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As one application of the Cauchy–Binet formula, the Ball–Barthe inequality plays a key role in solving reverse isoperimetric inequalities. Recently, a new Grassmannian Ball–Barthe inequality was established. With it, reverse isoperimetric inequalities on Grassmann manifolds were successfully proved. In this paper, we will establish its matrix form with a simpler proof than that of Grassmannian form. The matrix form also recovers the classical Ball–Barthe inequality in a special case. [ABSTRACT FROM AUTHOR]

Inspired by an old result by Georg Frobenius, we show that the unbiased version of Hall's marriage theorem is more transparent when reformulated in the language of matrices. At the same time, we obtain a more general statement applicable to bipartite graphs whose parts need not have the same size. [ABSTRACT FROM AUTHOR]

Estimating nonlinear effects between constructs is an important concern in the social sciences. In empirical studies, researchers often focus more on mediated moderation or moderated mediation as opposed to moderation by itself. This article generalizes the constrained approach with noncentered observed variables to a matrix form that encompasses the latent nonlinear effects of not only exogenous variables, but also endogenous variables or a combination of the two. Constraints are specified in matrix form and the matrices involved in model specification are partitioned to fit into the nonlinear model framework. The usage and validity of the procedure is demonstrated with a simulated data set example using the Mx program. [ABSTRACT FROM PUBLISHER]

Solvability and general solutions to dynamic systems in polynomial matrix descriptions are investigated. The polynomial matrix descriptions need not necessarily be regular. Consistency of initial values and inputs are discussed. The characterization of the general solution for the systems in polynomial matrix descriptions has an explicit separation of proportional, integral and differential terms with respect to initial values and inputs. The derivation is based on a decomposition form of a singular matrix pencil. [ABSTRACT FROM AUTHOR]

Modern data are often collected in a matrix form. In this paper, we consider modelling the varying coefficient regression with matrix valued covariate X and scalar index variable U. The proposed model simultaneously makes principal component analysis for both the row and column dimensions of the matrix objects, maintaining the matrix structure while achieving substantial dimension reduction. We develop an iterative estimation method for the involved principal parameters and nonparametric functions. Under regularity conditions, the asymptotic distributions of the estimators are derived. In addition, by incorporating the estimation with the adaptive group Lasso and the group SCAD penalties, variables of X in entire rows or columns are selected. The proximal gradient algorithm is further utilised to solve the regularised optimisation problems. The asymptotic properties of the penalised estimators are also studied. Our model and estimation methods are demonstrated by simulated experiments. Real applications to the primary biliary cirrhosis (PBC) data reveal that the effects of the blood measurements to the survival time vary with levels of age. [ABSTRACT FROM AUTHOR]

This study presents the spectral Chebyshev technique (SCT) for nonlinear vibrations of rotating beams based on a weak formulation. In addition to providing a fast-converging and precise solution for linear vibrations of structures with complex geometry, material, and physics, this method is further advanced to be able to analyze the nonlinear vibration behavior of continuous systems. Rotational motion and material gradation further complicate this nonlinear behavior. Accordingly, the beam is considered to be axially functionally graded (FG) and a model representing the forced nonlinear vibrations of the beam about steady-state equilibrium deformations (SSEDs) is developed. The model includes Coriolis, centrifugal softening, and nonlinear stiffening effects caused by coupling of the axial, chordwise, and flapwise motions, and large amplitude deformations. The integral boundary value problem for the rotating structure is discretized using the SCT and element-wise multiplication definition. As a result, mass, damping, and stiffness matrices, as well as internal nonlinear forcing functions and external forcing vectors, are obtained for a given rotating beam. This formulation provides a general representation of nonlinear strain relations in matrix form and circumvents the complexity rising from obtaining and solving the partial differential equations directly. In addition, nonlinear forcing functions are obtained in matrix form which facilitates the application of harmonic balance method easier to obtain the forced nonlinear response. [ABSTRACT FROM AUTHOR]

In this paper we consider the Gabriel form of cross-validation (CV) and we investigate how to estimate the optimum rank for lower rank approximations of any dataset that can be written in matrix form, with particular application in multivariate analysis and in the analysis of multienvironment trials. The literature related to the method suggests that it can produce overfitting and poor-quality predictions, characteristics that result in overestimation of the rank. Because of this, it is proposed to change the rank selection criterion, testing thirteen statistics both in the original method and in four proposed extensions that seek to solve the above problems. A comparison is made with two gold standard methods for CV through a simulation study and through the analysis of seventeen real datasets, two of which are general multivariate and fifteen are from experiments with genotype-by-environment interaction. It is concluded that from a predictive point of view, the highest accuracy in estimating the rank is obtained by using a regularized singular value decomposition. [ABSTRACT FROM AUTHOR]

We believe that developing cultural competencies can help students learn mathematics and conversely that learning mathematical content can help students learn about themselves and others. Using frameworks introduced by Rendón (2009) and Gutiérrez (2018), we present a five-part bundle of activities for undergraduate differential equations course instructors, including one pre-activity reflection assignment, three modeling activities, and a final project. The Pre-Activity Assignment engages students to draw on their own personal and/or cultural experiences with the concept of love. Three activities focus on developing revision skills in mathematical modeling and practicing methods of solving systems of ordinary differential equations (ODEs). In these activities, students would collaborate to construct a relationship model consisting of a system of first-order linear ODEs and solve different model iterations with the characteristic polynomial, matrix form, or Laplace transform method. The final project connects the reflections in Pre-Activity Assignment with the skills developed in the three activities by inviting students to create a relationship scenario, model, revise, solve it, and present the conclusions. By engaging in this set of assignments, students connect personal and cultural experiences with the concept of love and perceive themselves and their peers in the curriculum, fostering a sense of belonging and relevance. [ABSTRACT FROM AUTHOR]

Structural modal identification is generally implemented within a dynamic framework, requiring multidisciplinary knowledge and adequate operational experience. This preliminary study attempts to explore an easy-to-handle quasi-static alternative method for dynamics-based modal identification of beam-type structures. Acceleration time-history data are replaced by quasi-static deflections induced by slow moving loads. A concept of quasi-static deflection influence surface is proposed based on the theory of influence lines and the principle of virtual work. Its analytical expression is simplified into a deflection matrix by choosing specific points on the surface according to deflection measurement coordinates. The matrix form is divided by external loads to obtain a generalised quasi-static flexibility matrix, which is used to replace the inversion of the global stiffness matrix in the modal eigenvalue equation. The lumped-mass method is also employed to establish the mass matrix. Subsequently, the eigenvalue equation is analytically solved seeking for modal frequencies and mode shapeswithout performing modal tests. The feasibility of the proposed method has been successfully verified against three experimental examples including a continuous box girder with variable cross sections. It was observed that the modal frequencies and mode shapes estimated by the proposed method were very close to those given by the dynamically modal tests. [ABSTRACT FROM AUTHOR]

Support matrix machine (SMM) is a matrix classification method that effectively utilises information between rows and columns in matrix-form data. However, the presence of abnormal data in the feature matrix fed into the model can result in model non-convergence and hyperplane shift, greatly affecting classification accuracy. To address this issue, this paper introduces a matrix classification method, called asymmetric robust least squares support matrix machine (ARLSSMM). To construct ARLSSMM, a novel optimisation model based on a matrix with asymmetric constraints is designed to obtain the hyperplane, which can not only use the data set to dynamically determine the position of the hyperplane to obtain the maximum margin space but also reduce the influence of abnormal data on the model classification performance. Two different roller bearing types of test data are used for experimental validation, and the results show that ARLSSMM demonstrates excellent classification performance. [ABSTRACT FROM AUTHOR]

Motivated by the notions of the MP- -WGI and 1WGI, we further generalize these concepts and extend recent researches about them. Precisely, using an inner inverse and -WGI, we solve the system of matrix equation and introduce a new type of generalized inverses named the inner- -WGI. The MP- -WGI and 1WGI are known particular cases of inner- -WGI, and inner-CEP and inner-GGI are special types of inner- -WGI which present new generalized inverses in literature. We propose characterizations and formulae for the inner- -WGI. A canonical matrix form of the inner- -WGI is established. The -WG-inner inverse is defined and characterized as a dual inner- -WGI. To solve some systems of linear equations and represent their general solutions, we apply the -WG-inner inverse and inner- -WGI. [ABSTRACT FROM AUTHOR]

Jeongganbo is a unique music representation invented by Sejong the Great. Contrary to the Western music notation, the pitch of each note is encrypted and the length is visualized directly in a matrix form. We use topological data analysis (TDA) to analyze the Korean music written in Jeongganbo for Suyeonjang, Songuyeo, and Taryong, those well-known pieces played among noble community. We define the nodes of each music with pitch and length and transform the music into a graph with the distance between the nodes defined as their adjacent occurrence rate. The graph homology is investigated by TDA. We identify cycles of each music and show how those cycles are interconnected. We found that the cycles of Suyeonjang and Songuyeo, categorized as a special type of cyclic music, frequently overlap each other in the music, while those of Taryong, which does not belong to the same class, appear only individually. [ABSTRACT FROM AUTHOR]

In this article, an M/M/1 queueing model with bi-level network service provider, balking process and bi-level vacation policy that comprises of working vacation and complete vacation after fixed service, is developed. Matrix form expressions have been derived for the distributions of the queued customers with some performance metrics with the help of matrix geometric method. The maximum entropy principle is also used to derive the distributions of the steady state probabilities of queue size. The cost function has been formed to optimize the decision variables of the system. We perform the cost optimization by employing the steepest descent search method. Numerical illustrations along with the sensitivity analysis have been drawn to validate the model. Finally, the conclusions of the investigation done are drawn by mentioning the novel features and future scope. [ABSTRACT FROM AUTHOR]

Public key cryptography is based on two popular mathematical hard problems namely the integer factorization and discrete logarithm problem. Number Field Sieve (NFS) and Function Field Sieve (FFS) are the most efficient and widely used algorithms to solve integer factorization and discrete logarithm problems. The main phases of these algorithms are polynomial selection, relation collection and linear algebra. Among these steps, relation collection and linear algebra are the most computationally costly. The filtering step is used in between relation collection and linear algebra step, which employs several strategies to reduce the coefficient matrix size and makes the matrix suitable for linear algebra, so that linear algebra takes comparatively lesser time. This paper presents a complete framework for the filtering step in the NFS class of algorithms. In this paper, the filtering step is considered as two main sub-phases. The two phases are namely matrix construction and matrix reduction. In the first sub-phase, the relations collected from the relation collection step are structured to represent in a matrix form. The main goal of this phase is to construct a relation from the smooth elements obtained in the relation collection phase along with the other necessary inputs with respect to NFS class of algorithms. The second sub-phase deals with matrix reduction in which various strategies such as duplicate removal, singleton removal, clique removal and merge are applied to reduce the overall matrix size preserving the sparsity at the same time. Algorithms for the first and second phases are designed and analyzed in the paper. The experiments are conducted on the relations collected from standard tool CADO-NFS and the results are reported. From the results, it is shown that the filter map structure presented in the current work for matrix representation helps to improve the overall performance of filtering module. Specifically, the method to handle duplicates in the matrix instead of the traditional method improves the duplicate removal module of filtering. Additionally, an optimized clique removal method of filtering which is introduced in the present work further improves the performance of filtering. [ABSTRACT FROM AUTHOR]

In this paper, we explore the use of multiscale bubble entropy and power metric for feature extraction procedure and extend it with MLA and stability analysis to design a reliable multichannel seizure detection technique. First, we represent the multichannel EEG signal in 2D matrix form and then apply AM FM model to exploit the decomposed form of EEG. Thereafter, we construct the complexity coefficient using multiscale bubble entropy analysis from decomposed EEG wave. Then, second feature set is formed by using simple and efficient power procedure to obtain absolute power index and relative power index. Using two machine learning approaches, classification performance of proposed approach is explored to correctly identify the epileptic seizures. To show the robustness of multiscale bubble entropy, the stability analysis is performed with normal EEG dataset. Experimental results demonstrate that our proposed technique can effectively detect the epileptic seizures and achieve a superior classification performance with the ANN classifier compared to KNN classifier. This method provides higher discriminating capability with greater stability, so that they could detect wider range of seizure and thus help advance the current diagnosis system. [ABSTRACT FROM AUTHOR]

Hyperspectral images are easily contaminated by multi-modal noise in the process of data acquisition. Generally, hyperspectral signatures and noise appear unexpectedly scattered in the spatial-spectral domain. Conversely, in the transform domain, the principle components of an image are gathered in the low-frequency bands, while the details and noise often occur in high-frequency parts. The existing denoising methods usually divide the whole frequency domain into two parts, that is, high frequency and low frequency, which can not make the most of the knowledge contained at different frequencies or scales, especially in the multiscale transform domain. Furthermore, aiming to restore a clean image from the noise-corrupted data, hyperspectral image denoising often amounts to an ill-posed problem, in which reshaping cubic data into matrix form results in the loss of structure information. To address the aforementioned issues, this paper incorporates the reweighted smoothing regularization in the transform domain into the noise-perturbed degradation model to reformulate a novel optimization problem. First, the multiscale curvelet is leveraged to transform the spatial matrix into frequency domain, where the coefficients are carefully designed to weight the components at different scales and orientations. Second, ${l_1}$ l 1 -norm is imposed on the abundance term to promote sparsity in the transform domain for performance enhancement. Finally, using proximal alternating optimization, an efficient algorithm is well developed to obtain the closed-form solutions to the proposed denoising problem. The experimental results on several synthetic and real datasets, illustrate that the proposed method improves PSNR by at least 1.5 dB and reduces ERGAS error by more than 35% than the state-of-the-art approaches under the multi-modal noise mixed environments, which verifies the validity of regularization terms in hyperspectral images denoising. [ABSTRACT FROM AUTHOR]

An analytical modelling approach is developed in this article to simulate the pull-out behaviour of a single straight/hooked end fibre that is embedded in concrete matrix. The partial-interaction model is used to simulate the interfacial bond between the fibre and matrix along the entire fibre length throughout all stages of loading where additional axial and frictional forces due to straightening a hook is incorporated by simulating it as plastic hinges at the apex of bends. The analytical model is presented in a concise matrix form that helps to minimise the number of solution steps for the involved individual cases and provides a monolithic simplified implementation. A significant advantage of the approach is that it does not require fitting of a smoothing polynomial to show the full-range of fibre load-slip behaviour as it simulates the forces for straightening the fibre as it pulls through a bend and directly couples this to the interfacial bond forces. [ABSTRACT FROM AUTHOR]

The tremendous attention of researchers has been attracted to the unusual properties of quasicrystals (QCs). In this article, the thermo-elastic problems of imperfectly bonded, multilayered, two-dimensional decagonal QC plates with mixed boundary conditions are investigated based on the QC linear elasticity theory. The temperature, heat flux, displacement, and stress components are expressed in terms of differential quadrature regional discrete point expansions in any rectangular plate, from which the state equations with thermomechanical coupling effects in a concise and compact matrix form is obtained. The different imperfect interface conditions are introduced to characterize specific structural and thermal contact properties at the interfaces and are further converted into the interface propagator matrix. Different from the conventional propagator matrix method, the new global propagator relation for the composite laminate with the presence of perfect/imperfect interfaces is recursively obtained by means of the reduced propagator distance and the exponential term between the layer to layer propagator matrix. The numerical examples indicate that numerical results are stability and precision, different boundary conditions have hardly influenced temperature and heat fluxes, and interlaminar thermal stresses strengthen with increasing interface coefficients. The methods and results can also serve as a reference for verifying existing or future QC laminate theories. [ABSTRACT FROM AUTHOR]

A deadlock avoidance supervisory controller for Discrete Event (DE) Systems is implemented. The DE controller uses a novel rule-based matrix dispatching formulation (US patent received). This matrix formulation makes it easy to write down the DE controller from standard manufacturing tools such as the bill of materials or the assembly tree. It is shown that the DE controller's matrix form equations plus the Petri Net (PN) marking transition equation provide a complete dynamical description of DE systems. We provide circular wait analysis (CW) for deadlock-free dispatching rules for Multipart Re-entrant Flow line (MRF) regular systems, and provide a regularity test for these systems in PN and matrix notations. We analyse the so-called critical siphons, and certain critical subsystems to develop a DE controller that guaranties deadlock-free dispatching by limiting the work-in-progress in the critical subsystems associated with each CW. This least-restrictive dispatching policy avoids deadlock. The deadlock-free dispatching rules are implemented by the DE controller on a three-robot, two-machine re-entrant flow line, the Intelligent Material Handling cell at the Automation and Robotics Research Institute of UTA. Technical information given includes the development of the deadlock-free controller in LabVIEW. [ABSTRACT FROM AUTHOR]

Convolutive models, linking a local or average temperature to a thermal excitation in transient regime are as good as analytical or numerical solutions of the heat equation and of its associated boundary conditions, provided that the corresponding equations are linear with coefficients that do not depend on time, but with possible dependence on the space dimensions. These convolutive models are based on an impulse response function which can be identified, using measurements of input and output signals, together with some kind of regularization because of the ill-posed character of this inverse problem. Here, another exploratory approach is tested. It is based i) on a parameterization of the three functions involved by projection onto a Dirac comb basis to get a vector/matrix form of the convolution model derived in terms of doses, ii) on an alternate model based on an exact analytical relationship between the time moments of these functions and iii) on the different ways to use this last model in an inversion procedure using the parsimony principle. This is applied to a heat transfer configuration of one-dimensional heat diffusion in a slab, where conclusions and perspectives are drawn for this type of dosal-moment model. [ABSTRACT FROM AUTHOR]

In this paper, we propose an efficient finite-element method based on dimension reduction scheme to solve the fourth-order elliptic equation in a circular domain. First of all, by using polar coordinate transformation and Fourier basis function expansion, the necessary pole conditions are derived and the original problem is decomposed into a series of equivalent one-dimensional fourth-order problems. Based on the pole conditions, the appropriate weighted Sobolev spaces are introduced and the error estimate of finite-element solution is proved for each one-dimensional fourth-order problem. Then we construct the cubic Hermite interpolation basis functions and derive the matrix form corresponding to the discrete scheme. Furthermore, the sparsity of mass matrix and stiffness matrix are illustrated. Finally, we provide some numerical experiments, and the numerical results show that our method is very effective. [ABSTRACT FROM AUTHOR]

In this work, we represent free metabelian Leibniz algebras as the wreath product of abelian Leibniz algebras. We obtained an explicit matrix form for the IA-automorphisms of free metabelian Leibniz algebras of finite rank over a field K of characteristic zero. Then we describe a set of generators for the group of all automorphisms of the free metabelian Leibniz algebras of rank n. [ABSTRACT FROM AUTHOR]

Solving the well-known Lyapunov and Sylvester matrix equations appears in a wide range of applications such as in control theory and signal processing. This article establishes the matrix form of the biconjugate residual (BCR) algorithm for computing the generalized reflexive solution X and the generalized anti-reflexive solution Y of the generalized Sylvester matrix equation It is proven that the proposed BCR algorithm converges within a finite number of iterations in the absence of round-off errors. At the end, various numerical implementations illustrating the effectiveness and accuracy of the proposed BCR algorithm are presented and discussed. [ABSTRACT FROM AUTHOR]

A trigonometric quintic B-spline method is proposed for the solution of a class of turning point singularly perturbed boundary value problems (SP-BVPs) whose solution exhibits either twin boundary layers near both endpoints of the interval of consideration or an interior layer near the turning point. To resolve the boundary/interior layer(s) trigonometric quintic B-spline basis functions are used with a piecewise-uniform mesh generated with the help of a transition parameter that separates the layer and regular regions. The proposed method reduces the problem into a system of algebraic equations which can be written in matrix form with the penta-diagonal coefficient matrix. The well-known fast penta-diagonal system solver algorithm is used to solve the system. The method is shown almost fourth-order convergent irrespective of the size of the diffusion parameter ϵ. The theoretical error bounds are verified by taking some relevant test examples computationally. [ABSTRACT FROM AUTHOR]

In order to further alleviate computational burdens and enhance accuracies, we propose an efficient amelioration on the complex-frequency-shifted perfectly matched layer (CFS- PML) via introducing both direct Z-transform (DZT) and matrix exponential (ME) methods for terminating the finite-difference time-domain (FDTD) region. The method is here referred as the DZT-ME-PML. Due to introducing the DZT method, the proposal can avoid the disadvantages of approximate bilinear and matched Z-transform in modeling fine and course structures, leading to achieving higher accuracies. Moreover, by employing the ME technique, the proposal develops into the compact first-order differential matrix form applied to evading the convolution manipulations, the variable replacements, and the formulation rearrangements during the mathematical derivations. Besides, the proposed DZT-ME-PML can not only flexibly terminate the arbitrary media when adding the DB constitutive relation, but efficiently attenuate evanescent waves, and reduce the late-time reflections due to the CFS scheme. Three-dimensional (3D) numerical examples have been carried out to illustrate the validity and accuracy of the proposed DZT-ME-PML. Eventually, applied to solving geophysical problem with the very low frequency (VLF) case, the DZT-ME-PML shows stronger absorption accuracy than the general ME-PML method. [ABSTRACT FROM AUTHOR]

Networks have been widely employed to represent interactive relationships among individual units in complex systems such as the Internet of Things. Assignable causes in systems can lead to abrupt increased or decreased frequency of communications within the corresponding network, which allows us to detect such assignable causes by monitoring the communication level of the network. However, existing statistical process control methods for unweighted networks have scarcely incorporated either the network sparsity or the direction of interactions between two network nodes, i.e., dyadic interaction. Regarding this, we establish a matrix-form model to characterize directional dyadic interactions in time-independent unweighted networks. With inactive dyadic interactions excluded, the proposed procedure of parameter estimation achieves higher consistency with less computational cost than its alternative when networks are large-scale and sparse. Using the generalized likelihood ratio test, the work derives two schemes for monitoring directed unweighted networks. The first can be used in general cases whereas the second incorporates a priori shift information to improve change detection efficiency in some cases and estimate the location of a single shifted parameter. Simulation study and a real application are provided to demonstrate the advantages and effectiveness of proposed schemes. [ABSTRACT FROM AUTHOR]

A solution to the problem of a closed-form representation for the inverse of a matrix polynomial about a unit root is provided by resorting to a Laurent expansion in matrix notation, whose principal-part coefficients turn out to depend on the non-null derivatives of the adjoint and the determinant of the matrix polynomial at the root. Some basic relationships between principal-part structure and rank properties of algebraic function of the matrix polynomial at the unit root as well as informative closed-form expressions for the leading coefficient matrices of the matrix-polynomial inverse are established. [ABSTRACT FROM AUTHOR]

In this article, we propose an iterative algorithm to compute the minimum norm least-squares solution of AXB+CYD=E, based on a matrix form of the algorithm LSQR for solving the least squares problem. We then apply this algorithm to compute the minimum norm least-squares centrosymmetric solution of min X|AXB-E|F. Numerical results are provided to verify the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

A new 3D hydrodynamic model was developed to simulate water quality transport in surface waterbodies. The governing equations are the continuity equation, free surface equation, momentum equation and transport equation. The 2D numerical scheme of CE-QUAL-W2 was expanded in three dimensions and modified to solve for the free surface elevation. A time splitting technique was employed to solve the momentum and transport equation. The numerical formulation of the 3D scheme used a novel solution, which resulted in a tri-diagonal matrix form for solving the free surface equation rather than a more computationally intensive penta-diagonal matrix solution. In addition, the hydrodynamic and water quality equations were solved at the same time step in order to allow feedback between water quality and hydrodynamics. The verification of the model hydrodynamics and temperature was performed by comparing the model predictions to known analytical solutions and field data from Lake Chaplain, Washington, USA. There was good agreement of the solution of the hydrodynamic equations to analytical solutions and field data. [ABSTRACT FROM AUTHOR]

In this paper, we give a new, simple, and efficient method for evaluating the pth derivative of the Jacobi polynomial of degree n. The Jacobi polynomial is written in terms of the Bernstein basis, and then the pth derivative is obtained. The results are given in terms of both Bernstein basis of degree n - p and Jacobi basis form of degree n - p and presented in a matrix form. Numerical examples and comparisons with other well-known methods are presented. [ABSTRACT FROM AUTHOR]

A new stochastic model for the point kinetics equations with I-delayed neutron precursor groups is presented. In this stochastic model, the point kinetics equations are separated into three terms: prompt neutrons, delayed neutrons and external neutrons source. The matrix form of the efficient stochastic model is solved by a semi-analytical method. The semi-analytical method is based on the exponential function of the coefficient matrix. The eigenvalues of the coefficient matrix and Gaussian elimination are used to calculate this exponential function. The mean and standard deviation of neutron and precursor populations of the efficient stochastic model with step, ramp, and sinusoidal reactivities are computed. The results of the efficient stochastic model are compared with the results of Allen's stochastic model for the point kinetics equations. This comparison confirms that the efficient stochastic model is an accurate model compared with the deterministic point kinetics equations. This stochastic model is efficient to study the natural behavior of neutron and precursor populations in the nuclear reactor dynamics. [ABSTRACT FROM PUBLISHER]

This study presents the analytical characterisation of a low-cost, selective and sensitive method for inorganic Hg (as Hg22+/Hg2+) determination in liquid matrices based on spectrophotometry. The novelty of the study lies in combining the pre-concentration of i-Hg with spectrophotometry after chelation with the 2-aminobenzimidazole modified amidic copolymer to increase the selectivity and sensitivity of the method. The method involves ultrasonic extraction of the samples in a dilute acid mixture of HClO4-HCl-CH3COOH and mixture of Cu(II)-oxalic acid-KCl adjusted to pH 5.0 in parallel, pre-con centration using UA-CPE process on modified amide copolymer, and absorbance measurement at 332 nm using a micro-volume UV-spectrophotometer. The figures of merit were discussed in relation with the demands in the national/international regulations and standards on the determination of toxic i-Hg in water intended for human consumption. After a pre-concentration of 62.5-fold, the limits of detection and quantification (LODs, LOQs) were 0.24 and 0.22 μg L−1 allowing the use of the method for i-Hg determination in liquid matrices such as cold-/hot-spring waters, plain soda, bottled drinking waters, and carbonated soft drinks. For concentrations of Hg22+, Hg2+ and total Hg in the range of −1, the precision was 3.3–8.3%, below and little above the maximum limits of 1.0 µg L−1 set in the mentioned legislation. The recovery of 92–96.4% and the precision in the range of 4.1–5.4% in the analysis of two certified waters were found to be satisfactory, so as to validate the method. The method developed is cost-effective and enables us to achieve i-Hg determination in liquid matrices complying with European legislation. The system has a good potential for the future and analytical perspectives. [ABSTRACT FROM AUTHOR]

It's common to use multi-stage hydraulic fracturing in horizontal wells for the development of tight gas reservoirs. Therefore, accurate productivity prediction is crucial. Concerning the theory of equivalent wellbore radius and the principle of pressure drop superposition, the effects of secondary fractures and water-blocking damage were treated as distinct skin effects innovatively. Consequently, the productivity model for tight gas reservoirs in hydraulic fracturing horizontal wells was established, taking into account the effects of slippage effect, stress sensitivity, threshold pressure gradient and high-velocity non-Darcy flow. Then the accuracy of the model was verified in two ways. The calculated results are basically consistent with different models from the literature without considering the influence of various factors. In addition, the open flow capability of the proposed model by using the data of a gas field block is 1617.85Mscfd, while that of one fractured well through field well testing is 1696.79Mscfd, resulting in a relative error of 4.65%. Furthermore, the factors affecting productivity were subjected to a sensitivity analysis using this model. The results indicate that water-blocking damage can significantly impact productivity, while threshold pressure gradient, fracture number, and high-velocity non-Darcy flow have a relatively small influence on productivity. [ABSTRACT FROM AUTHOR]

The Duvernay Formation of Simonette Block is rich in shale oil and gas resources. The present-day in-situ stress field is a crucial parameter during the exploration and development in this block, a better understanding of which can assist with drilling and completion engineering, fracturing stimulation, and well deployment. In this study, the present-day in-situ stress in the Duvernay shale is predicted and analyzed based on well calculations and geomechanical modeling. The findings indicate that, I, NE-SW-trending is the dominant SHmax orientation. The SHmax and Shmin are the maximum and minimum principal stress, indicating that the Duvernay shale of Simonette Block is under a strike-slip faulting stress regime. II, The present-day in-situ stress in the Duvernay shale is heterogeneously distributed, which is controlled by lithology difference, fault development, and distribution. High stress values in the upper shale member D layer are mainly in the northwestern and central parts of Simonette Block. III, The present-day differential stress in the Duvernay shale mainly ranges from 15 MPa to 30 MPa. Bedding-parallel fractures are relatively developed, aiding in the creation of complex fracture networks. The results are expected to offer geological references for further development of shale oil and gas in the Simonette Block. [ABSTRACT FROM AUTHOR]

Multi-atlas based segmentation techniques constitute an effective approach in the automatic segmentation of medical images. Existing methods usually rely on single spectral descriptors extracted from a specific imaging modality. In this paper, we propose the Multi-View Knee Cartilage Segmentation (MV-KCS) approach, for segmenting the knee joint articular cartilage from MR images. Operating under the Semi-supervised learning framework, MV-KCS leverages spectral content from multiple feature spaces by constructing sparse graphs for each view individually, and aggregating them via optimisation to obtain a common data graph. In We consider two multi-view scenarios: in the former case views correspond to multiple feature descriptors, while on the latter, the views correspond to multiple image modalities. We propose two effective labelling schemes, implementing label propagation from the atlas library to the target image. The proposed methodology is applied to the publicly available Osteoarthritis Initiative repository. We devise a comprehensive experimental design to validate different test cases, comparing single-feature vs multi-features, multi-features vs feature stacking and multi-features vs multi-modalities. Comparative results and statistical analysis reveal that the proposed MV-KCS provides enhanced performance ($DSC = 92.56\% \left({FC} \right), 89.91\% \left({TC} \right)$ DSC = 92.56 % FC , 89.91 % TC ), outperforming a series of patch-based approaches, six recent state-of-the-art deep supervised models and three deep semi-supervised ones, in terms of both classification and volumetric measures. [ABSTRACT FROM AUTHOR]

Shale is a complex porous medium with multi-scale pores and well-developed fracture networks. This paper aims to use modeling and numerical simulation methods to study the transport of shale gas in a complex multi-scale matrix-fracture system. In this study, mathematical modeling and programming was used to establish digital models of shale gas multi-scale matrix and 3D discrete fracture network. Based on the transport mechanisms of shale gas, this study derives the mathematical models of shale gas transport in different transport media, and uses the finite element method to solve and analysis the transport of shale gas in the multi-scale matrix-fracture system. The model is verified by real shale gas field data. The results show that the fractal dimension of organic pores have great effects on shale gas transport. When the fractal dimension is greater than 1.4, the increase on gas production is particularly obvious. Compared with organic pores, the effect of fractal dimension of inorganic pores is smaller. The existence of the fracture network has an effect of up to 25% on gas production, and the optimal fracture density is 200. [ABSTRACT FROM AUTHOR]

To overcome the drawbacks of a single-stage evaporative cooler, an indirect-direct type evaporative cooler was proposed and fabricated. An alternative arrangement of mild steel plates wherein unmixed heat transfer occurs between air and water to form an indirect evaporative cooler. This is followed by a packing arrangement made of biomass-based coconut coir that forms a direct evaporative cooler. Experiments were conducted by varying the air and water flow rates, and the performance of the coconut coir was compared with that of a commercially available celdek packing. Experimental results indicated that a combination of an indirect-direct evaporative cooler helped cool air without an appreciable increase in air-specific humidity. The performance of the coconut coir is slightly lower than that of the Celdek coir in terms of the drop in DBT and wet-bulb effectiveness. A maximum wet bulb effectiveness of 0.78 and 0.63 was achieved for the celdek and coconut coir packings, respectively. The maximum performance was attained at an air velocity of 6 m/s and a water flow rate of 3 LPM. Owing to the different advantages of coconut coir over celdek packings, it is recommended to use coconut coir as an alternative packing in indirect-direct evaporative coolers. [ABSTRACT FROM AUTHOR]

Long-term mining activities without proper protections can cause geo-environmental problems. These problems have negative effects on the environment and agriculture, and also pose risks to the safety of local residents. This paper aims to propose an assessment system with authority and practicality for evaluating the influence of mining on the geo-environment in China. The proposed assessment system is based on the national technical specification and considers the natural conditions of the mining area. The study area for this research is the Huodong Mining Area (HMA) in Shanxi Province, China. To evaluate the impact of mining activities on the geo-environment, an assessment system with 5 criteria and 17 factors was established. The weights of the criteria and factors were calculated using the Analytic Hierarchy Process (AHP) method. The membership degrees of impact factors to the evaluation grades were determined using the Fuzzy Comprehensive Evaluation (FCE) method. The evaluation results of each divided element were then combined to obtain the final evaluation results for the entire study area. The final results demonstrate that the geo-environment in the HMA has been significantly affected by mining activities. [ABSTRACT FROM AUTHOR]

A computational technique for analysing coupled system of singularly perturbed convection-diffusion delay differential equations with large delay is presented in this study. We solve this problem using non-polynomial spline technique and arrive at a system that can potentially be solved. To show the theoretical investigation, an example is solved for different perturbation parameter values, and the computational results are shown in tables. The model we have proposed is of first order convergent, and this technique indicated that the acquired findings were more accurate than earlier results. [ABSTRACT FROM AUTHOR]

In this article, we propose three mathematical models of mosquito dynamics. The first model describes the dynamics of wild mosquitoes in combination with mechanical control and larvicide. For this model, we derive a threshold parameter $ \mathcal {N} $ N , called the basic number of offspring, and show that the trivial equilibrium is globally asymptotically stable when $ \mathcal {N}\leq ~1 $ N ≤ 1 , while if $ \mathcal {N} \gt 1 $ N > 1 , the non-trivial equilibrium is globally asymptotically stable. In the second model, we evaluated a constant release of Wolbachia-infected males in the wild mosquito population. Our analysis identified a critical threshold for releasing Wolbachia-infected male mosquitoes $ M_{i}^{\rm crit} $ M i crit to reduce or eliminate the wild mosquito population. In the third model, we assessed wild mosquito dynamics by periodically releasing Wolbachia-infected male mosquitoes. The analysis of this model produced two thresholds, $ T^{*} $ T ∗ the threshold on the release period and $ \Lambda ^{*} $ Λ ∗ the threshold on the release quantity. The existence of trivial periodic solutions is obtained, and the corresponding local and global stability conditions are proved by Floquet's theory and Lyapunov's stability theorem, respectively. We also prove the existence conditions for non-trivial periodic solutions and their local stability. Finally, we perform some numerical simulations to illustrate our theoretically pertinent results. [ABSTRACT FROM AUTHOR]

This paper considers the generalized sectorial decompositions of semi-sectorial operators and quasi-sectorial operators on the complex Hilbert space. Under an invariant subspace condition, a necessary and sufficient condition for the existence of the generalized sectorial decomposition of a semi-sectorial operator is given. The generalized sectorial decomposition of a quasi-sectorial operator is given without any conditions. Some sufficient conditions for a block upper triangular operator matrix to be a semi-sectorial operator or a quasi-sectorial operator are given. [ABSTRACT FROM AUTHOR]

The 400-degree-of-freedom deformed in-plane rigid-elastic-coupled tire model was enhanced by incorporating the vertical movement of the wheel as a rigid body. This refined model was then utilised to build the tire modal model. The tire modal model was developed to derive the transfer function (TF) covering a range of 0–300 Hz, which connects road irregularities as input to the contact patch and the wheel's vertical motion as output. The TF was operated under a quasi-static condition to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was combined with the quarter car model to analyse the vehicle's response when passing through short wavelength obstacles and random road profiles. This analysis was performed under varying load conditions represented by the contact patch length. The model and methodology demonstrated their effectiveness in handling rolling tires over short-wavelength obstacles and random road profiles. [ABSTRACT FROM AUTHOR]

This letter addresses the issue of mobile source localization using time of arrival (TOA) measurements in scenarios where the source and sensors are not synchronized, and the start transmission time is unknown. We propose a non-convex weighted least squares (WLS) minimization problem for estimating the source position, velocity and start transmission time from the distance measurement equation, without the need for Taylor approximation commonly used in traditional processing approaches. To effectively solve the non-convex WLS optimization problem, we use the semi-positive definite relaxation (SDR) technique to transform the original problem into a convex semi-positive definite programming (SDP) problem. Additionally, we further extend the proposed method to scenarios where the positions of sensors are uncertain. Computer simulation results demonstrate that the proposed method surpasses the existing methods, whether the positions of sensors are known or uncertain. [ABSTRACT FROM AUTHOR]

The hydroelasticity of ships is a complex fluid-solid interaction topic. The CFD-FEM technology has become a trend for studying ship hydroelasticity. Different numerical strategies, including mesh-based methods (mainly FVM-FEM) and meshless methods (mainly SPH-FEM, MPS-FEM) for hydroelastic solutions, are summarized and discussed. The two main categories include monolithic and partitioned schemes, and the latter can be further divided into one-way and two-way coupling methods. The computation cost of the one-way coupling method is lower than that of the two-way coupling method for small structural deformations. However, for large structural deformations, the two-way coupling model has significant advantages. Additionally, conservatism and efficiency of data interaction are core issues for all solution strategies. Therefore, the research and application of different data interpolation methods are summarized. Finally, the key factors of CFD and FEM technology to solve hydroelasticity and some prospects for its future development are proposed. [ABSTRACT FROM AUTHOR]

An improved optimization method is proposed which combines the particle swarm optimization (PSO) algorithm with the dimension reduction kriging surrogate model (DK), namely PSO + DK. In this method, a surrogate model is dynamically constructed and updated between the lower dimensional principal components and the response, instead of between the high-dimensional design variables and the response as in traditional methods. The key point of DK is that the principal components analysis (PCA) is integrated with the active learning kriging surrogate model (AK). Since PCA can reduce the dimension effectively, DK makes surrogate model construction possible for complex high-dimensional optimization problems. Numerical examples and four classical engineering problems are presented to validate the effectiveness of the proposed method. The results show that the proposed method can decrease the computational cost significantly while guaranteeing the precision compared with PSO and PSO + AK for high-dimensional optimization problems. [ABSTRACT FROM AUTHOR]

This work investigates the two-scale design optimization of graded plates with variable-height parallelogram microstructures based on asymptotic homogenization. First, updated unit cell problems, with an emphasis on rotational degrees of freedom, are proposed to evaluate shell-structured microstructures, so that a pointwise effective stiffness calculation can be efficiently conducted with shell elements, which is otherwise computationally prohibitive with solid elements. Then, a two-scale optimization framework seeking minimum compliance is established, where the design variables controlling both in-plane parallelogram shape and out-of-plane stiffener height are introduced to enlarge the design space. In addition, mapping functions are integrated into the optimization formulation and concurrently optimized, enabling the production of well-defined dehomogenized plates. Finally, numerical examples are presented to validate the effectiveness and correctness of the proposed method by comparing the deflections of the graded plates with those of the homogenized plates. [ABSTRACT FROM AUTHOR]