Integral Domain Research Articles

Integration of Cognitive, Affective, and Psychomotor Domain Scoring in Islamic Religious Education

An educator must consider the levels in each domain (cognitive, affective and psychomotor) when compiling scores and weighting questions. This is also the case in Islamic Religious Education lessons. The purpose of writing this article is to explain the integration of scoring for cognitive, affective, and psychomotor domains along with examples in Islamic religious education questions. Using literature studies, there are conclusions obtained from this article, namely the benefits for students, 1). Helps students to develop balanced competencies. 2). Helps students to understand the relationship between knowledge, attitudes, and skills. 3). Helps students to become a whole person with integrity. So it is highly recommended for educators to be able to carry out the right application, with the integration of cognitive, affective, and psychomotor domain scoring in order to become one of the important instruments to improve the quality of Islamic religious education in the world of education.

Maritime Security: Lost in Translation? Developing a Common Lexicon to Enhance Data Integrity and Global Maritime Domain Awareness

With the proliferation of post-Cold War globalisation, the international community began to appreciate the immense importance of maritime security. In recent decades, numerous national, regional, and global information sharing centres have been established with an aim to provide relevant stakeholders with an assessment of the risks and threats within the maritime domain. Unfortunately, international organisations failed to simultaneously emphasise the importance of standardised terminology and definitions for use in the global maritime security context. Instead of using other standardised areas of the maritime industry such as maritime safety as a guide, dozens of government agencies, regional reporting centres, private maritime security companies, and information sharing/fusion centres have now been established. Each of these uses its own unique categories, terminology, and definitions to measure and catalogue regional and global incidents of violent maritime crime. In this article, that includes acts of piracy and armed robbery against ships. In some cases, political and economic bias has played a significant role in how maritime security incident data is officially recorded and presented to the public. This lack of data cohesion has resulted in significant confusion and distrust amongst the shipping industry and policymakers. It has also created an uncertain environment for seafarers, who largely depend on their employers and regulators to keep them safe and secure at sea. The research includes an analysis of several sets of qualitative and quantitative data from prominent agencies and reporting centres. Case studies are also presented to illustrate why harmonised terminology, definitions, and incident reporting protocols are integral to achieving global maritime domain awareness. The numerous challenges to achieving this goal are then explored and proposed solutions are presented. The paper concludes by proposing a lexicon for incidents of violent maritime crime, as a first step in creating a common lexicon for global maritime security. As stated in earlier issues, this journal does not seek to promote a common definition of maritime security, but a common lexicon is of more practical use. This article is based on a dissertation completed as part of the master’s degree in Maritime Security at Coventry University in 2022.

The fast multipole method–accelerated line integration boundary element method for 3D heat conduction analysis with heat source

Purpose3D steady heat conduction analysis considering heat source is conducted on the fundamental of the fast multipole method (FMM)-accelerated line integration boundary element method (LIBEM).Design/methodology/approachDue to considering the heat source, domain integral is generated in the traditional heat conduction boundary integral equation (BIE), which will counteract the well-known merit of the BEM, namely, boundary-only discretization. To avoid volume discretization, the enhanced BEM, the LIBEM with dimension reduction property is introduced to transfer the domain integral into line integrals. Besides, owing to the unsatisfactory performance of the LIBEM when it comes to large-scale structures requiring massive computation, the FMM-accelerated LIBEM (FM-LIBEM) is proposed to improve the computation efficiency further.FindingsAssuming N and M are the numbers of nodes and integral lines, respectively, the FM-LIBEM can reduce the time complexity from O(NM) to about O(N+ M), and a full discussion and verification of the advantage are done based on numerical examples under heat conduction.Originality/value(1) The LIBEM is applied to 3D heat conduction analysis with heat source. (2) The domain integrals can be transformed into boundary integrals with straight line integrals by the LIM. (3) A FM-LIBEM is proposed and can reduce the time complexity from O(NM) to O(N+ M). (4) The FM-LIBEM with high computational efficiency is exerted to solve 3D heat conduction analysis with heat source in massive computation successfully.

Implementation of DRBEM for coupled sine-Gordon equations

In this study, two-dimensional, time dependent, nonlinear, coupled sine-Gordon equations (CSGE) is solved using the dual reciprocity boundary element method (DRBEM). The DRBEM provides to transform the domain integral, caused by the inhomogeneous terms, into the boundary integral by approximating with thin plate spline. DRBEM formulation is derived using the fundamental solution of the modified Helmholtz equations (MHE)’s. In order to write the original equations in the form of MHE, time dervatives are expanded using finite difference. The principle purpose of this study is to show that DRBEM is a successful alternative for the solution of CSGE. Method is tested with the examples which have the analitical solution. The study also includes the solutions of other examples in the literature. Numerical experiments show that obtained results are in good agreement with other studies where the problem has been solved before and thus DRBEM is effective and accurate for the solution of CSGE.

A new meshless local integral equation method

This paper proposes a novel meshless local integral equation (LIE) method for numerical solutions of two and three-dimensional Poisson equations. The proposed method can be regarded as a new variant of the meshless local Petrov-Galerkin (MLPG) method which already has six variants, and so the proposed method can be called MLPG7. A variant of MLPG called local boundary integral equation (LBIE) method, uses a localized fundamental solution of Laplace equation as test function. This test function vanishes on local boundaries and therefore, the derived local equations do not involve the gradient of field variables. The motivation for new formulation is using an average of LBIE equation over radius of local sub-domains instead of a single sub-domain. A new kernel is introduced which is a new modification of fundamental solutions of Laplace equation. It is proved that using the new kernel as test function leads to the same local equations as averaging. Infact, the new formulation is a modification of the LBIE method for which the boundary integral is replaced with a domain integral. It is proved that new local weak formulation is equivalent with strong form. The convergence of the method for the case of regularly spaced nodal points is proved. For trial approximation, this paper uses Gaussian radial basis functions (Gaussian RBF), however, derivative free property of the method allows the use of any non-differentiable basis functions. Stability and convergence of the method are numerically studied by considering both 2D and 3D problems with regular and irregular nodal points. The method is compared with LBIE, finite differences (FD) and RBF-FD methods and the numerical results reveal the significance of the proposed method.

The dynamic analysis of axisymmetric bodies with damping effects using the modified radial integration boundary elements method (MRIBEM)

This paper investigates the elastodynamic analysis of axisymmetric bodies under axisymmetric dynamic loads using the modified radial integration boundary elements method (MRIBEM). Purposely, the governing integral equations have been developed in cylindrical coordinates by employing the three-dimensional (3D) static fundamental solution. The axisymmetric bodies can be modeled as a two-dimensional (2D) problem, which is much simpler than 3D analysis and only requires a one-dimensional boundary mesh. In the proposed formulation, the effects of inertial and damping forces appear as 2D domain integrals. The domain variables are approximated using global radial basis functions (RBFs), and the modified radial integration method (MRIM) is employed to deal with the domain integral as the main idea of the present research. Various sample problems are provided in order to illustrate the capability of the presented method for analyzing axisymmetric bodies with concave geometry and damping effect under different types of transient loads. The Newmark and Houbolt methods were applied for time marching, and their efficiency was examined. The results of the present study were also validated by the axisymmetric FEM formulation and other available references.

A reduced-order modeling for thermo-mechanical coupling analyses by using radial integration boundary element method

In order to efficiently solve thermo-mechanical coupling problems, this work combines the radial integration boundary element method (RIBEM) and the proper orthogonal decomposition (POD) to construct a fast reduced-order model. This model transforms high-dimensional systems into low-dimensional ones, enabling faster computation of thermo-mechanical coupling problems under thermal loads. Firstly, RIBEM is employed to solve coupled thermoelastic dynamic problems under thermal shock loads. Domain integrals are converted to boundary integrals using the radial integration method, establishing a purely boundary element algorithm without internal cells. Subsequently, finite difference techniques are applied to calculate the discretized algebraic equations, and the obtained field variables are used as a snapshot matrix to establish POD modes and construct the POD reduced-order model. Numerical examples demonstrate that the results of the reduced-order model are essentially consistent with the full-order model across various physical parameters and boundary conditions. Therefore, this reduced-order model significantly improves computational efficiency while maintaining high accuracy, especially when solving large-scale problems.

Non-local gradients in bounded domains motivated by continuum mechanics: Fundamental theorem of calculus and embeddings

Abstract In this article, we develop a new set of results based on a non-local gradient jointly inspired by the Riesz s s -fractional gradient and peridynamics, in the sense that its integration domain depends on a ball of radius δ > 0 \delta \gt 0 (horizon of interaction among particles, in the terminology of peridynamics), while keeping at the same time the singularity of the Riesz potential in its integration kernel. Accordingly, we define a functional space suitable for non-local models in calculus of variations and partial differential equations. Our motivation is to develop the proper functional analysis framework to tackle non-local models in continuum mechanics, which requires working with bounded domains, while retaining the good mathematical properties of Riesz s s -fractional gradients. This functional space is defined consistently with Sobolev and Bessel fractional ones: we consider the closure of smooth functions under the natural norm obtained as the sum of the L p {L}^{p} norms of the function and its non-local gradient. Among the results showed in this investigation, we highlight a non-local version of the fundamental theorem of calculus (namely, a representation formula where a function can be recovered from its non-local gradient), which allows us to prove inequalities in the spirit of Poincaré, Morrey, Trudinger, and Hardy as well as the corresponding compact embeddings. These results are enough to show the existence of minimizers of general energy functionals under the assumption of convexity. Equilibrium conditions in this non-local situation are also established, and those can be viewed as a new class of non-local partial differential equations in bounded domains.

Autonomy for UAVS: Integration of Multiple Technology Domains

This paper looks at the science technology required to develop an autonomous group of UAVs to perform a specified mission. It details a three level approach which describes the bottom level where UAV guidance algorithms are examined. The second level describes the path planning requirements to allow for area research object tracking and rendezvous. The top level is where mission planning takes place. The use of Kripke Temporal Logic is described which allows the UAV behaviours to be determined and verified. A simple example of a UAV as part of a UAV group is given.

A Semantic Framework for Decision Making in Forest Fire Emergencies

Forest fires can have devastating effects on the environment, communities, individuals, economy, and climate change in many countries. During a forest fire crisis, massive amounts of data, such as weather patterns and soil conditions, become available. Efficient management, intelligent integration, and processing the available information in order to extract useful insights and knowledge to facilitate advanced whereas and support human operators and authorities in a real operational scenario is a challenge. In this work, we present ONTO-SAFE, an ontology-based framework for wildfire events, adopting Semantic Web technologies for data integration and infusion of domain and background knowledge. More specifically, the framework creates a unified representation of the available assets, taking into account data generated from different sources, such as sensors, weather forecasts, earth observations, etc. To this end, previously existing ontologies and standards are used, such as Empathi and EmergencyFire ontology, to provide the conceptual model and the necessary level of abstraction in the form of interconnected knowledge graphs to satisfy the modeling requirements. On top of the generated knowledge graphs, a declarative framework extracts facts and higher-level inferred knowledge from asserted data to support users in decision making. In addition, the framework supports the generation of recommendations, such as sharing important wildfire information with citizens and professionals, that can be adjusted based on user-defined factors and the current disaster risk management phase.

Polynomial chaos Kriging-based structural reliability analysis via the expected margin volume reduction

Integral learning functions are theoretically sound but suffer from intensive computational complexity induced by the associated double integral. Based on a new notation of limit-state margin volume, a computationally-cheap integral learning function called Expected margin volume reduction (EMVR) is proposed for structural reliability analysis. EMVR has two key contributions. First, closed-form expression for the inner integral is well derived based on Kriging update formulas, due to tractable definition of the margin volume. This gets rid of cumbersome numerical quadrature or drawing massive realizations of Gaussian process. Second, a confined integral domain is rationally defined for the outer integral, by virtue of exploring the locality of its integrand. This bypasses annoying computer memory issue. Moreover, a hybrid stopping condition coupled with two different settings of the associated parameters is deployed, accommodating to reliability problems with different features. Then, the performance of EMVR-based reliability algorithm is illustrated on four numerical examples. The results show that the evaluation time of EMVR is reduced to a level comparable to pointwise learning functions. Moreover, it outperforms those existing learning functions in terms of both computational accuracy and efficiency.

Tonal partition algebras: fundamental and geometrical aspects of representation theory

For we define tonal partition algebra over . We construct modules for over , and hence over any integral domain containing (such as ), that pass to a complete set of irreducible modules over the field of fractions. We show that is semisimple there. That is, we construct for the tonal partition algebras a modular system in the sense of Brauer. Using a “geometrical” index set for the Δ-modules, we give an order with respect to which the decomposition matrix over (with ) is upper-unitriangular. We establish several crucial properties of the Δ-modules. These include a tower property, with respect to n, in the sense of Green and Cox-Martin-Parker-Xi; contravariant forms with respect to a natural involutive antiautomorphism; a highest weight category property; and branching rules.

Petrov–Galerkin zonal free element method for 2D and 3D mechanical problems

AbstractIn this article, a novel weak‐form zonal Petrov–Galerkin free element method is proposed for two‐ and three‐dimensional linear mechanical problems. By absorbing the advantages of finite block method and strong‐form finite element method, the block mapping technique is used in the free element method. Combining the characteristics of the meshless local Petrov–Galerkin method, the local Petrov–Galerkin formulation based on the zonal free element method is formed at last. Besides, the local integral domain selected in the local collocation element is circular or spherical to simplify programming. The transformation of the local integral domain between the physical and normalized spaces is given for two‐ and three‐dimensional problems. The comparison of accuracy and convergence between the new proposed Petrov–Galerkin method and the conventional methods is carried out. Some challenging examples including fracture mechanics problems and a complex 3D problem are given to validate the convergence and accuracy of the proposed method.

Graded almost pseudo-valuation domains

Let Γ be a nonzero commutative cancellative monoid (written additively), be a Γ-graded integral domain with for all , and H be the set of nonzero homogeneous elements of R. A homogeneous ideal P of R will be said to be strongly homogeneous primary if implies or for some integer , for every homogeneous elements x, y of RH . We say that R is a graded almost pseudo-valuation domain (gr-APVD) if each homogeneous prime ideal of R is strongly homogeneous primary. In this paper, we study some ring-theoretic properties of gr-APVDs and graded integral domains R such that is a gr-APVD for all homogeneous maximal ideals (resp., homogeneous maximal t-ideals) P of R.

Error Correction for Discrete Tomography

Discrete tomography focuses on the reconstruction of functions from their line sums in a finite number d of directions. In this paper we consider functions f : A → R where A is a finite subset of ℤ2 and R an integral domain. Several reconstruction methods have been introduced in the literature. Recently Ceko, Pagani and Tijdeman developed a fast method to reconstruct a function with the same line sums as f. Up to here we assumed that the line sums are exact. Some authors have developed methods to recover the function f under suitable conditions by using the redundancy of data. In this paper we investigate the case where a small number of line sums are incorrect as may happen when discrete tomography is applied for data storage or transmission. We show how less than d/2 errors can be corrected and that this bound is the best possible. Moreover, we prove that if it is known that the line sums in k given directions are correct, then the line sums in every other direction can be corrected provided that the number of wrong line sums in that direction is less than k/2.

A Valuation Theorem for Noetherian Rings

Let A⊂B be integral domains. Suppose A is Noetherian and B is a finitely generated A-algebra. Denote by A‾ the integral closure of A in B. We show that A‾ is determined by finitely many unique discrete valuation rings. Our result generalizes Rees’ classical valuation theorem for ideals. We also obtain a variant of Zariski’s main theorem.

A Self-supervised Framework for Learning Biological Entities Representation by Fusing Class Information.

Ontologies are widely utilized in the biological domain for data annotation, integration, and analysis. Some representation learning methods have been proposed to learn the representation of entities to assist intelligent applications, such as knowledge discovery. However, most of them neglect the class information of entities in the ontology. In this paper, we propose a unified framework, named ERCI, which jointly optimizes the knowledge graph embedding model and self-supervised learning. In this way, we can generate embeddings of bio-entities by fusing the class information. Moreover, ERCI is a pluggable framework that can be easily incorporated with any knowledge graph embedding model. We validate ERCI in two different ways. In the first way, we utilize the protein embeddings learned by the ERCI to predict protein-protein interactions on two different datasets. In the second way, we leverage the gene and disease embeddings generated by the ERCI to predict gene-disease associations. In addition, we create three datasets to simulate the long-tail scenario and evaluate ERCI on these. Experimental results show that ERCI has superior performance on all metrics compared with the state-of-the-art methods.

A New Approach to Deriving Closed-Form Bit Error Probability Expressions of MPSK Signals

In conventional approach, the bit error probability (BEP) expressions of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary phase-shift keying (MPSK) signals over additive white Gaussian noise (AWGN) channel are derived by averaging error probabilities for all bits of MPSK symbol. The closed-form BEP expressions of MPSK signals over AWGN channel can also be derived by using the weighted conditional symbol error probability (SEP) expressions, which has not been reported. In this paper, we derive the conditional SEP expressions of MPSK signals in terms of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions by changing the domain of integration from a plane bounded by two rays into a quadrant. By weighting the conditional SEP expressions according to average distance spectrum, the closed-form BEP expressions of MPSK signals over AWGN channel are obtained. Only two summations involving two parameters are required. The closed-form BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are derived by using the BEP expressions over AWGN channel and the moment generating function-based approach. The approximate BEP expressions of MPSK signals over Nakagami- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading channel are obtained by using elementary functions-based approximations of Gaussian <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> and Owen’s <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> functions. The conciseness and computational complexity of our BEP expressions are verified by the comparison with existing results.

A node elimination algorithm for cubature of high-dimensional polytopes

Node elimination is a numerical approach for obtaining cubature rules for the approximation of multivariate integrals. Beginning with a known cubature rule, nodes are selected for elimination, and a new, more efficient rule is constructed by iteratively solving the moment equations. This paper introduces a new criterion for selecting which nodes to eliminate that is based on a linearization of the moment equation. In addition, a penalized iterative solver is introduced, that ensures that weights are positive and nodes are inside the integration domain. A strategy for constructing an initial cubature rule for various polytopes in several space dimensions is described. High efficiency rules are presented for two, three and four dimensional polytopes. The new rules are compared with rules that are obtained by combining tensor products of one dimensional quadrature rules and domain transformations, as well as with known analytically constructed cubature rules.

Influence of different magnetic configurations on plasma parameters in SPIDER device

The ITER fusion reactor will be heated by fast neutral beams generated by accelerating and neutralizing negative ions, produced in a RF inductively-coupled plasma which expands through a region featuring a magnetic filter. During the current shut down of the SPIDER device (until 2023) some modifications of the device have been planned to improve the system performance. These modifications are based on the experience gained during operation of SPIDER in previous years and include, among others, the addition of further sets of permanent magnets in the expansion chamber of the plasma source and around the RF drivers. The purpose of these modifications is to improve plasma confinement, and thus increase its density and homogeneity. The present paper reports the results of numerical studies of the plasma parameters in SPIDER source with different types of modifications of SPIDER device including new permanent magnets configurations. Analysis are done by means of the numerical code FSFS2D in which a self-consistent two-dimensional fluid description of the source is implemented. In order to partially account for the 3D flow pattern within our 2D model, simulations are run in two different layouts, in the vertical plane with the magnetic filter being perpendicular to the integration domain and in the horizontal plane with the filter field in the integration surface. Simulation results indicate, that the permanent magnets around the RF driver tends to increase the plasma density in the driver.