Remark on Algorithm 982: Explicit Solutions of Triangular Systems of First-order Linear Initial-value Ordinary Differential Equations with Constant Coefficients

Algorithm 982: Explicit solutions of triangular systems of first-order linear initial-value ordinary differential equations with constant coefficients provides an explicit solution for an homogeneous system, and a brief description of how to compute a solution for the inhomogeneous case. The method described is not directly useful if the coefficient matrix is singular. This remark explains more completely how to compute the solution for the inhomogeneous case and for the singular coefficient matrix case.

Nonlinear Beamforming Based on Group-Sparsities of Periodograms for Phased Array Weather Radar

<div>We propose nonlinear beamforming for phased array weather radars (PAWRs). Conventional beamforming is linear in the sense that a backscattered signal arriving from each elevation is reconstructed by a weighted sum of received signals, which can be seen as a linear transform for the received signals. For distributed targets such as raindrops, however, the number of scatterers is significantly large, differently from the case of point targets that are standard targets in array signal processing. Thus, the spatial resolution of the conventional linear beamforming is limited. To improve the spatial resolution, we exploit two characteristics of a periodogram of each backscattered signal from the distributed targets. The periodogram is a series of the powers of the discrete Fourier transform (DFT) coefficients of each backscattered signal and utilized as a nonparametric estimate of the power spectral density. Since each power spectral density is proportional to the Doppler frequency distribution, (i) major components of the periodogram are concentrated in the vicinity of the mean Doppler frequency, and (ii) frequency indices of the major components are similar between adjacent elevations. These are expressed as group-sparsities of the DFT coefficient matrix of the backscattered signals, and we propose to reconstruct the signals through convex optimization exploiting the group-sparsities. We consider two optimization problems. One problem roughly evaluates the group-sparsities and is relatively easy to solve. The other evaluates the group-sparsities more accurately, but requires more time to solve. Both problems are solved with the alternating direction method of multipliers including nonlinear mappings. Simulations using synthetic and real-world PAWR data show that the proposed method dramatically improves the spatial resolution.</div>

On the numerical solutions for nonlinear Volterra-Fredholm integral equations

In this note, we study a class of multistep collocation methods for the numerical integration of nonlinear Volterra-Fredholm Integral Equations (V-FIEs). The derived method is characterized by a lower triangular or diagonal coefficient matrix of the nonlinear system for the computation of the stages which, as it is known, can beexploited to get an efficient implementation. Convergence analysis and linear stability estimates are investigated. Finally numerical experiments are given, which confirm our theoretical results.

Stock Market Volatility

Researchers examine stock volatility in emerging (E7) nations prior to and during COVID-19 announcements using multiple volatility estimations. The correlation coefficient matrix indicates that there is a strong positive correlation between the specified volatility estimators in the pre-COVID-19 and post-COVID-19 periods. Rogers-Satchell standard deviation has the first rank, and Garman-Klass has the last position in the pre-post-COVID-19 analysis volatility estimators. However, the authors discover a considerable influence of pre-post COVID-19 on the world's E7 countries. The findings' primary implication is that post-COVID-19 volatility is greater than pre-COVID-19 volatility. This means that investors' financial portfolios should be rebalanced to favor industries that are less impacted by COVID-19. Additionally, it serves as an early warning signal for investors and the government to take preventative measures in the event that it occurs again in the future.

Prevalence of Musculoskeletal Disorders of Odisha Farmers in Selected Agricultural Tasks

In the chapter, there are dual main contributions. In the first phase, based on the extensive review of literature on the application of cuckoo search (CS) methodology, its application for the optimization of agricultural pesticide sprayers for maximum efficiency was suggested. In the second phase of study, 75 farmers of Odisha in India were considered to assess their musculoskeletal disorders (MSDs) during seeding, fertilizing, and weeding of crops using a Standardized Nordic Questionnaire with a five point rating scale (i.e., 1 = Very less, 2 =Less, 3 = Nil, 4 = Strong, 5 = Very Strong). Factor analysis was performed for “seeding, fertilizing, and weeding characteristics,” “economical characteristics,” and “tools and equipment characteristics of farmers.” Then Pearson correlation coefficient matrix was generated for the seeding, fertilizing, and weeding characteristics of farmers, followed by regression analysis for the economic characteristics of farmers.

Mathematical framework for describing multipartite entanglement in terms of rows or columns of coefficient matrices

In this paper, we develop a mathematical framework for describing entanglement quantitatively and qualitatively for multipartite qudit states in terms of rows or columns of coefficient matrices. More specifically, we propose an entanglement measure and separability criteria based on rows or columns of coefficient matrices. This entanglement measure has an explicit mathematical expression by means of exterior products of all pairs of rows or columns in coefficient matrices. It is introduced via our result that the [Formula: see text]-concurrence coincides with the entanglement measure based on two-by-two minors of coefficient matrices. Depending on our entanglement measure, we obtain the separability criteria and maximal entanglement criteria in terms of rows or columns of coefficient matrices. Our conclusions show that just like every two-by-two minor in a coefficient matrix of a multipartite pure state, every pair of rows or columns can also exhibit its entanglement properties, and thus can be viewed as its smallest entanglement contribution unit too. The great merit of our entanglement measure and separability criteria is two-fold. First, they are very practical and convenient for computation compared to other methods. Second, they have clear geometric interpretations.

Roots of Characteristic Polynomial Sequences in Iterative Block Cyclic Reductions

The block cyclic reduction method is a finite-step direct method used for solving linear systems with block tridiagonal coefficient matrices. It iteratively uses transformations to reduce the number of non-zero blocks in coefficient matrices. With repeated block cyclic reductions, non-zero off-diagonal blocks in coefficient matrices incrementally leave the diagonal blocks and eventually vanish after a finite number of block cyclic reductions. In this paper, we focus on the roots of characteristic polynomials of coefficient matrices that are repeatedly transformed by block cyclic reductions. We regard each block cyclic reduction as a composition of two types of matrix transformations, and then attempt to examine changes in the existence range of roots. This is a block extension of the idea presented in our previous papers on simple cyclic reductions. The property that the roots are not very scattered is a key to accurately solve linear systems in floating-point arithmetic. We clarify that block cyclic reductions do not disperse roots, but rather narrow their distribution, if the original coefficient matrix is symmetric positive or negative definite.

Research On Arc Fault Detection Using Morlet Wavelet Features And ResNet

Series arc fault is the main cause of electrical fire in low-voltage distribution system. A fast and accurate detection system can reduce the risk of fire effectively. In this paper, series arc experiment is carried out for different kinds of electrical load. The time-domain current is analyzed by Morlet wavelet. Then, the multiscale wavelet coefficients are expressed as the coefficient matrix. We use HSV color index to map the coefficient matrix to the phase space image. Random gamma transform and random rotation are applied to data enhancement. Finally, typical deep residual network (ResNet) is established for image recognition. Training results show that this method can detect faults in real time. The accuracy of ResNet50 is 96.53% by using the data set in this paper.

3D full-time anisotropic TEM modelling using a mixed BDF2/SAI method

Transient electromagnetic (TEM) data are affected by resistivity anisotropy, which should be considered in 3D modelling. The influence of anisotropy on full-time response is the main focus of this research. For spatial discretisation of an anisotropic model, the mimetic finite volume approach was applied. The accuracy of the shift-and-invert (SAI) Krylov subspace approach and the two-step backward differentiation formula (BDF2) for modelling 3D full-time electromagnetic data has been demonstrated. However, both algorithms require time-consuming calculations. The SAI technique requires a number of projection subspace constructions, whereas the BDF2 algorithm necessitates numerous coefficient matrix decompositions. We proposed a novel mixed BDF2/SAI algorithm in this paper, which combines the advantages of the two algorithms. The on-time response is computed using BDF2, while the off-time response is computed using the SAI-Krylov subspace method. The forward results of a 1D model with a half-sine waveform demonstrated that the new algorithm is accurate and faster than both the BDF2 algorithm and the SAI algorithm. During the full-time period, the forward results of a 3D anisotropic model with half-sine waveform show that abnormal responses can be induced. It was shown that the relative abnormal of ${{{\bf b}}_{\boldsymbol{z}}}$ is higher during the on-time period, while the relative abnormal of $\partial {{{\bf b}}_{\boldsymbol{z}}}/\partial t$ is higher during the off-time period. Furthermore, the change in relative anomaly is more obvious as the anisotropic block rotates around the x-axis. And the larger the rotation angle, the larger the relative anomaly.

Algorithms for forming the coefficient matrix of a system of differential equations Chapman-Kolmogorov models of non-stationary service systems

The paper considers a new approach to building models of nonstationary service systems based on: the formation of all possible states of a nonstationary service system with a finite number of applications and rules of transition between them; the formation of the coefficient matrix of Chapman-Kolmogorov differential equation system; the numbering procedure for all states. A critical analysis is made of the algorithms for the formation of the coefficient matrix and the numbering procedure for all states: sequential, recursive and recursive with grouping. Its comparison with the recursive algorithm is given, as well as the optimal structure for storing the list of states for the sequential algorithm. Recommendations for the practical application of software implementations of the considered algorithms are discussed. Theoretical foundations for building and calculating models of nonstationary service systems have been developed. It is compared to the recursive algorithm. The optimal structure for storing the list of states for a sequential algorithm is given.