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Inhomogeneous damping distribution leads to the occurrence of complex modes of structures. Complex modes' vibration and acoustic radiation characteristics are different from real modes. This paper studies the complex modal characteristics of inhomogeneously damped plates for forced vibration. We used the state space method to obtain the complex eigenvalues and eigenvectors of the vibration system and calculated the relationship between modal coordinates and frequency under unit force. The results show that the absolute values of the modal coordinates of two conjugate complex eigenvectors are different, and the structure's vibration is dominated by the eigenvectors corresponding to eigenvalues with positive imaginary parts near natural frequencies. When investigating the structural sound radiation in the vibration mode space, each mode's acoustic radiation is not independent but coupled with each other. The influence of the coupling between complex modes on the calculation results of the acoustic radiation power of the plate is studied in this paper. The results show that the coupling effect between modes cannot be ignored when calculating the acoustic radiation power based on complex modes. Finally, the error of calculating acoustic power using the decoupling approximation instead of the complex mode method is analyzed. [ABSTRACT FROM AUTHOR]

The breeding and selection of resistant varieties is an effective way to minimize wheat Fusarium head blight (FHB) hazards, so it is important to identify and evaluate resistant varieties. The traditional resistance phenotype identification is still largely dependent on time-consuming manual methods. In this paper, the method for evaluating FHB resistance in wheat ears was optimized based on the fusion feature wavelength images of the hyperspectral imaging system and the Faster R-CNN algorithm. The spectral data from 400-1000 nm were preprocessed by the multiple scattering correction (MSC) algorithm. Three feature wavelengths (553 nm, 682 nm and 714 nm) were selected by analyzing the X-loading weights (XLW) according to the absolute value of the peaks and troughs in different principal component (PC) load coefficient curves. Then, the different fusion methods of the three feature wavelengths were explored with different weight coefficients. Faster R-CNN was trained on the fusion and RGB datasets with VGG16, AlexNet, ZFNet, and ResNet-50 networks separately. Then, the other detection models SSD, YOLOv5, YOLOv7, CenterNet, and RetinaNet were used to compare with the Faster R-CNN model. As a result, the Faster R-CNN with VGG16 was best with the mAP (mean Average Precision) ranged from 97.7% to 98.8%. The model showed the best performance for the Fusion Image-1 dataset. Moreover, the Faster R-CNN model with VGG16 achieved an average detection accuracy of 99.00%, which was 23.89%, 1.21%, 0.75%, 0.62%, and 8.46% higher than SSD, YOLOv5, YOLOv7, CenterNet, and RetinaNet models. Therefore, it was demonstrated that the Faster R-CNN model based on the hyperspectral feature image fusion dataset proposed in this paper was feasible for rapid evaluation of wheat FHB resistance. This study provided an important detection method for ensuring wheat food security. [ABSTRACT FROM AUTHOR]

Roller bearings are critical components in various mechanical systems, and the timely detection of potential failures is essential for preventing costly downtimes and avoiding substantial machinery breakdown. This research focuses on finding and verifying a robust method that can detect failures early, without creating false positive failure states. Therefore, this paper introduces a novel algorithm for the early detection of roller bearing failures, particularly tailored to high-precision bearings and automotive test bed systems. The featured method (AFI—Advanced Failure Indicator) utilizes the Fast Fourier Transform (FFT) of wideband accelerometers to calculate the spectral content of vibration signals emitted by roller bearings. By calculating the frequency bands and tracking the movement of these bands within the spectra, the method provides an indicator of the machinery's health, mainly focusing on the early stages of bearing failure. The calculated channel can be used as a trend indicator, enabling the method to identify subtle deviations associated with impending failures. The AFI algorithm incorporates a non-static limit through moving average calculations and volatility analysis methods to determine critical changes in the signal. This thresholding mechanism ensures the algorithm's responsiveness to variations in operating conditions and environmental factors, contributing to its robustness in diverse industrial settings. Further refinement was achieved through an outlier detection filter, which reduces false positives and enhances the algorithm's accuracy in identifying genuine deviations from the normal operational state. To benchmark the developed algorithm, it was compared with three industry-standard algorithms: VRMS calculations per ISO 10813-3, Mean Absolute Value of Extremums (MAVE), and Envelope Frequency Band (EFB). This comparative analysis aimed to evaluate the efficacy of the novel algorithm against the established methods in the field, providing valuable insights into its potential advantages and limitations. In summary, this paper presents an innovative algorithm for the early detection of roller bearing failures, leveraging FFT-based spectral analysis, trend monitoring, adaptive thresholding, and outlier detection. Its ability to confirm the first failure state underscores the algorithm's effectiveness. [ABSTRACT FROM AUTHOR]

In recent years, there has been extensive research and application of unsupervised monocular depth estimation methods for intelligent vehicles. However, a major limitation of most existing approaches is their inability to predict absolute depth values in physical units, as they generally suffer from the scale problem. Furthermore, most research efforts have focused on ground vehicles, neglecting the potential application of these methods to unmanned aerial vehicles (UAVs). To address these gaps, this paper proposes a novel absolute depth estimation method specifically designed for flight scenes using a monocular vision sensor, in which a geometry-based scale recovery algorithm serves as a post-processing stage of relative depth estimation results with scale consistency. By exploiting the feature correspondence between successive images and using the pose data provided by equipped navigation sensors, the scale factor between relative and absolute scales is calculated according to a multi-view geometry model, and then absolute depth maps are generated by pixel-wise multiplication of relative depth maps with the scale factor. As a result, the unsupervised monocular depth estimation technology is extended from relative depth estimation in semi-structured scenes to absolute depth estimation in unstructured scenes. Experiments on the publicly available Mid-Air dataset and customized data demonstrate the effectiveness of our method in different cases and settings, as well as its robustness to navigation sensor noise. The proposed method only requires UAVs to be equipped with monocular camera and common navigation sensors, and the obtained absolute depth information can be directly used for downstream tasks, which is significant for this kind of vehicle that has rarely been explored in previous depth estimation studies. [ABSTRACT FROM AUTHOR]

In this paper, we propose a modified spectral conjugate gradient (MSCG) method for solving absolute value equations associated with second-order cones (SOCAVEs). Some properties of the SOCAVEs are analyzed, and the global convergence of the MSCG method is discussed in depth. Numerical experiments are given to illustrate the effectiveness and competitiveness of our algorithm. [ABSTRACT FROM AUTHOR]

This paper concentrates on addressing fractional inequalities for exponential type convex functions. By means of exponential-type convexity, we firstly establish Hermite-Hadamard (HH) type inequalities for fractional integrals with exponential kernels. Secondly, based on the discovered fractional identity by separating [a; b] to n equal subintervals, and the fact that the twice derivative in absolute value is exponential type convex, we present multipoint-based HH inequalities, which cover the trapezoid- and Bullen-type inequalities for n = 1 and 2, correspondingly. During the period, some numerical examples with graphs are provided to show the validity of the deduced inequalities. [ABSTRACT FROM AUTHOR]

Gabor phase retrieval is the problem of recovering a signal from the absolute values of Gabor transform, which has turned into a very active research area. In the paper, we define a generalized Paley–Wiener space, which is obtained by applying the special affine Fourier transform to L p ([ - B , B ]) (2 ≤ p ≤ ∞) and provide the uniqueness of the Gabor phase retrieval in the generalized Paley–Wiener space. When the window function ψ is the inverse special affine Fourier transform of ϕ = 2 1 4 e - π x 2 , we show that every signal in the generalized Paley–Wiener space can be uniquely recovered, up to a global sign, from its the magnitudes of Gabor measurement sampled on a rectangular lattice. Recently, Grohs, Liehr and Wellershoff studied the Gabor phase retrieval problems in the conventional Paley–Wiener space. The paper extends their results to the generalized Paley–Wiener space. Since the generalized Paley–Wiener space includes a broader class of signals, our results expand the applied range of the Gabor phase retrieval. [ABSTRACT FROM AUTHOR]

Positive and unlabeled learning (PU learning) is a significant binary classification task in machine learning; it focuses on training accurate classifiers using positive data and unlabeled data. Most of the works in this area are based on a two-step strategy: the first step is to identify reliable negative examples from unlabeled examples, and the second step is to construct the classifiers based on the positive examples and the identified reliable negative examples using supervised learning methods. However, these methods always underutilize the remaining unlabeled data, which limits the performance of PU learning. Furthermore, many methods require the iterative solution of the formulated quadratic programming problems to obtain the final classifier, resulting in a large computational cost. In this paper, we propose a new method called the absolute value inequality support vector machine, which applies the concept of eccentricity to select reliable negative examples from unlabeled data and then constructs a classifier based on the positive examples, the selected negative examples, and the remaining unlabeled data. In addition, we apply a hyperparameter optimization technique to automatically search and select the optimal parameter values in the proposed algorithm. Numerical experimental results on ten real-world datasets demonstrate that our method is better than the other three benchmark algorithms. [ABSTRACT FROM AUTHOR]

The spectral radius of a square matrix is the maximum among absolute values of its eigenvalues. Suppose a square matrix is nonnegative; then, by Perron–Frobenius theory, it will be one among its eigenvalues. In this paper, Perron–Frobenius theory for adjacency matrix of graph with self-loops A G S will be explored. Specifically, it discusses the nontrivial existence of Perron–Frobenius eigenvalue and eigenvector pair in the matrix A G S − σ n I , where σ denotes the number of self-loops. Also, Koolen–Moulton type bound for the energy of graph G S is explored. In addition, the existence of a graph with self-loops for every odd energy is proved. [ABSTRACT FROM AUTHOR]

Graph polynomials is one of the important research directions in mathematical chemistry. The coefficients of some graph polynomials, such as matching polynomial and permanental polynomial, are related to structural properties of graphs. The Hosoya index of a graph is the sum of the absolute value of all coefficients for the matching polynomial. And the permanental sum of a graph is the sum of the absolute value of all coefficients of the permanental polynomial. In this paper, we characterize the second to sixth minimal Hosoya indices of all bicyclic graphs. Furthermore, using the results, the second to sixth minimal permanental sums of all bicyclic graphs are also characterized. [ABSTRACT FROM AUTHOR]

Simpson inequalities for first-order differentiable convex functions and various fractional integrals have been studied extensively. However, Simpson type inequalities for twice-differentiable functions are researched slightly. Therefore, in the present paper, we endeavor to study fractional inequalities of Simpson type for twice-differentiable convex functions. To achieve this goal, we establish a new twicedifferentiable Simpson's identity by using tempered fractional integral operators. Based upon it, we prove several fractional Simpson type inequalities whose second derivatives in absolute value are convex. Finally, we give some examples to illustrate the correctness of the obtained results. [ABSTRACT FROM AUTHOR]

The leakage flow has a significant impact on the aerodynamic losses and efficiency of the compressor. This paper investigates the loss mechanism in the tip region based on a high-load cantilevered stator cascade. Firstly, a high-fidelity flow field structure was obtained based on the Enhanced Delay Detached Eddy Simulation (EDDES) method. Subsequently, the Liutex method was employed to study the vortex structures in the tip region. The results indicate the presence of a tip leakage vortex (TLV), passage vortex (PV), and induced vortex (IV) in the tip region. At i = 4 ° , 8 ° , the induced vortex interacts with the PV and low-energy fluid, forming a "three-shape" mixed vortex. Finally, a qualitative and quantitative analysis of the loss sources in the tip flow field was conducted based on the entropy generation rate, and the impact of the incidence on the losses was explored. The loss sources in the tip flow field included endwall loss, blade profile loss, wake loss, and secondary flow loss. At i = 0 ° , the loss primarily originated from the endwall and blade profile, accounting for 40 % and 39 % , respectively. As the incidence increased, the absolute value of losses increased, and the proportion of loss caused by secondary flow significantly increased. At i = 8 ° , the proportion of secondary flow loss reached 47%, indicating the most significant impact. [ABSTRACT FROM AUTHOR]

This paper established the idea of minimum evdominating matrix of semigraph and calculated its energy. The minimum ev-dominating energy EmeD(G) of a semigraph G is the sum of the absolute values of the eigenvalues of the minimum ev-dominating matrix. Here some results are also derived in connection with the energy of minimum evdominating matrix. Some lower bounds are also established. [ABSTRACT FROM AUTHOR]

Time series forecasting is an important application of many statistical methods. When it is appropriate to assume that the data may be projected towards the future based on the past history of the dataset, a preliminary examination is usually required to ensure that the data sequence is autocorrelated. This is a quite obvious assumption that has to be made and can be the object of a formal test of hypotheses. The most widely used test is the portmanteau test, i.e., a sum of the squared standardized autocorrelations up to an appropriate maximum lag (the truncation point). The choice of the truncation point is not obvious and may be data-driven exploiting supplementary information, e.g. the largest autocorrelation and the lag where such maximum is found. In this paper, we propose a portmanteau test with a truncation point equal to the lag of the largest (absolute value) estimated autocorrelation. Theoretical and simulation-based comparisons based on size and power are performed with competing portmanteau tests, and encouraging results are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we construct a new class of convex functions, so-called generalized n-polynomial p-convex functions. We investigate their algebraic properties and provide some relationships between these functions and other types of convex functions. We establish Hermite–Hadamard (H–H) inequality for the newly defined class of functions. Additionally, we derive refinements of H–H inequality for functions whose first derivatives in absolute value at certain power are generalized n-polynomial p-convex. When p = − 1 , our definition evolves into a new definition for the class of convex functions so-called generalized n-polynomial harmonically convex functions. The results obtained in this study generalize regarding those found in the existing literature. By extending these particular types of inequalities, the objective is to unveil fresh mathematical perspectives, attributes and connections that can enhance the evolution of more resilient mathematical methodologies. This study aids in the progression of mathematical instruments across diverse scientific fields. [ABSTRACT FROM AUTHOR]

Variable selection is one of the most important contents of machine learning research and a large number of variable selection methods have been proposed at present. From deep learning perspective, we propose a new variable selection method based on multi-layer artificial neural networks in this paper. The method propagates errors gained form a trained network model through the network from output layer to input layer and the values gained by input layer give information about the relative contribution. The variables with big contribution value are selected, which we call neural inverse propagation (NIP). Specifically, after training a neural network, the gained errors between the actual network outputs and the desired outputs go through the network from top to down and arrive at the input layer. The absolute values gained by input units provide information about the relative importance (contribution) of input units, which is that the larger the value is, the more important the corresponding input variable is. We remove k variables corresponding to the first k minimum absolute value gained by input units to the predictive variables, to perform variable selection. The efficiency of the proposed method is illustrated through its application to classification and regression tasks on a number of synthetic datasets and a real-world image classification dataset. [ABSTRACT FROM AUTHOR]

Newton-type methods have been successfully applied to solve the absolute value equation Ax − |x| = b (denoted by AVE). This class of methods usually solves a system of linear equations exactly in each iteration. However, for large-scale AVEs, solving the corresponding system exactly may be expensive. In this paper, we propose an inexact Newton-type method for solving the AVE. In each iteration, the proposed method solves the corresponding system only approximately. Moreover, it adopts a new line search technique, which is well-defined and easy to implement. We prove that the proposed method has global and local superlinear convergence under the condition that the interval matrix [A − I, A + I] is regular. This condition is much weaker than those used in some Newton-type methods. Numerical results show that our method has fairly good practical efficiency for solving large-scale AVEs. [ABSTRACT FROM AUTHOR]

The purpose of the paper is to present new q-parametrized Hermite–Hadamard-like type integral inequalities for functions whose third quantum derivatives in absolute values are s-convex and  (α , m) -convex, respectively. Two new q-integral identities are presented for three time q-differentiable functions. These lemmas are used like basic elements in our proofs, along with several important tools like q-power mean inequality, and q-Holder's inequality. In a special case, a non-trivial example is considered for a specific parameter and this case illustrates the investigated results. We make links between these findings and several previous discoveries from the literature. [ABSTRACT FROM AUTHOR]

Lateral roots, including adventitious roots, are the main component of rapeseed roots with support, absorb, and synthesis functions and their morphological parameters directly affecting the plant's aboveground growth and yield. Root biomass, as a material base for lateral root growth, can be used as a link between plant phenotypes and their physiological processes, as well as to enhance root 3D growth model mechanisms and accuracy. To quantify the relationships between lateral root morphological indices and the corresponding organ biomass for rapeseed, we used two cultivars, NY 22 (conventional) and NZ 1818 (hybrid), and conducted cultivar and fertilizing cylindrical tube experiments during the 2016–2019, with two fertilizer levels, no fertilizer, and 180 kg N ha−1 fertilizer. The lateral root biomass and morphological parameters were determined during the whole growth period. The biomass‐based lateral root morphological parameter models were developed by analyzing the quantitative relationship between the lateral root morphological indices and their corresponding biomass, and the descriptive models were verified with independent experimental data. The results showed that the correlation (r) of simulated and observed values for the lateral root morphological parameters are all greater than 0.9 with significant levels at p < 0.001. The absolute values of the average absolute difference (da) of simulated and observed values for the lateral root length (LLR), lateral root average diameter (ADLR), lateral root surface area (SALR), and lateral root volume (VLR) are −30.408 cm, −0.003 mm, 12.902 cm2, and 0.039 cm3, respectively. The RMSE values are 175.183 cm, 0.010 mm, 59.710 cm2, and 1.513 cm3, respectively. The ratio of da to the average observed values (dap) for the LLR and VLR are all less than 5%, and the ADLR and SALR are all <6%. The models developed in this paper have good performance and reliability for predicting lateral root morphological parameters of rapeseed. The study provides a mechanistic method for linking the rapeseed growth model with the morphological model using corresponding organic biomass and laying a good foundation for establishing a 3D morphological model for rapeseed root system based on biomass. [ABSTRACT FROM AUTHOR]

The stress state of a fault plane influences the mode of sliding and characteristics of slide behaviour. Existing researchers have mainly focused on studying the effect of shear stiffness on fault behaviour under the constant normal load (CNL) boundary conditions. However, the impact of the normal stiffness effect of deep faults on fault sliding stability and seismic source parameters remains uncertain. Addressing the issue, this paper conducts friction tests on granite-simulated faults under the constant normal stiffness (CNS) boundary conditions. It analyzes the impact of normal stiffness on the mechanical behaviour of fault sliding. The results of this paper demonstrate the following findings: (1) Under both normal boundary conditions, various sliding modes occur, including creep-slip, chaotic stick-slip, regular inclusion chaotic stick-slip, and regular stick-slip. (2) The normal stiffness effect reduces the duration of creep-slip and chaotic stick-slip behaviour and decreases the frequency of regular inclusion chaotic stick-slip behaviour. (3) Shear stress and normal stress of the regular stick-slip mode exhibit periodic changes under the CNS boundary conditions. (4) Compared to the CNL boundary conditions, the CNS boundary conditions show a larger shear stress drop and a positive correlation between the normal stress drop and normal stiffness. (5) The CNS boundary conditions result in larger shear stiffness, the absolute value of stick-slip stiffness, characteristic sliding displacement, and fracture energy compared to the relevant seismic source parameters of the CNL boundary conditions. These parameters display positive correlations with normal stiffness. The stick-slip period and normal stiffness initially decrease and then increase, while the normal displacement drop and normal stiffness display a negative correlation trend. These analyses provide comprehensive insights into the mechanical characteristics of fault-slip behaviour and can contribute to improving models and predictions related to fault-sliding behaviour and seismic activity. • We discover a new fault-slip pattern known as regular inclusion chaotic stick-slip. • The normal stiffness effect shortens the duration of fault-slip behaviour. • Under CNS condition, the shear and normal stress exhibit synchronous changes. • The values of seismic source parameters tend to be larger for the CNS condition. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to solve tensor absolute value equation by using preconditioned techniques and the inexact fixed point iteration method. For an existing preconditioner, we present a new inexact fixed point iteration method for solving tensor absolute value equation. Theoretically, we give the convergence of the proposed method. Numerically, we show the efficiency of the proposed method by two numerical examples. [ABSTRACT FROM AUTHOR]

Engine performance models are used in various fields, such as operation optimization, control, and diagnosis. In order to effectively apply an engine performance model in these fields, a high level of prediction accuracy is required. When improving the accuracy of an engine model through performance adaptation using measurement data, it is important to functionalize the component adaptation factors calculated at each measurement point to enable them to be utilized at other operating points. A method of curve fitting to find the adaptation factor for a single performance parameter was previously used to functionalize the component adaptation factor. In this paper, machine learning techniques are newly applied to functionalize component adaptation factors for several parameters, including engine operation characteristics, and their effectiveness is analyzed. The prediction accuracy of the adapted model for a two-spool mixed-flow turbofan engine is compared based on the fan exit total pressure, high-pressure compressor (HPC) exit static pressure, exhaust gas temperature (EGT), and high-pressure spool speed. For an engine model adapted using the existing functionalization method, the average absolute value of the relative errors in the fan exit total pressure, HPC exit static pressure, EGT, and high-pressure spool speed in the validation dataset were 2.91 %, 2.20 %, 5.32 %, and 1.84 %, respectively, whereas for an engine model adapted using the proposed machine learning-based functionalization method, these errors were 0.70 %, 1.00 %, 2.56 %, and 0.26 %, respectively, under the same conditions. As a result, it was confirmed that the performance prediction accuracy of the engine model adapted using the proposed method was improved compared to the existing method. [ABSTRACT FROM AUTHOR]

In this paper, the tracking control problem of the uncertain control system is studied in the frame of uncertainties estimation and compensation. To eliminate the influence of external disturbances and internal uncertainties on the control system, the error-driven nonlinear extended state observer (EDN-ESO), whose gain is set as an increasing function with respect to the absolute value of estimation error of the system output, is proposed to improve the estimation performance for the "total disturbance". Next, both the estimation error of proposed ESO and the tracking error of system output are proven to be bounded by selecting the lower bound and variation range of ESO's bandwidth. Moreover, the convergence of the estimation error as well as the tracking error to zero is proven under certain conditions. Finally, the proposed design method is applied to the air–fuel ratio control system of gasoline engines, and the experimental results show that the proposed EDN-ESO can effectively adjust the observer gain, so as to enhance the tracking performance. • A novel error-driven nonlinear ESO is designed to achieve faster response of ESO. • The stability of the proposed ESO and the closed-loop system are both proven. • The AFR experiment shows that the proposed method can enhance the tracking effect. [ABSTRACT FROM AUTHOR]

• Stable and homogeneous of droplets for the aqueous two-phase system is achieved. • Neck evolution of water-in-water droplets in flow-focusing devices is self-similar. • Four flow patterns were observed and analyzed. • Formation process of droplet includes slow and fast squeezing, and pinch-off stages. • Evolution regulations of droplet neck interface in three stages were described. In ATPS, the ultra-low interfacial tension makes the stable generation of droplets very difficult. In this paper, the stable and homogeneous preparation of ATPS droplets is achieved over a wide range of flow rates, and the self-similarity analysis and formation dynamics of the droplets are studied. Formation of ATPS droplets show good self-similarity. The generation process of ATPS droplets can be divided into slow squeezing, fast squeezing and rapid pinch-off stages. In the slow squeezing stage, the dimensionless minimum neck width w m / w c is linear with the time, and the absolute value of the slope increases with the capillary number of continuous phase Ca c. In the rapid squeezing and rapid pinch-off stages, the w m / w c satisfies the power-law relationship with time, and the absolute value of the power-law indexes decrease with increasing Ca c , and the pre-exponential factor of pinch-off stage increases with increasing Ca c. [ABSTRACT FROM AUTHOR]