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Mathematics, Volume 10, Issue 3 (February-1 2022) – 246 articles

Cover Story (view full-size image): A challenging problem in submanifold theory is to obtain simple relationships between the main intrinsic and extrinsic invariants of submanifolds. There is an increased interest in providing answers for this open problem, establishing inequalities for submanifolds in a statistical manifold, a concept introduced by Amari in 1985 in the context of information geometry. The statistical manifolds also have applications in physics, machine learning, statistics, etc. Here, the authors prove some inequalities involving the Chen first invariant and the mean curvature of totally real and holomorphic spacelike submanifolds in statistical manifolds of type para-Kähler space forms. A calculus of optimization theory is used.  In addition, the case of equalities is studied, and some examples are revealed. View this paper
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Article
On Undecidability of Finite Subsets Theory for Torsion Abelian Groups
Mathematics 2022, 10(3), 533; https://doi.org/10.3390/math10030533 - 08 Feb 2022
Viewed by 417
Abstract
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M. Earlier, we [...] Read more.
Let M be a commutative cancellative monoid with an element of infinite order. The binary operation can be extended to all finite subsets of M by the pointwise definition. So, we can consider the theory of finite subsets of M. Earlier, we have proved the following result: in the theory of finite subsets of M elementary arithmetic can be interpreted. In particular, this theory is undecidable. For example, the free monoid (the sets of all words with concatenation) has this property, the corresponding algebra of finite subsets is the theory of all finite languages with concatenation. Another example is an arbitrary Abelian group that is not a torsion group. But the method of proof significantly used an element of infinite order, hence, it can’t be immediately generalized to torsion groups. In this paper we prove the given theorem for Abelian torsion groups that have elements of unbounded order: for such group, the theory of finite subsets allows interpreting the elementary arithmetic. Full article
(This article belongs to the Special Issue Combinatorial Algebra, Computation, and Logic)
Article
Chaotic Oscillations in Cascoded and Darlington-Type Amplifier Having Generalized Transistors
Mathematics 2022, 10(3), 532; https://doi.org/10.3390/math10030532 - 08 Feb 2022
Viewed by 376
Abstract
This paper describes, based on both numerical and experimental bases, the evolution of chaotic and, in some cases, hyperchaotic attractors within mathematical models of two two-port analog functional blocks commonly used inside radio-frequency systems. The first investigated electronic circuit is known as the [...] Read more.
This paper describes, based on both numerical and experimental bases, the evolution of chaotic and, in some cases, hyperchaotic attractors within mathematical models of two two-port analog functional blocks commonly used inside radio-frequency systems. The first investigated electronic circuit is known as the cascoded class C amplifier and the second network represents a resonant amplifier with Darlington’s active part. For the analysis of each mentioned block, fundamental configurations that contain coupled generalized bipolar transistors are considered; without driving force or interactions with other lumped circuits. The existence of the structurally stable strange attractors is proved via the high-resolution composition plots of the Lyapunov exponents, numerical sensitivity analysis and captured oscilloscope screenshots. Full article
(This article belongs to the Special Issue Chaotic Systems: From Mathematics to Real-World Applications)
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Article
Multi-Objective Feeder Reconfiguration Using Discrete Particle Swarm Optimization
Mathematics 2022, 10(3), 531; https://doi.org/10.3390/math10030531 - 08 Feb 2022
Cited by 1 | Viewed by 427
Abstract
Electric power distribution systems have been heavily engaged in evolutionary changes toward effective usage of distribution networks for dependability, quality, and improvement of services delivered to customers throughout the years. This was accomplished via a procedure known as reconfiguration. Several strategies have been [...] Read more.
Electric power distribution systems have been heavily engaged in evolutionary changes toward effective usage of distribution networks for dependability, quality, and improvement of services delivered to customers throughout the years. This was accomplished via a procedure known as reconfiguration. Several strategies have been offered by various authors for successful distribution feeder reconfiguration with a novel optimization method. As a result, this work developed a Discrete Particle Swarm Optimization (DPSO) method to address the issue of distribution system feeder reconfiguration during both steady-state and dynamic power system operations. In a dynamic state, the power demand and generation required are continually changing over time, and the DPSO algorithm finds a new set of solutions to fulfill the power demand. Many network topologies are investigated for the dynamic operation. The feeder reconfiguration single-objective optimization problem was transformed into a multi-objective optimization problem by taking into account both real power loss reduction and distribution system load balancing. The suggested technique was verified using various IEEE 16, 33, and 69 bus standard test distribution systems to determine the efficiency of the developed DPSO algorithm. The simulation findings reveal that DPSO outperforms other optimization algorithms in terms of actual power loss reduction and load balancing, while solving multi-objective distribution system feeder reconfiguration. Full article
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Article
An Efficient Network Intrusion Detection and Classification System
Mathematics 2022, 10(3), 530; https://doi.org/10.3390/math10030530 - 08 Feb 2022
Viewed by 539
Abstract
Intrusion detection in computer networks is of great importance because of its effects on the different communication and security domains. The detection of network intrusion is a challenge. Moreover, network intrusion detection remains a challenging task as a massive amount of data is [...] Read more.
Intrusion detection in computer networks is of great importance because of its effects on the different communication and security domains. The detection of network intrusion is a challenge. Moreover, network intrusion detection remains a challenging task as a massive amount of data is required to train the state-of-the-art machine learning models to detect network intrusion threats. Many approaches have already been proposed recently on network intrusion detection. However, they face critical challenges owing to the continuous increase in new threats that current systems do not understand. This paper compares multiple techniques to develop a network intrusion detection system. Optimum features are selected from the dataset based on the correlation between the features. Furthermore, we propose an AdaBoost-based approach for network intrusion detection based on these selected features and present its detailed functionality and performance. Unlike most previous studies, which employ the KDD99 dataset, we used a recent and comprehensive UNSW-NB 15 dataset for network anomaly detection. This dataset is a collection of network packets exchanged between hosts. It comprises 49 attributes, including nine types of threats such as DoS, Fuzzers, Exploit, Worm, shellcode, reconnaissance, generic, and analysis Backdoor. In this study, we employ SVM and MLP for comparison. Finally, we propose AdaBoost based on the decision tree classifier to classify normal activity and possible threats. We monitored the network traffic and classified it into either threats or non-threats. The experimental findings showed that our proposed method effectively detects different forms of network intrusions on computer networks and achieves an accuracy of 99.3% on the UNSW-NB15 dataset. The proposed system will be helpful in network security applications and research domains. Full article
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Article
Fuzzy-Logic-Based Comparative Analysis of Different Maximum Power Point Tracking Controllers for Hybrid Renewal Energy Systems
Mathematics 2022, 10(3), 529; https://doi.org/10.3390/math10030529 - 08 Feb 2022
Viewed by 453
Abstract
There is an increasing demand for power production day by day all over the globe; thus, hybrid frameworks have an essential role in producing sufficient power for the desirable load due to increasing power demand. The proposed hybrid renewable energy (HRE) systems are [...] Read more.
There is an increasing demand for power production day by day all over the globe; thus, hybrid frameworks have an essential role in producing sufficient power for the desirable load due to increasing power demand. The proposed hybrid renewable energy (HRE) systems are used to provide power in different areas to conquer the intermittence of wind and solar resources. The HRE system incorporates more than one renewable energy (RE) system. In this research article, the optimum power generation of different combinations of RE using different Maximum Power Point Tracking (MPPT) control methods is presented. The Fuel Cell (FC), FC–Photovoltaic (PV), FC–Wind (W), and FC–PV–W systems are developed to examine different MPPT controllers. The results show that the FC–PV–W HRE system produces the maximum power as compared to the FC, FC–PV, and FC–W systems. The FC–PV–W HRE system produces increased power compared to 94.24% from the FC system, 37.17% from the FC–PV hybrid system, and 15.8% from the FC–W hybrid framework with a Perturb and Observe (P&O) controller and, similarly, 74.57% from the FC system, 10.3% from the FC-PV hybrid system, and 31.64% from the FC-W hybrid system using a fuzzy logic (FL) controller, indicating that the best combination is the FC-PV-W hybrid system using an FL controller, which is useful for maximum power generation with reduced oscillations. Full article
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Article
A Note on Pareto-Type Distributions Parameterized by Its Mean and Precision Parameters
Mathematics 2022, 10(3), 528; https://doi.org/10.3390/math10030528 - 08 Feb 2022
Viewed by 351
Abstract
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression [...] Read more.
Pareto-type distributions are well-known distributions used to fit heavy-tailed data. However, the standard parameterizations used for Pareto-type distributions are poorly suited to modeling. On this note, we suggest new parameterizations that are better suited to the purpose. In addition, we propose many regression models where the response variable is Pareto-type distributed using new parameterizations that are indexed by mean and precision parameters. The main motivation for these new parametrizations is the useful interpretation of the regression coefficients in terms of the mean and precision, as is usual in the context of regression models. The parameter estimation of these new models is performed, based on the maximum likelihood paradigm. Some numerical illustrations of the estimators are presented with a discussion of the obtained results. Finally, we illustrate the practicality of the new models by means of two applications to real data sets. Full article
(This article belongs to the Special Issue New Frontiers in Applied Mathematics and Statistics)
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Article
A Methodology for Estimating Vehicle Route Choice from Sparse Flow Measurements in a Traffic Network
Mathematics 2022, 10(3), 527; https://doi.org/10.3390/math10030527 - 08 Feb 2022
Viewed by 261
Abstract
While traffic speed data and travel time estimates are increasingly more available from commercial vendors, they are not sufficient for proper management and performance evaluation of transportation networks. Effective traffic control and demand management requires information about volumes, which is provided by fixed [...] Read more.
While traffic speed data and travel time estimates are increasingly more available from commercial vendors, they are not sufficient for proper management and performance evaluation of transportation networks. Effective traffic control and demand management requires information about volumes, which is provided by fixed location sensors, such as loop detectors or cameras, and those are sparse. This paper proposes a method for estimating route choice using sparse flow measurements and estimated speed on the road network based on compressed sensing technology widely used in image processing, where from a handful of scattered pixels, a full image is recovered. What is known includes flows at origins and at selected links of the road network, where the detection is present; speed estimates are available for all network links. We find coefficients that split origin flows among routes starting at those origins. The advantage of the proposed methodology is that it does not rely on simulation that is prone to calibration errors but only on measured data. We also show how vehicle flows can be estimated at links with no detection, which enables computing performance measures for road networks lacking complete sensor coverage. Finally, we propose a method for selecting plausible routes between origins and destinations. Full article
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Article
Impulsive Control of Complex-Valued Neural Networks with Mixed Time Delays and Uncertainties
Mathematics 2022, 10(3), 526; https://doi.org/10.3390/math10030526 - 08 Feb 2022
Viewed by 334
Abstract
This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs [...] Read more.
This paper investigates the global exponential stability of uncertain delayed complex-valued neural networks (CVNNs) under an impulsive controller. Both discrete and distributed time-varying delays are considered, which makes our model more general than previous works. Unlike most existing research methods of decomposing CVNNs into real and imaginary parts, some stability criteria in terms of complex-valued linear matrix inequalities (LMIs) are obtained by employing the complex Lyapunov function method, which is valid regardless of whether the activation functions can be decomposed. Moreover, a new impulsive differential inequality is applied to resolve the difficulties caused by the mixed time delays and delayed impulse effects. Finally, an illustrative example is provided to back up our theoretical results. Full article
(This article belongs to the Special Issue Impulsive Control Systems and Complexity II)
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Article
Optimal Management of Energy Consumption in an Autonomous Power System Considering Alternative Energy Sources
Mathematics 2022, 10(3), 525; https://doi.org/10.3390/math10030525 - 08 Feb 2022
Cited by 1 | Viewed by 596
Abstract
This work aims to analyze and manage the optimal power consumption of the autonomous power system within the Pamir region of Republic of Tajikistan, based on renewable energy sources. The task is solved through linear programming methods, production rules and mathematical modeling of [...] Read more.
This work aims to analyze and manage the optimal power consumption of the autonomous power system within the Pamir region of Republic of Tajikistan, based on renewable energy sources. The task is solved through linear programming methods, production rules and mathematical modeling of power consumption modes by generating consumers. It is assumed that power consumers in the considered region have an opportunity to independently cover energy shortage by installing additional generating energy sources. The objective function is to minimize the financial expenses for own power consumption, and to maximize them from both the export and redistribution of power flows. In this study, the optimal ratio of power generation by alternative sources from daily power consumption for winter was established to be hydroelectric power plants (94.8%), wind power plant (3.8%), solar photovoltaic power plant (0.5%) and energy storage (0.8%); while it is not required in summer due to the ability to ensure the balance of energy by hydroelectric power plants. As a result, each generating consumer can independently minimize their power consumption and maximize profit from the energy exchange with other consumers, depending on the selected energy sources, thus becoming a good example of carbon-free energy usage at the micro- and mini-grid level. Full article
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Article
A k,n-Threshold Secret Image Sharing Scheme Based on a Non-Full Rank Linear Model
Mathematics 2022, 10(3), 524; https://doi.org/10.3390/math10030524 - 07 Feb 2022
Cited by 2 | Viewed by 374
Abstract
Secret image sharing is a hot issue in the research field of data hiding schemes for digital images. This paper proposes a general k,n threshold secret image sharing scheme, which distributes secret data into n meaningful image shadows based on a [...] Read more.
Secret image sharing is a hot issue in the research field of data hiding schemes for digital images. This paper proposes a general k,n threshold secret image sharing scheme, which distributes secret data into n meaningful image shadows based on a non-full rank linear model. The image shadows are indistinguishable from their corresponding distinct cover images. Any k combination of the n shares can perfectly restore the secret data. In the proposed scheme, the integer parameters k,n, with kn, can be set arbitrarily to meet the application requirement. The experimental results demonstrate the applicability of the proposed general scheme. The embedding capacity, the visual quality of image shadows, and the security level are satisfactory. Full article
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Article
Minty Variational Principle for Nonsmooth Interval-Valued Vector Optimization Problems on Hadamard Manifolds
Mathematics 2022, 10(3), 523; https://doi.org/10.3390/math10030523 - 07 Feb 2022
Viewed by 319
Abstract
This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the [...] Read more.
This article deals with the classes of approximate Minty- and Stampacchia-type vector variational inequalities on Hadamard manifolds and a class of nonsmooth interval-valued vector optimization problems. By using the Clarke subdifferentials, we define a new class of functions on Hadamard manifolds, namely, the geodesic LU-approximately convex functions. Under geodesic LU-approximate convexity hypothesis, we derive the relationship between the solutions of these approximate vector variational inequalities and nonsmooth interval-valued vector optimization problems. This paper extends and generalizes some existing results in the literature. Full article
Article
Sobolev-Slobodeckij Spaces on Compact Manifolds, Revisited
Mathematics 2022, 10(3), 522; https://doi.org/10.3390/math10030522 - 07 Feb 2022
Viewed by 317
Abstract
In this manuscript, we present a coherent rigorous overview of the main properties of Sobolev-Slobodeckij spaces of sections of vector bundles on compact manifolds; results of this type are scattered through the literature and can be difficult to find. A special emphasis has [...] Read more.
In this manuscript, we present a coherent rigorous overview of the main properties of Sobolev-Slobodeckij spaces of sections of vector bundles on compact manifolds; results of this type are scattered through the literature and can be difficult to find. A special emphasis has been put on spaces with noninteger smoothness order, and a special attention has been paid to the peculiar fact that for a general nonsmooth domain Ω in Rn, 0<t<1, and 1<p<, it is not necessarily true that W1,p(Ω)Wt,p(Ω). This has dire consequences in the multiplication properties of Sobolev-Slobodeckij spaces and subsequently in the study of Sobolev spaces on manifolds. We focus on establishing certain fundamental properties of Sobolev-Slobodeckij spaces that are particularly useful in better understanding the behavior of elliptic differential operators on compact manifolds. In particular, by introducing notions such as “geometrically Lipschitz atlases” we build a general framework for developing multiplication theorems, embedding results, etc. for Sobolev-Slobodeckij spaces on compact manifolds. To the authors’ knowledge, some of the proofs, especially those that are pertinent to the properties of Sobolev-Slobodeckij spaces of sections of general vector bundles, cannot be found in the literature in the generality appearing here. Full article
(This article belongs to the Special Issue Recent Developments of Function Spaces and Their Applications I)
Article
Application of Fractional Order-PID Control Scheme in Automatic Generation Control of a Deregulated Power System in the Presence of SMES Unit
Mathematics 2022, 10(3), 521; https://doi.org/10.3390/math10030521 - 06 Feb 2022
Cited by 1 | Viewed by 389
Abstract
A fractional order PID (FOPID) control technique for automatic generation control (AGC) in a multi-area power system is presented in this study. To create a reliable controller, a variety of control strategies were used. The load frequency control (LFC) problem in a power [...] Read more.
A fractional order PID (FOPID) control technique for automatic generation control (AGC) in a multi-area power system is presented in this study. To create a reliable controller, a variety of control strategies were used. The load frequency control (LFC) problem in a power system implementing different power transactions, such as bilateral and Poolco transactions, are investigated here. Because any control scheme’s performance is only as good as its parameters, the parameters of the designed control scheme were determined using the big bang big crunch (BBBC) algorithm. Furthermore, in this work, the effect of a superconductive magnetic energy storage (SMES) unit is addressed in the given test (two and four area) systems. When confronted with a fluctuation in immediate load, the SMES unit is thought to follow the initial drop in frequency and tie-line power in order to increase LFC. It is evident that the performance of an FOPID control scheme is improved in the presence of an SMES unit and it provides frequency, tie-line power, change in generation with reduced oscillations and settling time. Full article
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Article
A Decision-Making Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring
Mathematics 2022, 10(3), 520; https://doi.org/10.3390/math10030520 - 06 Feb 2022
Cited by 1 | Viewed by 484
Abstract
The workers operating and supervising machining tools are often in charge of monitoring a high number of parameters of the machining process, and they usually make use of, among others, cutting sound signals, for following-up and assessing that process. The interpretation of those [...] Read more.
The workers operating and supervising machining tools are often in charge of monitoring a high number of parameters of the machining process, and they usually make use of, among others, cutting sound signals, for following-up and assessing that process. The interpretation of those signals is closely related to the operational conditions of the machine and to the work environment itself, because such signals are sensitive to changes in the process’ input parameters. Additionally, they could be considered as a valid indicator for detecting working conditions that either negatively affect the tools’ lifespan, or might even put the machine operators themselves at risk. In light of those circumstances, this work deals with the proposal and conceptual development of a new methodology for monitoring the work conditions of machining tools, based on expert systems that incorporate a reinforcement strategy into their knowledge base. By means of the combination of sound-processing techniques, together with the use of fuzzy-logic inference engines and hierarchization methods based on vague fuzzy numbers, it will be possible to determine existing undesirable behaviors in the machining tools, thus reducing errors, accidents and harmful failures, with consequent savings in time and costs. Aiming to show the potential for the use of this methodology, a concept test has been developed, implemented in the form of a short case study. The results obtained, even if they require more extensive validation, suggest that the methodology would allow for improving the performance and operation of machining tools, as well as the ergonomic conditions of the workplace. Full article
(This article belongs to the Special Issue Fuzzy Applications in Industrial Engineering)
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Article
Identification of Homogeneous Groups of Actors in a Local AHP-Multiactor Context with a High Number of Decision-Makers: A Bayesian Stochastic Search
Mathematics 2022, 10(3), 519; https://doi.org/10.3390/math10030519 - 06 Feb 2022
Viewed by 316
Abstract
The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a [...] Read more.
The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a new Bayesian stochastic search methodology for large-scale problems (number of decision-makers greater than 20). The new methodology, based on Bayesian tools for model comparison and selection, takes advantage of the individual preference structures distributions obtained from stochastic AHP to allow the identification of homogeneous groups of actors with a maximum common incompatibility threshold. The methodology offers a heuristic approach with several near-optimal partitions, calculated by the Occam’s window, that capture the uncertainty that is inherent when considering intangible aspects (AHP). This uncertainty is also reflected in the graphs that show the similarities of the decision-maker’s opinions and that can be used to achieve representative collective positions by constructing agreement paths in negotiation processes. If a small number of actors is considered, the proposed algorithm (AHP Bayesian clustering) significantly reduces the computational time of group identification with respect to an exhaustive search method. The methodology is illustrated by a real case of citizen participation based on e-Cognocracy. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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Article
Secure Data Transmission and Image Encryption Based on a Digital-Redesign Sliding Mode Chaos Synchronization
Mathematics 2022, 10(3), 518; https://doi.org/10.3390/math10030518 - 05 Feb 2022
Viewed by 482
Abstract
In this paper, a novel image encryption algorithm based on chaotic synchronization is proposed. First, a digital-redesign sliding mode controller (SMC) is developed to guarantee the chaos synchronization. The digital redesign method makes it possible to transform a proposed continuous-time SMC to discrete-time [...] Read more.
In this paper, a novel image encryption algorithm based on chaotic synchronization is proposed. First, a digital-redesign sliding mode controller (SMC) is developed to guarantee the chaos synchronization. The digital redesign method makes it possible to transform a proposed continuous-time SMC to discrete-time SMC whilst maintaining the performance of the robust synchronization. Then, the secret keys are embedded in the state equations of the master chaotic system, such that the secret keys do not appear in the public channel, and utilize the chaotic synchronization to achieve secure communication for transmitting the secret keys from transmitter to receiver. Second, an image encryption algorithm integrating the S-box with chaotic synchronization is established, where the S-box is created by the secret key transmitted from the transmitter. Finally, a detailed analysis of the image encryption algorithm based on chaos synchronization is included to verify the feasibility and effectiveness of this proposed approach. Full article
(This article belongs to the Special Issue Stability Analysis for Hybrid Systems)
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Article
A Study on the Experimental Design for the Lifetime Performance Index of Rayleigh Lifetime Distribution under Progressive Type I Interval Censoring
Mathematics 2022, 10(3), 517; https://doi.org/10.3390/math10030517 - 05 Feb 2022
Viewed by 425
Abstract
With the rapid development of technology, improving product life performance has become a very important issue in recent decades. The lifetime performance index is used in this research for the assessment of the lifetime performance of products following the Rayleigh distribution. Based on [...] Read more.
With the rapid development of technology, improving product life performance has become a very important issue in recent decades. The lifetime performance index is used in this research for the assessment of the lifetime performance of products following the Rayleigh distribution. Based on the hypothesis testing procedure with this index, using the maximum likelihood estimator as a testing statistic, the sampling design is determined and the related values are tabulated for practical use to reach the given power level and minimize the total experimental cost under progressive type I interval censoring. When the inspection interval length is fixed and the number of inspection intervals is not fixed, the required number of inspection intervals and sample size with the minimum total cost are determined and tabulated. When the termination time is not fixed, the required number of inspection intervals, sample size and equal interval length reaching the minimum total cost are determined and tabulated. Lastly, a practical example is given to illustrate the use of this sampling design for the testing procedure to determine whether the process is capable. Full article
(This article belongs to the Special Issue Applications of Partial Differential Equations in Engineering)
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Article
Connections between Campos-Bolanos and Murofushi–Sugeno Representations of a Fuzzy Measure
Mathematics 2022, 10(3), 516; https://doi.org/10.3390/math10030516 - 05 Feb 2022
Cited by 1 | Viewed by 394
Abstract
Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy [...] Read more.
Nonadditivity of a fuzzy measure, as an indicator of defectiveness, makes a fuzzy mea-sure less useful in applications compared to additive, probabilistic measures. In order to neutralize this indicator of defectiveness to some degree, it is important to study the representations of fuzzy measures, including, in particular, additive, probabilistic representations. In this paper, we discuss a couple of probability representations of a fuzzy measure: the Campos-Bolanos representation (CBR) and the Murofushi–Sugeno representation (MSR). The CBR is mainly represented by the Associated Probability Class (APC). The APC is well studied and the aspects of its use can be found in many interesting studies. This is especially true for the environment of interactive attributes in their identification and multi-attribute group decision-making (MAGDM) models, related to the attributes’ Shapley values and interaction indexes. The MSR is a less-used tool in practice today. The main motivation of the research presented here was to explore the connections between these two representations, which will help increase the usability of the MSR in practice in the future. In the MSR, we constructed the nonequivalent representation class (NERC) of a fuzzy measure. This probabilistic new representation is somewhat similar to the APC in the CBR environment. The proposition on the existence of the MSR induced by the CBR was proven. The presented formula of the APC by the NERC was obtained. The duality property of fuzzy measures for the CBR is well studied with respect to fuzzy measures—Choquet second-order dual capacities. Significant properties were proven for the representation of a monotone expectation (ME) under the NERC conditions: as is known, the necessary and sufficient conditions for the existence of the second-order Choquet dual capacities are proven in the terms of the APC of a CBR and ME. After establishing the links between the APC of a CBR and the NERC of a MSR, we proved the same in the case of the MSR. A recursive connection formula between the interaction indexes, Shapley values, and the probability distribution of the NERC of a two-order additive fuzzy measure was obtained in the environment of a general MAGDM. A new distance concept was introduced for all fuzzy measures’ classes defined in finite sets in terms of the NERC. The distance between two fuzzy measures was defined as the distance between their NERCs. This distance is equivalent to the distance defined on the same class under the conditions of the APC of a CBR. The correctness proposition on the extension of the distance between fuzzy measures for the NERC was preserved: distances between any two fuzzy measures and between their dual fuzzy measures also coincided in the CBR as the MSR. After parameterization, the calculation formula of the new distance was obtained. An illustrative example was considered in order to easily present the obtained results. The connection schemes between the CBR and MSR and the sequential scheme of key facts and results obtained are presented at the end of this work. Full article
(This article belongs to the Special Issue Multi-Criteria Decision Making under Fuzzy Information)
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Article
A Hybrid Localized Meshless Method for the Solution of Transient Groundwater Flow in Two Dimensions
Mathematics 2022, 10(3), 515; https://doi.org/10.3390/math10030515 - 05 Feb 2022
Viewed by 339
Abstract
In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation [...] Read more.
In this work, a hybrid localized meshless method is developed for solving transient groundwater flow in two dimensions by combining the Crank–Nicolson scheme and the generalized finite difference method (GFDM). As the first step, the temporal discretization of the transient groundwater flow equation is based on the Crank–Nicolson scheme. A boundary value problem in space with the Dirichlet or mixed boundary condition is then formed at each time node, which is simulated by introducing the GFDM. The proposed algorithm is truly meshless and easy to program. Four linear or nonlinear numerical examples, including ones with complicated geometry domains, are provided to verify the performance of the developed approach, and the results illustrate the good accuracy and convergency of the method. Full article
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Article
Solution Approach for Bus Transit Model with a Rectangular Service Area
Mathematics 2022, 10(3), 514; https://doi.org/10.3390/math10030514 - 05 Feb 2022
Viewed by 260
Abstract
This paper studies the solution procedure of a bus transit system with a rectangular service area that had been cited more than two hundred times. We will point out that they applied relations suitable for continuous variables, which are not held for a [...] Read more.
This paper studies the solution procedure of a bus transit system with a rectangular service area that had been cited more than two hundred times. We will point out that they applied relations suitable for continuous variables, which are not held for a discrete variable and will result in invalid results. We provide our solution procedure to the same example proposed by the original paper to illustrate that their results are less accurate. Our findings will help researchers understand this kind of bus transit system. Full article
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Article
FMEA in Smartphones: A Fuzzy Approach
Mathematics 2022, 10(3), 513; https://doi.org/10.3390/math10030513 - 05 Feb 2022
Viewed by 399
Abstract
Smartphones are attracting increasing interest due to how they are revolutionizing our lives. On the other hand, hardware and software failures that occur in them are continually present. This work aims to investigate these failures in a typical smartphone by collecting data from [...] Read more.
Smartphones are attracting increasing interest due to how they are revolutionizing our lives. On the other hand, hardware and software failures that occur in them are continually present. This work aims to investigate these failures in a typical smartphone by collecting data from a class of people. Concerns have been raised that call into question the efficiency of applied methods for identifying and prioritizing the potential defects. The widely used hybridized engineering method, Fuzzy Failure Mode and Effect Analysis (F-FMEA), is an excellent approach to solving these problems. The F-FMEA method was applied to prioritize the potential failures based on their Severity (S), expected Occurrence (O), and the likelihood of Detectability (D). After collecting failure data from different users on a selected smartphone, two well-known defuzzification methods facing the Risk Priority Number (RPN) in F-FMEA were applied. Despite this interest, to the best of our knowledge, no one has studied smartphone failures with a technique that combines the results of different fuzzy applications. Thus, to combine the results of the derived fuzzy subsystems for the average value, we suggest a summative defuzzification method. Our findings indicate that F-FMEA with a summative defuzzification procedure is a clear improvement on the F-FMEA method. Even though the summation method modifies close results of the defuzzification one, it was shown that it provides more accurate results. Full article
(This article belongs to the Special Issue Applications of Fuzzy Modeling in Risk Management)
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Article
Multiscale Balanced-Attention Interactive Network for Salient Object Detection
Mathematics 2022, 10(3), 512; https://doi.org/10.3390/math10030512 - 05 Feb 2022
Viewed by 344
Abstract
The purpose of saliency detection is to detect significant regions in the image. Great progress on salient object detection has been made using from deep-learning frameworks. How to effectively extract and integrate multiscale information with different depths is an open problem for salient [...] Read more.
The purpose of saliency detection is to detect significant regions in the image. Great progress on salient object detection has been made using from deep-learning frameworks. How to effectively extract and integrate multiscale information with different depths is an open problem for salient object detection. In this paper, we propose a processing mechanism based on a balanced attention module and interactive residual module. The mechanism addressed the acquisition of the multiscale features by capturing shallow and deep context information. For effective information fusion, a modified bi-directional propagation strategy was adopted. Finally, we used the fused multiscale information to predict saliency features, which were combined to generate the final saliency maps. The experimental results on five benchmark datasets show that the method is on a par with the state of the art for image saliency datasets, especially on the PASCAL-S datasets, where the MAE reaches 0.092, and on the DUT-OMROM datasets, where the F-measure reaches 0.763. Full article
(This article belongs to the Special Issue Advances of Data-Driven Science in Artificial Intelligence)
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Article
Numerical Method for Solving of the Anomalous Diffusion Equation Based on a Local Estimate of the Monte Carlo Method
Mathematics 2022, 10(3), 511; https://doi.org/10.3390/math10030511 - 05 Feb 2022
Viewed by 355
Abstract
This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing [...] Read more.
This paper considers a method of stochastic solution to the anomalous diffusion equation with a fractional derivative with respect to both time and coordinates. To this end, the process of a random walk of a particle is considered, and a master equation describing the distribution of particles is obtained. It has been shown that in the asymptotics of large times, this process is described by the equation of anomalous diffusion, with a fractional derivative in both time and coordinates. The method has been proposed for local estimation of the solution to the anomalous diffusion equation based on the simulation of random walk trajectories of a particle. The advantage of the proposed method is the opportunity to estimate the solution directly at a given point. This excludes the systematic component of the error from the calculation results and allows constructing the solution as a smooth function of the coordinate. Full article
(This article belongs to the Special Issue Modeling and Simulation in Engineering)
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Article
Sparse and Low-Rank Joint Dictionary Learning for Person Re-Identification
Mathematics 2022, 10(3), 510; https://doi.org/10.3390/math10030510 - 05 Feb 2022
Viewed by 386
Abstract
In the past decade, the scientific community has become increasingly interested in the re-identification of people. It is still a challenging problem due to its low-quality images; occlusion between objects; and huge changes in lighting, viewpoint and posture (even for the same person). [...] Read more.
In the past decade, the scientific community has become increasingly interested in the re-identification of people. It is still a challenging problem due to its low-quality images; occlusion between objects; and huge changes in lighting, viewpoint and posture (even for the same person). Therefore, we propose a dictionary learning method that divides the appearance characteristics of pedestrians into a shared part, which comprises the similarity between different pedestrians, and a specific part, which reflects unique identity information. In the process of re-identification, by removing the shared part of a pedestrian’s visual characteristics and considering the unique part of each person, the ambiguity of the pedestrian’s visual characteristics can be reduced. In addition, considering the structural characteristics of the shared dictionary and special dictionary, low-rank, l0 norm and row sparsity constraints instead of their convex-relaxed forms are introduced into the dictionary learning framework to improve its representation and recognition capabilities. Therefore, we adopt the method of alternating directions to solve it. The experimental results of several commonly used datasets show the effectiveness of our proposed method. Full article
(This article belongs to the Special Issue Advances in Machine Learning, Optimization, and Control Applications)
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Article
Synchronization of Nonlinear Complex Spatiotemporal Networks Based on PIDEs with Multiple Time Delays: A P-sD Method
Mathematics 2022, 10(3), 509; https://doi.org/10.3390/math10030509 - 05 Feb 2022
Cited by 1 | Viewed by 282
Abstract
This paper studies the synchronization control of nonlinear multiple time-delayed complex spatiotemporal networks (MTDCSNs) based on partial integro-differential equations. Firstly, dealing with an MTDCSN with time-invariant delays, P-sD control is employed and the synchronization criteria are obtained in terms of LMIs. Secondly, this [...] Read more.
This paper studies the synchronization control of nonlinear multiple time-delayed complex spatiotemporal networks (MTDCSNs) based on partial integro-differential equations. Firstly, dealing with an MTDCSN with time-invariant delays, P-sD control is employed and the synchronization criteria are obtained in terms of LMIs. Secondly, this control method is further used in an MTDCSN with time-varying delays. An example illustrates the effectiveness of the proposed methods. Full article
(This article belongs to the Special Issue Advanced Control Theory with Applications)
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Article
Water-Cycle-Algorithm-Tuned Intelligent Fuzzy Controller for Stability of Multi-Area Multi-Fuel Power System with Time Delays
Mathematics 2022, 10(3), 508; https://doi.org/10.3390/math10030508 - 05 Feb 2022
Viewed by 348
Abstract
In this paper, a fuzzy (F) proportional (P)–integral (I)–derivative (D) (PID) (FPID) controller optimized with a water cycle algorithm is proposed for load frequency control of a multi-area multi-fuel (MAMF) power system. The MAMF system has the realistic feature of communication time delays [...] Read more.
In this paper, a fuzzy (F) proportional (P)–integral (I)–derivative (D) (PID) (FPID) controller optimized with a water cycle algorithm is proposed for load frequency control of a multi-area multi-fuel (MAMF) power system. The MAMF system has the realistic feature of communication time delays (CTDs), in order to conduct an analysis nearer to realistic practice. Initially, the MAMF system is analyzed when subjected to a step load disturbance (SLD) of 10% on area 1. The superiority of the fuzzy PID controller is revealed upon comparing it with PID plus double derivative (DD) (PIDD) and PID controllers. The MAMF system is investigated with and without CTDs, to demonstrate their impact on system performance. Later, an additional HVDC line is incorporated in parallel with the existing AC line for further enhancement of the system performance. Finally, the MAMF system is targeted with random loading to validate the robustness of the presented control scheme. Full article
(This article belongs to the Special Issue Dynamic Modeling and Simulation for Control Systems)
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Article
Operator Methods of the Maximum Principle in Problems of Optimization of Quantum Systems
Mathematics 2022, 10(3), 507; https://doi.org/10.3390/math10030507 - 05 Feb 2022
Viewed by 348
Abstract
In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space. The equivalence of the obtained operator optimality conditions to the well-known Pontryagin maximum principle is shown. [...] Read more.
In the class of optimal control problems for quantum systems, operator optimality conditions for control are constructed in the form of fixed-point problems in the control space. The equivalence of the obtained operator optimality conditions to the well-known Pontryagin maximum principle is shown. Based on the obtained operator forms of optimality conditions, new iterative methods for finding extreme equations satisfying the maximum principle are developed. A comparative analysis of the effectiveness of the proposed operator methods of the maximum principle with known methods is carried out on model examples of optimization of quantum systems. Full article
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Article
On Estimating the Parameters of the Beta Inverted Exponential Distribution under Type-II Censored Samples
Mathematics 2022, 10(3), 506; https://doi.org/10.3390/math10030506 - 05 Feb 2022
Viewed by 297
Abstract
This article aims to consider estimating the unknown parameters, survival, and hazard functions of the beta inverted exponential distribution. Two methods of estimation were used based on type-II censored samples: maximum likelihood and Bayes estimators. The Bayes estimators were derived using an informative [...] Read more.
This article aims to consider estimating the unknown parameters, survival, and hazard functions of the beta inverted exponential distribution. Two methods of estimation were used based on type-II censored samples: maximum likelihood and Bayes estimators. The Bayes estimators were derived using an informative gamma prior distribution under three loss functions: squared error, linear exponential, and general entropy. Furthermore, a Monte Carlo simulation study was carried out to compare the performance of different methods. The potentiality of this distribution is illustrated using two real-life datasets from difference fields. Further, a comparison between this model and some other models was conducted via information criteria. Our model performs the best fit for the real data. Full article
(This article belongs to the Section Probability and Statistics Theory)
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Article
Factors Influencing Physicians Migration—A Case Study from Romania
Mathematics 2022, 10(3), 505; https://doi.org/10.3390/math10030505 - 05 Feb 2022
Cited by 1 | Viewed by 555
Abstract
Brain drain is a phenomenon that, over time, has followed an upward trend. It is an important component represented by physicians’ migration. For the country of destination, the migration of physicians offers several advantages, whereas the country of origin loses skilled and sometimes [...] Read more.
Brain drain is a phenomenon that, over time, has followed an upward trend. It is an important component represented by physicians’ migration. For the country of destination, the migration of physicians offers several advantages, whereas the country of origin loses skilled and sometimes highly trained individuals. This process will be reflected both in the efficiency of the health system (severe employment shortage) and in the quality of the health system services. After Romania’s accession to the EU, the migration of doctors intensified, significantly increasing the shortage of physicians. The purpose of this article is to identify the push factors that influence the physicians’ decision to migrate from Romania. For this, a panel regression analysis was applied, highlighting that physicians’ migration is influenced by several factors, such as the number of beds in hospitals, the number of emigrants, unemployment rate, and income. At the same time, we analyzed the extent to which public policy measures addressed to the remuneration of medical staff influenced the propensity towards external mobility of the practicing doctors, already employed and/or graduates. The results confirm that public policies can be a tool for redistributing the labor force allocation on the labor market. Moreover, the results of our analysis highlight that specific measures do not solve the system crises facing the health sector. Systemic, multidimensional changes are needed, adapted to the needs of medical services specific to the geographical area and adequate to the health status of the population. Full article
(This article belongs to the Special Issue Time Series Analysis and Econometrics with Applications)
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Article
Influence of Bioconvection and Chemical Reaction on Magneto—Carreau Nanofluid Flow through an Inclined Cylinder
Mathematics 2022, 10(3), 504; https://doi.org/10.3390/math10030504 - 04 Feb 2022
Cited by 2 | Viewed by 447
Abstract
The present contribution focuses on heat transmission in the conjugate mixed bioconvection flow of Carreau nanofluid with swimming gyrotactic microorganisms through an inclined stretchable cylinder with variable magnetic field impact and binary chemical reaction. Additionally, the investigation involves the aspects of variable decrease [...] Read more.
The present contribution focuses on heat transmission in the conjugate mixed bioconvection flow of Carreau nanofluid with swimming gyrotactic microorganisms through an inclined stretchable cylinder with variable magnetic field impact and binary chemical reaction. Additionally, the investigation involves the aspects of variable decrease or increase in heat source and non-uniform thermal conductivity. A passively controlled nanofluid pattern is used to estimate this nano-bioconvection flow case, which is believed to be more physically accurate than the earlier actively controlled nanofluid typically employed. One of essential features of this investigation is the imposition of a zero-mass flux condition at the surface of the cylinder. Through the implementation of an appropriate transformation, the nonlinear PDE system is mutated into similar equations. The flow equations thus obtained are solved numerically to explore the influence of the physical constraints involved through implementation with the aid of the MATLAB bvp4c code. The solutions were captured for both zero and non-zero bioconvection Rayleigh number, i.e., for flow with and without microorganisms. The present numerical results are compared with the available data and are determined to be in excellent agreement. The significant result of the present article is that the degree of nanoparticle concentration in the nanofluid exhibits an increasing trend with higher values of activation energy constraint. Full article
(This article belongs to the Special Issue Computational Fluid Dynamics II)
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