Coupling ITO3dE model and GIS for spatiotemporal evolution analysis of agricultural non-point source pollution risks in Chongqing in China

To determine the risk state distribution, risk level, and risk evolution situation of agricultural non-point source pollution (AGNPS), we built an ‘Input-Translate-Output’ three-dimensional evaluation (ITO3dE) model that involved 12 factors under the support of GIS and analyzed the spatiotemporal evolution characteristics of AGNPS risks from 2005 to 2015 in Chongqing by using GIS space matrix, kernel density analysis, and Getis-Ord Gi* analysis. Land use changes during the 10 years had a certain influence on the AGNPS risk. The risk values in 2005, 2010, and 2015 were in the ranges of 0.40–2.28, 0.41–2.57, and 0.41–2.28, respectively, with the main distribution regions being the western regions of Chongqing (Dazu, Jiangjin, etc.) and other counties such as Dianjiang, Liangping, Kaizhou, Wanzhou, and Zhongxian. The spatiotemporal transition matrix could well exhibit the risk transition situation, and the risks generally showed no changes over time. The proportions of ‘no-risk no-change’, ‘low-risk no-change’, and ‘medium-risk no-change’ were 10.86%, 33.42%, and 17.25%, respectively, accounting for 61.53% of the coverage area of Chongqing. The proportions of risk increase, risk decline, and risk fluctuation were 13.45%, 17.66%, and 7.36%, respectively. Kernel density analysis was suitable to explore high-risk gathering areas. The peak values of kernel density in the three periods were around 1110, suggesting that the maximum gathering degree of medium-risk pattern spots basically showed no changes, but the spatial positions of high-risk gathering areas somehow changed. Getis-Ord Gi* analysis was suitable to explore the relationships between hot and cold spots. Counties with high pollution risks were Yongchuan, Shapingba, Dianjiang, Liangping, northwestern Fengdu, and Zhongxian, while counties with low risks were Chengkou, Wuxi, Wushan, Pengshui, and Rongchang. High-value hot spot zones gradually dominated in the northeast of Chongqing, while low-value cold spot zones gradually dominated in the Midwest. Our results provide a scientific base for the development of strategies to prevent and control AGNPS in Chongqing.

New formulations of algebraic criteria for controllability and observability of a linear MIMO-system

New formulations of algebraic criteria for controllability and observability of a linear dynamical system with multiple inputs and outputs (MIMO-systems) are given, the corresponding theorems are formulated. The criteria are based on algebraic relations between linear combinations of the control matrix columns and own vectors of the free dynamics matrix. Keywords algebraic criterion; controllability; observability; linear MIMO-system; own value; own vector; Krylov vector and matrix; kernel; cokernel

Spinning Wave Scattering From a Flow Pipe With Serrations

It is well known that trailing-edge serrations, which are also known as chevrons, are able to reduce the turbulent mixing noise from an aeroengine. The study of the associated control capability of the scattering of incident waves from the rotor–stator assembly is rare. To address this issue, a theoretical model is proposed to predict sound wave scattering from a cylindrical pipe with trailing-edge serrations in the presence of plug flows. The model incorporates Fourier series expansion into the Wiener–Hopf method and, therefore, is a natural extension of the previous aerofoil work by Huang (2017, “Theoretical Model of Acoustic Scattering From a Flat Plate With Serrations,” J. Fluid Mech., 819, pp. 228–257). The nature of the flow duct problem, however, leads to a much more complicated matrix kernel, and the associated factorization method is given in this article. The proposed model is validated by comparison with the numerical simulations at certain representative setups, which show the overall agreements to be satisfactory. The comparisons also show that the proposed model is so efficient that it can enable rapid predictions. A series of parametric studies are performed to study the two mechanisms behind the noise reduction of a serrated flow duct. One is the redistribution of acoustic energy to new higher cutoff modes. The other is the destructive interference due to multiple scattering from serrations. Overall, the proposed model should be helpful in offering deep physical insights and would be able to assist the aeroacoustic design and optimization of new low-noise aeroengines and flow duct systems after considering the tradeoff with aerodynamic impacts.

Spatiotemporal evolution analysis of agricultural non-point source pollution risks in Chongqing, China, based on the ITO3dE model and GIS

To determine the risk state distribution, risk level, and risk evolution situation of agricultural non-point source pollution (AGNPS), we built an ‘Input-Translate-Output’ three-dimensional evaluation (ITO3dE) model that involved 12 factors under the support of GIS and analyzed the spatiotemporal evolution characteristics of AGNPS risks from 2005 to 2015 in Chongqing by using GIS space matrix, kernel density analysis, and Getis-Ord Gi* analysis. Land use changes during the 10 years had a certain influence on the AGNPS risk. The risk values in 2005, 2010, and 2015 were in the ranges of 0.40–2.28, 0.41–2.57, and 0.41–2.28, respectively, with the main distribution regions being the western regions of Chongqing (Dazu, Jiangjin, etc.) and other counties such as Dianjiang, Liangping, Kaizhou, Wanzhou, and Zhongxian. The spatiotemporal transition matrix could well exhibit the risk transition situation, and the risks generally showed no changes over time. The proportions of ‘no-risk no-change’, ‘low-risk no-change’, and ‘medium-risk no-change’ were 10.86%, 33.42%, and 17.25%, respectively, accounting for 61.53% of the coverage area of Chongqing. The proportions of risk increase, risk decline, and risk fluctuation were 13.45%, 17.66%, and 7.36%, respectively. Kernel density analysis was suitable to explore high-risk gathering areas. The peak values of kernel density in the three periods were around 1,110, suggesting that the maximum gathering degree of medium-risk pattern spots basically showed no changes, but the spatial positions of high-risk gathering areas somehow changed. Getis-Ord Gi* analysis was suitable to explore the relationships between hot and cold spots. Counties with high pollution risks were Yongchuan, Shapingba, Dianjiang, Liangping, northwestern Fengdu, and Zhongxian, while counties with low risks were Chengkou, Wuxi, Wushan, Pengshui, and Rongchang. High-value hot spot zones gradually dominated in the northeast of Chongqing, while low-value cold spot zones gradually dominated in the Midwest. Our results provide a scientific base for the development of strategies to prevent and control AGNPS in Chongqing.

Scattering on a square lattice from a crack with a damage zone

A semi-infinite crack in an infinite square lattice is subjected to a wave coming from infinity, thereby leading to its scattering by the crack surfaces. A partially damaged zone ahead of the crack tip is modelled by an arbitrarily distributed stiffness of the damaged links. While an open crack, with an atomically sharp crack tip, in the lattice has been solved in closed form with the help of the scalar Wiener–Hopf formulation (Sharma 2015 SIAM J. Appl. Math. , 75 , 1171–1192 ( doi:10.1137/140985093 ); Sharma 2015 SIAM J. Appl. Math. 75 , 1915–1940. ( doi:10.1137/15M1010646 )), the problem considered here becomes very intricate depending on the nature of the damaged links. For instance, in the case of a partially bridged finite zone it involves a 2 × 2 matrix kernel of formidable class. But using an original technique, the problem, including the general case of arbitrarily damaged links, is reduced to a scalar one with the exception that it involves solving an auxiliary linear system of N × N equations, where N defines the length of the damage zone. The proposed method does allow, effectively, the construction of an exact solution. Numerical examples and the asymptotic approximation of the scattered field far away from the crack tip are also presented.

Feature Extraction with Discrete Non-Separable Shearlet Transform and Its Application to Surface Inspection of Continuous Casting Slabs

A new feature extraction technique called DNST-GLCM-KSR (discrete non-separable shearlet transform-gray-level co-occurrence matrix-kernel spectral regression) is presented according to the direction and texture information of surface defects of continuous casting slabs with complex backgrounds. The discrete non-separable shearlet transform (DNST) is a new multi-scale geometric analysis method that provides excellent localization properties and directional selectivity. The gray-level co-occurrence matrix (GLCM) is a texture feature extraction technology. We combine DNST features with GLCM features to characterize defects of the continuous casting slabs. Since the combination feature is high-dimensional and redundant, kernel spectral regression (KSR) algorithm was used to remove redundancy. The low-dimension features obtained and labels data were inputted to a support vector machine (SVM) for classification. The samples collected from the continuous casting slab industrial production line—including cracks, scales, lighting variation, and slag marks—and the proposed scheme were tested. The test results show that the scheme can improve the classification accuracy to 96.37%, which provides a new approach for surface defect recognition of continuous casting slabs.

Improving the Quality of Digital Images Using the Median Filter Technique to Reduce Noise

The combination of point, line, shape and color elements combined to create a physical imitation of an object is called an image. The arrangement of the box elements in the image forms pixels or matrices. each image experiences degradation or loss of quality called noise. The effect of gaussian noise is the number of colored dots that are equal to the percentage of noise. This study raises the topic of improving the quality of digital images using median filter techniques to reduce noise. In this study using color image data (Red Green Blue) as test data and then converted into grayscale images to determine the gray degree of the image. The grayscale image is stored in the database. Then noise is generated by using random numbers. Noise in the form of impulse can be positive or negative in the form of adding pixel values to the original image, or it can reduce the value of the original image. The noise type used is salt & pepper. Gray degrees 0-255 spread. Can be calculated through image histograms. To reduce noise the median filter technique is used. Image histogram as a measure of the spread of numbers from the median filter. The result is a median filter can reduce noise salt and pepper by using a matrix kernel.

The Problem of Determining the Matrix Kernel of the Anisotropic Viscoelasticity Equations System

Рассматривается обратная задача определения матричного ядра K(t)(K1,K2,K3)(t), t0,T, входящего в систему интегродифференциальных уравнений анизотропной вязкоупругости. Прямая начальнокраевая задача состоит в определении векторфункции смещения u(x,t)(u1,u2,u3)(x,t), x(x1,x2,x3)R3, x30. Предполагается, что коэффициенты уравнений системы (плотность и модули упругости) зависят только от пространственной переменной x30. Источник возмущения упругих волн сосредоточен на границе области x30 и представляет собой дельтафункцию Дирака (граничное условие Неймана специального вида). Обратная задача сводится к изученным ранее задачам определения скалярных ядер Ki(t), i1,2,3. В качестве дополнительного условия задается значение преобразования Фурье по x2 от функции u(x,t) на поверхности x30. Приводятся теоремы глобальной однозначной разрешимости и устойчивости решения обратной задачи. Идея доказательства глобальной разрешимости состоит в применении принципа сжатых отображений к системе нелинейных интегральных уравнений Вольтерра второго рода в банаховом пространстве с весовыми нормами.

Sound wave scattering in a flow duct with azimuthally non-uniform liners

Novel acoustic liner designs often incorporate new materials with non-uniform impedance distributions. Therefore, new methods are required for their modelling and analysis. In this paper, a theoretical model is developed to investigate the scattering of sound waves from an axially symmetrical flow duct with a semi-infinite, azimuthally non-uniform acoustic lining on the duct wall. More specifically, the incorporation of Fourier series expansions into the Wiener–Hopf method leads to an analytical model with a matrix kernel, which is further factorised by using the pole-removal method to obtain a closed-form solution. A new mathematical method is developed to solve the residues associated with the pole-removal technique. The proposed model has been verified and validated by comparing with corresponding computational results. In addition to shedding light on the possible physical effect of azimuthally non-uniform liners along with an axial hard–soft interface, the current model enhances the theoretical modelling capability for a complicated set-up of practical importance, and can be used to investigate new liner designs for passive noise control in flow ducts.