Mohammad Hosein Sabzalian, Nurkhat Zhakiyev, Didar Yedilkhan
et al.
This paper presents a novel intelligent control strategy for Unmanned Aerial Vehicles (UAVs) using Type-3 fuzzy-logic systems (T3-FLSs). UAVs are widely adopted in diverse fields due to their efficiency and versatility; however, they face significant control challenges under uncertain dynamics and environmental disturbances. Addressing these issues requires control strategies with high adaptability and robustness. T3-FLSs offer superior capabilities in modeling and managing uncertainties, making them well-suited for complex UAV environments. In this study, a robust T3-FLS-based nonlinear control framework is proposed. Novel online adaptation laws are developed to optimize the T3-FLS for dynamic modeling and to identify unknown uncertainty bounds. Using these estimations, a supplementary controller is designed to operate in parallel with the T3-FLS controller, enhancing overall robustness. Theoretical analysis confirms the system’s stability under the proposed adaptation mechanisms. The effectiveness and resilience of the control scheme are validated through extensive simulations, demonstrating strong performance under structured disturbances (modeled as sinusoidal disturbances) stochastic turbulence/measurement noise (modeled as random noise) and unknown nonlinear dynamics.
Saikh Shahjahan Miah, M. Ali Akar, Kamruzzaman Khan
The space-time fractional Yu-Toda-Sasa-Fukuyama equation (YTSFE) is widely used to describe elastic quasi-plane waves in a two-layer fluid system, characterizing the behavior of the interface between two immiscible fluid layers of differing densities, relevant to interfacial wave dynamics in such systems. In this work, we explore solitary wave solutions to the (3+1)-dimensional space-time fractional YTSFE and analyze in detail using the extended modified auxiliary equation mapping technique. We construct a variety of solitary wave solutions to this equation, including trigonometric, rational, and hybrid solutions. The solutions include a range of waveforms such as kink, anti-kink, general, and plane-type solitons, which hold numerous applications in physical sciences and engineering. The solutions of this work have been compared with existing results, and new solutions have been identified. The effect of fractional order derivative on the soliton has been shown graphically. The stability, bifurcation, chaotic, and sensitivity analysis of the dynamical system of the governing model have been assessed. The graphical representations of the solutions are provided in 2D, 3D, and contour formats, using MATLAB with appropriately selected parameter values. The method proves to be effective and efficient for investigating nonlinear integrable equations, confirming its potential for addressing the space-time fractional YTSFE.
Applying artificial intelligence methods, the paper frames the algorithm structure and software for the formalized determination of the type of distribution (automatic classification) of the probability density function and the vector of limit values by justifying theoretically security gradations and determining quantitatively security indicators. The methodological basis of the research is the applied systems theory, statistical analysis, and methods of artificial intelligence (cluster analysis). The study of the approaches applied showed the absence of a theoretical basis for determining security gradations and the absence of their theoretical quantitative justification. The theoretical basis for determining security gradations is the concept of an extended "homeostatic plateau", which connects three levels of security in both directions: optimal, crisis, and critical with spheres of positive, neutral and negative feedback. To determine the bifurcation points (vector of limit values), the “t-criterion” method is used, which consists in constructing the probability density function of a “benchmark” sample, determining whether it belongs to the type of distribution with the calculation of statistical characteristics (mathematical expectation, mean square deviation, and asymmetry coefficient) and formalized calculation of the vector of limit values for characteristic types of distribution (normal, lognormal, exponential). To solve the problem of recognising (automatic classifying) the type of distribution of probability density functions of security indicators, artificial intelligence methods are used, namely, a discriminant method from the class of cluster analysis methods using quantitative and qualitative metrics: Euclidean distance, Manhattan metric and recognition by characteristic features. To digitize the determination of the vector of safety indicators limit values, an algorithm structure and software in the C++ programming language (version 6) have been developed, which ensures full automation of all stages of the algorithm and the adequacy of recognising graphic digital data with a predetermined number of clusters (types of distribution). A distinctive feature of the proposed method of formalized determination of the security indicators limit values is a complete absence of subjectivity and complete mathematical formalization, which significantly increases the speed, quality and reliability of the results obtained when evaluating the level of sustainable development, economic security, national security or national stability, regardless of the level of a researcher's qualification.
Abstract In legal practice litigation cases, the selection of a litigation strategy significantly impacts both the litigation process and the overall outcome of the case. The study mainly applies quantitative methods to evaluate the effectiveness of legal strategies for litigation. We collect relevant legal strategy texts after analyzing relevant civil litigation cases in China. We then use text mining methods, such as regular expressions, jieba participles, and Word2Vec training word vectors, to refine high-frequency words in text data related to litigation legal strategies. This process establishes a quantitative evaluation index system for assessing the effectiveness of litigation legal strategies. We select litigation legal strategy cases as the evaluation object, utilizing the PMC index to determine and evaluate the effectiveness of each strategy. The sample litigation legal strategies have a mean PMC index of 6.69, indicating a good overall level. Only one strategy is considered acceptable, with the remaining 87.5% rated as good. Deficient litigation solutions and thought paths, with a mean value below 0.8, hinder the effectiveness of litigation legal strategies. We recommend optimizing and improving them to enhance their effectiveness.
Oluwaseun F. Egbelowo, Oluwaseun F. Egbelowo, Justin B. Munyakazi
et al.
The co-infection of visceral leishmaniasis (VL) and tuberculosis (TB) patients pose a major public health challenge. In this study, we develop a mathematical model to study the transmission dynamics of VL and TB co-infection by first analyzing the VL and TB sub-models separately. The dynamics of these sub-models and the full co-infection model are determined based on the reproduction number. When the associated reproduction number (R1) for the TB-only model and (R2) for the VL-only are less than unity, the model exhibits backward bifurcation. If max{R1,R2}=R1, then the TB-VL co-infection model exhibits backward bifurcation for values of R1. Furthermore, if max{R1,R2}=R2, and by choosing the transmission probability, βL as the bifurcation parameter, then the phenomenon of backward bifurcation occurs for values of R2. Consequently, the full model, whose associated reproduction number is R0, also exhibits backward bifurcation when R0=1. The equilibrium points and their stability for the models are determined and analyzed based on the magnitude of the respective reproduction numbers. Finally, some numerical simulations are presented to show the reliability of our theoretical results.
Sunday O. Edeki, Sunday E. Fadugba, Chaudry Masood Khalique
Deposit insurance is a mechanism by which financial institutions are stabilized. The danger of a bank’s inability to meet its consumer commitments due to its suspended license is insured through deposit insurance practices. A flat-rate insurance scheme would contribute to moral hazard and a financial panic when banks indulge in dangerous practices. Hence, a reliable model with an explicit solution is required. This paper considers a risk rate model for deposit insurance engendered by the classical Black Scholes Option Pricing Model. The solutions are obtained via the application of Banach Contraction Mapping or Method. The procedures involved are straightforward, easy, and flexible, even without giving up accuracy. The desired explicit solutions are obtained with less computational time.
| Inequalities (Mathematics) Harmonic analysis on Euclidean spaces – Harmonic analysis in several variables – Maximal functions, Littlewood-Paley theory. | Functional analysis – Linear function spaces and their duals – Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems. | Real functions – Inequalities – Inequalities involving derivatives and differential and integral operators. | Measure and integration – Classical measure theory – Contents, measures, outer measures, capacities. | Potential theory – Higher-dimensional theory – Potentials and capacities, extremal length and related notions in higher dimensions. | Partial differential equations – General topics in partial differential equations – Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals. | Partial differential equations – Elliptic equations and systems – Quasilinear elliptic equations with p -Laplacian. | Harmonic analysis on Euclidean spaces – Harmonic analysis in several variables – Harmonic analysis and This book discusses advances in maximal function methods related to Poincaré and Sobolev inequalities, pointwise estimates and approximation for Sobolev functions, Hardy’s inequalities, and partial differential equations. Capacities are needed for fine properties of Sobolev functions and characterization of Sobolev spaces with zero boundary values. The authors consider several uniform quantitative conditions that are self-improving, such as Hardy’s inequalities, capacity density conditions, and reverse Hölder inequalities. They also study Muckenhoupt weight properties of distance functions and combine these with weighted norm inequalities; notions of dimension are then used to characterize density conditions and to give sufficient and necessary conditions for Hardy’s inequalities. At the end of the book, the theory of weak solutions to the p -Laplace equation and the use of maximal function techniques is this context are discussed. The book is to researchers and graduate students interested in applications of geometric and harmonic analysis in Sobolev spaces and partial differential equations.
With the increasing depth of coal mining, the quantitative evaluation of the degree of geological structure development is becoming increasingly important for the control of mine water hazards in coal mining areas. Understanding the complexity of geological structure development can improve the safety and efficiency of coal production. At present, various evaluation indicators of the geological structure development cannot fully reflect the complexity of faults and folds, and the evaluation process is usually affected by subjective human factors. In this paper, the fractal dimension from fractal theory is used as the evaluation indicator to quantitatively analyze and evaluate the complexity of fault and fold structure in the mining area. To verify the evaluation results, the mathematical geology method is applied in an analysis of the trend surface of fault and fold networks. The results indicate that the fractal dimension can be applied for the quantitative analysis and evaluation of the complexity of fault and fold networks. In addition, the outcome of this work provides new insights into how to characterize the fault and fold structures of coal mining areas in northern China, and has some important implications to ensure the coal production safety.
Quantitative MRI methods and learning-based algorithms require exact forward simulations. One critical factor to correctly describe magnetization dynamics is the effect of slice-selective RF pulses. While contemporary simulation techniques correctly capture their influence, they only provide final magnetization distributions, require to be run for each parameter set separately, and make it hard to derive general theoretical conclusions and to generate a fundamental understanding of echo formation in the presence of slice-profile effects. This work aims to provide a mathematically exact framework, which is equally intuitive as extended phase graphs (EPGs), but also considers slice-profiles through their natural spatial representation. We show, through an analytical, hybrid Bloch-EPG formalism, that the spatially-resolved EPG approach allows to exactly predict the signal dependency on off-resonance, spoiling moment, microscopic dephasing, and echo time. We also demonstrate that our formalism allows to use the same phase graph to simulate both gradient-spoiled and balanced SSFP-based MR sequences. We present a derivation of the formalism and identify the connection to existing methods, i.e. slice-selective Bloch, slice-selective EPG, and the partitioned EPG. As a use case, the proposed hybrid Bloch-EPG framework is applied to MR Fingerprinting.
ABSTRACT Background: STEM (science, technology, engineering, mathematics) education is attracting increasing public interest and policy attention and being promoted at different educational levels in Cambodia. Purpose: The study seeks to identify factors associated with Cambodian university freshmen’s choice of STEM major and how significant associations differ by gender and university location. Sample: The study draws on primary data collected from a survey of 2,016 freshmen at 15 universities across Cambodia. Design and method: Binary logistic regression was applied to detect correlates of major choice (dichotomized into STEM major and non-STEM major). Results: Students who choose a STEM major are likely to be male, have clearly prioritized the major since high school, have high self-efficacy in the chosen major, want a career in STEM, enrol at a Phnom Penh-based university, excel at mathematics at high school, excel at science at high school, have no job while studying, and value the importance of science and technology to society. When moderated by gender and university location, only excellence in mathematics, excellence in science, and STEM career prospects remained significantly associated with STEM major choice. Conclusion: Student experience in learning mathematics and science subjects at high school and their exposure to career information and guidance are vital in widening participation in STEM disciplines at higher education level in Cambodia.
This paper aims to find a solution of interval uncertainty to multiobjective variational problems. For this, we consider an interval-valued multiobjective variational problem. Then, by using the modified F-objective function method, we construct associated interval-valued multiobjective variational problem with the modified F-objective functions. We establish a relationship between LU-pareto optimal solution of original problem and its associated modified problem by using the concept of LU-F-convexity and LU-F-pseudoconvexity. Further, we define LU-Lagrange function and its saddle point to discuss the efficient solution of original problem through it. We provide an example to validate our results numerically.
O conteúdo de triângulo retângulo e suas razões trigonométricas apresenta diversas aplicações e sua compreensão é de grande relevância no cotidiano e em exames posteriores. Diante desta relevância, estratégias de ensino são pensadas para criar um momento de aprendizagens. Este trabalho tem como objetivo principal abordar o ensino de trigonometria do aplicativo Triângulo Retângulo Grátis, através de uma Sequência de Ensino Investigativa (SEI). Dessa forma, este trabalho apresenta a aplicação de uma sequência de ensino investigativo ao trabalhar este conteúdo de forma remota auxiliado por tecnologias móveis e atividades experimentais. A investigação mostrou que há expectativa discente por novas metodologias e o vídeo aulas foram eficazes na compreensão do conteúdo, visto a inserção de aplicativos e experimentos. As respostas ao questionário final apontam que, mesmo em período de adaptação ao ensino remoto, os meios utilizados são adequados ao ensino de triângulo retângulo e suas razões trigonométricas gerando motivação e proporcionando interação entre teoria e prática.
Special aspects of education, Applied mathematics. Quantitative methods
Abstract We derive an analytical expression for the mean load at each node of an arbitrary undirected graph for the non-uniform multicommodity flow problem under weighted random routing. We show the mean load at each node, net of its demand and normalized by its (weighted) degree, is a constant equal to the trace of the product of two matrices: the Laplacian of the demand matrix and the generalized inverse of the graph Laplacian. For the case of uniform demand, this constant reduces to the sum of the inverses of the non-zero eigenvalues of the graph Laplacian. We note that such a closed-form expression for the network capacity for the general multicommodity network flow problem has not been reported before, and even though (weighted) random routing is not a practical procedure, it enables us to derive a (tight) upper bound for the capacity of the network under more standard routing policies. Using this new expression, we compute network capacity for a sample of demand matrices for some prototypical networks, including uniform demand (one unit between all node pairs) and broadcast demand (one unit between a source node and each other node as destination), and finally derive estimates of the mean load in some asymptotic cases.
Nowadays, in addition to traditional qualitative methods, quantitative techniques are also a standard tool to describe biological systems behavior. An example is the broad class of mathematical models, based on differential equations, used in ecology, biochemical kinetics, epidemiology, gene regulatory networks, etc. Independent of their simplicity or complexity, all these models have in common (generally unknown a priori) parameters that need to be identified from observations (data) of the real system, usually available on the literature, obtained by specific assays or surveyed by public health offices. Before using this data to calibrate the models, a good practice is to judge the most influential parameters. That can be done with aid of the Sobol’ indices, a variance-based statistical technique for global sensitivity analysis, which measures the individual importance of each parameter, as well as their joint-effect, on the model output (a.k.a. quantity of interest). These variance-based indexes may be computed using Monte Carlo simulation but, depending on the model, this task can be very costly. An alternative approach for this scenario is the use of surrogate models to speed-up the calculations. Using simple biological models, from different areas, we develop a tutorial that illustrates how practitioners can use Sobol’ indices to quantify, in a probabilistic manner, the relevance of the parameters of their models. This tutorial describes a very robust framework to compute Sobol’ indices employing a polynomial chaos surrogate model constructed with the UQLab package.
FRET (Fluorescence Resonance Energy Transfer) measurements are commonly applied to proof protein-protein interactions. However, standard methods of live cell FRET microscopy and signal normalization only allow a principle assessment of mutual binding and are unable to deduce quantitative information of the interaction. We present an evaluation and normalization procedure for 3-filter FRET measurements, which reflects the process of complex formation by plotting FRET-saturation curves. The advantage of this approach relative to traditional signal normalizations is demonstrated by mathematical simulations. Thereby, we also identify the contribution of critical parameters such as the total amount of donor and acceptor molecules and their molar ratio. When combined with a fitting procedure, this normalization facilitates the extraction of key properties of protein complexes such as the interaction stoichiometry or the apparent affinity of the binding partners. Finally, the feasibility of our method is verified by investigating three exemplary protein complexes. Altogether, our approach offers a novel method for a quantitative analysis of protein interactions by 3-filter FRET microscopy, as well as flow cytometry. To facilitate the application of this method, we created macros and routines for the programs ImageJ, R and MS-Excel, which we make publicly available.