Shaher Momani, Fatimah Noor Harun, Rasha Amryeen
et al.
This work concerns the construction of the approximate analytical solutions for the nonlinear complex conformable Ginzburg-Landau equations with external potential using the conformable residual series method. The governing model plays a pivotal role in modeling complex physical phenomena such as Bose-Einstein condensation and building approximate analytical solutions for this model, which is considered a distinctive addition given the scarcity of work presented in the literature in this context. The methodology lies in combines of generalized multivariable power series and residual error function. Convergence analysis is provided to illustrate the theoretical framework of our scheme in handling the projected nonlinear models. For a sake of practical computation, several naturalistic applications for Bose-Einstein condensates are examined involving zero trapping, periodic box, optical lattice, and harmonic potentials. In this orientation, numeric computations and graphical representations are provided to verify the correctness and accuracies of the tested applications. The dynamic behaviors of wave soliton solutions are captured at different parameters in addition to the comparison of acquired wave solutions with previous studies. The overall impact of this work lies in the ease with which the proposed approach can be applied to construct efficient and systematic approximate analytical solutions for complex nonlinear partial differential equations arising in quantum optics, quantum gases, quantum fluids, and other quantum mechanical phenomena.
In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.
Maissa Farhat, Azzeddine Dekhane, Abdelhak Djellad
et al.
The accurate prediction of the Maximum Power Point (PMPP) in photovoltaic (PV) systems is critical for optimizing energy yield and enhancing solar energy harvesting efficiency. This study explores the application of data-driven methods to improve PMPP prediction, utilizing advanced regression techniques such as Ridge Regression, Lasso Regression, Decision Tree Regression, and Random Forest Regression. By analyzing a dataset of irradiance, temperature, and PMPP measurements, the research compares the performance of these models in capturing complex nonlinear relationships between key variables. Results indicate that tree-based models, particularly Random Forest Regression, outperform linear models, demonstrating superior predictive accuracy and robustness. Feature importance analysis further highlights the dominant influence of irradiance (GPOA) on PMPP, emphasizing the value of precise irradiance data. These findings underscore the potential of machine learning techniques in optimizing PV system performance. Future research should focus on integrating additional features, such as atmospheric conditions and panel characteristics, and exploring deep learning methods to enhance prediction accuracy further.
Biological research traditionally relies on experimental methods, which can be inefficient and hinder knowledge transfer due to redundant trial-and-error processes and difficulties in standardizing results. The complexity of biological systems, combined with large volumes of data, necessitates precise mathematical models like ordinary differential equations (ODEs) to describe interactions within these systems. However, the practical use of ODE-based models is limited by the need for curated data, making them less accessible for routine research. To overcome these challenges, we introduce LazyNet, a novel machine learning model that integrates logarithmic and exponential functions within a Residual Network (ResNet) to approximate ODEs. LazyNet reduces the complexity of mathematical operations, enabling faster model training with fewer data and lower computational costs. We evaluate LazyNet across several biological applications, including HIV dynamics, gene regulatory networks, and mass spectrometry analysis of small molecules. Our findings show that LazyNet effectively predicts complex biological phenomena, accelerating model development while reducing the need for extensive experimental data. This approach offers a promising advancement in computational biology, enhancing the efficiency and accuracy of biological research.
In this paper, we discuss how theoretical results from one family of fuzzy sets can be carried over immediately to another family of fuzzy sets by the use of lattice isomorphisms. We also show that these families can occur naturally and that applications may not necessarily be carried over using these isomorphisms. We illustrate this using techniques from the study of human trafficking and its analysis using mathematics of uncertainty. We also consider the new definition of fuzzy set provided by Trillas and de Soto.
The standard Lane–Emden equations model several physical phenomena such as isotropic continuous media, thermal behaviour of a spherical cloud of gas, and isothermal gas spheres. Systems of Lane–Emden-type equations appear in the modelling of the concentration of carbon substrate and oxygen, catalytic diffusion reactions, the steady state concentration of carbon dioxide, dusty fluid models, and pattern formation. In solving singular boundary value problems, one faces challenges resulting from the divergence of the associated variable coefficients at the singular points. This research article explores the power series approach to analytically approximate solutions to a class of systems of strongly nonlinear singular boundary value problems of Lane–Emden-type. The nonlinear terms in the proposed problems are transformed into power series using the generalised Cauchy product before establishing explicit recursion formulae for the expansion coefficients of the system of series solutions. The initial conditions required in the proposed boundary value problems are assumed and determined from a set of nonlinear algebraic equations resulting from the given right boundary conditions. Three special systems of nonlinear singular boundary value problems of Lane–Emden type are presented to demonstrate the proposed method’s reliability, effectiveness, and accuracy. The obtained approximate solutions are compared with the exact solutions (where they are available), or with other existing results (where the exact solution is not readily available). The series solution of the first example has a slow convergent rate, while the results of the other two examples are in excellent agreement with the exact solutions and other published results.
Christos Sammoutos, Angeliki Kitsopoulou, Panagiotis Lykas
et al.
The exploitation of solar irradiation is a critical weapon for facing the energy crisis and critical environmental problems. One of the most emerging solar technologies is the use of solar towers (or central receiver systems) coupled with high-performance thermodynamic cycles. In this direction, the present investigation examines a solar tower coupled to a closed-loop Brayton cycle which operates with supercritical CO<sub>2</sub> (sCO<sub>2</sub>) as the working medium. The system also includes a storage system with two molten salt tanks for enabling proper thermal storage. The sCO<sub>2</sub> is an efficient fluid that presents significant advancements, mainly reduced compression work when it is compressed close to the critical point region. The novelty of the present work is based on the detailed dynamic investigation of the studied configuration for the year period using adjustable time step and its sizing for achieving a continuous operation, something that makes possible the establishment of this renewable technology as a reliable one. The analysis is conducted with a developed model in the Modelica programming language by also using the Dymola solver. According to the simulation results, the yearly solar thermal efficiency is 50.7%, the yearly thermodynamic cycle efficiency is 42.9% and the yearly total system efficiency is 18.0%.
We re-examine the old question to what extent mathematics may be compared with a game. Mainly inspired by Hilbert and Wittgenstein, our answer is that mathematics is something like a rhododendron of language games, where the rules are inferential. The pure side of mathematics is essentially formalist, where we propose that truth is not carried by theorems corresponding to whatever independent reality and arrived at through proof, but is defined by correctness of rule-following (and as such is objective given these rules). Goedel's theorems, which are often seen as a threat to formalist philosophies of mathematics, actually strengthen our concept of truth. The applied side of mathematics arises from two practices: first, the dual nature of axiomatization as taking from heuristic practices like physics and informal mathematics whilst giving proofs and logical analysis; and second, the ability of using the inferential role of theorems to make surrogative inferences about natural phenomena. Our framework is pluralist, combining various (non-referential) philosophies of mathematics.
Michael Byamukama, Damian Kajunguri, Martin Karuhanga
The control of opportunistic infections among HIV infected individuals should be one of the major public health concerns in reducing mortality rate of individuals living with HIV/AIDS. In this study a deterministic co-infection mathematical model is employed to provide a quantification of treatment at each contagious stage against Pneumocystis Pneumonia (PCP) among HIV infected individuals on ART. The disease-free equilibrium for the HIV/AIDS sub model, PCP sub model and the co-infection model are shown to be locally asymptotically stable when their associated disease threshold parameter is less than a unity. By use of suitable Lyapunov functions, the endemic equilibrium corresponding to HIV/AIDS and PCP sub models are globally asymptotically stable whenever $\mathcal{R}_{0H}>1$ and $\mathcal{R}_{0P}>1$ respectively. The sensitivity analysis results implicate that the effective contact rates are the main mechanisms fueling the proliferation of the two diseases and on the other hand treatment efforts play an important role in reducing the incidence. Numerical simulations show that treatment of PCP at all contagious stages reduces its burden on HIV/AIDS patients and dual treatment of the co-infected individuals significantly reduces the burden of the co-infection.
The paper aims to provide a brief overview of soliton solutions obtained through the Hirota direct method. A bilinear formulation of soliton solutions in both (1+1)-dimensions and (2+1)-dimensions is discussed, together with applications to various integrable equations. The Hirota conditions for N-soliton solutions are analyzed and a few open questions regarding higher-dimensional cases and generalized bilinear equations are presented.
Olawale O. Kehinde, Justin B. Munyakazi, Appanah R. Appadu
Despite the availability of an abundant literature on singularly perturbed problems, interest toward non-linear problems has been limited. In particular, parameter-uniform methods for singularly perturbed semilinear problems are quasi-non-existent. In this article, we study a two-dimensional semilinear singularly perturbed convection-diffusion problems. Our approach requires linearization of the continuous semilinear problem using the quasilinearization technique. We then discretize the resulting linear problems in the framework of non-standard finite difference methods. A rigorous convergence analysis is conducted showing that the proposed method is first-order parameter-uniform convergent. Finally, two test examples are used to validate the theoretical findings.
The interactions between predators and their prey in the real world are usually affected by diverse ecological phenomena acting on both the prey and the predators.
Collaboration or cooperation between predators is one of those behaviors, which has received less attention from researchers than competition among consumers. These contacts are important aspects of the dynamics of food chains and trophic webs.
In this work, we will study the influence of collaboration or cooperation (hunting cooperation) between predators to consume (or capture) their favorite prey, which are affected by an effect Allee weak.
We extend the results obtained in a previously published model, considering only collaboration between predators and in which the Allee effect is absent.
هدف: روند تشخیص اختلال روانی در رویکردهای سنتی، متکی بر پرسشنامه، مصاحبه و بررسیهای بالینی است؛ درحالیکه ابزارهای غربالگری خودکار میتوانند مسیر کوتاهتری را طی کنند و بهعنوان استراتژیهای ارزیابی نوین، سیستمهای پشتیبان تصمیم و راهبردهای پیشگیری برای کمک به افراد مستعد توسعه یابند. با توجه به تمایل افراد به اشتراکگذاری افکار و احساسات در سکوهای اجتماعی، دادههای میکروبلاگینگ حاوی اطلاعات ارزشمندی هستند که میتوانند برای شناسایی حالات روانی مورد تحلیل قرار گیرند. هدف از این پژوهش تشریح سازوکار تحلیل داده در زمینه مورد بحث است.روششناسی پژوهش: در این مقاله، در ابتدا مفاهیمی مانند سلامت روان الکترونیک و سکوهای میکروبلاگینگ معرفی شده و با ارائه توضیحاتی در خصوص علم داده و تحلیل داده اجتماعی، ارتباط مفاهیم با یکدیگر مورد بحث قرار میگیرد. در ادامه در قالب بخشی جداگانه، پیشبینی اختلال در شبکههای اجتماعی شرح داده میشود. در نهایت با بررسی سوابق تحقیق و مسائل باز، به چگونگی جمعآوری داده، پیشپردازش و روند استفاده از ویژگیهای متفاوت به کمک ابزارهای تحلیل گوناگون میپردازیم.یافتهها: این پژوهش با پیادهسازی نمونهای کاربردی از تجزیهوتحلیل داده اجتماعی روی دادههای دنیای واقعی نشان میدهد، ویژگیهای استخراج شده از نمایه کاربر، تأثیر قابل توجهی در پیشبینی علائم افسردگی دارند و حتی میتوان با اطلاعات استخراج شده از نمایه عمومی کاربر، وضعیت روانی را با دقتی مناسب پیشبینی نمود.اصالت/ارزش افزوده علمی: در این پژوهش چگونگی تحلیل خودکار داده اجتماعی با هدف شناسایی اختلال روانی شرح داده شده و در پیادهسازی مشخص میشود که علائم تقریباً در تمام ویژگیهای مورد مطالعه قابل پیگیری هستند.
In this paper we provide a quantitative analysis to the concept of arbitrage, that allows to deal with model uncertainty without imposing the no-arbitrage condition. In markets that admit ``small arbitrage", we can still make sense of the problems of pricing and hedging. The pricing measures here will be such that asset price processes are close to being martingales, and the hedging strategies will need to cover some additional cost. We show a quantitative version of the Fundamental Theorem of Asset Pricing and of the Super-Replication Theorem. Finally, we study robustness of the amount of arbitrage and existence of respective pricing measures, showing stability of these concepts with respect to a strong adapted Wasserstein distance.
Image stitching can be employed to stitch images taken from different times, perspectives, or devices into a panorama with a wider view. However, the imaging specification of images to be stitched is strict. If the imaging specification is not satisfied, artefacts caused by inaccurate alignment and unnatural distortion will occur. Semantic segmentation can solve the classification problem at the pixel level; however, image stitching significantly depends on the accuracy of feature points. Therefore, this paper proposes an image stitching algorithm based on semantic segmentation to guide feature point classification and seam fusion. First, the images are recognized by a cascade semantic segmentation network, and the image feature points are classified. Thereafter, the corresponding homography transformations are calculated using different class feature points, and the best homography mapping for the entire target image is selected. Finally, a seam-cutting algorithm based on semantic segmentation is used to compute the seam, and a feathering Poisson fusion with distance transformation is used to eliminate artefacts and light differences. Experiments show that the algorithm can generate transitional natural and perceptual stitching results even under the influence of perspective and light differences.
Annalisa Buffa, Gregor Gantner, Carlotta Giannelli
et al.
This paper reviews the state of the art and discusses recent developments in the field of adaptive isogeometric analysis, with special focus on the mathematical theory. This includes an overview of available spline technologies for the local resolution of possible singularities as well as the state-of-the-art formulation of convergence and quasi-optimality of adaptive algorithms for both the finite element method (FEM) and the boundary element method (BEM) in the frame of isogeometric analysis (IGA).
This paper presents approximation methods for time-dependent thermal radiative transfer problems in high energy density physics. It is based on the multilevel quasidiffusion method defined by the high-order radiative transfer equation (RTE) and the low-order quasidiffusion (aka VEF) equations for the moments of the specific intensity. A large part of data storage in TRT problems between time steps is determined by the dimensionality of grid functions of the radiation intensity. The approximate implicit methods with reduced memory for the time-dependent Boltzmann equation are applied to the high-order RTE, discretized in time with the backward Euler (BE) scheme. The high-dimensional intensity from the previous time level in the BE scheme is approximated by means of the low-rank proper orthogonal decomposition (POD). Another version of the presented method applies the POD to the remainder term of P2 expansion of the intensity. The accuracy of the solution of the approximate implicit methods depends of the rank of the POD. The proposed methods enable one to reduce storage requirements in time dependent problems. Numerical results of a Fleck-Cummings TRT test problem are presented.
Ramón Escobedo, Valentin Lecheval, Vaios Papaspyros
et al.
Group-living organisms that collectively migrate range from cells and bacteria to human crowds, and include swarms of insects, schools of fish and flocks of birds or ungulates. Unveiling the behavioural and cognitive mechanisms by which these groups coordinate their movements is a challenging task. These mechanisms take place at the individual scale and they can be described as a combination of pairwise interactions between individuals and interactions between these individuals and the physical obstacles in the environment. Thanks to the development of novel tracking techniques that provide large and accurate data sets, the main characteristics of individual and collective behavioural patterns can be quantified with an unprecedented level of precision. However, in a large number of works, social interactions are usually described by force map methods that only have a limited capacity of explanation and prediction, being rarely suitable for a direct implementation in a concise and explicit mathematical model. Here, we present a general method to extract the interactions between individuals that are involved in the coordination of collective movements in groups of organisms. We then apply this method to characterize social interactions in two species of shoaling fish, the rummynose tetra (Hemigrammus rhodostomus) and the zebrafish (Danio rerio), which both present a burst-and-coast motion. The detailed quantitative description of microscopic individual-level interactions thus provides predictive models of the emergent dynamics observed at the macroscopic group-level. This method can be applied to a wide range of biological and social systems.
Abstract Fires can be an important hazard for the safety of chemical and process industries. Particularly, pool fires are the most frequent fire scenarios in such facilities and can affect other equipment of the plant with severe consequences due to the domino effect. During the last decades, simplified fire modelling tools were used to predict some of the harmful effects that hydrocarbon pool fires may entail. Although these can be applied to limited number of scenarios, they cannot cover the overall characteristics governing the fire behaviour. Computational Fluid Dynamics (CFD) modelling can provide more detailed insights of the related fire effects, can consider complex geometries and can represent from small to large scale fires. However, simulation results should be firstly compared to experimental measurements in order to assess the predictive capabilities of these tools. This paper investigates the predictive capabilities of CFD modelling when performing a priori simulations of medium and large scale hydrocarbon pool fires. The main objective is to assess the fire effects prediction performance of two CFD codes that may be used to evaluate the hazard of hydrocarbon pool fires. FLACS-Fire and FDS codes have been used to simulate medium and large scale pool fires (1.5, 3, 4, 5 and 6 m-diameter) of diesel and gasoline fuels in unconfined environments. Given the notable differences between the mathematical methods applied to solve the CFD sub-models, the mesh resolution and the boundary conditions in each investigated tool, this study is not aimed at directly comparing both codes (i.e. using identical sub-models choices). However, the present CFD analysis is intended to reveal the potential of each software separately by applying the most appropriate modelling options for each tool. Based on a qualitative assessment of the predictions and a quantitative error estimation of the variables measured (i.e. flame temperature, burning rate, heat flux, flame height, flame surface, and surface emissive power), the main strengths and weaknesses of FLACS-Fire and FDS are identified when modelling hydrocarbon pool fires.