compressed by Huffman coding. The compressed prediction errors are used to vacate additional room with no loss. After image encryption, the vacated room is reserved for data embedding. The receiver can extract the secret data and recover the image with no errors. Compared with existing approaches, the proposed method efficiently improves the embedding capacity. Full article

(This article belongs to the Special Issue Recent Advances in Security, Privacy, and Applied Cryptography)

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30 pages, 5932 KiB

Open AccessArticle

On the Modelling of Emergency Ambulance Trips: The Case of the Žilina Region in Slovakia

by Ľuboš Buzna and Peter Czimmermann

Mathematics 2021, 9(17), 2165; https://doi.org/10.3390/math9172165 - 5 Sep 2021

Cited by 7 | Viewed by 2971

Abstract

The efficient operation of emergency medical services is critical for any society. Typically, optimisation and simulation models support decisions on emergency ambulance stations’ locations and ambulance management strategies. Essential inputs for such models are the spatiotemporal characteristics of ambulance trips. Access to data [...] Read more.

The efficient operation of emergency medical services is critical for any society. Typically, optimisation and simulation models support decisions on emergency ambulance stations’ locations and ambulance management strategies. Essential inputs for such models are the spatiotemporal characteristics of ambulance trips. Access to data on the movements of ambulances is limited, and therefore modelling efforts often rely on assumptions (e.g., the Euclidean distance is used as a surrogate of the ambulance travel time; the closest available ambulance is dispatched to a call; or the travel time estimates, offered by application programming interfaces for ordinary vehicles, are applied to ambulances). These simplifying assumptions are often based on incomplete data or common sense without being fully supported by the evidence. Thus, data-driven research to model ambulance trips is required. We investigated a unique dataset of global positioning system-based measurements collected from seventeen emergency ambulances over three years. We enriched the data by exploring external sources and designed a rule-based procedure to extract ambulance trips for emergency cases. Trips were split into training and test sets. The training set was used to develop a series of statistical models that capture the spatiotemporal characteristics of emergency ambulance trips. The models were used to generate synthetic ambulance trips, and those were compared with the test set to decide which models are the most suitable and to evaluate degrees to which they fit the statistical properties of real-world trips. As confirmed by the low values of the Kullback–Leibler divergence (

0.004

–

0.229

) and by the Kolmogorov–Smirnov test at the significance level of

0.05

, we found a very good fit between the probability distributions of spatiotemporal properties of synthetic and real trips. A reasonable modelling choice is a model where the exponential dependency on the population density is used to locate emergency cases, emergency cases are allocated to hospitals following empirical probabilities, and ambulances are routed using the fastest paths. The models we developed can be used in optimisations and simulations to improve their validity. Full article

(This article belongs to the Special Issue Multi-Criteria Decision Making and Data Mining)

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13 pages, 362 KiB

Open AccessArticle

Evaluation of the Work-Integrated Learning Methodology: Teaching Marketing through Practitioner Experience in the Classroom

by Luis-Alberto Casado-Aranda, Juan Sánchez-Fernández, Francisco Javier Montoro-Ríos and María Isabel Arias Horcajadas

Mathematics 2021, 9(17), 2164; https://doi.org/10.3390/math9172164 - 5 Sep 2021

Cited by 7 | Viewed by 2452

Abstract

The teaching methodology in university marketing subjects has traditionally been based on “lecture classes”, which have proved to be insufficient for providing students with professional skills that can be directly applied in the workplace. This research aims to reduce this gap between the [...] Read more.

The teaching methodology in university marketing subjects has traditionally been based on “lecture classes”, which have proved to be insufficient for providing students with professional skills that can be directly applied in the workplace. This research aims to reduce this gap between the university and business by applying the active teaching methodology of work-integrated learning (WIL), which consists of providing students with knowledge and experiences directly from professionals that are invited to the classroom. We evaluated the effects of the WIL methodology on university students in a marketing degree course through self-administered questionnaires. During a semester, perceived personal, academic, and professional outcomes were assessed in two groups of students of the same module, one of which participated in the WIL program (i.e., they received lectures by professional marketing experts who were invited to the classroom and explained, through real examples, the content of the subject being taught), and the other served as a control (i.e., they learned the content only through traditional lectures from the college instructor). The results revealed that the students who took part in the WIL program experienced increased motivation, enjoyment, and interest in the subject. Furthermore, they had an increased understanding and acquisition of the concepts, as well as a greater perceived ability to manage companies and a comprehension of the economic environment. These findings constitute an advance because they identify the benefits of applying WIL in knowledge fields where the acquisition of professional skills is crucial for graduates’ entry into the labor market. Full article

(This article belongs to the Special Issue Business Games and Numeric Simulations in Economics and Management)

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22 pages, 1017 KiB

Open AccessArticle

A Novel MADM Framework under q-Rung Orthopair Fuzzy Bipolar Soft Sets

by Ghous Ali, Hanan Alolaiyan, Dragan Pamučar, Muhammad Asif and Nimra Lateef

Mathematics 2021, 9(17), 2163; https://doi.org/10.3390/math9172163 - 4 Sep 2021

Cited by 22 | Viewed by 2634

Abstract

In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework [...] Read more.

In many real-life problems, decision-making is reckoned as a powerful tool to manipulate the data involving imprecise and vague information. To fix the mathematical problems containing more generalized datasets, an emerging model called q-rung orthopair fuzzy soft sets offers a comprehensive framework for a number of multi-attribute decision-making (MADM) situations but this model is not capable to deal effectively with situations having bipolar soft data. In this research study, a novel hybrid model under the name of q-rung orthopair fuzzy bipolar soft set (q-ROFBSS, henceforth), an efficient bipolar soft generalization of q-rung orthopair fuzzy set model, is introduced and illustrated by an example. The proposed model is successfully tested for several significant operations like subset, complement, extended union and intersection, restricted union and intersection, the ‘AND’ operation and the ‘OR’ operation. The De Morgan’s laws are also verified for q-ROFBSSs regarding above-mentioned operations. Ultimately, two applications are investigated by using the proposed framework. In first real-life application, the selection of land for cropping the carrots and the lettuces is studied, while in second practical application, the selection of an eligible student for a scholarship is discussed. At last, a comparison of the initiated model with certain existing models, including Pythagorean and Fermatean fuzzy bipolar soft set models is provided. Full article

(This article belongs to the Special Issue Multiple Criteria Decision Making)

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20 pages, 343 KiB

Open AccessArticle

Algorithmic Determination of a Large Integer in the Two-Term Machin-like Formula for π

by Sanjar M. Abrarov, Rajinder K. Jagpal, Rehan Siddiqui and Brendan M. Quine

Mathematics 2021, 9(17), 2162; https://doi.org/10.3390/math9172162 - 4 Sep 2021

Cited by 2 | Viewed by 2326

Abstract

In our earlier publication we have shown how to compute by iteration a rational number

u_{2, k}

in the two-term Machin-like formula for

π

of the kind [...] Read more.

In our earlier publication we have shown how to compute by iteration a rational number

u_{2, k}

in the two-term Machin-like formula for

π

of the kind

\frac{π}{4} = 2^{k - 1} arctan (\frac{1}{u_{1, k}}) + arctan (\frac{1}{u_{2, k}}),

k \in Z, k \geq 1,

where

u_{1, k}

can be chosen as an integer

u_{1, k} = ⌊a_{k} / \sqrt{2 - a_{k - 1}}⌋

with nested radicals defined as

a_{k} = \sqrt{2 + a_{k - 1}}

and

a_{0} = 0

. In this work, we report an alternative method for determination of the integer

u_{1, k}

. This approach is based on a simple iteration and does not require any irrational (surd) numbers from the set

\{a_{k}\}

in computation of the integer

u_{1, k}

. Mathematica programs validating these results are presented. Full article

(This article belongs to the Section Computational and Applied Mathematics)

13 pages, 299 KiB

Open AccessFeature PaperArticle

Joint Universality of the Zeta-Functions of Cusp Forms

by Renata Macaitienė

Mathematics 2021, 9(17), 2161; https://doi.org/10.3390/math9172161 - 4 Sep 2021

Viewed by 1578

Abstract

Let F be the normalized Hecke-eigen cusp form for the full modular group and

ζ (s, F)

be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts [...] Read more.

Let F be the normalized Hecke-eigen cusp form for the full modular group and

ζ (s, F)

be the corresponding zeta-function. In the paper, the joint universality theorem on the approximation of a collection of analytic functions by shifts

(ζ (s + i h_{1} τ, F), \dots, ζ (s + i h_{r} τ, F))

is proved. Here,

h_{1}, \dots, h_{r}

are algebraic numbers linearly independent over the field of rational numbers. Full article

27 pages, 1842 KiB

Open AccessArticle

Fractional Dynamics of Stuxnet Virus Propagation in Industrial Control Systems

by Zaheer Masood, Muhammad Asif Zahoor Raja, Naveed Ishtiaq Chaudhary, Khalid Mehmood Cheema and Ahmad H. Milyani

Mathematics 2021, 9(17), 2160; https://doi.org/10.3390/math9172160 - 4 Sep 2021

Cited by 30 | Viewed by 3036

Abstract

The designed fractional order Stuxnet, the virus model, is analyzed to investigate the spread of the virus in the regime of isolated industrial networks environment by bridging the air-gap between the traditional and the critical control network infrastructures. Removable storage devices are commonly [...] Read more.

The designed fractional order Stuxnet, the virus model, is analyzed to investigate the spread of the virus in the regime of isolated industrial networks environment by bridging the air-gap between the traditional and the critical control network infrastructures. Removable storage devices are commonly used to exploit the vulnerability of individual nodes, as well as the associated networks, by transferring data and viruses in the isolated industrial control system. A mathematical model of an arbitrary order system is constructed and analyzed numerically to depict the control mechanism. A local and global stability analysis of the system is performed on the equilibrium points derived for the value of

α

= 1. To understand the depth of fractional model behavior, numerical simulations are carried out for the distinct order of the fractional derivative system, and the results show that fractional order models provide rich dynamics by means of fast transient and super-slow evolution of the model’s steady-state behavior, which are seldom perceived in integer-order counterparts. Full article

(This article belongs to the Special Issue Control, Optimization, and Mathematical Modeling of Complex Systems)

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12 pages, 4660 KiB

Open AccessArticle

Non-Uniform Spline Quasi-Interpolation to Extract the Series Resistance in Resistive Switching Memristors for Compact Modeling Purposes

by María José Ibáñez, Domingo Barrera, David Maldonado, Rafael Yáñez and Juan Bautista Roldán

Mathematics 2021, 9(17), 2159; https://doi.org/10.3390/math9172159 - 4 Sep 2021

Cited by 10 | Viewed by 1615

Abstract

An advanced new methodology is presented to improve parameter extraction in resistive memories. The series resistance and some other parameters in resistive memories are obtained, making use of a two-stage algorithm, where the second one is based on quasi-interpolation on non-uniform partitions. The [...] Read more.

An advanced new methodology is presented to improve parameter extraction in resistive memories. The series resistance and some other parameters in resistive memories are obtained, making use of a two-stage algorithm, where the second one is based on quasi-interpolation on non-uniform partitions. The use of this latter advanced mathematical technique provides a numerically robust procedure, and in this manuscript, we focus on it. The series resistance, an essential parameter to characterize the circuit operation of resistive memories, is extracted from experimental curves measured in devices based on hafnium oxide as their dielectric layer. The experimental curves are highly non-linear, due to the underlying physics controlling the device operation, so that a stable numerical procedure is needed. The results also allow promising expectations in the massive extraction of new parameters that can help in the characterization of the electrical device behavior. Full article

(This article belongs to the Section Computational and Applied Mathematics)

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(a) RRAM structure cross-section. (b) Circuit scheme to explain the different voltages employed in this work. (c) Current versus modified voltage for different series resistances. We choose the curve with the maximum slope (in fact, it is a vertical region, shown in symbols) as the one that allows us to extract the correct series resistances, as depicted in [<a href="#B18-mathematics-09-02159" class="html-bibr">18</a>]. Full article ">Figure 2
Current versus voltage for some resistive switching cycles. The original measured curves are shown in black, the modified curves in red, the corresponding series resistances are also shown. See the points marked by <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>T</mi> <mi>S</mi> </mrow> </msub> </semantics></math> (threshold set voltages) and <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>T</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </mrow> </msub> </semantics></math>, the points where the slope of the curve changes sign, marked with red dots in the modified curves. Full article ">Figure 3
(a) Current versus modified voltage for several series resistances. The selected series resistance corresponds to the curve with the vertical slope, shown with symbols. (b) Modified voltage versus current for the same curves shown on the left. The plots shown are parts of the graphs in (a) with the X-axis and Y-axis exchanged. The curve with the vertical section in (a) presents in this case a horizontal slope, as it is expected. In this manner, the algorithm to extract the series resistance can be applied more easily in (b). Full article ">Figure 4
Extended partition with multiple endpoints. Full article ">Figure 5
Supports of the B-splines defined on an extended partition with multiple endpoints. Full article ">Figure 6
Current versus voltage curves for two different cycles (a) cycle 2 and (b) cycle 106. The original measured curves are shown in black symbols and the modified curves in red symbols. See in lines, with the corresponding colors, the parametrized curves in each case. The <math display="inline"><semantics> <msub> <mi>V</mi> <mrow> <mi>T</mi> <msub> <mi>S</mi> <mn>2</mn> </msub> </mrow> </msub> </semantics></math> points are also shown. The cycle numbers correspond to the order of these cycles in the sequence that forms the resistive switching series measured, i.e., cycle 2 consists of the processes employed to change the device resistance for the second time in the series. Full article ">

16 pages, 1778 KiB

Open AccessArticle

Arbitrary Coefficient Assignment by Static Output Feedback for Linear Differential Equations with Non-Commensurate Lumped and Distributed Delays

by Vasilii Zaitsev and Inna Kim

Mathematics 2021, 9(17), 2158; https://doi.org/10.3390/math9172158 - 4 Sep 2021

Cited by 5 | Viewed by 1871

Abstract

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and [...] Read more.

We consider a linear control system defined by a scalar stationary linear differential equation in the real or complex space with multiple non-commensurate lumped and distributed delays in the state. In the system, the input is a linear combination of multiple variables and its derivatives, and the output is a multidimensional vector of linear combinations of the state and its derivatives. For this system, we study the problem of arbitrary coefficient assignment for the characteristic function by linear static output feedback with lumped and distributed delays. We obtain necessary and sufficient conditions for the solvability of the arbitrary coefficient assignment problem by the static output feedback controller. Corollaries on arbitrary finite spectrum assignment and on stabilization of the system are obtained. We provide an example illustrating our results. Full article

(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)

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19 pages, 314 KiB

Open AccessArticle

A Hybrid Genetic Algorithm for the Simple Assembly Line Balancing Problem with a Fixed Number of Workstations

by Eduardo Álvarez-Miranda, Jordi Pereira, Harold Torrez-Meruvia and Mariona Vilà

Mathematics 2021, 9(17), 2157; https://doi.org/10.3390/math9172157 - 4 Sep 2021

Cited by 10 | Viewed by 2997

Abstract

The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid [...] Read more.

The assembly line balancing problem is a classical optimisation problem whose objective is to assign each production task to one of the stations on the assembly line so that the total efficiency of the line is maximized. This study proposes a novel hybrid method to solve the simple version of the problem in which the number of stations is fixed, a problem known as SALBP-2. The hybrid differs from previous approaches by encoding individuals of a genetic algorithm as instances of a modified problem that contains only a subset of the solutions to the original formulation. These individuals are decoded to feasible solutions of the original problem during fitness evaluation in which the resolution of the modified problem is conducted using a dynamic programming based approach that uses new bounds to reduce its state space. Computational experiments show the efficiency of the method as it is able to obtain several new best-known solutions for some of the benchmark instances used in the literature for comparison purposes. Full article

(This article belongs to the Special Issue Mathematical Modeling and Optimization)

20 pages, 732 KiB

Open AccessArticle

Evaluation of Clustering Algorithms on HPC Platforms

by Juan M. Cebrian, Baldomero Imbernón, Jesús Soto and José M. Cecilia

Mathematics 2021, 9(17), 2156; https://doi.org/10.3390/math9172156 - 4 Sep 2021

Cited by 3 | Viewed by 2078

Abstract

Clustering algorithms are one of the most widely used kernels to generate knowledge from large datasets. These algorithms group a set of data elements (i.e., images, points, patterns, etc.) into clusters to identify patterns or common features of a sample. However, these algorithms [...] Read more.

Clustering algorithms are one of the most widely used kernels to generate knowledge from large datasets. These algorithms group a set of data elements (i.e., images, points, patterns, etc.) into clusters to identify patterns or common features of a sample. However, these algorithms are very computationally expensive as they often involve the computation of expensive fitness functions that must be evaluated for all points in the dataset. This computational cost is even higher for fuzzy methods, where each data point may belong to more than one cluster. In this paper, we evaluate different parallelisation strategies on different heterogeneous platforms for fuzzy clustering algorithms typically used in the state-of-the-art such as the Fuzzy C-means (FCM), the Gustafson–Kessel FCM (GK-FCM) and the Fuzzy Minimals (FM). The experimental evaluation includes performance and energy trade-offs. Our results show that depending on the computational pattern of each algorithm, their mathematical foundation and the amount of data to be processed, each algorithm performs better on a different platform. Full article

(This article belongs to the Special Issue Current Trends in Computer Architecture and High Performance Computing (HPC) with Their Mathematical Foundations)

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22 pages, 4870 KiB

Open AccessArticle

A Method of Image Quality Assessment for Text Recognition on Camera-Captured and Projectively Distorted Documents

by Julia Shemiakina, Elena Limonova, Natalya Skoryukina, Vladimir V. Arlazarov and Dmitry P. Nikolaev

Mathematics 2021, 9(17), 2155; https://doi.org/10.3390/math9172155 - 3 Sep 2021

Cited by 6 | Viewed by 3276

Abstract

In this paper, we consider the problem of identity document recognition in images captured with a mobile device camera. A high level of projective distortion leads to poor quality of the restored text images and, hence, to unreliable recognition results. We propose a [...] Read more.

In this paper, we consider the problem of identity document recognition in images captured with a mobile device camera. A high level of projective distortion leads to poor quality of the restored text images and, hence, to unreliable recognition results. We propose a novel, theoretically based method for estimating the projective distortion level at a restored image point. On this basis, we suggest a new method of binary quality estimation of projectively restored field images. The method analyzes the projective homography only and does not depend on the image size. The text font and height of an evaluated field are assumed to be predefined in the document template. This information is used to estimate the maximum level of distortion acceptable for recognition. The method was tested on a dataset of synthetically distorted field images. Synthetic images were created based on document template images from the publicly available dataset MIDV-2019. In the experiments, the method shows stable predictive values for different strings of one font and height. When used as a pre-recognition rejection method, it demonstrates a positive predictive value of 86.7% and a negative predictive value of 64.1% on the synthetic dataset. A comparison with other geometric quality assessment methods shows the superiority of our approach. Full article

(This article belongs to the Special Issue Mathematical Approaches to Image Processing with Applications)

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19 pages, 372 KiB

Open AccessArticle

On the Convergence of the Benjamini–Hochberg Procedure

by Dean Palejev and Mladen Savov

Mathematics 2021, 9(17), 2154; https://doi.org/10.3390/math9172154 - 3 Sep 2021

Cited by 3 | Viewed by 1951

Abstract

The Benjamini–Hochberg procedure is one of the most used scientific methods up to date. It is widely used in the field of genetics and other areas where the problem of multiple comparison arises frequently. In this paper we show that under fairly general [...] Read more.

The Benjamini–Hochberg procedure is one of the most used scientific methods up to date. It is widely used in the field of genetics and other areas where the problem of multiple comparison arises frequently. In this paper we show that under fairly general assumptions for the distribution of the test statistic under the alternative hypothesis, when increasing the number of tests, the power of the Benjamini–Hochberg procedure has an exponential type of asymptotic convergence to a previously shown limit of the power. We give a theoretical lower bound for the probability that for a fixed number of tests the power is within a given interval around its limit together with a software routine that calculates these values. This result is important when planning costly experiments and estimating the achieved power after performing them. Full article

(This article belongs to the Section Probability and Statistics)

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13 pages, 291 KiB

Open AccessArticle

Weaker Forms of Soft Regular and Soft T₂ Soft Topological Spaces

by Samer Al Ghour

Mathematics 2021, 9(17), 2153; https://doi.org/10.3390/math9172153 - 3 Sep 2021

Cited by 19 | Viewed by 2126

Abstract

Soft

ω

-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft

ω

-regularity as a weaker form of both soft regularity and soft

ω

-local indiscreetness is defined and investigated. Additionally, soft

ω

[...] Read more.

Soft

ω

-local indiscreetness as a weaker form of both soft local countability and soft local indiscreetness is introduced. Then soft

ω

-regularity as a weaker form of both soft regularity and soft

ω

-local indiscreetness is defined and investigated. Additionally, soft

ω

-

T_{2}

as a new soft topological property that lies strictly between soft

T_{2}

and soft

T_{1}

is defined and investigated. It is proved that soft anti-local countability is a sufficient condition for equivalence between soft

ω

-locally indiscreetness (resp. soft

ω

-regularity) and soft locally indiscreetness (resp. soft

ω

-regularity). Additionally, it is proved that the induced topological spaces of a soft

ω

-locally indiscrete (resp. soft

ω

-regular, soft

ω

-

T_{2}

) soft topological space are (resp.

ω

-regular,

ω

-

T_{2}

) topological spaces. Additionally, it is proved that the generated soft topological space of a family of

ω

-locally indiscrete (resp.

ω

-regular,

ω

-

T_{2}

) topological spaces is soft

ω

-locally indiscrete and vice versa. In addition to these, soft product theorems regarding soft

ω

-regular and soft

ω

-

T_{2}

soft topological spaces are obtained. Moreover, it is proved that soft

ω

-regular and soft

ω

-

T_{2}

are hereditarily under soft subspaces. Full article

(This article belongs to the Special Issue Computing Mathematics with Fuzzy Sets)

9 pages, 269 KiB

Open AccessArticle

On a One-Dimensional Hydrodynamic Model for Semiconductors with Field-Dependent Mobility

by Giuseppe Alì, Francesco Lamonaca, Carmelo Scuro and Isabella Torcicollo

Mathematics 2021, 9(17), 2152; https://doi.org/10.3390/math9172152 - 3 Sep 2021

Cited by 4 | Viewed by 1953

Abstract

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that [...] Read more.

We consider a one-dimensional, isentropic, hydrodynamical model for a unipolar semiconductor, with the mobility depending on the electric field. The mobility is related to the momentum relaxation time, and field-dependent mobility models are commonly used to describe the occurrence of saturation velocity, that is, a limit value for the electron mean velocity as the electric field increases. For the steady state system, we prove the existence of smooth solutions in the subsonic case, with a suitable assumption on the mobility function. Furthermore, we prove uniqueness of subsonic solutions for sufficiently small currents. Full article

(This article belongs to the Special Issue Modeling and Numerical Analysis of Energy and Environment 2021)

20 pages, 1593 KiB

Open AccessArticle

Instruments and Methods for Identifying Indicators of a Digital Entrepreneurial System

by Jelena Raut, Đorđe Ćelić, Branislav Dudić, Jelena Ćulibrk and Darko Stefanović

Mathematics 2021, 9(17), 2151; https://doi.org/10.3390/math9172151 - 3 Sep 2021

Cited by 3 | Viewed by 2361

Abstract

Entrepreneurial ecosystems are the main driver of the widespread trend of digitalization, and they open opportunities for the advancement of the digital economy. The digital economy makes its progress through innovative enterprises that can ensure global progress. In order to effectively use the [...] Read more.

Entrepreneurial ecosystems are the main driver of the widespread trend of digitalization, and they open opportunities for the advancement of the digital economy. The digital economy makes its progress through innovative enterprises that can ensure global progress. In order to effectively use the opportunities that open up the process of digitalization, information is needed on how much the Republic of Serbia is able to support the process of discovering entrepreneurship, which is stimulated by digitalization, which is the subject of this paper. The aim of this paper is to analyze the digital entrepreneurial system of the Republic of Serbia, as well as to identify indicators that hinder the development of this system, using appropriate instruments and methods that will be presented in detail in the paper. The results have demonstrated that the starting point for improvement of the digital entrepreneurial system is in the field of finance, with a particular focus on companies in the startup and stand-up phases. Furthermore, a comparative analysis will showcase the digital entrepreneurial system of the Republic of Serbia and the member states of the European Union, where it will be seen that the digital entrepreneurial system of the Republic of Serbia is lagging behind the member states of the European Union in its growth and development. The results will serve as the starting point for policymakers to improve the process of digitalization and the digital entrepreneurial system as a whole. The results show the starting point for the improvement of entrepreneurship in the Republic of Serbia, that is, how small, and medium-sized enterprises can be encouraged on the path to their successful management. Full article

(This article belongs to the Special Issue Recent Advances in Business and Industry: Mathematical Analysis, Sustainability Assessment Instruments and Methods)

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12 pages, 281 KiB

Open AccessArticle

The Link between Corporate Reputation and Financial Performance and Equilibrium within the Airline Industry

by Andreas-Daniel Cocis, Larissa Batrancea and Horia Tulai

Mathematics 2021, 9(17), 2150; https://doi.org/10.3390/math9172150 - 3 Sep 2021

Cited by 11 | Viewed by 4040

Abstract

This study examines how corporate reputation is perceived by investors through the financial performance and equilibrium of several airline companies. We used a sample of 22 companies. Nineteen are listed in the World Airline Awards 2018 ranking based on client satisfaction, and three [...] Read more.

This study examines how corporate reputation is perceived by investors through the financial performance and equilibrium of several airline companies. We used a sample of 22 companies. Nineteen are listed in the World Airline Awards 2018 ranking based on client satisfaction, and three companies are included in the Fortune ranking and enjoying the best corporate reputations in the airline industry. The analyzed period was 2016–2018. The purpose of this study was to rank airline companies based on financial indicators by means of the TOPSIS method to see whether the companies included in the Fortune ranking would keep a similar hierarchy. Results indicated that companies maintained a similar order in the TOPSIS ranking after considering financial performance and equilibrium indicators. The overall conclusion was that companies with a good financial performance and equilibrium enjoyed a good corporate reputation from investors’ point of view. Full article

(This article belongs to the Special Issue Statistical Methods of Analyzing Financial Equilibrium, Performance and Risk)

15 pages, 2618 KiB

Open AccessArticle

Time-Delay Synchronization and Anti-Synchronization of Variable-Order Fractional Discrete-Time Chen–Rossler Chaotic Systems Using Variable-Order Fractional Discrete-Time PID Control

by Joel Perez Padron, Jose Paz Perez, José Javier Pérez Díaz and Atilano Martinez Huerta

Mathematics 2021, 9(17), 2149; https://doi.org/10.3390/math9172149 - 3 Sep 2021

Cited by 7 | Viewed by 1848

Abstract

In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory [...] Read more.

In this research paper, we solve the problem of synchronization and anti-synchronization of chaotic systems described by discrete and time-delayed variable fractional-order differential equations. To guarantee the synchronization and anti-synchronization, we use the well-known PID (Proportional-Integral-Derivative) control theory and the Lyapunov–Krasovskii stability theory for discrete systems of a variable fractional order. We illustrate the results obtained through simulation with examples, in which it can be seen that our results are satisfactory, thus achieving synchronization and anti-synchronization of chaotic systems of a variable fractional order with discrete time delay. Full article

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Figure 1
Phase portrait of discrete-time chaotic Chen system. Full article ">Figure 2
Phase portrait of discrete-time chaotic Rossler system. Full article ">Figure 3
Time response (a–c) of synchronized states of master and slave. Full article ">Figure 4
Phase space of synchronization of original master–slave system. Full article ">Figure 5
Phase space of synchronization of master–slave system with fractional order given by c = 0.9, c1 = 0.8, c2 = 0.7. Full article ">Figure 6
Synchronization errors with time delay between states of master and slave system of variable fractional order derivative. Full article ">Figure 7
Time response (a–c) of synchronized states of master and slave. Full article ">Figure 8
Phase space of anti-synchronization of an original master–slave system. Full article ">Figure 9
Phase space of anti-synchronization of master–slave systems with fractional orders given by c = 0.9, c1 = 0.8, and c2 = 0.7. Full article ">Figure 10
Anti-synchronization errors with time delay between states of master and slave systems of a variable fractional-order derivative. Full article ">

16 pages, 18541 KiB

Open AccessArticle

Planar Typical Bézier Curves with a Single Curvature Extremum

by Chuan He, Gang Zhao, Aizeng Wang, Shaolin Li and Zhanchuan Cai

Mathematics 2021, 9(17), 2148; https://doi.org/10.3390/math9172148 - 3 Sep 2021

Cited by 2 | Viewed by 2390

Abstract

This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given [...] Read more.

This paper focuses on planar typical Bézier curves with a single curvature extremum, which is a supplement of typical curves with monotonic curvature by Y. Mineur et al. We have proven that the typical curve has at most one curvature extremum and given a fast calculation formula of the parameter at the curvature extremum. This will allow designers to execute a subdivision at the curvature extremum to obtain two pieces of typical curves with monotonic curvature. In addition, we put forward a sufficient condition for typical curve solutions under arbitrary degrees for the G1 interpolation problem. Some numerical experiments are provided to demonstrate the effectiveness and efficiency of our approach. Full article

(This article belongs to the Special Issue Approximation Theory and Methods 2020)

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