Next Issue
Volume 10, May-1
Previous Issue
Volume 10, April-1
 
 

Mathematics, Volume 10, Issue 8 (April-2 2022) – 150 articles

Cover Story (view full-size image):

Lepage forms represent a far-going generalization of a 1-form, introduced by E. Cartan in the 1920s within the framework of the calculus of variations of simple integrals and classical mechanics. The generalization, offered by D. Krupka, is motivated by the work of Th. Lepage in the 1940s. These objects define the same variational functional as it is prescribed by a given Lagrangian, and moreover, variational objects (as variations, extremals, or Noether’s type invariance) are globally characterized in terms of geometric operations acting on the Lepage equivalents of a Lagrangian.

Here, a second-order extension of the fundamental Lepage form of the calculus of variations over fibered manifolds with 2-dimensional base is described via order-reducibility of the generalized Poincaré–Cartan form. View this paper

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Readerexternal link to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:
Article
Fourth Cumulant Bound of Multivariate Normal Approximation on General Functionals of Gaussian Fields
Mathematics 2022, 10(8), 1352; https://doi.org/10.3390/math10081352 - 18 Apr 2022
Cited by 1 | Viewed by 706
Abstract
We develop a technique for obtaining the fourth moment bound on the normal approximation of F, where F is an Rd-valued random vector whose components are functionals of Gaussian fields. This study transcends the case of vectors of multiple stochastic [...] Read more.
We develop a technique for obtaining the fourth moment bound on the normal approximation of F, where F is an Rd-valued random vector whose components are functionals of Gaussian fields. This study transcends the case of vectors of multiple stochastic integrals, which has been the subject of research so far. We perform this task by investigating the relationship between the expectations of two operators Γ and Γ*. Here, the operator Γ was introduced in Noreddine and Nourdin (2011) [On the Gaussian approximation of vector-valued multiple integrals. J. Multi. Anal.], and Γ* is a muilti-dimensional version of the operator used in Kim and Park (2018) [An Edgeworth expansion for functionals of Gaussian fields and its applications, stoch. proc. their Appl.]. In the specific case where F is a random variable belonging to the vector-valued multiple integrals, the conditions in the general case of F for the fourth moment bound are naturally satisfied and our method yields a better estimate than that obtained by the previous methods. In the case of d=1, the method developed here shows that, even in the case of general functionals of Gaussian fields, the fourth moment theorem holds without conditions for the multi-dimensional case. Full article
(This article belongs to the Special Issue Probability, Stochastic Processes and Optimization)
Article
A Comparative Study of SSA-BPNN, SSA-ENN, and SSA-SVR Models for Predicting the Thickness of an Excavation Damaged Zone around the Roadway in Rock
Mathematics 2022, 10(8), 1351; https://doi.org/10.3390/math10081351 - 18 Apr 2022
Cited by 4 | Viewed by 817
Abstract
Due to the disturbance effect of excavation, the original stress is redistributed, resulting in an excavation damaged zone around the roadway. It is significant to predict the thickness of an excavation damaged zone because it directly affects the stability of roadways. This study [...] Read more.
Due to the disturbance effect of excavation, the original stress is redistributed, resulting in an excavation damaged zone around the roadway. It is significant to predict the thickness of an excavation damaged zone because it directly affects the stability of roadways. This study used a sparrow search algorithm to improve a backpropagation neural network, and an Elman neural network and support vector regression models to predict the thickness of an excavation damaged zone. Firstly, 209 cases with four indicators were collected from 34 mines. Then, the sparrow search algorithm was used to optimize the parameters of the backpropagation neural network, Elman neural network, and support vector regression models. According to the optimal parameters, these three predictive models were established based on the training set (80% of the data). Finally, the test set (20% of the data) was used to verify the reliability of each model. The mean absolute error, coefficient of determination, Nash–Sutcliffe efficiency coefficient, mean absolute percentage error, Theil’s U value, root-mean-square error, and the sum of squares error were used to evaluate the predictive performance. The results showed that the sparrow search algorithm improved the predictive performance of the traditional backpropagation neural network, Elman neural network, and support vector regression models, and the sparrow search algorithm–backpropagation neural network model had the best comprehensive prediction performance. The mean absolute error, coefficient of determination, Nash–Sutcliffe efficiency coefficient, mean absolute percentage error, Theil’s U value, root-mean-square error, and sum of squares error of the sparrow search algorithm–backpropagation neural network model were 0.1246, 0.9277, −1.2331, 8.4127%, 0.0084, 0.1636, and 1.1241, respectively. The proposed model could provide a reliable reference for the thickness prediction of an excavation damaged zone, and was helpful in the risk management of roadway stability. Full article
(This article belongs to the Topic Artificial Intelligence (AI) Applied in Civil Engineering)
Show Figures

Figure 1

Article
A New Alternative Regularization Method for Solving Generalized Equilibrium Problems
Mathematics 2022, 10(8), 1350; https://doi.org/10.3390/math10081350 - 18 Apr 2022
Cited by 2 | Viewed by 644
Abstract
The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’s extragradient method and [...] Read more.
The purpose of this paper is to present a numerical method for solving a generalized equilibrium problem involving a Lipschitz continuous and monotone mapping in a Hilbert space. The proposed method can be viewed as an improvement of the Tseng’s extragradient method and the regularization method. We show that the iterative process constructed by the proposed method converges strongly to the smallest norm solution of the generalized equilibrium problem. Several numerical experiments are also given to illustrate the performance of the proposed method. One of the advantages of the proposed method is that it requires no knowledge of Lipschitz-type constants. Full article
Show Figures

Figure 1

Article
The Dynamics between Structural Conditions and Entrepreneurship in Europe: Feature Extraction and System GMM Approaches
Mathematics 2022, 10(8), 1349; https://doi.org/10.3390/math10081349 - 18 Apr 2022
Viewed by 754
Abstract
Structural conditions and population characteristics of countries have been identified in the literature as factors for an individual to become, or to have intentions of becoming, an entrepreneur. However, this is still a subject under research, which has become increasingly relevant and could [...] Read more.
Structural conditions and population characteristics of countries have been identified in the literature as factors for an individual to become, or to have intentions of becoming, an entrepreneur. However, this is still a subject under research, which has become increasingly relevant and could be crucial in the current challenges of European countries. In this work, the factors for entrepreneurial intentions and entrepreneurship activity are studied. More precisely, the structural conditions of European countries, which has changed over the last two decades, is analysed. The aim is to describe this behaviour and to state the main conditions for developing entrepreneurship activities and the intentions to become an entrepreneur. To achieve this purpose, feature extraction, namely, principal component analysis and dynamic longitudinal approaches are used. In particular, we propose that the system-generalised method of moments (GMM) model is adequate in this situation. The results suggest that the structure of the European framework conditions for entrepreneurship, obtained using the Factor Analysis year by year, is quite diversified until 2008, while after 2008, it is more stable. Moreover, it is concluded that the conditions associated with entrepreneurial intentions and entrepreneurial activity differ between these two time periods. Hence, the dynamic aspect of the structural conditions that affect entrepreneurial activities or intentions should be acknowledged. Full article
(This article belongs to the Special Issue Industrial Mathematics in Management and Engineering)
Show Figures

Figure 1

Article
Artificial Neural Based Speed and Flux Estimators for Induction Machine Drives with Matlab/Simulink
Mathematics 2022, 10(8), 1348; https://doi.org/10.3390/math10081348 - 18 Apr 2022
Cited by 1 | Viewed by 956
Abstract
In this paper, an Artificial Neural Network (ANN) for accurate estimation of the speed and flux for induction motor (IM) drives has been presented for industrial applications such as electric vehicles (EVs). Two ANN estimators have been designed, one for the rotor speed [...] Read more.
In this paper, an Artificial Neural Network (ANN) for accurate estimation of the speed and flux for induction motor (IM) drives has been presented for industrial applications such as electric vehicles (EVs). Two ANN estimators have been designed, one for the rotor speed estimation and the other for the stator and rotor flux estimation. The input training data has been collected based on the currents and voltage data, while the output training data of the speed and stator and rotor fluxes has been established based on the measured speed and flux estimator-based mathematical model of the IM. The designed ANN estimators can overcome the problem of the parameter’s variations and drift integration problems. Matlab/Simulink has been used to develop and test the ANN estimators. The results prove the ANN estimators’ effectiveness under various operation conditions. Full article
(This article belongs to the Special Issue Modeling and Simulation of Control System)
Show Figures

Figure 1

Article
MHD Natural Convection and Radiation over a Flame in a Partially Heated Semicircular Cavity Filled with a Nanofluid
Mathematics 2022, 10(8), 1347; https://doi.org/10.3390/math10081347 - 18 Apr 2022
Cited by 8 | Viewed by 757
Abstract
The numerical analysis of MHD-free convective heat transfer and its interaction with the radiation over a heated flame inside a porous semicircular cavity loaded with SWCNTs–water nanofluid was explored for the very first time in the present work. The two circular arcs of [...] Read more.
The numerical analysis of MHD-free convective heat transfer and its interaction with the radiation over a heated flame inside a porous semicircular cavity loaded with SWCNTs–water nanofluid was explored for the very first time in the present work. The two circular arcs of the upper wall of the enclosure were preserved at a constant cold temperature, whereas the middle region of it was considered adiabatic. The midland region of the lower wall was heated partially, while other regions were also assumed adiabatic. An internal hot flame was included inside the cavity, while the cavity was exposed to a magnetic field. The results were illustrated for Hartmann number (0 ≤ Ha ≤ 100), Rayleigh number (104 ≤ Ra ≤ 106), heated region length (0.1 ≤ L ≤ 0.3), solid volumetric fraction (0 ≤ φ ≤ 0.04), Darcy number (10−3 ≤ Da ≤ 10−5) and radiation parameter (0 ≤ Rd ≤ 1). It was found that decreasing L is the best option for enhancing natural convection. Moreover, it was noted that (Nuout) is directly proportion to (Ra), (ϕ), (Rd) and (Da) increase. In contrast, it was in reverse proportion to (Ha). Furthermore, the results showed that augmentation of about (4%) and a decrement of (56.55%) are obtained on the average (Nu) on the heated length by increasing the radiation and the Hartmann number, respectively. Moreover, raising the radiation number from (0 to 1) causes an augmentation of about (73%) in the average (Nu) of the heated flame. Results also indicated that increasing the Hartmann number will cause a decrement of about (82.4%) of the maximum velocity profile in the vertical direction. Full article
Show Figures

Figure 1

Article
Sliding Mode Controller Based on the Extended State Observer for Plant-Protection Quadrotor Unmanned Aerial Vehicles
Mathematics 2022, 10(8), 1346; https://doi.org/10.3390/math10081346 - 18 Apr 2022
Cited by 1 | Viewed by 812
Abstract
Owing to the complex dynamics of quadrotor unmanned aerial vehicles (UAVs) and their susceptibility to unknown interferences in an actual working environment, the flight control accuracy of UAVs is extremely high. Moreover, their anti-interference ability is particularly important. This study designed a sliding-mode [...] Read more.
Owing to the complex dynamics of quadrotor unmanned aerial vehicles (UAVs) and their susceptibility to unknown interferences in an actual working environment, the flight control accuracy of UAVs is extremely high. Moreover, their anti-interference ability is particularly important. This study designed a sliding-mode controller based on the extended state observer. The position control was obtained through the outer-loop position controller. The attitude control was determined through the inner-loop attitude controller. The input of the UAV system was obtained through the controller. The boundary-layer function was used to weaken the oscillatory response of the system, and the traditional extended state observer was improved to improve the response speed, robustness, and tracking accuracy of the controller. For the entire process, the input and output state information of the system and total internal and external disturbances were estimated in real-time through the extended state observer. A sliding-mode control law was designed to compensate for the estimated disturbance in real-time to realize attitude control. Finally, Lyapunov theory was used to confirm the stability of the system. The simulation results demonstrated the improved anti-interference and tracking ability of the designed controller. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
Show Figures

Figure 1

Article
Diffusion Mechanism of Slurry during Grouting in a Fractured Aquifer: A Case Study in Chensilou Coal Mine, China
Mathematics 2022, 10(8), 1345; https://doi.org/10.3390/math10081345 - 18 Apr 2022
Cited by 2 | Viewed by 719
Abstract
Grouting is one of the main technical means to prevent water inrush hazards in coal seam floor aquifers. It is of great significance to elucidate the diffusion law of slurry in the process of grouting in fractured aquifers for safe mining in coal [...] Read more.
Grouting is one of the main technical means to prevent water inrush hazards in coal seam floor aquifers. It is of great significance to elucidate the diffusion law of slurry in the process of grouting in fractured aquifers for safe mining in coal mines. In this paper, the mechanism of slurry diffusion in horizontal fractures of fractured aquifers was studied based on the Bingham slurry with time-varying characteristics; additionally, a one-dimensional seepage grouting theoretical model considering the temporal and spatial variation of slurry viscosity under constant grouting rate was established. In this model, the grouting pressure required by the predetermined slurry diffusion radius can be obtained by knowing the grouting hole pressure and injection flow. Slurry properties, fracture parameters, grouting parameters, and water pressure were the parameters affecting the slurry diffusion process. Looking at the problem of water disaster prevention of coal seam floor in the Working Face 2509 of the Chensilou Coal Mine, according to the aquifer parameters and model calculation results, a grouting scheme with a slurry diffusion radius of 20 m and grouting pressure of 12 MPa was proposed. Finally, with the comparative analysis of the transient electromagnetic method (TEM) and water inflow before and after grouting, it was verified that the design grouting pressure and the spacing of grouting holes were reasonable and the grouting effect was good. Full article
Show Figures

Figure 1

Article
Contextual Semantic-Guided Entity-Centric GCN for Relation Extraction
Mathematics 2022, 10(8), 1344; https://doi.org/10.3390/math10081344 - 18 Apr 2022
Viewed by 785
Abstract
Relation extraction tasks aim to predict potential relations between entities in a target sentence. As entity mentions have ambiguity in sentences, some important contextual information can guide the semantic representation of entity mentions to improve the accuracy of relation extraction. However, most existing [...] Read more.
Relation extraction tasks aim to predict potential relations between entities in a target sentence. As entity mentions have ambiguity in sentences, some important contextual information can guide the semantic representation of entity mentions to improve the accuracy of relation extraction. However, most existing relation extraction models ignore the semantic guidance of contextual information to entity mentions and treat entity mentions in and the textual context of a sentence equally. This results in low-accuracy relation extractions. To address this problem, we propose a contextual semantic-guided entity-centric graph convolutional network (CEGCN) model that enables entity mentions to obtain semantic-guided contextual information for more accurate relational representations. This model develops a self-attention enhanced neural network to concentrate on the importance and relevance of different words to obtain semantic-guided contextual information. Then, we employ a dependency tree with entities as global nodes and add virtual edges to construct an entity-centric logical adjacency matrix (ELAM). This matrix can enable entities to aggregate the semantic-guided contextual information with a one-layer GCN calculation. The experimental results on the TACRED and SemEval-2010 Task 8 datasets show that our model can efficiently use semantic-guided contextual information to enrich semantic entity representations and outperform previous models. Full article
Show Figures

Figure 1

Article
The Generalization of the Brusov–Filatova–Orekhova Theory for the Case of Payments of Tax on Profit with Arbitrary Frequency
Mathematics 2022, 10(8), 1343; https://doi.org/10.3390/math10081343 - 18 Apr 2022
Cited by 1 | Viewed by 650
Abstract
Both main theories of capital cost and capital structure—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory—consider the payments of tax on profit once per year, while in real economy these payments are made more frequently (semi-annual, quarterly, monthly etc.). Recently [...] Read more.
Both main theories of capital cost and capital structure—the Brusov–Filatova–Orekhova (BFO) theory and its perpetuity limit, the Modigliani–Miller theory—consider the payments of tax on profit once per year, while in real economy these payments are made more frequently (semi-annual, quarterly, monthly etc.). Recently the Modigliani–Miller theory has been generalized by us for the case of tax on profit payments with an arbitrary frequency. Here for the first time, we generalized the Brusov–Filatova–Orekhova (BFO) theory for this case. The main purpose of the paper is bringing the BFO theory closer to economic practice, taking into account one of the features of the real functioning of companies, the frequent payments of tax on profit. We derive modified BFO formulas and show that: (1) All BFO formulas change; (2) all main financial parameters of the company, such as company value, V, equity cost, ke, and the weighted average cost of capital, WACC, depend on the tax on profit payments frequency. The increase of the frequency of payments of income tax leads to a decrease in the cost of attracting capital, WACC, and increase in the capitalization of the company, V. At a certain age n of the company and at certain frequency of tax on profit payments p, a qualitatively new anomalous effect takes place: the equity cost, ke(L), decreases with an increase in the level of leverage L. This radically changes the company′s dividend policy, since the economically justified amount of the dividends is equal to the cost of equity. For both parties–for the company and for the tax regulator more frequent payments of tax on profit are beneficial: for the company, because this increases the company capitalization, and for the tax regulator, because earlier payments are beneficial for it due to the time value of money. Full article
(This article belongs to the Special Issue Recent Development of Mathematical Methods in Financial Management)
Show Figures

Figure 1

Article
Static and Dynamic Analysis of 6-DOF Quasi-Zero-Stiffness Vibration Isolation Platform Based on Leaf Spring Structure
Mathematics 2022, 10(8), 1342; https://doi.org/10.3390/math10081342 - 18 Apr 2022
Cited by 1 | Viewed by 932
Abstract
Multi-degree-of-freedom isolator with low stiffness is a fair prospect in engineering application. In this paper, a novel 6-DOF QZS vibration isolation platform based on leaf spring structure is presented. Its bearing capacity is provided through four leaf springs, and the quasi-zero-stiffness is realized [...] Read more.
Multi-degree-of-freedom isolator with low stiffness is a fair prospect in engineering application. In this paper, a novel 6-DOF QZS vibration isolation platform based on leaf spring structure is presented. Its bearing capacity is provided through four leaf springs, and the quasi-zero-stiffness is realized by the force balance between the central spring and the suspension spring. 6-DOF vibration isolation is realized by the ball-hinge fixed design of a leaf spring. Through static and dynamic analysis, the following conclusions are brought. The stiffness of the leaf spring and the deformation of the central spring under static load are directly proportional to the bearing capacity of the isolation table. Besides, in order to ensure that the stiffness of the system is close to zero, the stiffness of the suspension spring and the inner spring should be as similar as possible. The vertical and horizontal displacement transmissibility tests of the isolation platform are carried out, in which the jumping phenomenon in the QZS vibration isolation platform is analyzed. By improving the damping of the structure and the length of the suspension spring, the dynamic vibration isolation process of the system can be more stable, the transmissibility can be reduced, and the vibration isolation effect can be enhanced. Full article
(This article belongs to the Special Issue Control Problem of Nonlinear Systems with Applications)
Show Figures

Figure 1

Article
Influence Maximization Based on Snapshot Prediction in Dynamic Online Social Networks
by and
Mathematics 2022, 10(8), 1341; https://doi.org/10.3390/math10081341 - 18 Apr 2022
Viewed by 755
Abstract
With the vigorous development of the mobile Internet, online social networks have greatly changed the way of life of human beings. As an important branch of online social network research, influence maximization refers to finding K nodes in the network to form the [...] Read more.
With the vigorous development of the mobile Internet, online social networks have greatly changed the way of life of human beings. As an important branch of online social network research, influence maximization refers to finding K nodes in the network to form the most influential seed set, which is an abstract model of viral marketing. Most of the current research is based on static network structures, ignoring the important feature of network structures changing with time, which discounts the effect of seed nodes in dynamic online social networks. To address this problem in dynamic online social networks, we propose a novel framework called Influence Maximization based on Prediction and Replacement (IMPR). This framework first uses historical network snapshot information to predict the upcoming network snapshot and then mines seed nodes suitable for the dynamic network based on the predicted result. To improve the computational efficiency, the framework also adopts a fast replacement algorithm to solve the seed nodes between different snapshots. The scheme we adopted exhibits four advantages. First, we extended the classic influence maximization problem to dynamic online social networks and give a formal definition of the problem. Second, a new framework was proposed for this problem and a proof of the solution is given in theory. Third, other classical algorithms for influence maximization can be embedded into our framework to improve accuracy. More importantly, to reveal the performance of the scheme, a series of experiments based on different settings on real dynamic online social network datasets were carried out, and the experimental results are very promising. Full article
(This article belongs to the Special Issue Complex Network Modeling: Theory and Applications)
Show Figures

Figure 1

Article
Combinatorial and Proportional Task: Looking for Intuitive Strategies in Primary Education
Mathematics 2022, 10(8), 1340; https://doi.org/10.3390/math10081340 - 18 Apr 2022
Viewed by 640
Abstract
The development of probabilistic thinking at school requires enhancing combinatorial and proportional reasoning. For this reason, 190 sixth-grade elementary school students (11–12-year-old), without previous instruction in the topic, solve a task consisting of five questions that address both types of reasoning. This study [...] Read more.
The development of probabilistic thinking at school requires enhancing combinatorial and proportional reasoning. For this reason, 190 sixth-grade elementary school students (11–12-year-old), without previous instruction in the topic, solve a task consisting of five questions that address both types of reasoning. This study explores the problem-solving strategies used by schoolchildren. The results obtained indicate that, in general, the students do not show strategies in the answers to the combinatorial questions. In addition, it is observed that they have difficulties in understanding the proposed statements and arguing the issues that explicitly require a justification. Full article
(This article belongs to the Special Issue Statistics Education: An Immediate Need in a Changing World)
Show Figures

Figure 1

Article
Meanings Expressed by Primary Schoolchildren When Solving a Partitioning Task
Mathematics 2022, 10(8), 1339; https://doi.org/10.3390/math10081339 - 18 Apr 2022
Cited by 1 | Viewed by 613
Abstract
This study entailed an in-depth exploration of the meanings identified by a group of 105 fourth year primary schoolchildren when solving a task involving partitioning. The research was based on a semantic triangle consisting of a conceptual structure, representation systems, and sense. The [...] Read more.
This study entailed an in-depth exploration of the meanings identified by a group of 105 fourth year primary schoolchildren when solving a task involving partitioning. The research was based on a semantic triangle consisting of a conceptual structure, representation systems, and sense. The content of children’s answers was analysed qualitatively. One of the most prominent findings was that purposes or usages were recognised based on multiple strategies, new categories of which, not envisaged in earlier research, were defined. Most of the students deployed graphic, verbal, and numerical representation and established relationships among them. Concepts such as the part-whole relationship and fractioning appeared in their description of conceptual structure, although errors were detected in terms of inequities and confusion between numerator and denominator. Full article
Show Figures

Figure 1

Article
An Agent-Based Interpretation of Leukocyte Chemotaxis in Cancer-on-Chip Experiments
Mathematics 2022, 10(8), 1338; https://doi.org/10.3390/math10081338 - 18 Apr 2022
Viewed by 733
Abstract
The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, [...] Read more.
The present paper was inspired by recent developments in laboratory experiments within the framework of cancer-on-chip technology, an immune-oncology microfluidic chip aiming at studying the fundamental mechanisms of immunocompetent behavior. We focus on the laboratory setting where cancer is treated with chemotherapy drugs, and in this case, the effects of the treatment administration hypothesized by biologists are: the absence of migration and proliferation of tumor cells, which are dying; the stimulation of the production of chemical substances (annexin); the migration of leukocytes in the direction of higher concentrations of chemicals. Here, following the physiological hypotheses made by biologists on the phenomena occurring in these experiments, we introduce an agent-based model reproducing the dynamics of two cell populations (agents), i.e., tumor cells and leukocytes living in the microfluidic chip environment. Our model aims at proof of concept, demonstrating that the observations of the biological phenomena can be obtained by the model on the basis of the explicit assumptions made. In this framework, close adherence of the computational model to the biological results, as shown in the section devoted to the first calibration of the model with respect to available observations, is successfully accomplished. Full article
(This article belongs to the Special Issue Transport Phenomena Equations: Modelling and Applications)
Show Figures

Figure 1

Article
Bistability and Chaos Emergence in Spontaneous Dynamics of Astrocytic Calcium Concentration
Mathematics 2022, 10(8), 1337; https://doi.org/10.3390/math10081337 - 18 Apr 2022
Cited by 2 | Viewed by 896
Abstract
In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were [...] Read more.
In this work, we consider a mathematical model describing spontaneous calcium signaling in astrocytes. Based on biologically relevant principles, this model simulates experimentally observed calcium oscillations and can predict the emergence of complicated dynamics. Using analytical and numerical analysis, various attracting sets were found and investigated. Employing bifurcation theory analysis, we examined steady state solutions, bistability, simple and complicated periodic limit cycles and also chaotic attractors. We found that astrocytes possess a variety of complex dynamical modes, including chaos and multistability, that can further provide different modulations of neuronal circuits, enhancing their plasticity and flexibility. Full article
Show Figures

Figure 1

Article
Gradient and Parameter Dependent Dirichlet (p(x),q(x))-Laplace Type Problem
Mathematics 2022, 10(8), 1336; https://doi.org/10.3390/math10081336 - 18 Apr 2022
Cited by 2 | Viewed by 676
Abstract
We analyze a Dirichlet (p(x),μq(x))-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter μ varies on [...] Read more.
We analyze a Dirichlet (p(x),μq(x))-Laplace problem. For a gradient dependent nonlinearity of Carathéodory type, we discuss the existence, uniqueness and asymptotic behavior of weak solutions, as the parameter μ varies on the non-negative real axis. The results are obtained by applying the properties of pseudomonotone operators, jointly with certain a priori estimates. Full article
Article
Dense-to-Question and Sparse-to-Answer: Hybrid Retriever System for Industrial Frequently Asked Questions
Mathematics 2022, 10(8), 1335; https://doi.org/10.3390/math10081335 - 18 Apr 2022
Viewed by 916
Abstract
The term “Frequently asked questions” (FAQ) refers to a query that is asked repeatedly and produces a manually constructed response. It is one of the most important factors influencing customer repurchase and brand loyalty; thus, most industry domains invest heavily in it. This [...] Read more.
The term “Frequently asked questions” (FAQ) refers to a query that is asked repeatedly and produces a manually constructed response. It is one of the most important factors influencing customer repurchase and brand loyalty; thus, most industry domains invest heavily in it. This has led to deep-learning-based retrieval models being studied. However, training a model and creating a database specializing in each industry domain comes at a high cost, especially when using a chatbot-based conversation system, as a large amount of resources must be continuously input for the FAQ system’s maintenance. It is also difficult for small- and medium-sized companies and national institutions to build individualized training data and databases and obtain satisfactory results. As a result, based on the deep learning information retrieval module, we propose a method of returning responses to customer inquiries using only data that can be easily obtained from companies. We hybridize dense embedding and sparse embedding in this work to make it more robust in professional terms, and we propose new functions to adjust the weight ratio and scale the results returned by the two modules. Full article
Show Figures

Figure 1

Article
Robust Detection and Modeling of the Major Temporal Arcade in Retinal Fundus Images
Mathematics 2022, 10(8), 1334; https://doi.org/10.3390/math10081334 - 18 Apr 2022
Viewed by 768
Abstract
The Major Temporal Arcade (MTA) is a critical component of the retinal structure that facilitates clinical diagnosis and monitoring of various ocular pathologies. Although recent works have addressed the quantitative analysis of the MTA through parametric modeling, their efforts are strongly based on [...] Read more.
The Major Temporal Arcade (MTA) is a critical component of the retinal structure that facilitates clinical diagnosis and monitoring of various ocular pathologies. Although recent works have addressed the quantitative analysis of the MTA through parametric modeling, their efforts are strongly based on an assumption of symmetry in the MTA shape. This work presents a robust method for the detection and piecewise parametric modeling of the MTA in fundus images. The model consists of a piecewise parametric curve with the ability to consider both symmetric and asymmetric scenarios. In an initial stage, multiple models are built from random blood vessel points taken from the blood-vessel segmented retinal image, following a weighted-RANSAC strategy. To choose the final model, the algorithm extracts blood-vessel width and grayscale-intensity features and merges them to obtain a coarse MTA probability function, which is used to weight the percentage of inlier points for each model. This procedure promotes selecting a model based on points with high MTA probability. Experimental results in the public benchmark dataset Digital Retinal Images for Vessel Extraction (DRIVE), for which manual MTA delineations have been prepared, indicate that the proposed method outperforms existing approaches with a balanced Accuracy of 0.7067, Mean Distance to Closest Point of 7.40 pixels, and Hausdorff Distance of 27.96 pixels, while demonstrating competitive results in terms of execution time (9.93 s per image). Full article
Show Figures

Figure 1

Article
A Novel Dynamic Mathematical Model Applied in Hash Function Based on DNA Algorithm and Chaotic Maps
Mathematics 2022, 10(8), 1333; https://doi.org/10.3390/math10081333 - 17 Apr 2022
Cited by 2 | Viewed by 910
Abstract
This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal—namely, improved logistic, cosine logistic [...] Read more.
This paper aims to improve SHA-512 security without increasing complexity; therefore, we focused on hash functions depending on DNA sequences and chaotic maps. After analysis of 45 various chaotic map types, only 5 types are selected in this proposal—namely, improved logistic, cosine logistic map, logistic sine system, tent sine system, and hybrid. Using DNA features and binary coding technology with complementary rules to hide information is a key challenge. This article proposes improving SHA-512 in two aspects: the modification of original hash buffer values, and the modification of additive constants Kt. This proposal is to make hash buffer values (a, b, c, d, e, f, g, and h) and Kt dependent on one-dimensional discrete chaotic maps and DNA sequences instead of constant. This modification complicates the relationship between the original message and hash value, making it unexpected. The performance of the proposed hash function is tested and analyzed the confusion, diffusion, and distributive and compared with the original SHA-512. The performance of security is analyzed by collision analysis, for which the maximum number of hits is only three, showing that the proposed hash function enhances the security and robustness of SHA-512. The statistical data and experimental analysis indicate that the proposed scheme has good properties and satisfies high-performance requirements for secure hash functions. Full article
Show Figures

Figure 1

Article
Fractional Evolution Equations with Infinite Time Delay in Abstract Phase Space
Mathematics 2022, 10(8), 1332; https://doi.org/10.3390/math10081332 - 17 Apr 2022
Cited by 1 | Viewed by 681
Abstract
In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative of non-integer-order 1<α2 and the [...] Read more.
In the presented research, the uniqueness and existence of a mild solution for a fractional system of semilinear evolution equations with infinite delay and an infinitesimal generator operator are demonstrated. The generalized Liouville–Caputo derivative of non-integer-order 1<α2 and the parameter 0<ρ<1 are used to establish our model. The ρ-Laplace transform and strongly continuous cosine and sine families of uniformly bounded linear operators are adapted to obtain the mild solution. The Leray–Schauder alternative theorem and Banach contraction principle are used to demonstrate the mild solution’s existence and uniqueness in abstract phase space. The results are applied to the fractional wave equation. Full article
Article
The Instability and Response Studies of a Top-Tensioned Riser under Parametric Excitations Using the Differential Quadrature Method
Mathematics 2022, 10(8), 1331; https://doi.org/10.3390/math10081331 - 17 Apr 2022
Viewed by 626
Abstract
The differential quadrature method (DQM) is a numerical technique widely applied in structure mechanics problems. In this work, a top-tensioned riser conveying fluid is considered. The governing equation of this riser under parametric excitations is deduced. Through Galerkin’s method, the partial differential governing [...] Read more.
The differential quadrature method (DQM) is a numerical technique widely applied in structure mechanics problems. In this work, a top-tensioned riser conveying fluid is considered. The governing equation of this riser under parametric excitations is deduced. Through Galerkin’s method, the partial differential governing equation with respect to time t and vertical coordinate z is reduced into a 1D differential equation with respect only to time. Moreover, the DQM is applied to discretize the governing equation to give solution schemes for the risers’ parametric vibration problem. Furthermore, the instability region of Mathieu equation is studied by both the DQM and the Floquet theory to verify the effectiveness of the DQM, and the solutions of both methods show good consistency. After that, the influences of some factors such as damping coefficient, internal flow velocity, and wet-weight coefficient on the parametric instability of a top-tensioned riser are discussed through investigating the instability regions solved by the DQM solution scheme. Hence, conclusions are obtained that the increase of damping coefficient will save the riser from parametric resonance while increasing internal flow velocity, or the wet-weight coefficient will deteriorate the parametric instability of the riser. Finally, the time-domain responses of several specific cases in both stable region and unstable region are presented. Full article
Show Figures

Figure 1

Article
Investigation of 2D Seismic DDA Method for Numerical Simulation of Shaking Table Test of Rock Mass Engineering
Mathematics 2022, 10(8), 1330; https://doi.org/10.3390/math10081330 - 17 Apr 2022
Viewed by 675
Abstract
Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and [...] Read more.
Since the basic theory of the discontinue deformation analysis (DDA) method was proposed, the DDA open source has gone through a long development process. At present, different kinds of programs have been widely applied in rock mass engineering such as slope, dam, and tunnel. This paper introduces the solution principle of DDA motion equations in detail, as well as the development status of the 2D open-source program. Numerical simulation of shaking table test of rock mass engineering using 2D DDA program is highlighted, and investigations of seismic wave pre-processing and seismic input method are carried out. First, based on the Newmark integration scheme, the integration algorithms of synthetic or measured seismic wave time history, correction function of seismic wave, and DDA simulation are unified. Then, three seismic input methods are implanted in the DDA program, and the applicability of various seismic input methods is discussed. On this basis, using the improved seismic 2D DDA program, a shaking table test of typical rock mass engineering is simulated. Through the comparison between the theoretical/test data and simulation results, the reliability of the improved DDA program in seismic response analysis is verified; the large mass method and the large stiffness method are more suitable for rigid foundation, such as shaking table test; the propagation of the seismic wave presents a significant amplification effect due to the reflection, refraction, and diffraction in the tunnel. The research results provide DDA theory and an open-source program for analyzing the seismic response of rock mass engineering. Full article
Show Figures

Figure 1

Article
A Comparative Study of Forecasting Electricity Consumption Using Machine Learning Models
Mathematics 2022, 10(8), 1329; https://doi.org/10.3390/math10081329 - 17 Apr 2022
Cited by 6 | Viewed by 1478
Abstract
Production of electricity from the burning of fossil fuels has caused an increase in the emission of greenhouse gases. In the long run, greenhouse gases cause harm to the environment. To reduce these gases, it is important to accurately forecast electricity production, supply [...] Read more.
Production of electricity from the burning of fossil fuels has caused an increase in the emission of greenhouse gases. In the long run, greenhouse gases cause harm to the environment. To reduce these gases, it is important to accurately forecast electricity production, supply and consumption. Forecasting of electricity consumption is, in particular, useful for minimizing problems of overproduction and oversupply of electricity. This research study focuses on forecasting electricity consumption based on time series data using different artificial intelligence and metaheuristic methods. The aim of the study is to determine which model among the artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), least squares support vector machines (LSSVMs) and fuzzy time series (FTS) produces the highest level of accuracy in forecasting electricity consumption. The variables considered in this research include the monthly electricity consumption over the years for different countries. The monthly electricity consumption data for seven countries, namely, Norway, Switzerland, Malaysia, Egypt, Algeria, Bulgaria and Kenya, for 10 years were used in this research. The performance of all of the models was evaluated and compared using error metrics such as the root mean squared error (RMSE), average forecasting error (AFE) and performance parameter (PP). The differences in the results obtained via the different methods are analyzed and discussed, and it is shown that the different models performed better for different countries in different forecasting periods. Overall, it was found that the FTS model performed the best for most of the countries studied compared to the other three models. The research results can allow electricity management companies to have better strategic planning when deciding on the optimal levels of electricity production and supply, with the overall aim of preventing surpluses or shortages in the electricity supply. Full article
Show Figures

Figure 1

Article
Synthesized Landing Strategy for Quadcopter to Land Precisely on a Vertically Moving Apron
Mathematics 2022, 10(8), 1328; https://doi.org/10.3390/math10081328 - 17 Apr 2022
Cited by 5 | Viewed by 872
Abstract
Quadcopter unmanned aerial vehicles have become increasingly popular for various real-world applications, and a significant body of literature exists regarding the improvement of their flight capabilities to render them fully autonomous. The precise landing onto moving platforms, such as ship decks, is one [...] Read more.
Quadcopter unmanned aerial vehicles have become increasingly popular for various real-world applications, and a significant body of literature exists regarding the improvement of their flight capabilities to render them fully autonomous. The precise landing onto moving platforms, such as ship decks, is one of the remaining challenges that is largely unresolved. The reason why this operation poses a considerable challenge is because landing performance is considerably degraded by the ground effect or external disturbances. In this paper, we propose a synthesized landing algorithm that allows a quadcopter to land precisely on a vertically moving pad. Firstly, we introduce a disturbance observer-based altitude controller that allows the vehicle to perform robust altitude flight in the presence of external disturbances and the ground effect, strictly proving the system’s stability using Lyapunov’s theory. Secondly, we derive an apron state estimator to provide information on the landing target’s relative position. Additionally, we propose a landing planner to ensure that the landing task is completed in a safe and reliable manner. Finally, the proposed algorithms are implemented in an actual quadcopter, and we demonstrate the effectiveness and applicability of our method through real flight experiments. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
Show Figures

Figure 1

Article
Algebraic Systems with Positive Coefficients and Positive Solutions
Mathematics 2022, 10(8), 1327; https://doi.org/10.3390/math10081327 - 16 Apr 2022
Viewed by 641
Abstract
The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference [...] Read more.
The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state equations in continuous and discrete dynamical models, Dirichlet problems, difference equations, boundary value problems, periodic solutions and numerical solutions for differential equations. We apply Brouwer’s fixed point theorem, Krasnoselskii’s fixed point theorem and monotone iterative methods in order to extend some known results and to obtain new results. We relax some hypotheses used in the literature concerning the strict monotonicity of the involved functions. We show that, in some cases, the unique positive solution can be obtained by a monotone increasing iterative method or by a monotone decreasing iterative method. As a consequence of one of our results, we recover the existence of a non-negative solution of the Leontief system and describe a monotone iterative method to find it. Full article
(This article belongs to the Special Issue Mathematical Inequalities, Models and Applications)
Article
An Evolutionary Game Analysis of Periodical Fluctuation in Food Safety Supervision
Mathematics 2022, 10(8), 1326; https://doi.org/10.3390/math10081326 - 15 Apr 2022
Viewed by 689
Abstract
Periodical fluctuation is a common phenomenon in food safety supervision. The existing literature on China’s food safety supervision mainly analyzes periodical fluctuation by statistical methods. This paper provides a theoretical explanation by building an evolutionary game model between food enterprises and supervision institutions [...] Read more.
Periodical fluctuation is a common phenomenon in food safety supervision. The existing literature on China’s food safety supervision mainly analyzes periodical fluctuation by statistical methods. This paper provides a theoretical explanation by building an evolutionary game model between food enterprises and supervision institutions under bounded rationality. The “Sanlu milk powder” food safety incident is taken as a typical example to conduct numerical simulations of the food safety supervision game. Moreover, the determining factors in the periodical fluctuation in food safety supervision are analyzed in detail by numerical simulations, including the initial states and benefit–cost parameters. The results show that the periodical fluctuation and probability of supervision failure are influenced by the initial states. Supervision institutions should discard historical path dependence and adjust their supervision-intensity timing according to its actual effects. In addition, blindly increasing rewards or punishments cannot effectively restrain the fluctuation or reduce food safety incidents. To reduce the occurrence of food safety incidents and decrease periodical fluctuation, supervision institutions should reduce supervision costs by using information technology, establish strict food safety standards to eliminate “small-workshop” enterprises, be more aware of risks and appropriately overestimate the added benefits for food enterprises of becoming involved in illegal production. Full article
Show Figures

Figure 1

Article
Influence of Context on Greatest Common Divisor Problem Solving: A Qualitative Study
Mathematics 2022, 10(8), 1325; https://doi.org/10.3390/math10081325 - 15 Apr 2022
Viewed by 685
Abstract
This paper presents results from a study about problem solving related to the concept of the greatest common divisor with secondary school students. The perspective of the analysis is the meaningful learning of the constructivist theory. The main objectives are to assess the [...] Read more.
This paper presents results from a study about problem solving related to the concept of the greatest common divisor with secondary school students. The perspective of the analysis is the meaningful learning of the constructivist theory. The main objectives are to assess the students’ competence in the resolution of such problems and analyze if the difficulties in the acquisition of this competence are influenced by the kinds of magnitudes or the context of the problem. The results suggest that some contexts generate more difficulties to perform the use of the greatest common divisor. Moreover, some erroneous patterns have been detected. On one hand, students tend to relate and confuse the concepts of greatest common divisor and lowest common multiple. On the other hand, they have a predisposition to simplify problems, performing only the operation to obtain the greatest common divisor, and without thinking that additional arithmetic operations can be performed. Full article
Show Figures

Figure 1

Article
Localized Boundary Knot Method for Solving Two-Dimensional Inverse Cauchy Problems
Mathematics 2022, 10(8), 1324; https://doi.org/10.3390/math10081324 - 15 Apr 2022
Viewed by 602
Abstract
In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the local concept of the localization method [...] Read more.
In this paper, a localized boundary knot method is adopted to solve two-dimensional inverse Cauchy problems, which are controlled by a second-order linear differential equation. The localized boundary knot method is a numerical method based on the local concept of the localization method of the fundamental solution. The approach is formed by combining the classical boundary knot method with the localization method. It has the potential to solve many complex engineering problems. Generally, in an inverse Cauchy problem, there are no boundary conditions in specific boundaries. Additionally, in order to be close to the actual engineering situation, a certain level of noise is added to the known boundary conditions to simulate the measurement error. The localized boundary knot method can be used to solve two-dimensional Cauchy problems more stably and is truly free from mesh and numerical quadrature. In this paper, the stability of the method is verified by using multi-connected domain and simply connected domain examples in Laplace equations. Full article
Show Figures

Figure 1

Article
Towards Avoiding Cascading Failures in Transmission Expansion Planning of Modern Active Power Systems Using Hybrid Snake-Sine Cosine Optimization Algorithm
Mathematics 2022, 10(8), 1323; https://doi.org/10.3390/math10081323 - 15 Apr 2022
Cited by 2 | Viewed by 923
Abstract
In this paper, a transmission expansion planning (TEP) model is proposed to guarantee the resilience of power systems and mitigate cascading failures’ impacts. The energy storage systems and fault current limiters’ planning models are integrated into the TEP problem to minimize cascading outages [...] Read more.
In this paper, a transmission expansion planning (TEP) model is proposed to guarantee the resilience of power systems and mitigate cascading failures’ impacts. The energy storage systems and fault current limiters’ planning models are integrated into the TEP problem to minimize cascading outages and comply with short-circuit current reliability constraints. Most studies in the literature adopt a single strategy to simulate power systems’ cascading failures that may not be enough to guarantee networks’ resilience. This work elaborates on two scenarios for initiating cascading failures to study the impact of various initiating events on the planned system’s strength and the projects required. The TEP problem is formulated as a non-linear, non-convex large-scale problem. To avoid linearization issues and enhance meta-heuristics performance, a hybridization of two meta-heuristic techniques, namely snake optimizer and sine cosine algorithm (SO-SCA), is proposed to solve the problem. Two hybridization strategies are suggested to improve the exploration and exploitation stages. Defining future loads growth is essential for TEP. Hence, a load forecasting technique based on SO-SCA is investigated and compared with some methods reported in the literature. The results obtained proved the efficiency of the proposed approach in predicting load growth. TEP’s calculations were carried out on the Garver and the IEEE 24-bus system. The results demonstrated the superiority of the hybrid SO-SCA in solving the TEP problem. Moreover, the projects required to expand networks differed according to the type of cascading failures’ initiating scenario. Full article
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop