Integral Solution Research Articles

Muddy Waters: Design Thinking for Understanding the Multi-Organizational Problem Space of the Water Sector

Context and motivation: Climate change is manifested by climate variability, rising temperatures (and thus evaporation), and extreme events such as droughts and floods, which have a profound effect on the availability of natural resources, for example, high-quality water. While several technologies for addressing these challenges are available, their adoption is not widespread. In this study, a design thinking (DT) approach was applied to understand the problem space of floods and their handling by the Israeli water sector. Specifically, we aim at addressing the following question: What are the gaps in and barriers to adopting solutions that address sewerage flooding during extreme heavy rainfall events? The DT approach exposed major problems in the conduct of the water sector, including a lack of communication among organizations, the ill-defined distribution of responsibility, unclear and conflicting guidance, and insufficient funds and technological solutions, all hindering the possibility of adopting an integrative solution. This study demonstrates the role that DT plays in understanding a complex, multi-organizational problem space, in our case, the climate change readiness of the water sector, before delving into technological development. Any solution development should involve participants from the various organizations involved in the challenge. It is vital to address not only each organization’s requirements but also its technology adoption barriers and to initiate a comprehensive discussion, ultimately resulting in a shared understanding of all the facets of the challenge that can impact solution development and deployment.

Residual symmetry and interactions between solitons and periodic waves of the Drinfeld–Sokolov–Satsuma–Hirota system

In this paper, the Drinfeld–Sokolov–Satsuma–Hirota (DSSH) system is studied by using residual symmetry and the consistent Riccati expansion (CRE) method, respectively. The residual symmetry of the DSSH system is localized to Lie point symmetry in a properly prolonged system, based on which we get a new Bäcklund transformation for this system. New symmetry reduction solutions of the DSSH system are obtained by applying the classical Lie group approach on the prolonged system. Moreover, the DSSH system proves to be CRE integrable and new interesting interaction solutions between solitons and periodic waves are generated and analyzed.

A Real-Time Associative Feature-Based Customer Relationship Management and Enterprise Resource Planning Integration Model for Small- and Medium-Sized Enterprises

Abstract Customer relationship management (CRM) and enterprise resource planning (ERP) have been extensively discussed in the research literature respectively. However, existing studies do not reach a complete agreement on the CRM/ERP integration method, especially for small- and medium-sized enterprises (SMEs). Generally, this work proposed a novel method for CRM/ERP integration approach via associative feature technology. A new feature type, Real-time Data Link Board (RDLB), is developed and detailed as a generic information carrier solution for multisystem integration between CRM and ERP packages. Valuable data elements are mapped into such data boards dynamically and synchronized across different data sources, structures, and databases. The contribution of this work is to present a well-defined and generically reusable data carrier definition, alongside related methods for ensuring consistent data modeling during the system integration phase across various digitalization engineering implementation projects. With this approach, the consistent management of data integration across intricate systems is achievable throughout application lifecycles, supported by the object-oriented software engineering foundation.

Solving recurrence relations for multiloop integrals in the limit of large values of the dimensional regularization parameter

A method for calculating the 1/d expansion coefficients for solutions of integration by parts relations for Feynman integrals is presented. The idea is to use linear substitutions to transform these relations to an explicitly recursive form. A possible type of such substitutions is proposed for the case of vacuum integrals. Its applicability is shown for several families of massless (with one massive line) vacuum integrals up to the 7-loop level.

Modelling project activities for future teachers within the innovative infrastructure of pedagogical universities: integrative solutions

Introduction. In the quest to enhance the training of future teachers, particular emphasis is placed on identifying the educational potential of new learning environments within pedagogical universities under the Ministry of Education of Russia. These institutions have undergone infrastructure updates as part of federal programs designed to support education. Aim. The aim of this study is to develop an original model for organising the project activities of student teachers, taking into account the contemporary infrastructural capabilities of pedagogical universities under the Ministry of Education of Russia. Methodology, methods and techniques. The methodological foundation of this research is grounded in the principles of community development pedagogy and the design of evolving educational systems. The integration of integrative, synergetic, environmental, and system-activity approaches facilitated the identification and development of components within the author’s model for organising project activities for future teachers in the context of pedagogical technoparks, such as “Quantorium”, and technoparks focused on universal pedagogical competencies in higher education institutions under the Ministry of Education of the Russian Federation. The validation of the developed model was conducted through expert assessments. Results. The authors developed the model for organising project activities for future teachers within the innovative infrastructure of pedagogical universities. The main components of the model are outlined, including integrative objectives and anticipated outcomes of students’ project activities, interdisciplinary project content, and a technological component that facilitates the transformation of interdisciplinary project content into personally meaningful experiences through the technology of collaborative distributed project activities. The study identifies and justifies the conditions necessary for the effective implementation of the developed model, focusing on the management of processes, resources, and participants involved in interdisciplinary project activities. Scientific novelty. Integrative processes, within the context of this study, are regarded as a pedagogical phenomenon that reflects the interconnections among the objects, processes, and subjects involved in project activities. Practical significance. The research materials can be utilised in the development of programmes aimed at enhancing the infrastructure of pedagogical universities. They can also assist in the refinement of educational curricula for training teaching staff, particularly in disciplines that prepare future educators to effectively organise project-based activities within contemporary educational environments.

Energy Storage in Carbon Fiber-Based Batteries: Trends and Future Perspectives

Carbon fiber-based batteries, integrating energy storage with structural functionality, are emerging as a key innovation in the transition toward energy sustainability. Offering significant potential for lighter and more efficient designs, these advanced battery systems are increasingly gaining ground. Through a bibliometric analysis of scientific literature, the study identifies three primary research areas: (i) the development of anodes for lithium-ion batteries, tackling challenges such as dendrite formation and performance degradation; (ii) the creation of new carbon fiber-based cathodes with coatings of LiFePO4, LiCoO2, or other nanoparticles, alongside efforts to develop cobalt-free alternatives; and (iii) the advancement of solid electrolytes that achieve a balance between ionic conductivity and mechanical strength. These advancements position carbon fiber-based batteries as promising solutions for seamless integration into various structural applications. The analysis of publication trends, citation patterns, and collaboration networks provides critical insights into the ongoing technological developments, current research challenges, and emerging trends in this field. Moreover, the study highlights potential research directions, underscoring the importance of continuous innovation to fully realize the potential of carbon fiber-based energy storage technologies.

The asymptotic preserving unified gas kinetic scheme for the multi-scale kinetic SIR epidemic model

In this paper, we present an asymptotic preserving scheme for the two-dimensional space-dependent and multi-scale kinetic SIR epidemic model which is widely used to model the spread of infectious diseases in populations. The scheme combines a discrete ordinate method for the velocity variables and finite volume method for the spatial and time variables. The idea of unified gas kinetic scheme (UGKS) is used to construct the numerical boundary fluxes which needs the formal integral solutions of the model. Due to the coupling of the three transfer equations in the SIR model, it is difficult to obtain these integral solutions dependently. We decouple the system by constructing the fluxes in a separate way. Then following the framework of UGKS we can obtain the macro auxiliary quantities which is needed in the scheme. Thus the SIR model can be solved in the sequential way. In addition, we can show numerically that the scheme is second-order accurate both in space and time. Moreover, it can not only capture the solution of the diffusion limit equations without requiring the cell size and time step being related to the smallness of the scaling parameters, but also resolve the solution in hyperbolic regime in a natural way. Furthermore, the positive property of the UGKS is analyzed in detail, and through adding time step constraint conditions and applying nodal limiters together, the positive UGKS, called PPUGKS2−order, is obtained. Moreover, in order release the time step constraints in the diffusion regime, a temporal first-order accuracy positive preserving UGKS, called PPUGKS1−order, is proposed. Finally, several numerical tests are included to validate the performance of the proposed schemes.

Smart Grids: Integrating AI for Efficient Renewable Energy Utilization

The urgent global shift from fossil fuels to renewable energy sources necessitates innovative solutions to address energy system management challenges. Smart grids, equipped with sophisticated infrastructures, play a crucial role in this transition. This study integrates Artificial Intelligence (AI) into smart grids to enhance their efficiency and reliability, directly supporting the United Nations Sustainable Development Goals (SDGs), particularly SDG 7 (Affordable and Clean Energy), SDG 9 (Industry, Innovation, and Infrastructure), and SDG 11 (Sustainable Cities and Communities). Employing a mixed-methods approach, the research utilizes historical and real-time data, applying machine learning algorithms such as Linear Regression, Support Vector Regression (SVR), Recurrent Neural Networks (RNN), and Long ShortxTerm Memory (LSTM) for predictive accuracy in energy management. Optimization techniques like Genetic Algorithms and Particle Swarm Optimization (PSO) are also implemented for resource scheduling and grid balancing. The results demonstrate significant improvements, with an 11.76% increase in energy efficiency and grid stability, a 66.67% reduction in prediction errors, and a 20% decrease in operational costs compared to conventional systems. These enhancements highlight the transformative potential of AI in smart grids, promoting more efficient and sustainable energy utilization. The study concludes that AI-driven smart grids are pivotal in achieving the SDGs by providing scalable and efficient solutions for renewable energy integration, thereby fostering sustainable development and reducing environmental impacts.

An implicit unified gas-kinetic particle method with large time steps for gray radiation transport

For a long time, efficient algorithms for high-dimensional equations, represented by photon radiation transport, have been one important topic in the development of computational methods for particle transport processes. In this paper, we present an implicit unified gas-kinetic particle (IUGKP) method for multiscale gray radiative transfer. Based on the integral solution of the radiative transfer equation, the photon transport processes are categorized into non-equilibrium transport processes with a large photon free path and equilibrium transport processes with a small photon free path. The long-path processes are solved by an implicit Monte Carlo (IMC) method, and the short-path processes are solved by an implicit diffusion system. The closure formulation of photon distribution is derived from the local integral solution of the radiative transfer equation to couple the IMC and diffusion system. The improvement of the proposed IUGKP method over UGKP method is that particles can be tracked continuously instead of just until the first collision, making simulation with large time steps possible. The IUGKP method has the properties of asymptotic-preserving (AP) and regime-adaptive (RA). The AP property states that the IUGKP method converges to the consistent numerical methods for the asymptotic limiting equations of RTE in the limiting regimes. The RA property states that the computational accuracy of the IUGKP method adapts to the regimes. In this paper, the mathematical proof of the AP and RA properties is presented, and the multiscale numerical tests are performed to demonstrate the accuracy and efficiency of the IUGKP method.

Political-RAG: using generative AI to extract political information from media content

ABSTRACT In the digital era, media content is crucial for political analysis, providing valuable insights through news articles, social media posts, speeches, and reports. Natural Language Processing (NLP) has transformed Political Information Extraction (IE), automating tasks such as event extraction and sentiment analysis. Traditional NLP methods, while effective, are often task-specific and require specialized expertise. In contrast, Large Language Models (LLMs) powered by Generative Artificial Intelligence (GenAI) offer a more integrated solution. However, domain-specific challenges persist, which led to the development of the Retrieval-Augmented Generation (RAG) framework. RAG enhances LLMs by incorporating external data retrieval, addressing issues related to data availability. To demonstrate RAG’s capabilities, we introduce the Political-RAG system, designed to extract political event information from media content, including Twitter data and news articles. Initially developed for event extraction, the Political-RAG system lays the foundation for developing various complex Political IE tasks. These include detecting hate speech, analyzing conflicts, assessing political bias, and evaluating social trends, sentiment, and opinions.

Degenerate Parabolic Equation with Zero-flux Boundary Condition and its Approximations

We study a degenerate parabolic-hyperbolic equation with zero-flux boundary condition. The aim of this paper is to prove convergence of numerical approximate solutions towards the unique entropy solution. We propose an implicit finite volume scheme on admissible mesh. We establish fundamental estimates and prove that the approximate solution converge towards an entropy-process solution. Contrarily to the case of Dirichlet condition, in zero-flux problem unnatural boundary regularity of the flux is required to establish that entropyprocess solution is the unique entropy solution. In the study of well-posedness of the problem, tools of nonlinear semigroup theory (stationary, mild and integral solutions) were used in order to overcome this difficulty. Indeed, in some situations including the one-dimensional setting, solutions of the stationary problem enjoy additional boundary regularity. Here, similar arguments are developed based on the new notion of integral-process solution that we introduce for this purpose.

Understanding depression, anxiety and stress in young people living with HIV in Ghana

Ghanaians with perinatally acquired human immunodeficiency virus (HIV) infection now live into adulthood. It is known that adolescents and young adults living with HIV have a high risk of mental health comorbidity. Despite increasing global attention on HIV–mental health interactions, the field remains understudied in Ghana, with an attendant lack of national integrated care solutions. This study aimed to measure the burden and explore the context of depression, anxiety and stress symptoms among young people living with HIV receiving care at a tertiary care hospital in Ghana. This was an explanatory sequential mixed-methods study. Depression, anxiety and stress symptoms were measured using the Depression, Anxiety and Stress Scale, and their associations with quality of life (QoL), socioeconomic status, internalised stigma, disease stage and HIV-related risk-taking behaviours were explored. After preliminary quantitative data analysis, semi-structured interviews were conducted for those who screened positive for depression and/or anxiety to explore their experience with this comorbidity. This study found a low prevalence of depression and anxiety symptoms, which were associated with higher stigma scores and lower QoL. We believe this low prevalence to be attributable to the effect of several psychosocial interventional programmes, which were previously piloted with the study cohort that have gradually normalised mental health discussions. Participants also showed marked resilience and knowledge about their condition. The results of this study present an opportunity to advocate and scale up effective locally adapted and strength-based solutions to address the mental illness–HIV syndemic in Ghanaian young people living with HIV.

Seeing the Whole Together Through Relational Mapping: A Method for Engaging in Complex Systems Change

Complex global challenges cut across organizational and sectoral boundaries, increasing calls for holistic responses. Seeing the whole across diverse stakeholders is challenging for participants in complex systems, yet doing so is essential for engaging effectively in systems change. A promising new method known as relational mapping, based on relational coordination theory, has been used to facilitate complex systems change. Here, we propose that relational mapping can be applied to help participants (1) see the whole in relation to the parts, (2) share their explicit and tacit knowledge, (3) engage in dialogue across distinct perspectives supported by the map as a boundary object, (4) reduce the impact of power differences, and (5) prepare to co-design interventions from multiple perspectives. This paper presents an illustrative case of relational mapping in the context of public administration in a South Carolina community engaging in complex systems change. Our analysis suggests a set of boundary conditions for the success of relational mapping, including the willingness of participants to seek integrative solutions to a conflict or problem and facilitation that is attentive to differential power and status among stakeholders. We conclude that relational mapping is a powerful, theoretically grounded method that enables the visual assessment of multi-level stakeholder relationships, preparing participants to engage in complex systems change and then present a template for use of relational mapping more broadly.

Formation of a Unified Educational Space of the Union State from the Perspective of the Policy of Patriotic Education

Introduction. Awareness of the commonality of geopolitical and civilizational challenges of the Russian Federation and the Republic of Belarus pushes for deepening integration cooperation in different directions. Close attention is paid to the problem of security, interpreted in an expanded way. Its provision correlates with the strengthening of the humanitarian dimension of the Union State, including the formation of a unified educational space. In modern conditions, its correlation with the consolidation of the policy of patriotic education in the integration field is being actualized. The purpose of the article is to identify the specifics of their coupling, taking into account the dynamics of union construction. Materials and Methods. The research is based on the methods of binary comparison, traditional and discourse analysis of official texts. An additional method is a formalized correspondence expert survey. The key materials are normative legal acts of the Russian Federation and the Republic of Belarus, interstate, intergovernmental and integration agreements, information content of the web resources of the Union State. The theoretical and methodological foundations of the research are a new political institutionalism, a multidimensional model of social action, and the paradigm of “political unification”. Results. The article describes the normative foundations of state policy in the field of education and integration guidelines in the cultural and humanitarian plane within the framework of the movement towards the Union educational space. The demanded categories of the axiological plan are revealed, referring to the relationship between education and upbringing. The key lines of discursive practices at the sites of the union institutions are shown. The understanding of the need to adapt education systems to the requirements of the time and the linking of patriotic education with the protection and preservation of common historical memory are emphasized. Discussion and Conclusion. The results of the study and expert assessments suggest the articulation of not only positive changes, but also urgent vectors for improving national approaches and integration solutions. They correspond to the elimination of conflicts, the development and adoption of new documents at the level of the Union State, the implementation of value categories and new areas of unified policy. The results obtained may be of interest to public authorities and union institutions, participants in patriotic education in the territory of the Union State.

Evolution and Trends in Digital Wallet Research: A Bibliometric Analysis in Scopus and Web of Science

Digital wallets have become a driving force in the global economy, with 2.4 billion users worldwide in 2020, a figure projected to reach 3.6 billion by 2026. This study conducts an in-depth bibliometric analysis to evaluate the current state and future trends of digital wallet research using scientific databases such as Scopus and Web of Science. A scoping review methodology was applied, in which we analyzed 778 documents, following an eligibility process with the following search terms: “digital wallet”, “mobile wallet”, and “e-wallet”. Results show that India, the United States, and China are leading research efforts in this field. Key factors influencing the adoption of digital wallets include data security, ease of use, and integration with traditional payment systems. While much research has focused on technological innovation and adoption, significant gaps remain in areas such as blockchain integration and AI-driven solutions. This article provides the first comprehensive bibliometric analysis of digital wallets, offering crucial insights into emerging trends such as “blockchain”, “electronic commerce”, and “digital payments” and their role in shaping the future of financial technology.

Radial Kernels Collocation Method for the Solution of Volterra Integro-Differential Equations

Radial kernel interpolation is an advanced method in approximation theory for the construction of higher order accurate interpolants for scattered data up to higher dimensional spaces. In this manuscript, we formulate a radial kernel collocation approach for solving problems involving the Volterra integro-differential equations using two radial kernels: The Generalized Multi-quadrics and the linear Laguerre-Gaussians. This was achieved by simplifying the Volterra integral problem's solution to an algebraic system of equations. The impact of the shape parameter present in every kernel on the method's accuracy is examined and found to be significant. Two examples were used to illustrate the process; the numerical results are shown as tables and graphs. MATLAB 2018a was employed in the process.

A Glimpse on Integral Solutions of Ternary Uniform Second Degree Equation 𝟓 (𝐱𝟐 + 𝐲𝟐) − 𝟑𝑥𝑦 = 𝟐𝟎𝟎𝟎𝑧𝟐

Objectives: Many integer solutions to ternary homogeneous quadratic given by are determined. Various choices of integer solutions are secure from beginning to end employing linear modifications and used to simplify expressions. Methods: Different transformations are utilized to determine many solutions in integers for the considered polynomial equation. Findings: Five distinct transformations are applied to obtain choices of integral solutions for the considered second-degree equation having three unknowns. Novelty: The equation in the title has been reduced to a solvable ternary quadratic equation by employing suitable transformation. Mathematics Subject Classification: 11D09 Keywords: Quadratic having three unknowns, Homogeneous quadratic, Integer Solutions, Ternary Quadratic Equation, Pair of equations

Convex integration solution of two-dimensional hyperbolic Navier–Stokes equations*

Abstract Hyperbolic Navier–Stokes equations replace the heat operator within the Navier–Stokes equations with a damped wave operator. Due to this second-order temporal derivative term, there exist no known bounded quantities for its solution; consequently, various standard results for the Navier–Stokes equations such as the global existence of a weak solution, that is typically constructed via Galerkin approximation, are absent in the literature. In this manuscript, we employ the technique of convex integration on the two-dimensional hyperbolic Navier–Stokes equations to construct a weak solution with prescribed energy and thereby prove its non-uniqueness. The main difficulty is the second-order temporal derivative term, which is too singular to be estimated as a linear error. One of our novel ideas is to use the time integral of the temporal corrector perturbation of the Navier–Stokes equations as the temporal corrector perturbation for the hyperbolic Navier–Stokes equations.

Prediction of the acoustic particle velocity in aerodynamic flows and its applications to the boundary element method

The acoustic variables are essential for understanding sound energy transmission and redistribution. The previous methods focused on acoustic pressure without the acoustic particle velocity, which is not enough for acoustic field evaluation. In this paper, an analytical formula for acoustic particle velocity prediction is developed based on the permeable surface integral solution of a vector wave equation. The validation examples are presented with stationary dipole and rotational monopole. The acoustic quantities, pressure, and velocity are solved at the same time and will be applied as input for the boundary element method (BEM) to evaluate the sound scattering problem in the frequency domain. Furthermore, the method is applied to study the acoustic field of flow passing a cylinder. The acoustic pressure shows good agreement with the flow observer. The acoustic particle velocity is also investigated.

Using Symmetries to Investigate the Complete Integrability, Solitary Wave Solutions and Solitons of the Gardner Equation

In this paper, using a scaling symmetry, it is shown how to compute polynomial conservation laws, generalized symmetries, recursion operators, Lax pairs, and bilinear forms of polynomial nonlinear partial differential equations, thereby establishing their complete integrability. The Gardner equation is chosen as the key example, as it comprises both the Korteweg–de Vries and modified Korteweg–de Vries equations. The Gardner and Miura transformations, which connect these equations, are also computed using the concept of scaling homogeneity. Exact solitary wave solutions and solitons of the Gardner equation are derived using Hirota’s method and other direct methods. The nature of these solutions depends on the sign of the cubic term in the Gardner equation and the underlying mKdV equation. It is shown that flat (table-top) waves of large amplitude only occur when the sign of the cubic nonlinearity is negative (defocusing case), whereas the focusing Gardner equation has standard elastically colliding solitons. This paper’s aim is to provide a review of the integrability properties and solutions of the Gardner equation and to illustrate the applicability of the scaling symmetry approach. The methods and algorithms used in this paper have been implemented in Mathematica, but can be adapted for major computer algebra systems.