Integral Domain Research Articles

Worldline approach for spinor fields in manifolds with boundaries

The worldline formalism is a useful scheme in Quantum Field Theory which has also become a powerful tool for numerical computations. It is based on the first quantisation of a point-particle whose transition amplitudes correspond to the heat-kernel of the operator of quantum fluctuations of the field theory. However, to study a quantum field theory in a bounded manifold one needs to restrict the path integration domain of the point-particle to a specific subset of worldlines enclosed by those boundaries. In the present article it is shown how to implement this restriction for the case of a spinor field in a two-dimensional curved half-plane under MIT bag boundary conditions, and compute the first few heat-kernel coefficients as a verification of the proposed construction. This construction admits several generalisations.

An immersed boundary fast meshfree integration methodology with consistent weight learning

An immersed boundary fast integration methodology featured by a consistent weight learning is proposed to accelerate Galerkin meshfree computation. In the proposed approach, the problem domain is embedded in a rectangular spatial domain discretized by regular distributions of meshfree nodes and integration sampling points with virtual integration cells. A trimming operation of the rectangular spatial domain by the physical problem boundary with nodal discretization yields the discrete model for meshfree computation, where the integration sampling points are grouped into the interior sampling points and the near boundary sampling points which form a training set. For the interior sampling points, a natural alignment between the influence domains of meshfree shape functions and virtual integration cells can be easily realized through employing integer support sizes, which ensures a satisfactory accuracy for the basis degree correspondent normal order Gauss integration. The background cells for the domain integration are completely avoided, which greatly simplifies the preprocessing for numerical integration. Meanwhile, a machine learning module is devised to optimize the weights of near boundary integration sampling points. The key step to construct this machine learning module for weight optimization is the selection of the variational integration consistency condition as the loss function, which guarantees the convergence of Galerkin meshfree formulation. The accuracy and efficiency of the proposed weight learning immersed boundary fast integration methodology is thoroughly validated through numerical results.

Information Technology Integration and Classroom Learning Engagement in Selected Elementary Schools in Binangonan, Rizal

The objective of this study is to assess the correlation of information technology integration on the learning engagement of grade school pupils in selected elementary schools in Binangonan, Rizal. In an era where technological advancements are rapidly transforming educational landscapes, this study investigates how effectively integrating information technology (IT) into teaching practices impacts various dimensions of pupil engagement, including emotional, cognitive, motivational, behavioral, cognitive-behavioral, and social-behavioral engagement. The research sample consists of 655 pupils, highlighting a slight predominance of females over males and revealing significant socioeconomic diversity among the respondents. The study employs a comprehensive approach, evaluating teachers' proficiency in multiple domains of IT integration—Technological Knowledge, Content Knowledge, Pedagogical Knowledge, Pedagogical Content Knowledge, Technological Content Knowledge, Technological Pedagogical Knowledge, and Technological Pedagogical Content Knowledge. Findings indicate a consistently high level of IT integration across these domains, with slight variances based on factors such as sex, family income, and access to technology at home. Emotional and cognitive engagement among pupils are particularly influenced by these variables, while overall engagement levels remain robust across different demographics. The study also reveals significant positive correlations between teachers' IT integration and pupils' engagement across all dimensions, underscoring the critical role of proficient IT use in enhancing educational outcomes. Based on these insights, the study proposes an Enhanced Training Plan aimed at addressing the digital divide, empowering teachers through continuous professional development, fostering high levels of pupil engagement, and promoting collaborative and supportive classroom environments. This plan includes targeted activities, regular monitoring, and evaluation to ensure its effectiveness and adaptability to evolving educational needs. The findings highlight the necessity for ongoing support and professional development for teachers to maximize the benefits of IT integration, ultimately contributing to a more dynamic and inclusive educational experience for all pupils.

A Class of Functional Equations (Almost) Characterizing Polynomials on Integral Domains

A Class of Functional Equations (Almost) Characterizing Polynomials on Integral Domains

Extended mapping and systematic optimisation of the Carnot battery trilemma for sub-critical cycles with thermal integration

Thermally integrated pumped thermal energy storage (TI-PTES) is a flexibility option to recover low-grade heat and provide overnight storage. Common criteria when designing such systems are the power-to-power efficiency (electricity recovery), the exergy efficiency (combined heat and electricity recovery) and the energy density (storage size). However, these are generally conflicting and multi-criteria optimisation is therefore required. Design guidelines have been proposed for some specific case studies but are still lacking for the remaining wide range of possible integrations. This work therefore presents a systematic multi-criteria analysis of a TI-PTES, consisting of a vapour compression heat pump, a sensible heat storage and an organic Rankine cycle, in an extended integration domain. Results show that the storage temperature levels are key variables, as they directly influence the conflict between the performance of the heat pump and the organic Rankine cycle. Also, the intensity of the conflict between the three criteria increases with the temperature difference between the source and the sink, mainly because of the power-to-power efficiency (the density and the exergy efficiency are much less conflicting with each other). Finally, the relevance of thermal integration in TI-PTES is questioned when it leads to a sharp deterioration in exergy efficiency and density.

Precise integration boundary element method for solving nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity

The precise integration boundary element method (PIBEM) is used to solve nonlinear transient heat conduction problems with temperature dependent thermal conductivity and heat capacity in this article. At first, a boundary-domain integral equation can be obtained by using the fundamental solution for steady linear heat conduction problems. Secondly, the domain integrals are converted into boundary integrals by using the radial integration method to get a pure boundary integral equation, which can retain the advantage of dimension reduction of the boundary element method. Then, after discretization, a first-order nonlinear differential equation system in time is obtained, and the precise integration method with predictor-corrector technique is used to solve the system of nonlinear equations. In the end, several numerical examples are presented to verify the accuracy and stability of the presented method. The results obtained by the presented method are less affected by the time step size and satisfactory results can be obtained even for a large time step size.

Specht property for the graded identities of the pair (M2(D),sl2(D))

Let D be a Noetherian infinite integral domain, denote by M2(D) and by sl2(D) the 2×2 matrix algebra and the Lie algebra of the traceless matrices in M2(D), respectively. In this paper we study the weak polynomial identities for the natural grading by the cyclic group Z2 of order 2 on M2(D) and on sl2(D). We describe a finite basis of the graded polynomial identities for the pair (M2(D),sl2(D)). Moreover we prove that the ideal of the graded identities for this pair satisfies the Specht property, that is every ideal of graded identities of pairs (associative algebra, Lie algebra), satisfying the graded identities for (M2(D),sl2(D)), is finitely generated. The polynomial identities for M2(D) are known if D is any field of characteristic different from 2. The identities for the Lie algebra sl2(D) are known when D is an infinite field. The identities for the pair we consider were first described by Razmyslov when D is a field of characteristic 0, and afterwards by the second author when D is an infinite field. The graded identities for the pair (M2(D),gl2(D)) were also described, by Krasilnikov and the second author.In order to obtain these results we use certain graded analogues of the generic matrices, and also techniques developed by G. Higman concerning partially well ordered sets.

Accurate and efficient integrative reference-informed spatial domain detection for spatial transcriptomics.

Spatially resolved transcriptomics (SRT) studies are becoming increasingly common and large, offering unprecedented opportunities in mapping complex tissue structures and functions. Here we present integrative and reference-informed tissue segmentation (IRIS), a computational method designed to characterize tissue spatial organization in SRT studies through accurately and efficiently detecting spatial domains. IRIS uniquely leverages single-cell RNA sequencing data for reference-informed detection of biologically interpretable spatial domains, integrating multiple SRT slices while explicitly considering correlations both within and across slices. We demonstrate the advantages of IRIS through in-depth analysis of six SRT datasets encompassing diverse technologies, tissues, species and resolutions. In these applications, IRIS achieves substantial accuracy gains (39-1,083%) and speed improvements (4.6-666.0) in moderate-sized datasets, while representing the only method applicable for large datasets including Stereo-seq and 10x Xenium. As a result, IRIS reveals intricate brain structures, uncovers tumor microenvironment heterogeneity and detects structural changes in diabetes-affected testis, all with exceptional speed and accuracy.

A Review on Fake News Detection using Deep Learning Methods

The proliferation of fake news in online media platforms poses a significant threat to the integrity of information dissemination and public discourse. In response, researchers have increasingly turned to deep learning techniques to develop effective solutions for detecting and mitigating the spread of fake news. This review paper provides a comprehensive overview of recent advances in fake news detection using deep learning methodologies. We survey the literature on various deep learning architectures and approaches employed for fake news detection, including supervised, semi-supervised, and unsupervised learning methods. We discuss the challenges associated with data preprocessing, feature extraction, and model evaluation, and examine the ethical considerations and societal implications of deploying deep learning models for fake news detection. Furthermore, we identify emerging trends and future research directions in the field, with a focus on addressing the evolving nature of fake news and enhancing the robustness and interpretability of detection systems. This review contributes to the ongoing discourse on fake news detection and provides valuable insights for researchers, practitioners, and policymakers working in the domain of information integrity and online media governance.

Georgia-EU Cooperation in the Field of Culture in Multilateral and Bilateral International Format

In the realm of international relations, the significance of culture and soft power is steadily growing, particularly in the establishment of diplomatic ties and the fostering of cooperation among nations. As Georgia progresses in its integration into the European Union—a political and economic endeavor given the union's nature—its motto of "unity in diversity" exemplifies the European commitment to peace, citizen well-being, and the celebration of cultural diversity. The European Union stands as a prominent example of effective soft power utilization in international relations, with culture representing one of its most intricate integration domains. In the context of Georgia's deepening ties with the EU, a thorough examination of European and developed countries' cultural pathways and experiences becomes imperative. This analysis is essential for Georgia to chart a coherent, unified, and effective cultural policy, both domestically and on the global stage. Following the European Commission's recommendation on November 8, 2023, Georgia was granted the EU candidate status by the European Council on December 14, officially becoming part of the EU's enlargement policy. Consequently, it becomes even more pertinent for Georgia to scrutinize and understand the EU's cultural policy, a cornerstone of its foreign relations strategy. The influence of cultural policy on the EU-Eastern Partnership relations emerges as the significant force shaping their development. Cultural cooperation serves as a linchpin, fostering mutual understanding, identity preservation, and the cultivation of shared values. The analysis of progress and challenges within Georgia-EU cooperation, both bilaterally and multilaterally, offers insight into how cultural relations are cultivated within the Eastern Partnership framework. The EU cultural policy, operationalized through various mechanisms like association agreements and support packages, prioritizes democracy, human rights, and cultural cooperation, adapting to the unique circumstances of each partner country. Examining the EU's cultural policy within the Eastern Partnership context underscores culture's pivotal role in diplomacy, cooperation, and economic development. Establishing an effective vision centered on cultural cooperation is crucial for Georgia's engagement with the EU, positioning it as a cornerstone of the partnership's success. Keywords: EU cultural policy, soft power, European integration, European perspective.

The impact of heat pump load flexibility on its process integration and economics

The conventional methodology of heat pump integration has found application in various industries, including cheese production, spray drying, milk evaporation systems, brewing, and meat processing. While several approaches have been developed for optimizing direct and indirect heat recovery in non-continuous industrial processes, the optimal integration of heat pumps in non-continuous processes remains a challenge.This paper introduces a systematic methodology that leverages extensive datasets of time-resolved industrial process data to determine the optimal heat pump integration and the level of heat pump load flexibility that maximizes the economic benefit. Thus, the work establishes a connection between the domain of Process Integration and heat pump load flexibility. Additionally, the study provides insights on the requirements for load flexibility during the design phase of the heat pump, offering an estimation on the need for research on heat pump flexibility.The findings indicate the presence of a load flexibility threshold in the examined case study, beyond which additional load flexibility yields diminishing returns. Furthermore, the study shows that different heat pump integration parameters are chosen based on the heat pump’s capability for load flexibility. Within the investigated case, a heat pump with a minimum load of 55% increases the net present value by 19.3% compared to a load inflexible heat pump.

Shaping the Future of Destinations: New Clues to Smart Tourism Research from a Neuroscience Methods Approach

In the context of the technological era, the smart tourism construct serves as a bridge between human and the artificial worlds, combining social sciences and neurosciences. This study aims to explore smart tourism through neuroscientific methods in order to shape the future of tourism destinations, using a hybrid methodology combining bibliometric techniques and content analysis. The findings reveal the integration of diverse scientific domains, highlighting a transdisciplinary approach. They offer clear evidence that neuroscientific methods in smart tourism integrate multiple areas of scientific knowledge, surpassing disciplinary boundaries. “Destination” stands out alongside “emotion”, “visual attention” and eye tracking (ET). The collaboration network reveals the emergence of a new school, called neurotourism in the 21st century, formed mainly by actors and organizations from the Global North, evoking the need to include the Global South in the research scenario. The predominant methods include ET, heart rate (HR), and electroencephalography (EEG), suggesting triangulation with traditional methods for robust results. Virtual reality emerges as the primary immersive technology, promising insights when integrated with neurosciences. This study’s practical and theoretical contributions guide smart tourism strategies and enhance destination experiences through neuroscientific methods, addressing a gap in the scientific literature while advancing ontological and epistemological understanding.

Core of an ideal in Prüfer domains

This paper contributes to the study of the core of an ideal in integral domains. Our aim is to develop explicit formulas for the core in various classes of Prüfer domains. We pay particular attention to relevant ideal-theoretic notions such as stability, invertibility, and h-local property. We also provide decomposition results for the core of an ideal in integral domains with effectual ramifications to Prüfer domains. All main results are illustrated with original examples, where we explicitly compute the core. We also provide counter-examples to test the limits of the assumptions used in the main results.

PV based Systems with Advanced Control Strategies for Load Balancing in Multilevel Inverter

In an era driven by sustainable energy solutions, the synergy of photovoltaic (PV) system stands as a beacon of hope for meeting the world's growing energy demands while minimizing environmental impact. This research ventures into the domain of renewable energy integration by seamlessly including a PV system, ingeniously controlled by Chaotic Flower Pollination Optimized Adaptive Neuro Fuzzy Inference System (ANFIS) based MPPT (Maximum Power Point Tracking) controller capable of optimizing the efficiency in the face of ever-changing weather dynamics. The PV system's quest for optimal efficiency receives a substantial boost through the implementation of the High Gain Modified Luo Converter. Designed to achieve an optimal PV output voltage, this converter's prowess finds its true calling in grid applications, where precision and efficiency are paramount. Furthermore, this research extends its purview to incorporate a bidirectional converter linked to an energy storage solution, such as a battery, through a common DC link. The output power is then passed to the Flyback Converter, seamlessly connected to a 31 level Cascaded H Bridge Multi-Level Inverter (31-level CHB MLI) controlled by PI controller. This formidable inverter architecture facilitates the efficient delivery of power to the grid, ensuring a smooth and controlled integration of renewable energy resources. This strategic integration bolsters the system's adaptability, enabling the seamless management of energy flows and grid interactions along with load balancing in MLI. The MATLAB simulation platform is used for confirming the system's overall performance. According to the simulation results, the proposed approach achieves the maximum efficiency with the lowest THD value of 94.5% and 2.5%, respectively.

Use of waste plastic oil as a fuel in reactivity-controlled compression ignition engines: a bibliometric investigation from 2017–23

Abstract Waste plastic oil, generated through the pyrolysis of plastic without oxygen, known as plastic-to-fuel conversion, stands as a promising alternative fuel. This research employs bibliometric analysis, a quantitative method, to comprehensively assess publications in the domain of waste plastic oil integration within reactivity-controlled compression ignition engines. Utilizing Scopus as the primary repository post-2017, the study categorizes information into pivotal aspects, including influential journals, countries, authors, affiliations, document types, thematic areas, sponsors and keywords. The analysis reveals significant contributions from diverse nations, prominently India, China, Turkey and Malaysia. Noteworthy is the prevalence of Energy, Engineering and Chemical Engineering as thematic focal points, with the journal Fuel leading the count followed by the journal Energy emerging as a prominent conduit. Institutional contributions are prolific, led by Gandhi Institute of Technology and Management University and Vellore Institute of Technology. Renowned authors ‘Gugulothu S.K’ and ‘He Z’ play a pivotal role in shaping the discourse. The National Natural Science Foundation of China stands out as a primary patron. This bibliometric analysis provides a structured understanding of waste plastic oil integration in reactivity-controlled compression ignition engines, laying the groundwork for future research avenues. The study identifies potential research platforms beyond Scopus, including Web of Science, CrossRef, Science Direct and Google Scholar, as valuable repositories for further exploration. Moreover, after careful observation of the research articles published by the top 10 authors as found in the study, it was found that the authors share a few common characteristics that helped them in advancing the understanding and application of waste plastic oil in reactivity-controlled compression ignition engines. These are also summarized in the present study with supporting data.

Homogeneous star-operations on graded integral domains

Let Γ be a torsion-free cancellative monoid and let R = ⊕ α ∈ Γ R α be a graded integral domain. In this paper, we define the concept of homogeneous star-operations, which is a generalization of that of star-operations, and apply some properties of star-operations. Also, we define the concept of homogeneous divisor classes, which is the graded integral domain version of that of divisor classes, and study some equivalent conditions for the set of homogeneous divisor classes H D ( R ) of R to be a group.

The dispensability of VH-VL pairing and the indispensability of VL domain integrity in the IgG1 secretion process.

Introduction: The CH1 domain of IgG antibodies controls assembly and secretion, mediated by the molecular chaperone BiP via the endoplasmic reticulum protein quality control (ERQC) mechanism. However, it is not clear whether the variable domains are necessary for this process. Methods: Here, we generated IgG1 antibodies in which the V domain (VH and/or VL) was either removed or replaced, and then assessed expression, assembly, and secretion in HEK293 cells. Results: All Ig variants formed a covalent linkage between the Cγ1 and Cκ, were successfully secreted in an assembled form. Replacement of the cognate Vκ with a non-secretory pseudo Vκ (ψVκ) hindered secretion of individual or assembled secretion of neither heavy chains (HCs) nor light chains (LCs). The ψLC (ψVκ-Cκ) exhibited a less folded structure compared to the wild type (wt) LC, as evidenced by enhanced stable binding to the molecular chaperone BiP and susceptibility to proteolytic degradation. Molecular dynamics simulation demonstrated dramatic alterations in overall structure of ψFab (Fd-ψLC) from wt Fab. Discussion: These findings suggest that V domains do not initiate HC:LC assembly and secretion; instead, the critical factor governing IgG assembly and secretion is the CH-CL pairing. Additionally, the structural integrity of the VL domain is crucial for IgG secretion. These data offer valuable insight into the design of bioactive molecules based on an IgG backbone.

Integrating inquiry and mathematical modeling when teaching a common topic in lower secondary school: an iSTEM approach

The world has been increasingly shaped by Science, Technology, Engineering and Mathematics (STEM). This has resulted in educational systems across the globe implementing STEM education. To reap maximum benefits, researchers are now advocating for the integration of STEM domains. In recent studies, the integration of science and mathematics has become increasingly popular. The domains are much more suitable for integration because of their fields of application and their mutual approach toward problem-solving. However, there is little empirical evidence to drive the development of a practical model for classroom implementation. This study aims to cover that gap through integrating mathematics and science concepts when teaching a common topic to two classes of Form 1 (13–14 years) students. A mathematics and a science teacher went through two cycles of lesson study, integrating and teaching the concept of density. Results show a strong synergy between the BSCS 5E instructional model of inquiry and mathematical modeling; hence the methodological approaches can be used to integrate common topics like density. Further, teacher collaboration, teacher immersion in the iSTEM practices, teacher’s knowledge, and skills of the other subject and an in-depth understanding of a problem and its contextualization, are variables that can be capitalized on to enhance the teacher’s capacity to implement innovative and integrated STEM programs effectively.

Boundary element method for bending-extension coupling shear deformable laminated composite plates with multiple stiffeners

In general, the laminated composite plates and stiffeners may exhibit the bending-extension coupling effect with the transverse shear deformations significantly induced. In this paper, for the first time we develop the associated boundary element method (BEM) for bending-extension coupling shear deformable laminated composite plates with multiple beams attached as stiffeners. Based upon the first order shear deformation theory, the individual boundary integral equations (BIEs) for plates and stiffeners are obtained from their corresponding matrix-form basic equations. To account for perfect bonding conditions between plate and stiffeners, we establish displacement continuity and interaction load equilibrium relations at their interfaces. To calculate the domain integrals related to unknown interaction loads, we discretize each stiffener into a series of cells using quadratic interpolation. By collecting the individual BIEs for plates and stiffeners and employing the continuity and equilibrium relations at the interfaces, we construct the entire system of linear equations to solve for all the unknown nodal quantities. Additionally, the complete solutions at the plate boundary, at internal points or along a stiffener are provided. The correctness of our present BEM formulation is verified through two representative examples by comparison with the commercial finite element software ANSYS. The numerical results demonstrate that our BEM formulation surpasses the conventional finite element method and is highly desirable for general stiffened laminated plates with bending-extension coupling and transverse shear deformations.

Logical characterizations of algebraic circuit classes over integral domains

AbstractWe present an adapted construction of algebraic circuits over the reals introduced by Cucker and Meer to arbitrary infinite integral domains and generalize the $\mathrm{AC}_{\mathbb{R}}$ and $\mathrm{NC}_{\mathbb{R}}^{}$ classes for this setting. We give a theorem in the style of Immerman’s theorem which shows that for these adapted formalisms, sets decided by circuits of constant depth and polynomial size are the same as sets definable by a suitable adaptation of first-order logic. Additionally, we discuss a generalization of the guarded predicative logic by Durand, Haak and Vollmer, and we show characterizations for the $\mathrm{AC}_{R}$ and $\mathrm{NC}_R^{}$ hierarchy. Those generalizations apply to the Boolean $\mathrm{AC}$ and $\mathrm{NC}$ hierarchies as well. Furthermore, we introduce a formalism to be able to compare some of the aforementioned complexity classes with different underlying integral domains.