Integral Domain Research Articles

Numerical solution of the boundary value problem of elliptic equation by Levi function scheme

AbstractFor boundary value problem of an elliptic equation with variable coefficients describing the physical field distribution in inhomogeneous media, the parametrix can represent the solution in terms of volume and surface potentials, with the drawback that the volume potential involving in the solution expression requires heavy computational costs as well as the solvability of the integral equations with respect to the density pair. We introduce an modified integral expression for the solution to an elliptic equation in divergence form under the parametrix framework. The well‐posedness of the linear integral system with respect to the density functions to be determined is rigorously proved. Based on the singularity decomposition for the parametrix, we propose two schemes to deal with the volume integrals so that the density functions can be solved efficiently. One method is an adaptive discretization scheme for computing the integrals with continuous integrands, leading to the uniform accuracy of the integrals in the whole domain, and consequently the efficient computations for the density functions. The other method is the dual reciprocity method which is a meshless approach converting the volume integrals into boundary integrals equivalently by expressing the volume density as the combination of the radial basis functions determined by the interior grids. The proposed schemes are justified numerically to be of satisfactory computation costs. Numerical examples in 2‐dimensional and 3‐dimensional cases are presented to show the validity of the proposed schemes.

Some results on the total zero-divisor graph of a commutative ring

PurposeThe purpose of this paper is to characterize a commutative ring R with identity which is not an integral domain such that ZT(R), the total zero-divisor graph of R is connected and to determine the diameter and radius of ZT(R) whenever ZT(R) is connected. Also, the purpose is to generalize some of the known results proved by Duric et al. on the total zero-divisor graph of R.Design/methodology/approachWe use the methods from commutative ring theory on primary decomposition and strong primary decomposition of ideals in commutative rings. The structure of ideals, the primary ideals, the prime ideals, the set of zero-divisors of the finite direct product of commutative rings is used in this paper. The notion of maximal Nagata prime of the zero-ideal of a commutative ring is also used in our discussion.FindingsFor a commutative ring R with identity, ZT(R) is the intersection of the zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R. The zero-divisor graph of R and the total graph of R induced by the set of all non-zero zero-divisors of R are well studied. Hence, we determine necessary and sufficient condition so that ZT(R) agrees with the zero-divisor graph of R (respectively, agrees with the total graph induced by the set of non-zero zero-divisors of R). If Z(R) is an ideal of R, then it is noted that ZT(R) agrees with the zero-divisor graph of R. Hence, we focus on rings R such that Z(R) is not an ideal of R. We are able to characterize R such that ZT(R) is connected under the assumptions that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. With the above assumptions, we are able to determine the domination number of ZT(R).Research limitations/implicationsDuric et al. characterized Artinian rings R such that ZT(R) is connected. In this paper, we extend their result to rings R such that the zero ideal of R admits a strong primary decomposition and Z(R) is not an ideal of R. As an Artinian ring is isomorphic to the direct product of a finite number of Artinian local rings, we try to characterize R such that ZT(R) is connected under the assumption that R is ta finite direct product of rings R1, R2, … Rn with Z(Ri) is an ideal of Ri for each i between 1 to n. Their result on domination number of ZT(R) is also generalized in this paper. We provide several examples to illustrate our results proved.Practical implicationsThe implication of this paper is that the existing result of Duric et al. is applicable to large class of commutative rings thereby yielding more examples. Moreover, the results proved in this paper make us to understand the structure of commutative rings better. It also helps us to learn the interplay between the ring-theoretic properties and the graph-theoretic properties of the graph associated with it.Originality/valueThe results proved in this paper are original and they provide more insight into the structure of total zero-divisor graph of a commutative ring. This paper provides several examples. Not much work done in the area of total zero-divisor graph of a commutative ring. This paper is a contribution to the area of graphs and rings and may inspire other researchers to study the total zero-divisor graph in further detail.

Hyper-reduced-order model for estimating convection heat transfer coefficients of turbine rotors

Forced convection heat transfer occurs inside the steam turbine, and it is crucial for thermal and strength analysis to accurately estimate the convection heat transfer coefficients of the turbine rotor. This paper presents a hyper-reduced-order model for efficiently estimating the forced convection heat transfer coefficients of a steam turbine rotor. Unlike the full-order finite element method, the hyper-reduced-order model uses the discrete empirical interpolation method to approximate the domain integration of transient heat conduction simulations. This approach greatly reduces the degrees of freedom of numerical integration, thus substantially improving the computational efficiency of forward heat conduction problems. The hyper-reduced-order model and Levenberg–Marquardt algorithm are combined to minimize temperature errors between the numerical simulation results and remote sensor measurements and iteratively estimate the heat transfer coefficients of forced convection in the rotor. The accuracy and efficiency of the proposed model are verified through a transient heat conduction simulation. Moreover, the effects of the initial guess values and measurement errors are investigated to demonstrate the universality and robustness of the proposed approach in determining the convection heat transfer coefficient. Compared with the full-order finite element model, the proposed hyper-reduced-order model can increase the efficiency of forward heat conduction simulations of the turbine rotor by more than 10 times, and it only takes 0.87 s computer runtime in single transient step simulation, and then rapidly estimate the forced convection heat transfer coefficients. Furthermore, the performance of the proposed approach is insensitive to the initial guess values, and it exhibits great robustness under measurement error. The mean errors are 4.78 %, 2.67 % and 10.51 % when the initial values are 0.015 mW·mm−3·°C−1, 0.05 mW·mm−3·°C−1 and 0.15 mW·mm−3·°C−1 respectively. When there is no measurement error, the estimated error of the convection heat transfer coefficients is 2.67 %, and even if the measurement error reaches 5 %, and the accuracy loss is only 5.57 %. Consequently, this approach is highly suitable for estimating convection heat transfer coefficients during the dynamic operation of steam turbines, and this research provides reliable guidance for the optimization design and safe operation of steam turbines.

The periplectic q-Brauer category

We introduce the periplectic q-Brauer category over an integral domain of characteristic not 2. This is a strict monoidal supercategory and can be considered as a q-analogue of the periplectic Brauer category in [18]. We prove that the periplectic q-Brauer category admits a split triangular decomposition in the sense of [6]. When the ground ring is an algebraically closed field, the category of locally finite-dimensional right modules for the periplectic q-Brauer category is an upper finite fully stratified category in the sense of [6]. We prove that periplectic q-Brauer algebras defined in [1] are isomorphic to endomorphism algebras in the periplectic q-Brauer category. Furthermore, a periplectic q-Brauer algebra is a standardly based algebra in the sense of [13]. We construct a Jucys-Murphy basis for any standard module of the periplectic q-Brauer algebra with respect to a family of commutative elements called Jucys-Murphy elements. Via them, we classify blocks for both the periplectic q-Brauer category and periplectic q-Brauer algebras in the generic case. Our result shows that both the periplectic q-Brauer category and periplectic q-Brauer algebras are always not semisimple over any algebraically closed field.

Calculation of a Multidimensional Integral with a Singularity by Dividing the Integration Domain into Subsegments

Calculation of a Multidimensional Integral with a Singularity by Dividing the Integration Domain into Subsegments

Numerical Computation of 2D Domain Integrals in Boundary Element Method by (α, β) Distance Transformation for Transient Heat Conduction Problems

When the time-dependent boundary element method, also termed the pseudo-initial condition method, is employed for solving transient heat conduction problems, the numerical evaluation of domain integrals is necessitated. Consequently, the accurate calculation of the domain integrals is of crucial importance for analyzing transient heat conduction. However, as the time step decreases progressively and approaches zero, the integrand of the domain integrals is close to singular, resulting in large errors when employing standard Gaussian quadrature directly. To solve the problem and further improve the calculation accuracy of the domain integrals, an (α, β) distance transformation is presented. Distance transformation is a simple and efficient method for eliminating near-singularity, typically applied to nearly singular integrals. Firstly, the (α, β) coordinate transformation is introduced. Then, a new distance transformation for the domain integrals is constructed by replacing the shortest distance with the time step. With the new method, the integrand of the domain integrals is substantially smoothed, and the singularity arising from small time steps in the domain integrals is effectively eliminated. Thus, more accurate results can be obtained by the (α, β) distance transformation. Different sizes of time steps, positions of source point, and shapes of integration elements are considered in numerical examples. Comparative studies of the numerical results for the domain integrals using various methods demonstrate that higher accuracy and efficiency are achieved by the proposed method.

How and why does religion matter for the integration of Muslim minorities? Differentiating religiosity from religious orientations among Turkish Muslims in Germany

ABSTRACT The high level of religiosity of immigrants in general and Muslims in particular is often conceived of as a barrier to integration in European public and scholarly debates. However, existing survey research on the relation between religion and integration was limited to measures of religiosity and has yielded contradictory findings. For a broad range of outcomes spanning the domains of structural, social and cultural integration, there are studies showing positive, negative or no associations with immigrants’ religiosity. Arguing that religious cognitions are independent of religiosity, we examine whether the way immigrants reason about religion explains additional variation in immigrant integration. Drawing on original survey data of Turkish-origin Muslims in Germany (N = 500), we examine how religious literalism, symbolism and theological exclusivism relate to a broad range of integration outcomes (educational attainment, labour market participation, intergroup contact, civic and political participation, volunteering, sense of belonging to Germany and social distance), over and above levels of religiosity. Factor analyses reveal that a symbolic approach to religion (i.e. emphasizing the need to take the historical context into account when interpreting religious texts) is conceptually distinct from literalism and exclusivism and can explain variation beyond religiosity, particularly in the domain of civic integration.

N-prime elements and the primality of x − α in D⟦x⟧

Let D be an integral domain and D [ ​ [ x ] ​ ] be the power series ring over D. In this paper, we study the primality of x − α in D [ ​ [ x ] ​ ] , where α ∈ D . For this purpose, we generalize the definition of a prime element as follows. For a positive integer N, a nonzero nonunit α ∈ D is called an N-prime element if for any a , b ∈ D , α N | ab implies α | a or α | b . We prove that if α is an N-prime element for some N, then x − α is a prime element in D [ ​ [ x ] ​ ] . Surprisingly, it is shown that the converse also holds when D is a PID, a valuation domain, or a Dedekind domain. In other words, when D is a PID, a valuation domain, or a Dedekind domain, a necessary and sufficient condition for x − α to be a prime element in D [ ​ [ x ] ​ ] is α is an N-prime element in D for some N. This however does not hold for other types of integral domains such as UFDs or Krull domains. We also investigate the N-prime property in an arbitrary integral domain and give other (equivalent) conditions for an element α in the aforementioned types of integral domains to be an N-prime element.

FreqSNet: a multiaxial integration of frequency and spatial domains for medical image segmentation

Objective. In recent years, convolutional neural networks, which typically focus on extracting spatial domain features, have shown limitations in learning global contextual information. However, frequency domain can offer a global perspective that spatial domain methods often struggle to capture. To address this limitation, we propose FreqSNet, which leverages both frequency and spatial features for medical image segmentation. Approach. To begin, we propose a frequency-space representation aggregation block (FSRAB) to replace conventional convolutions. FSRAB contains three frequency domain branches to capture global frequency information along different axial combinations, while a convolutional branch is designed to interact information across channels in local spatial features. Secondly, the multiplex expansion attention block extracts long-range dependency information using dilated convolutional blocks, while suppressing irrelevant information via attention mechanisms. Finally, the introduced Feature Integration Block enhances feature representation by integrating semantic features that fuse spatial and channel positional information. Main results. We validated our method on 5 public datasets, including BUSI, CVC-ClinicDB, CVC-ColonDB, ISIC-2018, and Luna16. On these datasets, our method achieved Intersection over Union (IoU) scores of 75.46%, 87.81%, 79.08%, 84.04%, and 96.99%, and Hausdorff distance values of 22.22 mm, 13.20 mm, 13.08 mm, 13.51 mm, and 5.22 mm, respectively. Compared to other state-of-the-art methods, our FreqSNet achieves better segmentation results. Significance. Our method can effectively combine frequency domain information with spatial domain features, enhancing the segmentation performance and generalization capability in medical image segmentation tasks.

Partially Ordered Fields and Integral Domains

Partially Ordered Fields and Integral Domains

Structural insight into the Csx1-Crn2 fusion self-limiting ribonuclease of type III CRISPR system.

In the type III CRISPR system, cyclic oligoadenylate (cOA) molecules act as second messengers, activating various promiscuous ancillary nucleases that indiscriminately degrade host and viral DNA/RNA. Conversely, ring nucleases, by specifically cleaving cOA molecules, function as off-switches to protect host cells from dormancy or death, and allow viruses to counteract immune responses. The fusion protein Csx1-Crn2, combining host ribonuclease with viral ring nuclease, represents a unique self-limiting ribonuclease family. Here, we describe the structures of Csx1-Crn2 from the organism of Marinitoga sp., in both its full-length and truncated forms, as well as in complex with cA4. We show that Csx1-Crn2 operates as a homo-tetramer, a configuration crucial for preserving the structural integrity of the HEPN domain and ensuring effective ssRNA cleavage. The binding of cA4 to the CARF domain triggers significant conformational changes across the CARF, HTH, and into the HEPN domains, leading the two R-X4-6-H motifs to form a composite catalytic site. Intriguingly, an acetate ion was found to bind at this composite site by mimicking the scissile phosphate. Further molecular docking analysis reveals that the HEPN domain can accommodate a single ssRNA molecule involving both R-X4-6-H motifs, underscoring the importance of HEPN domain dimerization for its activation.

The Role of Premium Domains, COREDAO VIP Token, and 9NFTMania in the CORE Blockchain Ecosystem

The CORE blockchain ecosystem has witnessed significant advancements with the integration of premium domains, the COREDAO VIP token, and the rise of 9NFTMania. This paper explores their individual and collective impacts on decentralized finance (DeFi), governance, and digital asset ownership within the CORE blockchain. Analyzing their functionalities, economic implications, and future prospects sheds light on their transformative roles in shaping the decentralized landscape.

Integration of the DIAMONDS and CAPTION situation taxonomies based on the South Korean culture.

In this study, we developed an integrated situational taxonomy by merging the second-generation situational taxonomies of the DIAMONDS and CAPTION models. The study participants included 363 adults aged 25-39 years, residing in South Korea, with at least a college degree, and currently employed. To integrate the factors of both models, we conducted an exploratory factor analysis and further examined the hierarchical structure of these factors using bass-ackwards analysis. Our analysis revealed that the integrated situational taxonomy comprises seven domains with a confirmed hierarchical structure. Building on these findings, we further conducted a comparative analysis of the results with prior situational taxonomy research. It was found that the factors constituting integrated domains derived from previous studies that employed correlation analysis or factor analysis differed from those of our study. However, the taxonomy of the three domains in the third level (negativity, positivity, and tasks) aligned with that of previous relevant research, suggesting that these domains are universally applicable to situational taxonomy. Hence, although the taxonomy of the three domains does not encapsulate specific situational characteristics, like the seven domains, if one seeks a culturally universal, statistically clear, and concise structure of situational taxonomy, the three-domain one is a promising alternative to the seven domains. Moreover, this study is the first situational taxonomic research outside the United States and European cultural spheres that confirms that an integrated situational taxonomy is similarly applicable in East Asian cultures.

Development of aircraft noise simulation framework J-FRAIN based on component-wise sound source models

In order tomake detailed and accurate predictions of aircraft noise around airports, we have developed “J-FRAIN”, a new aircraft noise simulation framework that can precisely predict the time histories of noises emitted from each major aircraft noise source during the landing approach phase at ground observation points. This article describes the elements of the developed framework—data acquisition, sound source modeling, propagation modeling, and ground noise prediction—and present some application examples. To develop the framework, we first deployed a 30m-diameter microphone array under the final approach path to an international airport to measure acoustic maps of several civil aircraft types in flight. The sound powers of major aircraft noise-emitting components were then estimated quantitatively by domain integration of the deconvolved acoustic maps at five emission angles in the plane of the glideslope, and the directivities of each noise source were determined. Next, component-wise sound source regression models for engines and airframe noise sources were created based on the physical relationships between engine rotation speed, airspeed, and the deployment angle of high-lift devices, and the coefficients in each model were determined to minimize the root-mean-square error between the measured and predicted sound power levels. The phenomena of atmospheric absorption and ground effect during the propagation of radiated sounds were also incorporated into the framework. Actual flight parameter values were used as inputs to the completed framework, and it was confirmed that the predicted time histories of sound pressure levels on the ground agreed with measured data to within 2 dB if ground effect was properly considered. Finally, as sample applications that use the unique features of the proposed J-FRAIN framework, the article discusses the evaluation of the contributions of each aircraft noise source at noise observation points under the final approach path to the airport and the impact assessment of flight operations on noise.

Understanding Economic Integration in Immigrant and Refugee Populations: A Scoping Review of Concepts and Metrics in the United States

In an increasingly mobile world, the integration of immigrants and displaced individuals is an important factor in creating cohesive and inclusive societies. Integration has different dimensions; this scoping review examines the conceptualization and measurement of economic integration among immigrants and refugees in the United States. Quantitative peer-reviewed journal papers measuring or conceptualizing the economic integration of first-generation documented adult immigrants or refugees in the United States, as well as relevant conceptual or theory papers on this topic, were included in the review. The search strategy included an online search of the Web of Science Core Collection, PsycINFO, Applied Social Sciences Index and Abstracts (ASSIA), and EconLit. Additional search strategies included scanning the reference lists of studies identified as relevant in the initial database search. An analysis of 72 studies included in the review using a data extraction table reveals seven key domains of economic integration: income and economic security, employment and occupational categories, assets and use of financial services, neighborhood and housing, health, education, and use of public assistance. Income and economic security emerged as the most common indicators of integration in the reviewed studies. Notably, less than half of the reviewed publications had a multidimensional approach to defining or measuring economic integration, and the majority of studies were focused on immigrants, with a smaller proportion dedicated to refugees. This review emphasizes the need for comprehensive frameworks in assessing economic integration among immigrants and refugees, reflecting the multifaceted nature of their economic integration experiences.

Approximate averaged derivative moments and stochastic response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises

Stochastic response prediction is one of the principal topics in diverse branches of engineering, such as aerospace engineering, mechanical engineering, and vehicle engineering. However, the challenge of addressing high-dimensional partial differential equations or evaluating high-dimensional domain integrals in determining averaged derivative moments has limited the research. This study proposes a method to predict the stochastic response of high-degree-of-freedom (DOF) quasi-non-integrable Hamiltonian systems under Poisson white noises. The original finite DOF system is reduced to a one-dimensional one governing the Hamiltonian by applying the stochastic averaging method, and the associated reduced generalized Fokker–Planck–Kolmogorov (GFPK) equation is derived. Then, the two-step generalized elliptical coordinate transformation is extended to evaluate averaged derivative moments that are the key to obtaining the stationary probability density function (SPDF) for probabilistic information prediction. Moreover, the perturbation method is introduced to address the high-order GFPK equation. Finally, an 8-DOF strongly nonlinear system under purely additive Poisson white noises is given as an example to highlight the accuracy of the proposed method. Results from the proposed method show good agreement with those from Monte Carlo simulations, which indicates that the proposed method can be applied to assess the response of high-DOF quasi-non-integrable Hamiltonian systems under Poisson white noises. In addition, if the potential energy of an arbitrary finite n-DOF system is the same form as that in Appendix B, pertinent high-dimensional domain integrals are converted into explicit expressions when n is even.

Analytical solutions for the free vibration of cross-ply composite laminated plates with arbitrary biaxial symmetric geometry

This paper presents an analytical model for the free vibration of composite laminated plates with arbitrary biaxial symmetric geometry under elastic boundary conditions, applicable to cross-ply fiber-reinforced composites. In this model, the domain segmentation integral method proposed by the authors is extended to the first-order shear deformation theory (FSDT) and the laminated plate theory. The energy integrals pertaining to the FSDT are analytically simplified by segmenting the integration domains and synthesizing orthogonal polynomial displacement functions over the plate domain coordinate intervals. This synthesis is achieved through the amalgamation of the penalty function method and the Gram-Schmidt orthogonalization process. Then, using the Rayleigh-Ritz procedure, a series solution for the free vibration problem of cross-ply fiber-reinforced composite laminated plates is obtained. The model provides an analytical mathematical relationship between the profile curve of composite laminated plates with arbitrary biaxial symmetric geometry and the strain energy, kinetic energy, and boundary potential energy during vibrational processes. The correctness and applicability of the method are validated by comparing the obtained results with those from the literatures. New results for laminated plates, such as hexagonal and astroid-shaped plates, were presented as references for future research. Taking a track shaped plate as an example, the effect of the number of layers on the vibration characteristics of cross-ply fiber-reinforced composite laminated plates with a certain thickness is studied.

Machining quality prediction of multi-feature parts using integrated multi-source domain dynamic adaptive transfer learning

Machining quality prediction of multi-feature parts has been a challenging problem because of small dataset and inconsistent quality data distribution with respect to each machining feature. Transfer learning that leverages knowledge of one task and can be repurposed on another task seems a good solution for this purpose. However, traditional transfer learning typically has a single source domain and a target domain, which limits its applications in multi-source scenarios (e.g., multi-feature). To solve this issue, this paper proposes a novel integrated multi-source domain dynamic adaptive transfer learning (IMD-DATL) framework for machining quality prediction of multi-feature part machining systems. Specifically, a domain-sample similarity double matching multi-source domain integration method is designed to construct the integration knowledge transfer from multiple source domains to the target domain. A residual feature extraction network based on sample entropy-dynamic channel double-layer attention structure and a fine-grained transferable feature attention module are designed. These three attentions are used to improve the feature learning ability and the adaptation level to the predicted object in the three dimensions of sample, channel and data feature. Finally, multiple sets of comparative experiments in thin-walled part machining systems confirm the effectiveness and superiority of the proposed method for cross-domain quality prediction. Compared with other traditional transfer learning methods, the MAE, RMSE and Score on average of this method are increased by 5.47 %, 4.59 % and 4.84 %, respectively, compared with other multi-source domain adaptation methods, the MAE, RMSE and Score on average of this method are increased by 7.13 %, 7.37 % and 6.52 %, respectively.

Graded perinormality

An integral domain [Formula: see text] is perinormal if every local going-down overring is a localization of [Formula: see text] and globally perinormal if every going-down overring is a localization of [Formula: see text]. In this paper, I introduce notions of graded perinormal and graded globally perinormal domains and show that many results obtained for perinormal and globally perinormal domains have graded analogs. I also give some results for descent of properties between a graded domain and its [Formula: see text]th graded component.

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.