Integral Solution Research Articles

A Force Function Formula for Solutions of Nonlinear Weakly Singular Volterra Integral Equations

In this paper, we examine the nonlinear Weakly Singular Volterra Integral Equation(WSVIE), $u(x)=f(x)+\int_{0}^{x}\frac{t^{\mu-1}}{x^\mu}[u(t)]^\beta dt$. AL-Jawary and Shehan used Daftardar-Jafari Method(DJM) and solved the above integral equation for the investigation parameter $\mu>1$ using specific force functions with $\mu$ and $\beta$ values and obtained unique solutions. We have discovered a force function $f(x)=x^{k_1}-{\frac{x^{\gamma k_1}}{\gamma k_1+\mu}}$, that allows the introduction of noise terms phenomena discovered by Wazwaz; that cancel out the terms of the power series in the successive solution terms $u_m$, $m=0,1,2,...,n$: we thus obtain a maximum finite power series terms for each solution term called truncation point and denoted by $x^{g(n)}$. Such that the integral solution can be written as $u(x)=u_0+\sum_{m=1}^{n}u_m$, where $n$ is finite. Simplifying the solution terms we get the unique solution $u(x)=x^{k_1}$, irrespective of $n-$value in the truncation point. We discovered a formula relation between the last solution term $u_n$ and the truncation point as $u_n=a_nx^{g(n)}$. Our results confirm the results of the two solution examples of AL-Jawary and Shehan for the investigation parameter $\mu>1$. We extend the parameter range to include $\mu>1$ and $0<\mu\leq 1$ for our solution. In addition, for any chosen rational parameter $k_1$, the solution $u(x)=x^{k_1}$ is extrapolated to be valid for all integer parameter values $\beta\geq 2$, and positive rational parameter value $\mu>0$ and for any finite value of $n\geq2$.

Attached Flows for Reaction–Diffusion Processes Described by a Generalized Dodd–Bullough–Mikhailov Equation

This paper uses the attached flow method for solving nonlinear second-order differential equations of the reaction–diffusion type. The key steps of the method consist of the following: (i) reducing the differentiability order by defining the first derivative of the variable as a new variable called the flow and (ii) a forced decomposition of the derivative-free term so that the flow appears explicitly in it. The resulting reduced equation is solved using specific balancing rules. Only step (i) would lead to an Abel-type equation with complicated integral solutions. Completed with (ii) and with the graduation procedure, the attached flow method used in the paper, without requiring such a great effort, allows for the obtaining of accurate analytical solutions. The method is applied here to a subclass of reaction–diffusion equations, the generalized Dodd–Bulough–Mikhailov equation, which includes a translation of the variable and nonlinearities up to order five. The equation is solved for each order of nonlinearity, and the solutions are discussed following the values of the parameters involved in the equation.

Minimal graphs in Riemannian spaces

In this treatise, we discuss existence and uniqueness questions for parametric minimal surfaces in Riemannian spaces, which represent minimal graphs. We choose the Riemannian metric suitably such that the variational solution of the Riemannian Dirichlet integral under Dirichlet boundary conditions possesses a one-to-one projection onto a plane. At first we concentrate our considerations on existence results for boundary value problems. Then we study uniqueness questions for boundary value problems and for complete minimal graphs. Here we establish curvature estimates for minimal graphs on discs, which imply Bernstein-type results.

Mass transport in Couette flow

In this study we examine the large Péclet number, Pe, limit of a concentration boundary layer in Couette flow. The boundary layer has a thickness of order Pe−1/2. The asymptotic concentration is asymptotically obtained as an integral solution up to order Pe−1/2 using the Fourier sine transform. The asymptotic solution is found to be in good agreement with the full numerical solution for large Péclet numbers. Further, the effective diffusivity obtained from the asymptotic solution is found to be in good agreement with the effective diffusivity obtained from the full numerical solution for large Péclet numbers.

Noisecut: a python package for noise-tolerant classification of binary data using prior knowledge integration and max-cut solutions

BackgroundClassification of binary data arises naturally in many clinical applications, such as patient risk stratification through ICD codes. One of the key practical challenges in data classification using machine learning is to avoid overfitting. Overfitting in supervised learning primarily occurs when a model learns random variations from noisy labels in training data rather than the underlying patterns. While traditional methods such as regularization and early stopping have demonstrated effectiveness in interpolation tasks, addressing overfitting in the classification of binary data, in which predictions always amount to extrapolation, demands extrapolation-enhanced strategies. One such approach is hybrid mechanistic/data-driven modeling, which integrates prior knowledge on input features into the learning process, enhancing the model’s ability to extrapolate.ResultsWe present NoiseCut, a Python package for noise-tolerant classification of binary data by employing a hybrid modeling approach that leverages solutions of defined max-cut problems. In a comparative analysis conducted on synthetically generated binary datasets, NoiseCut exhibits better overfitting prevention compared to the early stopping technique employed by different supervised machine learning algorithms. The noise tolerance of NoiseCut stems from a dropout strategy that leverages prior knowledge of input features and is further enhanced by the integration of max-cut problems into the learning process.ConclusionsNoiseCut is a Python package for the implementation of hybrid modeling for the classification of binary data. It facilitates the integration of mechanistic knowledge on the input features into learning from data in a structured manner and proves to be a valuable classification tool when the available training data is noisy and/or limited in size. This advantage is especially prominent in medical and biomedical applications where data scarcity and noise are common challenges. The codebase, illustrations, and documentation for NoiseCut are accessible for download at https://pypi.org/project/noisecut/. The implementation detailed in this paper corresponds to the version 0.2.1 release of the software.

Iterated Robin problem, the case of various parameters

ABSTRACT Prescribing Robin boundary conditions for the iterated Poisson equation ( ∂ z ∂ z ¯ ) n w = f leads to Robin-n problems. Extending previous results by allowing an independent choice for the parameters α k , β k for every iteration k , 1 ≤ k ≤ n , leads to explicit integral representations depending on the data of the Robin-n problem. Parting from these integral representation explicit solutions with their respective solvability conditions are derived. For the unit disc of the complex plane, the Robin functions for n = 2 and 3 are explicitly constructed.

Kinematic and Joint Compliance Modeling Method to Improve Position Accuracy of a Robotic Vision System.

In the field of robotic automation, achieving high position accuracy in robotic vision systems (RVSs) is a pivotal challenge that directly impacts the efficiency and effectiveness of industrial applications. This study introduces a comprehensive modeling approach that integrates kinematic and joint compliance factors to significantly enhance the position accuracy of a system. In the first place, we develop a unified kinematic model that effectively reduces the complexity and error accumulation associated with the calibration of robotic systems. At the heart of our approach is the formulation of a joint compliance model that meticulously accounts for the intricacies of the joint connector, the external load, and the self-weight of robotic links. By employing a novel 3D rotary laser sensor for precise error measurement and model calibration, our method offers a streamlined and efficient solution for the accurate integration of vision systems into robotic operations. The efficacy of our proposed models is validated through experiments conducted on a FANUC LR Mate 200iD robot, showcasing notable improvements in the position accuracy of robotic vision system. Our findings contribute a framework for the calibration and error compensation of RVS, holding significant potential for advancements in automated tasks requiring high precision.

Solution for Integration of Renewable Energy Power Plants into Smart Grids with Active Power Control

This article addresses the integration of renewable energy power plants into smart grids and active power control. Renewable energy sources contribute to environmentally friendly and sustainable energy production, but the fluctuations inherent in these sources pose a challenge for energy grids. The article examines various technologies that can be used to overcome this challenge and make energy grids more reliable. Smart grids aim to improve energy grids by optimizing energy production, transmission, and distribution using data analytics, automation, and communication technologies. The integration of renewable energy power plants into these smart grids offers significant advantages, including the ability to predict energy production, integrate with energy storage systems, and manage energy demand. The article also emphasizes the importance of active power control. Active power control is used to manage energy production steadily, thereby maintaining grid stability. Balancing energy fluctuations from renewable energy sources and storing excess energy when needed enhances grid stability. In conclusion, this article discusses the crucial role of integrating renewable energy power plants into smart grids and implementing active power control in the energy sector. These integration and control methods are important steps in making energy grids more sustainable, efficient, and reliable.

Higher performance enhancement of direct torque control by using artificial neural networks for doubly fed induction motor

Recently Direct Torque Control is widely appreciated compared to other conventional control methods due to its numerous advantages, notably its speed and precision. However, despite its qualities, it often encounters torque ripples that limit its operational effectiveness. These variations can be attributed to the use of hysteresis comparators, leading to variable frequency operation and undesirable speed overshoots. To address these challenges and enhance overall motor control, this article introduces a new approach based on neural networks. Direct Torque Control method is specifically designed for Doubly Fed Induction Motors and utilizes an Artificial Neural Network. Unlike conventional methods, this approach eliminates the need for speed controllers, commutation tables, and hysteresis comparators, thus providing a more integrated and efficient solution. Simulations conducted in the Matlab/Simulink environment have demonstrated the significant advantages of this approach with a higher performance enhancement. Not only were torque ripples reduced, but speed overshoot was completely eliminated. Furthermore, significant reductions in Total Harmonic Distortion values of stator and rotor currents were achieved, indicating an overall improvement in system performance.

System for Biological Sensor-Based Stress Detection Using the Bohm-Jacopini Algorithm

Chronic stress has become a pervasive issue in modern society, particularly impacting professions like car driving. While mitigating stress entirely may not be feasible, exploring effective coping mechanisms is crucial. Although research on stress management is extensive, few studies have harnessed the power of modern technology to assess stress levels and simultaneously develop integrated management solutions.

Event Management to Connect Across Video Conferencing Platforms

Managing events across multiple video conferencing platforms poses challenges in coordination, resulting in inefficiencies and fragmented user experiences. To address these issues, this project develops a cross-platform integration solution, creating a unified platform for seamless management, scheduling, and tracking of meetings. Integration techniques, such as authentication mechanisms and request wrappers, are explored to facilitate interaction with major platforms like Zoom, Microsoft Teams, and Google Meet. The project aims to enhance user workflow efficiency across multiple platforms by introducing a suite of integrated components. The cornerstone is a secure User Authentication system with Single Sign-On support, ensuring streamlined access. A Unified Dashboard serves as a centralised hub for managing meetings, eliminating the need for platform-switching. Cross-Platform Scheduling enables seamless meeting arrangement from a single interface, while Real-Time Updates keep users informed of schedule changes. Additionally, the incorporation of Artificial Intelligence-driven chat for meeting scheduling facilitates intuitive, natural language-based interaction. Together, these components optimise user experience, saving time and effort. Keywords—Meet, Event Management, Zoom, Integration, video conference

Integrability and Symmetry of Positive Integrable Solutions for Weighted Wolff-Type Integral Systems

Integrability and Symmetry of Positive Integrable Solutions for Weighted Wolff-Type Integral Systems

Self-management of water: uses of rainwater harvesting. The case of Sierra de Mexico

Introduction: rainwater harvesting and self-management of water are promising approaches to address water scarcity and limited access to safe drinking water. These approaches require the active participation of individuals and communities, fostering solidarity, cooperation and trust among them. At the same time, it is essential to be supported by government policies that promote and facilitate the implementation of rainwater harvesting systems and establish a sound regulatory basis for their safe and effective use. Methods: a mixed approach was used, combining the benefits of qualitative research with documentary reviews. This approach allowed us to examine and describe key aspects related to water self-management, social capital and the role of government policies in the implementation of rainwater harvesting, especially in the community of La Lupita in Lerma, State of Mexico. Results: this community has implemented traditional self-management strategies to cope with water scarcity, such as rainwater harvesting and the use of community reservoirs. However, challenges in water supply persist, especially during the dry season. Conclusions: it is necessary to promote integral solutions that combine rainwater harvesting with governmental actions and promote education on responsible water use

Water–energy network provisioning services in Harare, Zimbabwe

Abstract Water-energy systems are interlinked. Energy is used in the treatment and pumping of water. Water is used to generate electricity. Effective and efficient water-energy network provisioning satisfies households' basic human needs. Most local authorities in developing countries have seen water and energy scarcity amid climate change. The research aims to understand the interlinkages of water-energy services and to develop integrated and innovative green solutions in line with sustainable development goals. This study explores water and energy network provisioning to promote an integrated approach to planning and managing service delivery in Harare, Zimbabwe. The paper also establishes how water and energy provisioning challenges have affected household activities. The study embraced a sequential mixed-methods approach. In-depth interviews were used to solicit information from relevant departments and focus group discussions from communities. A total of 314 questionnaires were administered to five communities based on five settlement classifications. The study hinges on the ‘collective action theory'. Findings revealed poor governance issues, lack of finance and public participation in water-energy service delivery. Integration of sectors and community participation can improve the provision of water -energy services and contribute to reducing carbon emissions through greening households.

Integral Transform Solution for Natural Convection Within Horizontal Concentric Annular Cavities

Abstract Natural convection inside horizontal concentric annular cavities is dealt with through the generalized integral transform technique (GITT), offering a hybrid numerical-analytical solution of the continuity, Navier–Stokes, and energy equations in cylindrical coordinates. The flow is in steady-state, laminar regime, two-dimensional, buoyancy-induced, and the governing equations are written in the streamfunction-only formulation. Two strategies of integral transformation are adopted to verify the best computational performance, namely, the usual one with eigenvalue problems for both streamfunction and temperature defined in the radial variable, and a novel alternative with eigenvalue problems defined in the azimuthal angular coordinate. First, the eigenfunction expansions convergence behavior is analyzed to critically compare the two integral transform solution strategies. Then, test cases for different aspect ratios and Rayleigh numbers are validated with experimental data from the classical work of Kuehn and Goldstein. A maximum relative deviation of 5% is found comparing the GITT results for the average Nusselt number against the experimental data, while an 8% maximum relative deviation is found comparing against an empirical correlation by the same authors. It is concluded that the GITT solution with the eigenvalue problem in the angular coordinate yields better convergence rates than the more usual eigenfunction expansion in the radial variable. This is due to the originally homogeneous boundary conditions in the angular direction, which do not require filtering for convergence enhancement, as opposed to the required filter in the radial direction that introduces a source term in the filtered equation for the streamfunction.

INTEGRATION OF GRID SCALE BATTERY ENERGY STORAGE SYSTEMS AND APPLICATION SCENARIOS

Integration of renewable energy sources (RESs) into the grid has profoundly gained a lot of attention in the energy domain, coupled with an ever-changing generation profile and dependency on weather conditions, RESs are commonly known to pose security of supply challenges and in case they are not monitored they can cause techno-economic losses and even lead to catastrophic failure of the electrical grids. However, their availability and negligible generation cost make them environmentally friendly when compared to conventional energy sources. For seamless connection of renewables to the grid network, battery energy storage system (BESS) has been suggested in literature, the technology has come to the fore recently, and has found application cases in the utility grid with enhanced functions to participate in both reserve and wholesale electricity markets such as day-ahead and intra-day markets. This technical brief presents various energy storage systems (ESSs) potentially used in large-scale grid networks, which are investigated, and their individual properties are compared, where necessary application areas with examples enabled by constituting material properties are outlined, in the same context their general advantages and disadvantages are given in reference to the specific application cases. In addition, the application of large-scale BESS is explained together with the integration solutions such as use of Virtual Power Plant (VPP) and microgrid.

FIFRA, ESA, and Pesticide Consultation: Understanding and Addressing the Complexities

This paper explores the complexities and challenges that arise when trying to align the mandates of the Endangered Species Act (ESA) and the Federal Insecticide, Fungicide, and Rodenticide Act (FIFRA), particularly in the context of pesticide regulation and the conservation of endangered species. It examines the difficulties faced by the Environmental Protection Agency (EPA) in approving pesticides under FIFRA in compliance with the ESA and discusses the differing definitions and approaches to risk between the two regulatory frameworks. The paper aims to propose solutions for better integration of the two acts to improve their functionality and effectiveness in achieving their respective goals.

Temporal and spectral signatures of the interaction between ultrashort laser pulses and Bloch surface waves

The resonant excitation of Bloch Surface Waves (BSWs) in dielectric one-dimensional photonic crystals is becoming a realistic photonic solution for surface integration in many domains, from spectroscopy to local field management. Bringing BSWs to ultrafast and nonlinear regimes requires a deep knowledge of the effects that the photonic crystal dispersion and the resonant surface wave excitation have on the ultrashort laser pulses. We report on the experimental evidence of spectral and temporal modifications of the radiation leaving a planar one-dimensional photonic crystal after coupling to BSWs. In such a resonant condition, a characteristic long temporal tail is observed in the outgoing pulses. Observations are performed by employing both frequency-resolved optical gating and field cross-correlation techniques.

Tackling Ternary Cubic Diophantine Equation

Abstract: A few interesting characteristics among the solutions and the patterns of non-zero integral solutions to the nonhomogeneous cubic equation with three unknowns represented by the Diophantine equation 2 2 3 4(   )  7( )  64 are examined.

On Integer Solutions of the Ternary Bi-Quadratic Diophantine Equation 14(x^2+y^2)-24xy=17z^4

Abstract: This analysis is discussed on the non-trivial distinct integral solution to the ternary bi-quadratic diophantine equation 4 ) 24 17 2 2 14(x  y  xy  z , in four dissimilar patterns. Few connections between the solutions are obtained and also unique polygonal numbers are described