Journal Description
Mathematics
Mathematics
is a peer-reviewed, open access journal which provides an advanced forum for studies related to mathematics, and is published semimonthly online by MDPI. The European Society for Fuzzy Logic and Technology (EUSFLAT) and International Society for the Study of Information (IS4SI) are affiliated with Mathematics and their members receive a discount on article processing charges.
- Open Access— free for readers, with article processing charges (APC) paid by authors or their institutions.
- High Visibility: indexed within Scopus, SCIE (Web of Science), RePEc, and many other databases.
- Journal Rank: JCR - Q1 (Mathematics) / CiteScore - Q1 (General Mathematics)
- Rapid Publication: manuscripts are peer-reviewed and a first decision provided to authors approximately 19 days after submission; acceptance to publication is undertaken in 3.6 days (median values for papers published in this journal in the second half of 2021).
- Recognition of Reviewers: reviewers who provide timely, thorough peer-review reports receive vouchers entitling them to a discount on the APC of their next publication in any MDPI journal, in appreciation of the work done.
- Sections: published in 13 topical sections.
- Companion journals for Mathematics include: Foundations, AppliedMath and Analytics.
Impact Factor:
2.258 (2020)
;
5-Year Impact Factor:
2.165 (2020)
Latest Articles
Measuring the Attractiveness of Cities to Receive Investments in Regional Airport Infrastructure
Mathematics 2022, 10(10), 1734; https://doi.org/10.3390/math10101734 (registering DOI) - 19 May 2022
Abstract
The vast Brazilian territory and the accelerated economic growth of the cities of the country’s interior in recent years have created a favourable environment for the expansion of regional aviation. In 2015, the Brazilian Government launched a program of investments in regional airports
[...] Read more.
The vast Brazilian territory and the accelerated economic growth of the cities of the country’s interior in recent years have created a favourable environment for the expansion of regional aviation. In 2015, the Brazilian Government launched a program of investments in regional airports equipping them to receive commercial flights. However, the economic crisis and the scarcity of resources drive the prioritisation of projects with a greater economic and social return. This article aims to present a multicriteria decision aid (MCDA) model to measure cities’ attractiveness to receive investments in regional airports. The MCDA approach can deal with multiple indicators and different points of view and provide systematised steps for supporting decision-makers. For this purpose, we selected 12 criteria among the evaluation parameters identified in the literature, which led to the construction of the evaluation model and elaborating the ranking of the localities participating in the investment program. This study can contribute scientifically by proposing the use of an MCDA approach to support decisions related to logistics and infrastructure. It can help managers and practitioners provide a structured and systematised model to address decisions related to airport investments.
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(This article belongs to the Topic Multi-Criteria Decision Making)
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Sequence-to-Sequence Remaining Useful Life Prediction of the Highly Maneuverable Unmanned Aerial Vehicle: A Multilevel Fusion Transformer Network Solution
Mathematics 2022, 10(10), 1733; https://doi.org/10.3390/math10101733 - 18 May 2022
Abstract
The remaining useful life (RUL) of the unmanned aerial vehicle (UAV) is primarily determined by the discharge state of the lithium-polymer battery and the expected flight maneuver. It needs to be accurately predicted to measure the UAV’s capacity to perform future missions. However,
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The remaining useful life (RUL) of the unmanned aerial vehicle (UAV) is primarily determined by the discharge state of the lithium-polymer battery and the expected flight maneuver. It needs to be accurately predicted to measure the UAV’s capacity to perform future missions. However, the existing works usually provide a one-step prediction based on a single feature, which cannot meet the reliability requirements. This paper provides a multilevel fusion transformer-network-based sequence-to-sequence model to predict the RUL of the highly maneuverable UAV. The end-to-end method is improved by introducing the external factor attention and multi-scale feature mining mechanism. Simulation experiments are conducted based on a high-fidelity quad-rotor UAV electric propulsion model. The proposed method can rapidly predict more precisely than the state-of-the-art. It can predict the future RUL sequence by four-times the observation length (32 s) with a precision of 83% within 60 ms.
Full article
(This article belongs to the Special Issue Advances of Intelligent Systems and Computing)
Open AccessArticle
Optimal Breeding Strategy for Livestock with a Dynamic Price
Mathematics 2022, 10(10), 1732; https://doi.org/10.3390/math10101732 - 18 May 2022
Abstract
China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of
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China’s livestock output has been growing, but domestic livestock products such as beef, mutton and pork have been unable to meet domestic consumers’ demands. The imbalance between supply and demand causes unstable livestock prices and affects profits on livestock. Therefore, the purpose of this paper is to provide the optimal breeding strategy for livestock farmers to maximize profits and adjust the balance between supply and demand. Firstly, when the price changes, livestock farmers will respond in two ways: by not adjusting the scale of livestock with the price or adjusting the scale with the price. Therefore, combining the model of price and the behavior of livestock farmers, two livestock breeding models were established. Secondly, we proposed four optimal breeding strategies based on the previously studied models and the main research method is Pontryagin’s Maximum Principle. Optimal breeding strategies are achieved by controlling the growth and output of livestock. Further, their existence was verified. Finally, we simulated two situations and found the most suitable strategy for both situations by comparing profits of four strategies. From that, we obtained several conclusions: The optimal strategy under constant prices is not always reasonable. The effect of price on livestock can promote a faster balance. To get more profits, the livestock farmers should adjust the farm’s productivity reasonably. It is necessary to calculate the optimal strategy results under different behaviors.
Full article
(This article belongs to the Special Issue Mathematical Population Dynamics and Epidemiology)
Open AccessArticle
A Note on Generalized Quasi-Einstein and (λ, n + m)-Einstein Manifolds with Harmonic Conformal Tensor
Mathematics 2022, 10(10), 1731; https://doi.org/10.3390/math10101731 - 18 May 2022
Abstract
Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a
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Sufficient conditions for a Lorentzian generalized quasi-Einstein manifold to be a generalized Robertson–Walker spacetime with Einstein fibers are derived. The Ricci tensor in this case gains the perfect fluid form. Likewise, it is proven that a -Einstein manifold having harmonic Weyl tensor, and reduces to a perfect fluid generalized Robertson–Walker spacetime with Einstein fibers. Finally, reduces to a perfect fluid manifold if is a -vector field on M and to an Einstein manifold if is a -vector field on M. Some consequences of these results are considered.
Full article
(This article belongs to the Special Issue Differential Geometry of Spaces with Special Structures)
Open AccessArticle
A Modified Conjugate Residual Method and Nearest Kronecker Product Preconditioner for the Generalized Coupled Sylvester Tensor Equations
Mathematics 2022, 10(10), 1730; https://doi.org/10.3390/math10101730 - 18 May 2022
Abstract
This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor
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This paper is devoted to proposing a modified conjugate residual method for solving the generalized coupled Sylvester tensor equations. To further improve its convergence rate, we derive a preconditioned modified conjugate residual method based on the Kronecker product approximations for solving the tensor equations. A theoretical analysis shows that the proposed method converges to an exact solution for any initial tensor at most finite steps in the absence round-off errors. Compared with a modified conjugate gradient method, the obtained numerical results illustrate that our methods perform much better in terms of the number of iteration steps and computing time.
Full article
(This article belongs to the Special Issue Selected Papers from The China-Korea-USA International Conference on Matrix Theory with Applications)
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Open AccessArticle
Study of Solutions for a Degenerate Reaction Equation with a High Order Operator and Advection
Mathematics 2022, 10(10), 1729; https://doi.org/10.3390/math10101729 - 18 May 2022
Abstract
The goal of the present study is to characterize solutions under a travelling wave formulation to a degenerate Fisher-KPP problem. With the degenerate problem, we refer to the following: a heterogeneous diffusion that is formulated with a high order operator; a non-linear advection
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The goal of the present study is to characterize solutions under a travelling wave formulation to a degenerate Fisher-KPP problem. With the degenerate problem, we refer to the following: a heterogeneous diffusion that is formulated with a high order operator; a non-linear advection and non-Lipstchitz spatially heterogeneous reaction. The paper examines the existence of solutions, uniqueness and travelling wave oscillatory properties (also called instabilities). Such oscillatory behaviour may lead to negative solutions in the proximity of zero. A numerical exploration is provided with the following main finding to declare: the solutions keeps oscillating in the proximity of the null stationary solution due to the high order operator, except if the reaction term is quasi-Lipschitz, in which it is possible to define a region where solutions are positive locally in time.
Full article
(This article belongs to the Special Issue Recent Advances in Oscillation Theory of Differential Equations: Problems, Solutions and Applications)
Open AccessArticle
Mathematics 2022, 10(10), 1728; https://doi.org/10.3390/math10101728 - 18 May 2022
Abstract
This paper mainly considers a class of non-weight modules over the Lie algebra of the Weyl type. First, we construct the -free modules of rank one over the differential operator algebra. Then, we characterize the tensor products of these
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This paper mainly considers a class of non-weight modules over the Lie algebra of the Weyl type. First, we construct the -free modules of rank one over the differential operator algebra. Then, we characterize the tensor products of these kind of modules and the quasi-finite highest weight modules. Finally, we undertake such research for the differential operator algebra of multi-variables.
Full article
(This article belongs to the Special Issue Rota-Baxter Algebra and Related Topics)
Open AccessArticle
Generalized Wintgen Inequality for Statistical Submanifolds in Hessian Manifolds of Constant Hessian Curvature
Mathematics 2022, 10(10), 1727; https://doi.org/10.3390/math10101727 - 18 May 2022
Abstract
The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who
[...] Read more.
The geometry of Hessian manifolds is a fruitful branch of physics, statistics, Kaehlerian and affine differential geometry. The study of inequalities for statistical submanifolds in Hessian manifolds of constant Hessian curvature was truly initiated in 2018 by Mihai, A. and Mihai, I. who dealt with Chen-Ricci and Euler inequalities. Later on, Siddiqui, A.N., Ahmad K. and Ozel C. came with the study of Casorati inequality for statistical submanifolds in the same ambient space by using algebraic technique. Also, Chen, B.-Y., Mihai, A. and Mihai, I. obtained a Chen first inequality for such submanifolds. In 2020, Mihai, A. and Mihai, I. studied the Chen inequality for -invariant. In the development of this topic, we establish the generalized Wintgen inequality for statistical submanifolds in Hessian manifolds of constant Hessian curvature. Some examples are also discussed at the end.
Full article
(This article belongs to the Special Issue Geometry of Manifolds and Applications)
Open AccessArticle
Identification and Classification of Aggregation Operators Using Bipolar Complex Fuzzy Settings and Their Application in Decision Support Systems
Mathematics 2022, 10(10), 1726; https://doi.org/10.3390/math10101726 - 18 May 2022
Abstract
The idea of bipolar complex fuzzy (BCF) sets, as a genuine modification of both bipolar fuzzy sets and complex fuzzy sets, gives a massive valuable framework for representing and evaluating ambiguous information. In intelligence decision making based on BCF sets, it is a
[...] Read more.
The idea of bipolar complex fuzzy (BCF) sets, as a genuine modification of both bipolar fuzzy sets and complex fuzzy sets, gives a massive valuable framework for representing and evaluating ambiguous information. In intelligence decision making based on BCF sets, it is a critical dilemma to compare or rank positive and negative membership grades. In this framework, we deliberated various techniques for aggregating the collection of information into a singleton set, called BCF weighted arithmetic averaging (BCFWAA), BCF ordered weighted arithmetic averaging (BCFOWAA), BCF weighted geometric averaging (BCFWGA), and BCF ordered weighted geometric averaging (BCFOWGA) operators for BCF numbers (BCFNs). To illustrate the feasibility and original worth of the diagnosed approaches, we demonstrated various properties of the diagnosed operators, in addition to their capability that the evaluated value of a set of BCF numbers is a unique BCF number. Further, multiattribute decision making (“MADM”) refers to a technique employed to compute a brief and dominant assessment of opinions with multiattributes. The main influence of this theory is implementing the diagnosed theory in the field of the MADM tool using BCF settings. Finally, a benchmark dilemma is used for comparison with various prevailing techniques to justify the cogency and dominancy of the evaluated operators.
Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making under Fuzzy Information)
Open AccessArticle
State Estimation for Complex-Valued Inertial Neural Networks with Multiple Time Delays
by
and
Mathematics 2022, 10(10), 1725; https://doi.org/10.3390/math10101725 - 18 May 2022
Abstract
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix
[...] Read more.
In this paper, the problem of state estimation for complex-valued inertial neural networks with leakage, additive and distributed delays is considered. By means of the Lyapunov–Krasovskii functional method, the Jensen inequality, and the reciprocally convex approach, a delay-dependent criterion based on linear matrix inequalities (LMIs) is derived. At the same time, the network state is estimated by observing the output measurements to ensure the global asymptotic stability of the error system. Finally, two examples are given to verify the effectiveness of the proposed method.
Full article
(This article belongs to the Topic Analysis and Controls of Time-Delay Systems with Perturbations: Theory and Application)
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Some Fixed-Point Theorems in Proximity Spaces with Applications
Mathematics 2022, 10(10), 1724; https://doi.org/10.3390/math10101724 - 18 May 2022
Abstract
Considering the -distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using -distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in
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Considering the -distance function defined by Kostić in proximity space, we prove the Matkowski and Boyd–Wong fixed-point theorems in proximity space using -distance, and provide some examples to explain the novelty of our work. Moreover, we characterize Edelstein-type fixed-point theorem in compact proximity space. Finally, we investigate an existence and uniqueness result for solution of a kind of second-order boundary value problem via obtained Matkowski-type fixed-point results under some suitable conditions.
Full article
(This article belongs to the Special Issue New Progress in General Topology and Its Applications)
Open AccessArticle
Supply Chain Pricing Models Considering Risk Attitudes under Free-Riding Behavior
Mathematics 2022, 10(10), 1723; https://doi.org/10.3390/math10101723 - 18 May 2022
Abstract
The free-riding behavior of companies that do not act will bring losses to companies that provide services. A market consists of two secondary supply chains: manufacturers and retailers. Each supply chain can choose to adopt promotional strategies to expand its market demand. This
[...] Read more.
The free-riding behavior of companies that do not act will bring losses to companies that provide services. A market consists of two secondary supply chains: manufacturers and retailers. Each supply chain can choose to adopt promotional strategies to expand its market demand. This paper constructs the centralized decision-making in the supply chain and the Nash game competition model between supply chains and primarily studies the impact of risk aversion and the free-riding coefficient on supply chain pricing, promotion strategy selection, and expected utility. We show that the supply chain with high-risk aversion has relatively low pricing, but the demand and a total expected utility are high. We also identify that, on the premise of the same risk aversion degree of the two supply chains, when the free-riding coefficient between the chains is small and equal, the supply chain tends to implement the promotion strategy. When consumers have the same preference for the products of two retailers, the pricing of the free-riding supply chain increases with the increase in the free-riding coefficient, while the supply chain with a promotion strategy is the opposite. Based on the numerical results, we further give the optimal one-way free-riding coefficient when the two supply chains have the same degree of risk aversion; when there is a bidirectional free-riding behavior in the market, competition among supply chains gradually tends to the first two scenarios.
Full article
(This article belongs to the Topic Game Theory and Applications)
Open AccessArticle
“Mixed” Meshless Time-Domain Adaptive Algorithm for Solving Elasto-Dynamics Equations
Mathematics 2022, 10(10), 1722; https://doi.org/10.3390/math10101722 - 18 May 2022
Abstract
A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in
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A time-domain adaptive algorithm was developed for solving elasto-dynamics problems through a mixed meshless local Petrov-Galerkin finite volume method (MLPG5). In this time-adaptive algorithm, each time-dependent variable is interpolated by a time series function of n-order, which is determined by a criterion in each step. The high-order series of expanded variables bring high accuracy in the time domain, especially for the elasto-dynamic equations, which are second-order PDE in the time domain. In the present mixed MLPG5 dynamic formulation, the strains are interpolated independently, as are displacements in the local weak form, which eliminates the expensive differential of the shape function. In the traditional MLPG5, both shape function and its derivative for each node need to be calculated. By taking the Heaviside function as the test function, the local domain integration of stiffness matrix is avoided. Several numerical examples, including the comparison of our method, the MLPG5–Newmark method and FEM (ANSYS) are given to demonstrate the advantages of the presented method: (1) a large time step can be used in solving a elasto-dynamics problem; (2) computational efficiency and accuracy are improved in both space and time; (3) smaller support sizes can be used in the mixed MLPG5.
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(This article belongs to the Special Issue Numerical Simulation and Computational Methods in Engineering and Sciences)
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Open AccessEditorial
Preface to the Special Issue on “Advances in Artificial Intelligence: Models, Optimization, and Machine Learning”
Mathematics 2022, 10(10), 1721; https://doi.org/10.3390/math10101721 - 18 May 2022
Abstract
Recent advancements in artificial intelligence and machine learning have led to the development of powerful tools for use in problem solving in a wide array of scientific and technical fields [...]
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(This article belongs to the Special Issue Advances in Artificial Intelligence: Models, Optimization, and Machine Learning)
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A Correlational Predictive Study of Teacher Well-Being and Professional Success in Foreign Language Student Teachers
Mathematics 2022, 10(10), 1720; https://doi.org/10.3390/math10101720 - 18 May 2022
Abstract
The teaching profession has an important emotional burden that, together with the erosion of different elements that compose it from continuous educational reform to the bad behavior and demotivation of students has led to many teachers experiencing physical and psychological illness or leaving
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The teaching profession has an important emotional burden that, together with the erosion of different elements that compose it from continuous educational reform to the bad behavior and demotivation of students has led to many teachers experiencing physical and psychological illness or leaving the profession. Nevertheless, studies and interventions in this regard are still insufficient in the Spanish context. This situation also exponentially affects pre-service teachers, which according to numerous studies is the stage during which the diminishing of teacher well-being begins and consolidates. Within this panorama, with this study the authors pursue to determine which dimensions of teacher well-being are capable of predicting the professional success of 88 pre-service primary education teachers who specialize in a foreign language so that they can be addressed in the training process. To this end, an ex post facto study was carried out correlating the following instruments: the Teacher Distress Questionnaire, the Trait Emotional Intelligence Questionnaire and the Maslach Burnout Inventory-Educators Survey with an adaptation of the Rueda de la vida escolar sobre el éxito y la satisfacción laboral del docente (Wheel of school life on teacher success and job satisfaction). Multiple linear regression revealed that of all the variables studied for teacher well-being (intrinsic motivation, expectations about good professional performance, professional distress, professional exhaustion, irrational beliefs, emotional intelligence and burnout) only emotional intelligence and intrinsic motivation have the ability to predict the success of teachers in training in their future professional performance. This result is of paramount importance for reconsidering the training that teachers receive during their university stage, which currently and substantially prioritizes the cognitive component over psychosocial and emotional components.
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(This article belongs to the Special Issue Advances in the Scientific Interplay of Mathematics and Language, Literature, and Education)
Open AccessArticle
New Properties and Identities for Fibonacci Finite Operator Quaternions
Mathematics 2022, 10(10), 1719; https://doi.org/10.3390/math10101719 - 17 May 2022
Abstract
In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions. Moreover, we derive many identities
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In this paper, with the help of the finite operators and Fibonacci numbers, we define a new family of quaternions whose components are the Fibonacci finite operator numbers. We also provide some properties of these types of quaternions. Moreover, we derive many identities related to Fibonacci finite operator quaternions by using the matrix representations.
Full article
(This article belongs to the Special Issue Algebraic, Analytic, and Computational Number Theory and Its Applications)
Open AccessArticle
Using Augmented Reality to Enhance Students’ Representational Fluency: The Case of Linear Functions
Mathematics 2022, 10(10), 1718; https://doi.org/10.3390/math10101718 - 17 May 2022
Abstract
Using multiple representations is advocated and emphasized in mathematics and science education. However, many students have difficulty connecting multiple representations of linear functions. Augmented Reality (AR) may affect these teaching and learning difficulties by offering dynamically linked representations. Inspired by this, our study
[...] Read more.
Using multiple representations is advocated and emphasized in mathematics and science education. However, many students have difficulty connecting multiple representations of linear functions. Augmented Reality (AR) may affect these teaching and learning difficulties by offering dynamically linked representations. Inspired by this, our study aims to develop, implement, and evaluate an AR-based multi-representational learning environment (MRLE) with three representations of linear functions. The data were collected from 82 seventh graders from two high-performing classes in an urban area in China, through a pre-test, a post-questionnaire, and follow-up interviews. The results reveal that students were satisfied with the AR-based MRLE, which assisted in enhancing their understanding of the real-life, symbolic, and graphical representations and connections among them. Regarding students’ interactions with multiple representations, apparent differences in learning sequences and preferences existed among students in terms of their representational learning profile. In sum, learning in the AR-based MRLE is a complex interaction process between the mathematics content, forms of representations, digital features, and students’ representational learning profile.
Full article
(This article belongs to the Special Issue International Perspectives for Technology Applications in Mathematics Education)
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Maximal Regularity Estimates and the Solvability of Nonlinear Differential Equations
by
and
Mathematics 2022, 10(10), 1717; https://doi.org/10.3390/math10101717 - 17 May 2022
Abstract
We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. We also consider a non-linear generalization with coefficients that depends on an unknown function. We establish sufficient conditions for the correctness of
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We study a type of third-order linear differential equations with variable and unbounded coefficients, which are defined in an infinite interval. We also consider a non-linear generalization with coefficients that depends on an unknown function. We establish sufficient conditions for the correctness of this linear equation and the maximal regularity estimate for their solution. Using these results, we prove the solvability of a nonlinear differential equation and estimate the norms of its terms.
Full article
(This article belongs to the Special Issue Mathematical Models and Methods in Engineering and Social Sciences)
Open AccessArticle
Inventory Management of Perishable Goods with Overconfident Retailers
Mathematics 2022, 10(10), 1716; https://doi.org/10.3390/math10101716 - 17 May 2022
Abstract
In recent years, many retailers sell their products through not only offline but also online platforms. The sales of perishable goods on e-commerce platforms recorded phenomenal growth in 2020. However, some retailers are overconfident and order more products than the optimal ordering quantity,
[...] Read more.
In recent years, many retailers sell their products through not only offline but also online platforms. The sales of perishable goods on e-commerce platforms recorded phenomenal growth in 2020. However, some retailers are overconfident and order more products than the optimal ordering quantity, resulting in great losses due to product decay. In this paper, we apply the newsvendor model to analyze the impacts of overconfident behavior on the retailer’s optimal pricing and order quantity decisions and profit. Our model provides the overconfident retailer with a feasible and effective method to adjust optimal ordering and pricing decisions. Through numerical studies, we examine the retailer’s optimal decisions under the scenarios of complete rationality, over-estimation, and over-precision. We find that the over-estimation retailer always orders more products than the optimal order quantity, and the over-precision retailer always orders fewer products than the optimal order quantity. Under some conditions, overconfidence hurts the retailer’s revenue to a large extent. Therefore, it is beneficial for the overconfident retailer to adjust its order quantity according to our research findings.
Full article
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity II)
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Design of an NSMCR Based Controller for All-Electric Aircraft Anti-Skid Braking System
Mathematics 2022, 10(10), 1715; https://doi.org/10.3390/math10101715 - 17 May 2022
Abstract
In this paper, a relative threshold event-triggered based novel complementary sliding mode control (NSMCR) algorithm of all-electric aircraft (AEA) anti-skid braking system (ABS) is proposed to guarantee the braking stability and tracking precision of reference wheel slip control. First, a model of the
[...] Read more.
In this paper, a relative threshold event-triggered based novel complementary sliding mode control (NSMCR) algorithm of all-electric aircraft (AEA) anti-skid braking system (ABS) is proposed to guarantee the braking stability and tracking precision of reference wheel slip control. First, a model of the braking system is established in strict-feedback form. Then a virtual controller with a nonlinear control algorithm is proposed to address the problem of constraint control regarding wheel slip rate with asymptotical stability. Next, a novel approaching law-based complementary sliding mode controller is developed to keep track of braking pressure. Moreover, the robust adaptive law is designed to estimate the uncertainties of the braking systems online to alleviate the chattering problem of the braking pressure controller. Additionally, to reduce the network communication and actuator wear of AEA-ABS, a relative threshold event trigger mechanism is proposed to transmit the output of NSMC in demand. The simulation results under various algorithms regarding three types of runway indicate that the proposed algorithms can improve the performance of braking control. In addition, the hardware-in-the-loop (HIL) experimental results prove that the proposed methods are practical for real-time applications.
Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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