Search results for: eigenvalues

Authors: Krish Jhurani

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The research paper presents an in-depth analysis of symmetry properties in linear algebraic systems under the operation of non-canonical scalar multiplication structures, specifically semirings, and near-rings. The objective is to unveil the profound alterations that occur in traditional linear algebraic structures when we replace conventional field multiplication with these non-canonical operations. In the methodology, we first establish the theoretical foundations of non-canonical scalar multiplication, followed by a meticulous investigation into the resulting symmetry properties, focusing on eigenvectors, eigenspaces, and invariant subspaces. The methodology involves a combination of rigorous mathematical proofs and derivations, supplemented by illustrative examples that exhibit these discovered symmetry properties in tangible mathematical scenarios. The core findings uncover unique symmetry attributes. For linear algebraic systems with semiring scalar multiplication, we reveal eigenvectors and eigenvalues. Systems operating under near-ring scalar multiplication disclose unique invariant subspaces. These discoveries drastically broaden the traditional landscape of symmetry properties in linear algebraic systems. With the application of these findings, potential practical implications span across various fields such as physics, coding theory, and cryptography. They could enhance error detection and correction codes, devise more secure cryptographic algorithms, and even influence theoretical physics. This expansion of applicability accentuates the significance of the presented research. The research paper thus contributes to the mathematical community by bringing forth perspectives on linear algebraic systems and their symmetry properties through the lens of non-canonical scalar multiplication, coupled with an exploration of practical applications.

Keywords: eigenspaces, eigenvectors, invariant subspaces, near-rings, non-canonical scalar multiplication, semirings, symmetry properties

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Authors: H. Jung, N. Kim, B. Kang, J. Choe

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History matching is a crucial procedure for predicting reservoir performances and making future decisions. However, it is difficult due to uncertainties of initial reservoir models. Therefore, it is important to have reliable initial models for successful history matching of highly heterogeneous reservoirs such as channel reservoirs. In this paper, we proposed a novel scheme for regenerating geological models using support vector machine (SVM) and principal component analysis (PCA). First, we perform PCA for figuring out main geological characteristics of models. Through the procedure, permeability values of each model are transformed to new parameters by principal components, which have eigenvalues of large magnitude. Secondly, the parameters are projected into two-dimensional plane by multi-dimensional scaling (MDS) based on Euclidean distances. Finally, we train an SVM classifier using 20% models which show the most similar or dissimilar well oil production rates (WOPR) with the true values (10% for each). Then, the other 80% models are classified by trained SVM. We select models on side of low WOPR errors. One hundred channel reservoir models are initially generated by single normal equation simulation. By repeating the classification process, we can select models which have similar geological trend with the true reservoir model. The average field of the selected models is utilized as a probability map for regeneration. Newly generated models can preserve correct channel features and exclude wrong geological properties maintaining suitable uncertainty ranges. History matching with the initial models cannot provide trustworthy results. It fails to find out correct geological features of the true model. However, history matching with the regenerated ensemble offers reliable characterization results by figuring out proper channel trend. Furthermore, it gives dependable prediction of future performances with reduced uncertainties. We propose a novel classification scheme which integrates PCA, MDS, and SVM for regenerating reservoir models. The scheme can easily sort out reliable models which have similar channel trend with the reference in lowered dimension space.

Keywords: history matching, principal component analysis, reservoir modelling, support vector machine

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Authors: Patsawut Sukserm

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Oracy proficiency, encompassing both speaking and listening skills, is vital for EFL learners, yet Thai university students often face significant challenges in developing these abilities. This study aims to identify and analyze the barriers that hinder oracy proficiency in EFL learners. To achieve this, a questionnaire was developed based on a comprehensive review of the literature and administered to a large cohort of Thai EFL students. The data were subjected to exploratory factor analysis (EFA) to validate the questionnaire and uncover the underlying factors influencing learners’ performance. The results revealed that the Kaiser-Meyer-Olkin (KMO) measure of sampling adequacy was 0.912, and Bartlett’s test of sphericity was significant at 2345.423 (p < 0.05), confirming the suitability for factor analysis. There are five main barriers in oracy proficiency, namely Listening and Comprehension Obstacles (LCO), Accent and Speech Understanding (ASU), Speaking Anxiety and Confidence Issues (SACI), Fluency and Expression Issues (FEI), and Grammar and Conversational Understanding (GCU), with eigenvalues ranging from 1.066 to 12.990, explaining 60.305 % of the variance of the 32 variables. These findings highlight the complexity of the challenges faced by Thai EFL learners and emphasize the need for diverse and authentic listening experiences, a supportive classroom environment, or balanced grammar instruction. The findings of the study suggest that educators, curriculum developers, and policy makers should implement evidence-based strategies to address these barriers in order to improve Thai EFL learners’ oral proficiency and enhance their overall academic and professional success. Also, this study will discuss these findings in depth, offering evidence-based strategies for addressing these barriers. Recommendations include integrating diverse and authentic listening experiences, fostering a supportive classroom environment, and providing targeted instruction in both speaking fluency and grammar. The study’s implications extend to educators, curriculum developers, and policymakers, offering practical solutions to enhance learners’ oracy proficiency and support their academic and professional development.

Keywords: exploratory factor analysis, barriers, oracy proficiency, EFL learners

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Authors: Mancho Manev

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The concept of almost paracontact Riemannian manifolds (abbr., apcR manifolds) was introduced by I. Sato in 1976 as an analogue of almost contact Riemannian manifolds. The notion of an apcR manifold of type (p,q) was defined by S. Sasaki in 1980, where p and q are respectively the numbers of the multiplicity of the structure eigenvalues 1 and -1. It also has a simple eigenvalue of 0. In our work, we consider (2n+1)-dimensional apcR manifolds of type (n,n), i.e., the paracontact distribution of the studied manifold can be considered as a 2n-dimensional almost paracomplex Riemannian distribution with almost paracomplex structure and structure group O(n) × O(n). The aim of the present study is to introduce a new class of apcR manifolds. Such a manifold is obtained using the construction of a certain Riemannian cone over it, and the resulting manifold is a paraholomorphic paracomplex Riemannian manifold (abbr., phpcR manifold). We call it a para-Sasaki-like Riemannian manifold (abbr., pSlR manifold) and give some explicit examples. We study the structure of pSlR spaces and find that the paracontact form η is closed and each pSlR manifold locally can be considered as a certain product of the real line with a phpcR manifold, which is locally a Riemannian product of two equidimensional Riemannian spaces. We also obtain that the curvature of the pSlR manifolds is completely determined by the curvature of the underlying local phpcR manifold. Moreover, the ξ-directed Ricci curvature is equal to -2n, while in the Sasaki case, it is 2n. Accordingly, the pSlR manifolds can be interpreted as the counterpart of the Sasaki manifolds; the skew-symmetric part of ∇η vanishes, while in the Sasaki case, the symmetric part vanishes. We define a hyperbolic extension of a (complete) phpcR manifold that resembles a certain warped product, and we indicate that it is a (complete) pSlR manifold. In addition, we consider the hyperbolic extension of a phpcR manifold and prove that if the initial manifold is a complete Einstein manifold with negative scalar curvature, then the resulting manifold is a complete Einstein pSlR manifold with negative scalar curvature. In this way, we produce new examples of a complete Einstein Riemannian manifold with negative scalar curvature. Finally, we define and study para contact conformal/homothetic deformations by deriving a subclass that preserves the para-Sasaki-like condition. We then find that if we apply a paracontact homothetic deformation of a pSlR space, we obtain that the Ricci tensor is invariant.

Keywords: almost paracontact Riemannian manifolds, Einstein manifolds, holomorphic product manifold, warped product manifold

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Authors: M. Maier, I. Dedigama, J. Majasan, Y. Wu, Q. Meyer, L. Castanheira, G. Hinds, P. R. Shearing, D. J. L. Brett

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Increasing the efficiency of electrolyser technology is commonly seen as one of the main challenges on the way to the Hydrogen Economy. There is a significant lack of understanding of the different states of operation of polymer electrolyte membrane water electrolysers (PEMWE) and how these influence the overall efficiency. This in particular means the two-phase flow through the membrane, gas diffusion layers (GDL) and flow channels. In order to increase the efficiency of PEMWE and facilitate their spread as commercial hydrogen production technology, new analytic approaches have to be found. Acoustic emission (AE) offers the possibility to analyse the processes within a PEMWE in a non-destructive, fast and cheap in-situ way. This work describes the generation and analysis of AE data coming from a PEM water electrolyser, for, to the best of our knowledge, the first time in literature. Different experiments are carried out. Each experiment is designed so that only specific physical processes occur and AE solely related to one process can be measured. Therefore, a range of experimental conditions is used to induce different flow regimes within flow channels and GDL. The resulting AE data is first separated into different events, which are defined by exceeding the noise threshold. Each acoustic event consists of a number of consequent peaks and ends when the wave diminishes under the noise threshold. For all these acoustic events the following key attributes are extracted: maximum peak amplitude, duration, number of peaks, peaks before the maximum, average intensity of a peak and time till the maximum is reached. Each event is then expressed as a vector containing the normalized values for all criteria. Principal Component Analysis is performed on the resulting data, which orders the criteria by the eigenvalues of their covariance matrix. This can be used as an easy way of determining which criteria convey the most information on the acoustic data. In the following, the data is ordered in the two- or three-dimensional space formed by the most relevant criteria axes. By finding spaces in the two- or three-dimensional space only occupied by acoustic events originating from one of the three experiments it is possible to relate physical processes to certain acoustic patterns. Due to the complex nature of the AE data modern machine learning techniques are needed to recognize these patterns in-situ. Using the AE data produced before allows to train a self-learning algorithm and develop an analytical tool to diagnose different operational states in a PEMWE. Combining this technique with the measurement of polarization curves and electrochemical impedance spectroscopy allows for in-situ optimization and recognition of suboptimal states of operation.

Keywords: acoustic emission, gas diffusion layers, in-situ diagnosis, PEM water electrolyser

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Authors: Getachew Weldemichael, Sentayehu Alamerew, Leta Tulu, Gezahegn Berecha

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Coffee quality improvement program is becoming the focus of coffee research, as the world coffee consumption pattern shifted to high-quality coffee. However, there is limited information on the genetic variation of C. Arabica for quality improvement in potential specialty coffee growing areas of Ethiopia. Therefore, this experiment was conducted with the objectives of determining the magnitude of variation among 105 coffee accessions collected from east Wollega coffee growing areas and assessing correlations between the different coffee qualities attributes. It was conducted in RCRD with three replications. Data on green bean physical characters (shape and make, bean color and odor) and organoleptic cup quality traits (aromatic intensity, aromatic quality, acidity, astringency, bitterness, body, flavor, and overall standard of the liquor) were recorded. Analysis of variance, clustering, genetic divergence, principal component and correlation analysis was performed using SAS software. The result revealed that there were highly significant differences (P<0.01) among the accessions for all quality attributes except for odor and bitterness. Among the tested accessions, EW104 /09, EW101 /09, EW58/09, EW77/09, EW35/09, EW71/09, EW68/09, EW96 /09, EW83/09 and EW72/09 had the highest total coffee quality values (the sum of bean physical and cup quality attributes). These genotypes could serve as a source of genes for green bean physical characters and cup quality improvement in Arabica coffee. Furthermore, cluster analysis grouped the coffee accessions into five clusters with significant inter-cluster distances implying that there is moderate diversity among the accessions and crossing accessions from these divergent inter-clusters would result in hetrosis and recombinants in segregating generations. The principal component analysis revealed that the first three principal components with eigenvalues greater than unity accounted for 83.1% of the total variability due to the variation of nine quality attributes considered for PC analysis, indicating that all quality attributes equally contribute to a grouping of the accessions in different clusters. Organoleptic cup quality attributes showed positive and significant correlations both at the genotypic and phenotypic levels, demonstrating the possibility of simultaneous improvement of the traits. Path coefficient analysis revealed that acidity, flavor, and body had a high positive direct effect on overall cup quality, implying that these traits can be used as indirect criteria to improve overall coffee quality. Therefore, it was concluded that there is considerable variation among the accessions, which need to be properly conserved for future improvement of the coffee quality. However, the variability observed for quality attributes must be further verified using biochemical and molecular analysis.

Keywords: accessions, Coffea arabica, cluster analysis, correlation, principal component

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Authors: Ali H. Daraji, Jack M. Hale, Ye Jianqiao

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With the extensive use of high specific strength structures to optimise the loading capacity and material cost in aerospace and most engineering applications, much effort has been expended to develop intelligent structures for active vibration reduction and structural health monitoring. These structures are highly flexible, inherently low internal damping and associated with large vibration and long decay time. The modification of such structures by adding lightweight piezoelectric sensors and actuators at efficient locations integrated with an optimal control scheme is considered an effective solution for structural vibration monitoring and controlling. The size and location of sensor and actuator are important research topics to investigate their effects on the level of vibration detection and reduction and the amount of energy provided by a controller. Several methodologies have been presented to determine the optimal location of a limited number of sensors and actuators for small-scale structures. However, these studies have tackled this problem directly, measuring the fitness function based on eigenvalues and eigenvectors achieved with numerous combinations of sensor/actuator pair locations and converging on an optimal set using heuristic optimisation techniques such as the genetic algorithms. This is computationally expensive for small- and large-scale structures subject to optimise a number of s/a pairs to suppress multiple vibration modes. This paper proposes an efficient method to determine optimal locations for a limited number of sensor/actuator pairs for active vibration reduction of a flexible structure based on finite element method and Hamilton’s principle. The current work takes the simplified approach of modelling a structure with sensors at all locations, subjecting it to an external force to excite the various modes of interest and noting the locations of sensors giving the largest average percentage sensors effectiveness measured by dividing all sensor output voltage over the maximum for each mode. The methodology was implemented for a cantilever plate under external force excitation to find the optimal distribution of six sensor/actuator pairs to suppress the first six modes of vibration. It is shown that the results of the optimal sensor locations give good agreement with published optimal locations, but with very much reduced computational effort and higher effectiveness. Furthermore, it is shown that collocated sensor/actuator pairs placed in these locations give very effective active vibration reduction using optimal linear quadratic control scheme.

Keywords: optimisation, plate, sensor effectiveness, vibration control

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Authors: Dragan Ribarić

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We employ the so-called problem-dependent linked interpolation concept to develop two cubic 4-node quadrilateral Mindlin plate finite elements with 12 external degrees of freedom. In the problem-independent linked interpolation, the interpolation functions are independent of any problem material parameters and the rotation fields are not expressed in terms of the nodal displacement parameters. On the contrary, in the problem-dependent linked interpolation, the interpolation functions depend on the material parameters and the rotation fields are expressed in terms of the nodal displacement parameters. Two cubic 4-node quadrilateral plate elements are presented, named Q4-U3 and Q4-U3R5. The first one is modelled with one displacement and two rotation degrees of freedom in every of the four element nodes and the second element has five additional internal degrees of freedom to get polynomial completeness of the cubic form and which can be statically condensed within the element. Both elements are able to pass the constant-bending patch test exactly as well as the non-zero constant-shear patch test on the oriented regular mesh geometry in the case of cylindrical bending. In any mesh shape, the elements have the correct rank and only the three eigenvalues, corresponding to the solid body motions are zero. There are no additional spurious zero modes responsible for instability of the finite element models. In comparison with the problem-independent cubic linked interpolation implemented in Q9-U3, the nine-node plate element, significantly less degrees of freedom are employed in the model while retaining the interpolation conformity between adjacent elements. The presented elements are also compared to the existing problem-independent quadratic linked-interpolation element Q4-U2 and to the other known elements that also use the quadratic or the cubic linked interpolation, by testing them on several benchmark examples. Simple functional upgrading from the quadratic to the cubic linked interpolation, implemented in Q4-U3 element, showed no significant improvement compared to the quadratic linked form of the Q4-U2 element. Only when the additional bubble terms are incorporated in the displacement and rotation function fields, which complete the full cubic linked interpolation form, qualitative improvement is fulfilled in the Q4-U3R5 element. Nevertheless, the locking problem exists even for the both presented elements, like in all pure displacement elements when applied to very thin plates modelled by coarse meshes. But good and even slightly better performance can be noticed for the Q4-U3R5 element when compared with elements from the literature, if the model meshes are moderately dense and the plate thickness not extremely thin. In some cases, it is comparable to or even better than Q9-U3 element which has as many as 12 more external degrees of freedom. A significant improvement can be noticed in particular when modeling very skew plates and models with singularities in the stress fields as well as circular plates with distorted meshes.

Keywords: Mindlin plate theory, problem-independent linked interpolation, problem-dependent interpolation, quadrilateral displacement-based plate finite elements

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Authors: Kaleeswari R. K., Seevagan L .

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Soil quality in an agroecosystem is influenced by the cropping system, water and soil fertility management. A valid soil quality index would help to assess the soil and crop management practices for desired productivity and soil health. The soil quality indices also provide an early indication of soil degradation and needy remedial and rehabilitation measures. Imbalanced fertilization and inadequate organic carbon dynamics deteriorate soil quality in an intensive cropping system. The rice soil ecosystem is different from other arable systems since rice is grown under submergence, which requires a different set of key soil attributes for enhancing soil quality and productivity. Assessment of the soil quality index involves indicator selection, indicator scoring and comprehensive score into one index. The most appropriate indicator to evaluate soil quality can be selected by establishing the minimum data set, which can be screened by linear and multiple regression factor analysis and score function. This investigation was carried out in intensive rice cultivating regions (having >1.0 lakh hectares) of Tamil Nadu viz., Thanjavur, Thiruvarur, Nagapattinam, Villupuram, Thiruvannamalai, Cuddalore and Ramanathapuram districts. In each district, intensive rice growing block was identified. In each block, two sampling grids (10 x 10 sq.km) were used with a sampling depth of 10 – 15 cm. Using GIS coordinates, and soil sampling was carried out at various locations in the study area. The number of soil sampling points were 41, 28, 28, 32, 37, 29 and 29 in Thanjavur, Thiruvarur, Nagapattinam, Cuddalore, Villupuram, Thiruvannamalai and Ramanathapuram districts, respectively. Principal Component Analysis is a data reduction tool to select some of the potential indicators. Principal Component is a linear combination of different variables that represents the maximum variance of the dataset. Principal Component that has eigenvalues equal or higher than 1.0 was taken as the minimum data set. Principal Component Analysis was used to select the representative soil quality indicators in rice soils based on factor loading values and contribution percent values. Variables having significant differences within the production system were used for the preparation of the minimum data set. Each Principal Component explained a certain amount of variation (%) in the total dataset. This percentage provided the weight for variables. The final Principal Component Analysis based soil quality equation is SQI = ∑ i=1 (W ᵢ x S ᵢ); where S- score for the subscripted variable; W-weighing factor derived from PCA. Higher index scores meant better soil quality. Soil respiration, Soil available Nitrogen and Potentially Mineralizable Nitrogen were assessed as soil quality indicators in rice soil of the Cauvery Delta zone covering Thanjavur, Thiruvavur and Nagapattinam districts. Soil available phosphorus could be used as a soil quality indicator of rice soils in the Cuddalore district. In rain-fed rice ecosystems of coastal sandy soil, DTPA – Zn could be used as an effective soil quality indicator. Among the soil parameters selected from Principal Component Analysis, Microbial Biomass Nitrogen could be used quality indicator for rice soils of the Villupuram district. Cauvery Delta zone has better SQI as compared with other intensive rice growing zone of Tamil Nadu.

Keywords: soil quality index, soil attributes, soil mapping, and rice soil

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