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We present a formalization of collections that Cornelius Castoriadis calls "magmas", especially the property which mainly characterizes them and distinguishes them from the usual cantorian sets. It is the property of their elements to depend on other elements, either in a one-way or a two-way manner, so that one cannot occur in a collection without the occurrence of those dependent on it. Such a dependence relation on a set A of atoms (or urelements) can be naturally represented by a pre-order relation ≼ of A with the extra condition that it contains no minimal elements. Then, working in a mild strengthening of the theory ZFA , where A is an infinite set of atoms equipped with a primitive pre-ordering ≼ , the class of magmas over A is represented by the class L O (A , ≼) of nonempty open subsets of A with respect to the lower topology of ⟨ A , ≼ ⟩ . The non-minimality condition for ≼ implies that all sets of L O (A , ≼) are infinite and none of them is ⊆ -minimal. Next the pre-ordering ≼ is shifted (by a kind of simulation) to a pre-ordering ≼ + on P (A) , which turns out to satisfy the same non-minimality condition as well, and which, happily, when restricted to L O (A , ≼) coincides with ⊆ . This allows us to define a hierarchy M α (A) , along all ordinals α ≥ 1 , the"magmatic hierarchy", such that M 1 (A) = L O (A , ≼) , M α + 1 (A) = L O (M α (A) , ⊆) , and M α (A) = ⋃ β < α M β (A) , for a limit ordinal α . For every α ≥ 1 , M α (A) ⊆ V α (A) , where V α (A) are the levels of the universe V(A) of ZFA . The class M (A) = ⋃ α ≥ 1 M α (A) is the "magmatic universe above A." The axioms of Powerset and Union (the latter in a restricted version) turn out to be true in ⟨ M (A) , ∈ ⟩ . Besides it is shown that three of the five principles about magmas that Castoriadis proposed in his writings (mildly modified and adapted to the needs of formalization), M 2 ∗ , M 3 ∗ and M 5 ∗ , are true of M(A). A selection of excerpts from these writings, in which the concept of magma was first introduced and elaborated, is presented in the Introduction. [ABSTRACT FROM AUTHOR]

In this article, we apply NURBS-based isogeometric method to solve a nonlocal degenerate parabolic problem. The isogeometric method has advantages over classical finite element method in terms of exact geometry representation and higher order smooth basis functions. We consider the NURBS-based semi-discretization of the problem. The second-order Crank–Nicolson method is applied for the complete discretization of the problem. Error estimates of the semi-discrete and fully-discrete problems are derived. Few numerical examples are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

Quantum field theories can be applied to compute various statistical properties of random tensors. In particular, signed distributions of tensor eigenvalues/vectors are the easiest, which can be computed as partition functions of four-fermi theories. Though signed distributions are different from genuine ones because of extra signs of weights, they are expected to coincide in vicinities of ends of distributions. In this paper, we perform a case study of the signed eigenvalue/vector distribution of the real symmetric order-three random tensor. The correct critical point and the correct end in the large N limit are obtained from the four-fermi theory, for which a method using the Schwinger-Dyson equation is very efficient. Since locations of ends are particularly important in applications, such as the largest eigenvalues and the best rank-one tensor approximations, signed distributions are the easiest and highly useful through the Schwinger-Dyson method. [ABSTRACT FROM AUTHOR]

To reduce the emission of fine particulate matter (PM) from gasoline engines, a gasoline particulate filter (GPF) filtration model that considers the fractal characteristics of both particulate matter and filters is designed and its filtration characteristics are analyzed based on several GPF filtration models. Based on the GPF filtration mechanism, a new mathematical model of fiber efficiency filtration is established after correcting the classical filtration formula based on correcting the particle size of particles and considering the relationship between the porosity of the fiber filter and the fractal dimension of the filter. Simulation of the filtration efficiency of the established mathematical filtration model is carried out to obtain visual filtration efficiency curves. The filtration efficiency and pressure drop of the model are analyzed, and the effects of parameters such as particle fractal dimension, filter fractal dimension, filter thickness, flow rate, and fiber diameter on filtration efficiency are also comprehensively analyzed. The results show that when the fractal dimension of particles is in the range of 1.8-2.8, the most penetrating particle size decreases with the increase of the fractal dimension of particles. When the particle size is small, the effect of fractal dimension on filtration efficiency is not obvious. When the particle size is larger than the most penetrating particle range, the larger the fractal dimension, the filtration efficiency increases obviously. Considering the relationship between the fractal dimension of the filter body and the porosity and the influence of each on the filtration efficiency, the optimal fractal dimension of the filter body should be between 1.82 and 1.925, and the thickness of the filter has some influence on the filtration efficiency. The slower the gas flow rate is, the better the trapping effect will be. However, considering the problem of automobile emission, a lower exhaust speed can be chosen. Increasing the fiber diameter can improve the trapping efficiency of the model, but will reduce the porosity of the trapping collective. Therefore, the fiber diameter should not be too large under the combined action.

In this article, we study how interactive digital art is applied in interior design under the ecological concept, focusing on color innovation and image technology to enhance the aesthetics and functionality of interior decoration. The article studies the three elements of color design and their application in product design. The K-Means clustering method is used to classify color imagery words in interior design, and the GAN model is combined to generate interior design colors. The results show that the error qualification rate for the color design scheme coding combination serial number is 88.2%. The composition of interior image decoration systems, digitization processing, and image fusion technology are also a part of this. A method for analyzing the impact of indoor digital decoration based on the ecological concept was proposed after studying the application range of interior decorative colors using cluster analysis. A questionnaire survey was conducted to analyze the perceptual imagery of interior decoration design. Interactive digital art can effectively enhance the aesthetics and functionality of interior design while reaffirming the ecological concept.

This study focuses on innovations in school social work methods and explores applying predictive control-based models to effectively support and improve students’ mental health and behavioral development. The XGBoost algorithm and support vector machine were employed to predict students’ mental health. The study was influenced by physiological, self, family, school, social, and network factors, and a questionnaire was developed based on the SCL-90 Symptom Self-Rating Scale. A validity rate of 94.32% was achieved by collecting 432 valid questionnaires. The results indicated a significant positive correlation between the influencing factors and students’ mental health, with physiological and family factors being the most influential. An AUC value of 93.6% and an accuracy rate of 93.9% were achieved by the XGBoost-SVM model when predicting students’ mental health. The prediction model can update students’ mental health status in real-time and provide an effective predictive control tool for school social work.

This study examines the optimization of digital resource management and sharing in preschool education, employing the Goodness of Fit (GoF) algorithm to assess eigenvalues’ suitability in this context. As digital educational materials proliferate, effectively managing and disseminating these resources is a critical challenge. We have developed a preschool educational digital resource management and sharing system grounded in GoF algorithmic principles through an in-depth evaluation of various GoF algorithms’ classification and detection capabilities. Our methodology combines theoretical exploration with empirical algorithm performance testing. Findings indicate that a GoF algorithm, explicitly leveraging the chi-square distribution, achieves over 95% accuracy in identifying preschool digital resources. Furthermore, this study introduces a novel dynamic fitting object model, addressing the GoF algorithm’s adaptability in fluctuating environments. Results affirm the algorithm’s broad adaptability and promising efficiency for managing and sharing digital resources in preschool education settings.

This study aimed to critically evaluate the effectiveness of casework intervention in addressing the interpersonal challenges encountered by de facto unsupported children. An in-depth analysis of casework practices revealed positive outcomes, with significant advancements observed in the children’s social interaction capabilities. Leveraging a psychosocial therapy framework, the intervention strategically provided emotional support and social skills development, crucial for bolstering self-esteem and improving communicative competences. The results of this study illuminate the substantial benefits of casework interventions, confirming their essential role in facilitating the holistic growth and interpersonal health of unsupported children.

Facing global climate change and energy crises, urban power grids, particularly in Guangxi, need resilience enhancements to cope with these unprecedented challenges. This study proposes a resilience improvement strategy by integrating distributed renewable energy with building systems, tailored to Guangxi’s unique conditions. We demonstrate that optimizing the network structure and protection settings significantly enhances fault recovery capabilities through system analysis, model development, and simulation. Implementing a distributed multi-microgrid system increased the resilience power supply rate by an average of 15% across eight cities in Guangxi, with a 20% improvement in the system’s resilience emergence rate. This was achieved by optimizing power interactions using a dynamic consistency algorithm, showcasing a viable pathway to bolster urban grid resilience through renewable integration and offering insights applicable to similar urban settings.

Exploring the intricacies of learning Chinese, this study leverages digital ink technology to observe the stroke writing behaviors of novice learners. We delved into the nuances of stroke order, direction, and the fluidity of writing, scrutinizing 2,131 Chinese characters to uncover the relationship between character structure and writing behavior. Our findings illuminate beginners’ challenges, offering a novel perspective on teaching Chinese characters that caters to the dynamic nature of writing and learning.

As digital technology advances, college aerobics instruction must evolve to enhance teaching efficiency and quality through tech-based solutions. Traditional aerobics evaluation faces challenges like subjectivity, delayed feedback, and inefficiency, hindering quality improvement and modern teaching management. This study introduces a novel, efficient, scientific evaluation platform for aerobics teaching, focusing on quantitative assessment and refined management. The platform demonstrates significant benefits by developing an evaluation index system, utilizing a genetic algorithm for index weight optimization, and employing a fuzzy comprehensive evaluation method for teacher performance. Results show enhanced student satisfaction, a notable 14.81% increase in assessment scores among the experimental group, and improved skill quality and application. This platform offers a fresh perspective and pathway for elevating aerobics teaching in higher education.

In the era of big data, establishing a sustainable school-enterprise collaboration framework for cultivating Civic and Political Education talents in higher education is crucial. This study employs the DEMATEL model and Structural Equation Modeling (SEM) to dissect this collaboration’s dynamics. Through DEMATEL, we unravel the complex interrelations among these factors, constructing a direct influence matrix and quantifying the centrality and causality indices. SEM further elucidates the causal interplays, underscoring the profound impact of university infrastructure, corporate culture, and governmental roles on the collaboration’s efficacy. Notably, the engagement of enterprise entities, academic institutions, and equitable benefit mechanisms emerge as pivotal, with path regression coefficients of 0.961, 0.943, and 0.925, respectively. The study highlights the indispensability of balanced benefit distribution, resource sharing, and strategic improvements in organizational management, pedagogical innovation, dual-expertise faculty development, and fostering industry-academia-research synergies. Offering theoretical insights and actionable strategies, this research advances the optimization of school-enterprise partnerships, ensuring the adept nurturing of Civic and Political Education professionals.

In the quest to safeguard and revitalize folk dance heritage, this study explores the transformative potential of virtual reality (VR) technology. We developed an immersive display system using the Unreal game engine, incorporating a dance movement database, virtual reality immersion, and precise inertial motion capture. This innovative approach captivates users with an immersive folk dance experience and boasts a high motion recognition accuracy (99.51%) and an overall accuracy of 96%. Comparative experiments highlight VR’s advantages in making folk dance education more interactive and enjoyable without sacrificing ease of use. Virtual reality emerges as a vital tool in engaging new generations with folk dance, suggesting a vibrant future for intangible cultural heritage preservation.

Image inpainting aims to fill the undetectable domain and has been studied using deep learning in recent years. This study investigates smoothness-informed convolutional neural network models for image inpainting. The total variation (TV) is considered and local smoothness constraints are also explored in this study. The local smoothness constraint is conducted by the fidelity of the low-order derivatives on mostly connected parts of the given image at training stage. Unlike most neural network-based inpainting methods using numerous images for training, only a single local image containing the domain to be filled is required for the whole training here. The convolutional neural network accepts the image and is trained using detectable data. Computational results indicate that the local smoothness constraint can conduct a more satisfactory inpainting in comparison to usual TV-based one. We also demonstrate how a deep learning approach is used to solve the Euler-Lagrange equation-based inpainting.

In this research work, we proposed a Haar wavelet collocation method (HWCM) for the numerical solution of first- and second-order nonlinear hyperbolic equations. The time derivative in the governing equations is approximated by a finite difference. The nonlinear hyperbolic equation is converted into its full algebraic form once the space derivatives are replaced by the finite Haar series. Convergence analysis is performed both in space and time, where the computational results follow the theoretical statements of convergence. Many test problems with different nonlinear terms are presented to verify the accuracy, capability, and convergence of the proposed method for the first- and second-order nonlinear hyperbolic equations.

As in the case of enhancing the performance of high-temperature superconductors, the dynamics of colloidal mixes of water and copper-based nanoparticles exposed to an inclined magnetic field owing to free convection is a recognized issue. However, nothing is known about the dynamics mentioned above when the radius and inter-particle spacing of copper nanoparticles grow in the presence of Joule dissipation, mass flux owing to a temperature gradient, internal heating, and heat flux due to concentration gradient. When the ratio of momentum to thermal diffusivities is incorporated into the momentum equation using appropriate models, the governing equation (i.e. Partial Differential Equations) that models the transport mentioned above was scaled, solved numerically, and simulated with a focus on the nanoparticle radius and the spacing between copper nanoparticles. The resultant non-linear coupled Ordinary Differential Equation was solved using the MATLAB integrated (i.e. bvp4c software package) and the shooting approach (i.e. fourth-order Runge–Kutta integration strategy shrk4). Just because of the resulting improvement in the temperature distribution, increasing the ratio of momentum to thermal diffusivities leads to a more pronounced local skin friction within the layers adjacent to the wall and heat transfer. Because buoyancy forces are exclusively associated with the growth of concentration difference, they cause the distance covered by the transport phenomenon in terms of the spatial domain to decrease. Higher ratios of momentum to thermal diffusivities cause the full-fledged sheer stress profile, which is proportional to friction across fluid layers, to rise.

In this paper, we present a new simple method for solving two integral equations of Love's type that have many applications, especially in electrostatic systems. The approach of the solution is based on an innovative technique using matrix algebra for the barycentric Lagrange interpolation. The unknown function is expressed through the product of four matrices. The kernel is interpolated twice, so we get it in the product of five matrices. Additionally, we derive an equivalent linear algebraic system to the solution by substituting the matrix-vector barycentric interpolated unknown function together with the double interpolated kernel into both sides of the integral equation. Thus, there was no need to employ the collocation method. The obtained results converge strongly with the approximate analytical solutions, in addition to being uniformly approximated, continuous, and even, which proves the validity of the solution by the presented method. [ABSTRACT FROM AUTHOR]

Regime-switching models have been heavily studied recently, as they have some clear advantages of over other non-constant volatility model to resolve the so-called smirk effect displayed when constant volatility models are used to price financial derivatives such as options. However, due to the increased model complexity, the associated computational effort usually increases as well, particularly when they are used to price American-style options. In this paper, a novel computational approach based on integral equations is presented. A distinctive feature of our approach, in comparison with other numerical approaches, is that the coupled partial differential equations (PDEs) in a PDE system have been decoupled in the Fourier space, resulting in a completely decoupled integral equation for each economical states, and thus has greatly reduced computational effort. Some examples with preliminary results for a two-state regime-switching model are used to demonstrate our approach. [ABSTRACT FROM AUTHOR]

This article establishes the actual movement mathematical model of CNC machine tools for the precision processing of jewelry. Through analyzing the general geometric error analysis model of CNC machine tools with less than five axes and the method of solving precision CNC instructions, the operating principle of the CNC machine tools is studied. At the same time, we use a transformation matrix to express the relationship between the various moving bodies. The article abstracts the complex motion relationship between entities as the relationship between mathematical matrices. The experimental results show that the theoretical method proposed in this paper can increase the machining accuracy of the machine tool by more than 50%.

The current work aims to present abundant families of the exact solutions of Mikhailov-Novikov-Wang equation via three different techniques. The adopted methods are generalized Kudryashov method (GKM), exponential rational function method (ERFM), and modified extended tanh-function method (METFM). Some plots of some presented new solutions are represented to exhibit wave characteristics. All results in this work are essential to understand the physical meaning and behavior of the investigated equation that sheds light on the importance of investigating various nonlinear wave phenomena in ocean engineering and physics. This equation provides new insights to understand the relationship between the integrability and water waves’ phenomena.

We present a method for optimal path planning of human walking paths inmountainous terrain, using a control theoretic formulation and aHamilton-Jacobi-Bellman equation. Previous models for human navigation wereentirely deterministic, assuming perfect knowledge of the ambient elevationdata and human walking velocity as a function of local slope of the terrain.Our model includes a stochastic component which can account for uncertainty inthe problem, and thus includes a Hamilton-Jacobi-Bellman equation withviscosity. We discuss the model in the presence and absence of stochasticeffects, and suggest numerical methods for simulating the model. We discuss twodifferent notions of an optimal path when there is uncertainty in the problem.Finally, we compare the optimal paths suggested by the model at differentlevels of uncertainty, and observe that as the size of the uncertainty tends tozero (and thus the viscosity in the equation tends to zero), the optimal pathtends toward the deterministic optimal path.

An animal is a planar shape formed by attaching congruent regular polygons along their edges. Usually, these polygons are a finite subset of tiles of a regular planar tessellation. These tessellations can be parameterized using the Schläfli symbol { p , q } , where p denotes the number of sides of the regular polygon forming the tessellation and q is the number of edges or tiles meeting at each vertex. If (p - 2) (q - 2) > 4 , = 4 , or < 4 , then the tessellation corresponds to the geometry of the hyperbolic plane, the Euclidean plane, or the sphere, respectively. In 1976, Harary and Harborth studied animals defined on regular tessellations of the Euclidean plane, finding extremal values for their vertices, edges, and tiles, when any one of these parameters is fixed. They named animals attaining these extremal values as extremal animals. Here, we study hyperbolic extremal animals. For each { p , q } corresponding to a hyperbolic tessellation, we exhibit a sequence of spiral animals and prove that they attain the minimum numbers of edges and vertices within the class of animals with n tiles. We also give the first results on enumeration of extremal hyperbolic animals by finding special sequences of extremal animals that are unique extremal animals, in the sense that any animal with the same number of tiles which is distinct up to isometries cannot be extremal. [ABSTRACT FROM AUTHOR]

We investigate the computation and stability of hierarchical Newton interpolation formulas using ℜ -Leja sequences. We carry out a thorough study, in particular from the angle of rounding errors (underflow/overflow), cost, and numerical stability. Furthermore, conditionings of Newton formulas are addressed and moderate estimates are derived. [ABSTRACT FROM AUTHOR]

The general theory of slender structure buckling by Grabovsky and Truskinovsky (Cont. Mech. Thermodyn. 19(3–4):211-243, 2007), (later extended in J. Nonlinear Sci. 26(1):83–119, 2016 by Grabovsky and the author), predicts that the critical buckling load of a thin shell under dead loading is closely related to the Korn's constant (in Korn's first inequality) of the shell under the Dirichlet boundary conditions resulting from the loading program. It is known that under zero Dirichlet boundary conditions on the thin part of the boundary of positive, negative, and zero (one principal curvature vanishing, and one apart from zero) Gaussian curvature shells, the optimal Korn constant in Korn's first inequality scales like the thickness to the power of −1, − 4 / 3 , and − 3 / 2 respectively. In this work we analyse the scaling of the optimal constant in Korn's first inequality for elliptic shells that contain a finite number of points where both principal curvatures vanish. We prove that the presence of at least one such point on the shell leads to the scaling drop from the thickness to the power of −1 to the thickness to the power of − 3 / 2 . To our best knowledge, this is the first result in the direction for constant-sign curvature shells, that do not contain a developable region. In addition, under the assumption that a suitable trivial branch exists, we prove that in fact the buckling deformation of such shells under dead loading, should be localized at the vanishing curvature points, as the shell thickness h goes to zero. [ABSTRACT FROM AUTHOR]

Numerical simulations of reactive flows are still a challenge when using full detailed kinetic mechanisms, which are becoming larger and larger to incorporate most of the combustion phenomena. One strategy to overcome this issue and simplify the treatment of the chemical kinetics is to use manifold-based methods, and one representative of this class is the Reaction–Diffusion Manifolds (REDIM). In the present work, the REDIM is applied for the first time to study soot formation in ethylene/air counterflow non-premixed flames. A simplified semi-empirical model for soot formation based on acetylene that describes nucleation, surface growth, and oxidation is used, and an uncoupled framework between gas phase and the formation of particulate matter is presented. Validation is carried out for laminar flames, and the results show that REDIM can predict with good accuracy the slow process of soot formation. [ABSTRACT FROM AUTHOR]

In the presented study, the hyperbolic telegraph equation is taken as the focus point. To solve such an equation, an accurate, reliable, and efficient method has been proposed. The developed method is mainly based on the combination of a kind of mesh-free method and an adaptive method. Multiquadric radial basis function mesh-free method is considered on spatial domain and the adaptive fifth-order Runge–Kutta method is used on time domain. The validity and the performance of the proposed method have been checked on several test problems. The approximate solutions are compared with the exact solution, it is shown that the proposed method has more preferable to the other methods in the literature. [ABSTRACT FROM AUTHOR]

We study the problem of recovering an atomic measure on the unit 2-sphere S 2 given finitely many moments with respect to spherical harmonics. The analysis relies on the formulation of this problem as an optimization problem on the space of bounded Borel measures on S 2 as it was considered by Y. de Castro & F. Gamboa (J. Math. Anal. Appl. 395(1):336–354, 2012) and E. Candés & C. Fernandez-Granda (J. Fourier Anal. Appl. 19(6):1229–1254, 2013). We construct a dual certificate using a kernel given in an explicit form and make a concrete analysis of the interpolation problem. Numerical examples are provided and analyzed. [ABSTRACT FROM AUTHOR]

New propulsion systems in aircrafts must meet strict regulations and emission limitations. The Flightpath 2050 goals set by the Advisory Council for Aviation Research and Innovation in Europe (ACARE) include reductions of 75%, 90%, and 65% in CO2, NOx, and noise, respectively. These goals are not fully satisfied by marginal improvements in gas turbine technology or aircraft design. A novel control design procedure for the next generation of turbofan engines is proposed in this paper to improve Full Authority Digital Engine Control (FADEC) systems and reduce the emission levels to meet the Flightpath 2050 regulations. Hence, an Adaptive Network–based Fuzzy Inference System (ANFIS), nonlinear autoregressive network with exogenous inputs (NARX) techniques, and the block-structure Hammerstein–Wiener approach are used to develop a model for a turbofan engine. The Min–Max control structure is chosen as the most widely used practical control algorithm for gas turbine aero engines. The objective function is considered to minimize the emission level for the engine in a pre-defined maneuver while keeping the engine performance in different aspects. The Genetic Algorithm (GA) is applied to find the optimized control structure. The results confirm the effectiveness of the proposed approach in emission reduction for the next generation of turbofan engines. [ABSTRACT FROM AUTHOR]

COVID-19 global outbreak has been significantly damaging the human well-being, life style of people and the global economy. It is clear that the entire world is moving into a dangerous phase of this epidemic at the moment. With absence of a preventive vaccine, the governments across world implement, monitor and manage various public health and social distancing measures to control the spread of this extremely contagious disease and it is found that most of these responses have been critical results of numerous mathematical and decision support models. In this study, SEIR compartment structure is used to model the COVID-19 transmission in Sri Lanka. Reported cases data during the first 80 days of the outbreak is used to model the time dependent transmission rate of the disease. Optimal transmission rates and initial size of the exposed and infected sizes of the populations are then estimated matching between clinically identified cases to model based simulated outcomes.

Electrodeposition in the presence of a DC field is an unstable process leading to morphological patterns on the cathode. The effect of a low-frequency and small amplitude AC forcing superimposed on a base DC field, Δ V , is investigated by perturbation theory and Floquet analysis. It is shown that we can forecast the stability behavior of the AC problem from the nature of the graph of electrode base speed, U, versus Δ V . The key finding is this: when this graph is always of negative curvature, the effect of AC forcing is stabilizing, whereas when the curvature changes sign, the effect of AC forcing can be either destabilizing or stabilizing. The difference in the two types of U– Δ V curves is characterized by a single dimensionless group that signals the change from diffusion-controlled transport to transport controlled by reaction kinetics at the electrodes. The critical value of this parameter that marks the transition is obtained analytically. [ABSTRACT FROM AUTHOR]

Queueing systems are modeled by equations which depend on a large number of input parameters. In practice, significant uncertainty is associated with estimates of these parameters, and this uncertainty must be considered in the analysis of the model. The objective of this paper is to propose a sensitivity analysis approach for a queueing model, presenting parameters that follow a Gaussian distribution. The approach consists in decomposing the output of the model (stationary distribution of the model) into a polynomial chaos. The sensitivity indices, allowing to quantify the contribution of each parameter to the variance of the output, are obtained directly from the coefficients of decomposition. The proposed approach is then applied to M/G/1/N queueing model. The most influential parameters are highlighted. Finally several numerical and data examples are sketched out to illustrate the accuracy of the proposed method and compare them with Monte Carlo simulation. The results of this work will be useful to practitioners in various fields of theoretical and applied sciences. [ABSTRACT FROM AUTHOR]

In this paper, we describe new hybrid genetic algorithm and particle swarm optimization to solve the sum of earliness and the number of tardy job on two-machines flow shop schedule problem is NP- hard. The study discusses a hybrid genetic algorithm and particle swarm optimization (HGA-PSO) to tackle the presented mission. Extensive experiments, based on computers, suggest that the proposed mathematical models are efficient in solving flow shop problems with GA solved to n = 3000 while PSO solved to n = 500 job. [ABSTRACT FROM AUTHOR]

This study provides a detailed exposition of in-hospital community-acquired methicillin-resistant S. aureus (CA-MRSA) which is a new strain of MRSA, and hospital-acquired methicillin-resistant S. aureus (HA-MRSA) employing Caputo fractional operator. These two strains of MRSA, referred to as staph, have been a serious problem in hospitals and it is known that they give rise to more deaths per year than AIDS. Hence, the transmission dynamics determining whether the CA-MRSA overtakes HA-MRSA is analyzed by means of a non-local fractional derivative. We show the existence and uniqueness of the solutions of the fractional staph infection model through fixed-point theorems. Moreover, stability analysis and iterative solutions are furnished by the recursive procedure. We make use of the parameter values obtained from the Beth Israel Deaconess Medical Center. Analysis of the model under investigation shows that the disease-free equilibrium existing for all parameters is globally asymptotically stable when both R 0 H and R 0 C are less than one. We also carry out the sensitivity analysis to identify the most sensitive parameters for controlling the spread of the infection. Additionally, the solution for the above-mentioned model is obtained by the Laplace-Adomian decomposition method and various simulations are performed by using convenient fractional-order α . [ABSTRACT FROM AUTHOR]

Emerging as a new field, quantum computation has reinvented the fundamentals of Computer Science and knowledge theory in a manner consistent with quantum physics. The fact that quantum computation has superior features and new events than classical computation provides benefits in proving mathematical theories. With advances in technology, the nonlinear partial differential equations are used in almost every area, and many difficulties have been overcome by the solutions of these equations. In particular, the complex solutions of KdV and Burgers equations have been shown to be used in modeling a simple turbulence flow. In this study, Burger-like equation with complex solutions is defined in Hilbert space and solved with an example. In addition, these solutions were analyzed. Thanks to the Quantum Burgers-Like equation, the nonlinear differential equation is solved by linearizing. The pattern changes of time made the result linear. This means that the Quantum Burgers-Like equation can be used to smoothen the sonic processing.

The benefit of this paper is to find the circular divison of the factor group when r is an odd number, where Q2r is denoted to Quaternion group of order 4r, such that for each positive integer r, there are two generators a and b for Q2r satisfies Q2r = {ah bk, 0 ≤ h ≤ 2r − 1, k = 0, 1} which has the following properties {a2r = b4 = I, barb−1 = a−r}. [ABSTRACT FROM AUTHOR]

In this study, we applied the generalized Kudryashov method to two different conformable fractional differential equations and one system namely Burgers' equation with conformable derivative, Wu-Zhang system with conformable derivative, and the conformable sinh-Gordon equation. Obtained solutions are soliton-type solutions. All obtained solutions have been verified and considered correct by placing them in the original equation with the help of the Maple software program. Also, we have plotted three-dimensional (3D) graphs of some of these solutions with the help of Maple. [ABSTRACT FROM AUTHOR]

This article addresses numerical simulation of the mechanical behaviour of materials comprising heterogeneous ductile micro-structures in the presence of voids using a multi-scale approach considering plasticity processes. This kind of material has been used in several applications as structural solutions. Therefore, for safety reasons, studies about stress analysis of porous ductile materials are essential to understand their mechanical behaviour. Numerical modelling is performed in micro-structures using the concept of representative volume element (RVE) where the matrix is considered as an ideally plastic material governed by the von Mises model with isotropic hardening, while inclusions are adopted as very stiff elastic materials. Also, fracture and contact finite elements are used to model the phase debonding. Different distributions of voids and inclusions are assumed in the RVE domain to investigate their influences on the proposed analyses. We conclude, for instance, that the concentration of voids in the RVE decreases its loading capacity. On the other hand, we show in the numerical examples that the RVEs containing random distributions of voids present loading capacity improved when compared to the RVEs containing symmetric distributions of voids. Moreover, the results show that the insertion of reinforcements into porous ductile media has limited efficiency when dealing with high values of loading. [ABSTRACT FROM AUTHOR]

Information propagation driven by the epidemic may cause individuals awareness to change their behavior to prevent themselves from being infected, as we observed in reality that aware individuals often migrate away from infected areas. In this work, we study the coupled interaction of epidemic spreading and information propagation over a two-layer metapopulation network, where aware and unaware individuals separately take different migration routes, and mainly explore how individual migration route affects the epidemic spreading. Combined with the transition probability tree of individual states, we use Markovian chain approach to derive the epidemic threshold for the proposed model. Through numerous Monte Carlo simulations, we verify the accuracy of the Markovian equations for the prediction of epidemic dynamics. The results show that the role of information transmission in suppressing the epidemic is limited. Further increase in the information transmission rate beyond some critical value will no longer affect the epidemic. Detailed analysis of information propagation has to consider the migration route of individuals, especially the aware individuals, and their mobility frequency. In addition, the initial population distribution is also a fundamental factor for the epidemic dynamic. With a heterogeneous population distribution, frequent mobility of individuals would delay the epidemic spread, while with the homogeneous population distribution, it does not. The study of the coupled interaction between epidemic and information over separate migration routes provides helpful guidance for the intervention of epidemic in reality. [ABSTRACT FROM AUTHOR]