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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]

In this paper, we focus on the nonlinear least squares problem: \min _{{\boldsymbol {x}}\in \mathbb {H}^d}\|\lvert A{\boldsymbol {x}}\rvert -{\boldsymbol {b}}\| where A\in \mathbb {H}^{m\times d}, {\boldsymbol {b}}\in \mathbb {R}^m with \mathbb {H}\in \left \{\mathbb {R},\mathbb {C}\right \} and consider the uniqueness and stability of solutions. This problem arises in applications such as phase retrieval and absolute value rectification neural networks. While several results have been developed to characterize the uniqueness and stability of solutions when {\boldsymbol {b}}=\lvert A{\boldsymbol {x}}_0\rvert for some {\boldsymbol {x}}_0\in \mathbb {H}^d, no existing results address the case where {\boldsymbol {b}} is arbitrary. In this paper, we investigate the uniqueness and stability of solutions for the more general case where {\boldsymbol {b}} is not necessarily equal to \lvert A{\boldsymbol {x}}_0\rvert for any {\boldsymbol {x}}_0\in \mathbb {H}^d. We prove that for any matrix A\in \mathbb {H}^{m\times d}, there is always a vector {\boldsymbol {b}}\in \mathbb {R}^m for which the solution to the nonlinear least squares problem is not unique. However, we show that such "bad" vectors {\boldsymbol {b}} are negligible in practice; specifically, if {\boldsymbol {b}}\in \mathbb {R}_{ }^m does not lie in some measure zero set, then the solution is unique. Furthermore, we establish certain conditions under which the solution is guaranteed to be unique. Regarding the stability of solutions, we prove that the solution is not uniformly stable. However, if we restrict the vectors {\boldsymbol {b}} to a convex set where the solution to the least squares problem is unique, then the solution becomes stable. To the best of our knowledge, our results represent the first theoretical results of the uniqueness and stability of solutions for the nonlinear least squares problem. [ABSTRACT FROM AUTHOR]

Text processing tasks commonly grapple with the challenge of high dimensionality. One of the most effective solutions to this challenge is to preprocess text data through feature selection methods. Feature selection can select the most advantageous features for subsequent operations (e.g., classification) from the native feature space of the text. This process effectively trims the feature space's dimensionality, enhancing subsequent operations' efficiency and accuracy. This paper proposes a straightforward and efficient filter feature selection method based on document-term matrix unitization (DTMU) for text processing. Diverging from previous filter feature selection methods that concentrate on scoring criteria definition, our method achieves more optimal feature selection by unitizing each column of the document-term matrix. This approach mitigates feature-to-feature influence and reinforces the role of the weighting proportion within the features. Subsequently, our scoring criterion subtracts the sum of weights for negative samples from positive samples and takes the absolute value. We conduct numerical experiments to compare DTMU with four advanced filter feature selection methods: max–min ratio metric, proportional rough feature selector, least loss, and relative discrimination criterion, along with two classical filter feature selection methods: Chi-square and information gain. The experiments are performed on four ten-thousand-dimensional feature space datasets: b o o k , d v d , m u s i c , m o v i e and two thousand-dimensional feature space datasets: i m d b , a m a z o n _ c e l l s , sourced from Amazon product reviews and movie reviews. Experimental findings demonstrate that DTMU selects more advantageous features for subsequent operations and achieves a higher dimensionality reduction rate than those of the other six methods used for comparison. Moreover, DTMU exhibits robust generalization capabilities across various classifiers and dimensional datasets. Notably, the average CPU time for a single run of DTMU is measured at 1.455 s. • This paper offers DTMU, a filter feature selection method enhancing feature quality via unitization for improved properties. • DTMU is notably user-friendly, involving only two straightforward steps. • This paper substantiates, through numerical experiments, that DTMU stands as an advanced and effective method. [ABSTRACT FROM AUTHOR]

Purpose: This study presents a two-step numerical iteration method specifically designed to solve absolute value equations. The proposed method is valuable and efficient for solving absolute value equations. Several numerical examples were taken to demonstrate the accuracy and efficiency of the proposed method. Design/methodology/approach: We present a two-step numerical iteration method for solving absolute value equations. Our two-step method consists of a predictor-corrector technique. The new method uses the generalized Newton method as the predictor step. The four-point open Newton-Cotes formula is considered the corrector step. The convergence of the proposed method is discussed in detail. This new method is highly effective for solving large systems due to its simplicity and effectiveness. We consider the beam equation, using the finite difference method to transform it into a system of absolute value equations, and then solve it using the proposed method. Findings: The paper provides empirical insights into how to solve a system of absolute value equations. Originality/value: This paper fulfills an identified need to study absolute value equations. [ABSTRACT FROM AUTHOR]

Shame we are told is as intense as it is unrelenting. Shame we are told, further still, is as contagious as it is transmittable. By fastidiously attending to clinical reports and theoretical depictions of shame's totalizing character, I argue in this paper that we can notice something that has broadly gone unnoticed: shame assumes for itself absolute value. To bear this out, I contrast my view with that of the dominant one: that shame has an instrumental value. I show some limitations of the dominant view by reflecting on the role of shame in psychoanalytic training. The picture that emerges may seem quaintly commonsensical, and even commonplace, but it has, I think, vast clinical implications. I believe that it certainly has the potential to open some new horizons. The arguments for such a bold claim will occupy the concluding section of my paper. [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]

The aim of this paper was to investigate intumescent coatings based on polyfurfuryl alcohol (PFA) resin as a binder benefiting from high char yield and low smoke emission. To this end, the coatings composition in terms of PFA binder resin, long oil alkyd plasticizing resin, TiO2 pigment, and flame-retardant additives (FR) was changed as input parameters according to a mixture design-of-experiments. The corresponding changes in the backside temperature of mild steel substrate (Tb), residual char expansion ratio, limiting oxygen index, and char residue (wt% @1000 °C) were studied as the response variables describing fire performance characteristics of the coatings. The results showed that the backside temperature of the plate increased and the expansion ratio decreased with increasing in the alkyd resin concentration. Also, the flame-retardant efficiency of coatings strongly depends on the content of FR additives. When the content of PFA and alkyd resin was increased at a high level (35 and 4 wt%, respectively), the Tb of the coated plates reached 415 °C rapidly, due to the cracking of the coating and the lower concentration of FR additives. However, the formula with higher FR content, i.e., 68 wt%, showed the lowest Tb value ca. 128 °C. Flame-retardant characteristics directly depended on the expansion ratio of the coatings and the morphology of the char layer remaining on the substrate after the flame test; therefore, coatings with a higher expansion ratio showed lower backside temperature. The findings were supported by examining of the remaining char morphology after a flame test by optical microscopy and validated by comparing the predicted and actual responses for optimization. The value of absolute relative deviation was obtained in the range of 1.6–7.9, which indicates a good agreement between the proposed and experimental results. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving the generalized absolute value equations (GAVE). We present a new method named as modulus-based block triangular splitting iteration (MBTS) method based on the block matrix structure resulting from the transformation of the GAVE into two equations. This method is developed by decomposing the matrix into diagonal and triangular matrices, as well as applying a series of suitable combination and modification techniques. The advantage of the MBTS method is that it is not necessary to solve the inverse of the coefficient matrix of the linear equation system during each iteration, which greatly improves the computational speed and reduces its storage requirements. In addition, we present some convergent theorems proving by different techniques and the estimate of the required number of iteration steps. Furthermore, in the accompanying corollaries, we provide some estimations for choosing appropriate parameter values. Finally, we validated the effectiveness and efficiency of our newly developed method through two numerical examples of the GAVE. [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]

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]

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]

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]

The paper presents monitoring of spatial displacements and deformation of hydraulic structures of hydroelectric power plants of the Dnipro and Dnister cascades using permanent deformation monitoring systems (PDMS). The architecture of the geodetic (measuring) component of monitoring systems deployed at Kaniv, Dnipro, Seredniodniprovska and Dnister HPP (all in Ukraine) are presented, as well as deformation monitoring structure of this systems. Analysis of the impact of geodynamic and seismic factors on the operation of selected monitoring systems are presented. The spatial deformations of the base points on all the studied monitoring systems were determined. As a result of the analysis of the obtained values, it was found that the deformations of the dam crest have a seasonal nature (with half-annual period) of movements, and are characterized by the corresponding vector field and the absolute value of spatial movements. [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]

The distance energy of a connected graph G is the sum of absolute values of the eigenvalues of the distance matrix of G. In this paper, we study how the distance energy of the complete split graph G S (m , n) = K m + K ¯ n changes when an edge is deleted from it. The complete split graph G S (m , n) consists of a clique on m vertices and an independent set on n vertices in which each vertex of the clique is adjacent to each vertex of the independent set. We prove that the distance energy of the complete split graph G S (m , n) always increases when an edge is deleted from it. [ABSTRACT FROM AUTHOR]

The Capra operation is a graph theoretical operation that transforms the given graph into a structurally different and larger graph. It is commonly used in statistical analysis, data processing, and scientific research to compare and analyze data. The Capra operation involves subtracting the reference value from each numerical value, taking the absolute value of the resultand raising it to a specified power. This operation is used to create a new set of values that are more sensitive to differences between numerical values and can help to identify outliers and other anomalous data points. The Capra operation has numerous applications in fields such as finance, engineering, and biology, where it is used to analyze data and make predictions about future trends. Its ability to transform data and highlight differences between values makes it a valuable tool for researchers and analysts seeking to gain deeper insights into the patterns and structures within their data. In this paper, we studied the distance-based topological indices of some graphs under the Capra operation. [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]

Rationale: SLAP is one of the two calibration materials for the isotopic water scale. By consensus the established δ18O value is −55.5‰, although several expert laboratories measure significantly more negative δ18OSLAP values. The real δ18OSLAP value as such does not influence the isotopic water scale; however, knowledge of the size of isotopic scale contraction in stable isotope measurements is vital for second‐order isotopes. This study describes the quantification of δ18OSLAP with respect to δ18OVSMOW. Methods: SLAP‐like water was quantitatively mixed with highly 18O‐enriched water to mimic VSMOW. The 18O concentration was determined using an electron ionization quadrupole mass spectrometer. The isotopic composition of the SLAP‐like and VSMOW‐like waters was measured using an optical spectrometer, alongside original VSMOW and SLAP. Results: This study resulted in a much more negative δ18O value for SLAP than expected. The averaged outcome of seven independent experiments is δ18OSLAP = −56.33 ± 0.03‰. There is a large discrepancy between the actual isotopic measurements of even the most carefully operating isotope laboratories and the true δ18O value. Conclusions: Although this finding as such does not influence the use of the VSMOW–SLAP scale, it raises the intriguing question of what we actually measure with our instruments and why even a fully corrected measurement can be so far off. Our result has consequences for issues like the transfer of δ18O from and to the VPDB scale, various fractionation factors, and Δ17O. The absolute 18O abundance for SLAP was calculated as (1887.98 ± 0.43) × 10−6 based on the absolute 18O abundance of VSMOW and the presented δ18OSLAP in this paper. [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]

The technique for order preference by similarity to ideal solution (TOPSIS) is a popular multi-attribute decision making method. However, the increasing uncertain information with probability and the psychological factor of regret aversion of experts in some complicated situations bring new challenges to the application of traditional TOPSIS. The probabilistic hesitant fuzzy set (P-HFS) is an effective tool to depict the hesitant fuzzy information with the corresponding probability, which can remain more information. In addition, the regret theory indicates that experts may care more about the regret values than the absolute values of alternatives under the fuzzy environment. This paper investigates a new probabilistic hesitant fuzzy TOPSIS (PHFTOPSIS) method based on the regret theory. We propose the corresponding concepts of utility function, reject–rejoice function and perceived utility value of the probabilistic hesitant fuzzy element (P-HFE). The maximum deviation model under the probabilistic hesitant fuzzy environment is presented to determine the weights of attributes. The detailed implementation process of the PHFTOPSIS method based on the regret theory is also provided. Moreover, we apply the proposed method to the investment strategy. Compared with earlier methods, the proposed method can consider both the probabilistic hesitant fuzzy information and regret aversion of experts at the same time in actual applications. A comparative analysis with traditional TOPSIS and probabilistic hesitant fuzzy weighted averaging (PHFWA) operator is further conducted to illustrate its advantages. [ABSTRACT FROM AUTHOR]

Periodic generalized autoregressive conditionally heteroscedastic (PGARCH) models were introduced by Bollerslev and Ghysels [T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Bus. Econom. Statist. 14 1996, 2, 139–151]; these models have gained considerable interest and continued to attract the attention of researchers. This paper is devoted to extensions of the standard absolute value GARCH (AVGARCH) model to the periodically time-varying coefficients (PAVGARCH) one. In this class of models, the parameters are allowed to switch between different regimes. Moreover, these models allow to integrate asymmetric effects in the volatility, Firstly, we give necessary and sufficient conditions ensuring the existence of stationary solutions (in the periodic sense). Secondary, a quasi-maximum likelihood (QML) estimation approach for estimating the PAVGARCH model is developed. The strong consistency and the asymptotic normality of the estimator are studied given mild regularity conditions, requiring strict stationarity and the finiteness of moments of some order for the errors term. Next, we present a set of numerical experiments illustrating the practical relevance of our theoretical results. Finally, we apply our model to two foreign exchange rates: of Algerian Dinar to the European currency Euro (Euro/Dinar) and the American currency Dollar (Dollar/Dinar). This empirical work shows that our approach also outperforms and fits the data well. [ABSTRACT FROM AUTHOR]

For the period of satellite altimetry observation 1993–2018, a comparison was made of estimates of the linear meridional shifts of the jet structure and variations in current intensity in the sector of the Antarctic Circumpolar Current (ACC) south of Africa (10° E–25° W), obtained on the basis of the parameters derived from the module of the absolute dynamic topography (ADT) gradient : directly , module of the velocity of geostrophic current |u| on the ocean surface, half of square of the ADT gradient , and specific kinetic energy . The analysis was carried out by a method developed earlier and refined in this paper using linear regression analysis. It is shown that qualitatively the characters of the meridional shifts (displacement of the curves of these parameters averaged over latitude and for each year) in latitude and the corresponding current intensity variations (i.e., variations in the parameters themselves) over 26-year observations, when calculated through each of the four parameters, turned out to be similar. The same similarity was obtained from the calculations with respect to the ADT scale. Meanwhile, the quantitative differences between calculations for different pairs of parameters can be significant even in the and pair. In quantitative terms, the absolute values of shifts of the jet structure and variations in the intensity of currents in the ACC band in the studied sector of the Southern Ocean generally increase from those linearly dependent on the ADT gradient module to quadratically dependent ones. [ABSTRACT FROM AUTHOR]

In this paper we resolve a conjecture of Kresch and Tamvakis [Duke Math. J. 110 (2001), pp. 359–376]. Our result is the following. Theorem : For any positive integer D and any integers i,j (0\leq i,j \leq D), \; the absolute value of the following hypergeometric series is at most 1: \begin{equation*} {_4F_3} \left [ \begin {array}{c} -i, \; i+1, \; -j, \; j+1 \\ 1, \; D+2, \; -D \end{array} ; 1 \right ]. \end{equation*} To prove this theorem, we use the Biedenharn-Elliott identity, the theory of Leonard pairs, and the Perron-Frobenius theorem. [ABSTRACT FROM AUTHOR]

Consider a quantum cat map M associated with a matrix A ∈ Sp (2 n , Z) , which is a common toy model in quantum chaos. We show that the mass of eigenfunctions of M on any nonempty open set in the position–frequency space satisfies a lower bound which is uniform in the semiclassical limit, under two assumptions: (1) there is a unique simple eigenvalue of A of largest absolute value and (2) the characteristic polynomial of A is irreducible over the rationals. This is similar to previous work (Dyatlov and Jin in Acta Math 220(2):297–339, 2018; Dyatlov et al. in J Am Math Soc 35(2):361–465, 2022) on negatively curved surfaces and (Schwartz in The full delocalization of eigenstates for the quantized cat map, 2021) on quantum cat maps with n = 1 , but this paper gives the first results of this type which apply in any dimension. When condition (2) fails we provide a weaker version of the result and discuss relations to existing counterexamples. We also obtain corresponding statements regarding semiclassical measures and damped quantum cat maps. [ABSTRACT FROM AUTHOR]

The spectral radius ρ (A) is the maximum absolute value of the eigenvalues of a matrix A. In this paper, we establish some relationship between the spectral radius of a symmetric matrix and its principal submatrices, i.e., if A is partitioned as a 2 × 2 block matrix A = ( 0 A 12 A 21 A 22 ) , then ρ (A) 2 ≤ ρ 2 2 + θ ⁎ , where θ ⁎ is the largest real root of the equation μ 2 = (x − ν) 2 (ρ 2 2 + x) and ρ 2 = ρ (A 22) , μ = ρ (A 12 A 22 A 21) , ν = ρ (A 12 A 21). Furthermore, the results are used to obtain several upper bounds of the spectral radius of graphs, which strengthen or improve some known results. [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]

In this paper, Mg 2.3 Y 0.1 Ni + x wt.% graphene (x = 1, 3, 5, 7) composite hydrogen storage alloys were fabricated by mechanical ball milling of Mg 2.3 Y 0.1 Ni alloy powder and graphene. The experimental results show that the phases of the composite alloy consist mainly of Mg 2 Ni, Mg, MgNi 2 and Ni 3 Y phases, and graphene tends to be distributed at the edges of the alloy, increasing the phase boundary resulting from the contact between the C-boundary and the Mg 2.3 Y 0.1 Ni alloy, providing more channels for the diffusion of H 2. In which 7 wt.% of graphene is added, the gestation period of the composite alloy completely disappears. And the ball-milled alloy with 3 wt.% graphene at different temperatures has the highest hydrogen uptake in 2 min and the highest hydrogen release in 10 min. At 573 K, the composite alloy has a hydrogen absorption capacity of 3.251 wt.% H 2 in 2 min and reaches 90.21% of the maximum hydrogen absorption, while it is able to release 3.389 wt.% H 2 in 10 min and reaches 99.04% of the maximum hydrogen release. And the composite alloy with 3 wt.% graphene has the smallest dehydrogenation activation energy. The absolute value of the enthalpy change is reduced from 60.1 kJ/mol to 54.8 kJ/mol, and the desorption enthalpy change is reduced from 73.4 kJ/mol to 67.5 kJ/mol. • Addition of graphene increases the phase boundary of the composite alloy. • Graphene lowers the reaction barrier of the alloy with hydrogen. • Graphene improves the kinetics of hydrogen absorption/release of the alloy. • Graphene reduces the thermodynamic stability of composite alloys. [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]

Let M n be the space of real matrices of order n. The sign-real spectral radius ξ : M n → R + , introduced in a 1997 paper by S.M. Rump, intervenes for instance in the problem of estimating the componentwise distance to singularity. The function ξ has also a bearing in the analysis of generalized absolute value equations and linear complementarity problems. Although ξ is not a norm, it is at least absolutely homogeneous and continuous. Furthermore, ξ is invariant under transposition, permutation similarity, and a few other linear isomorphisms on M n. A matrix A ∈ M n is called sign-real expansive if ξ (A) ≥ 1. Let Ω n be the set of such matrices. The purpose of this work is to discover new properties of the function ξ and to explore in detail the structure of the set Ω n. [ABSTRACT FROM AUTHOR]

Let G be a simple undirected graph. The Seidel energy of G , denoted by E s (G) , is the sum of absolute values of all Seidel eigenvalues of G. A complete r -partite graph with n vertices is called r -partite Turán graph, denoted by T (n , r) , if the number of vertices of each part is either ⌊ n r ⌋ or ⌈ n r ⌉. In 2021, Tian et al. proposed a problem that for any edge e of Turán graph T (n , r) with r ≥ 4 , does there exist a sufficiently large integer n 0 such that E s (T (n , r)) < E s (T (n , r) − e) whenever n ≥ n 0 . In this paper, we prove that the Seidel energy of T (n , 5) of order n ≥ 5 is always increased when an edge is deleted. [ABSTRACT FROM AUTHOR]

In this note, we give the two counterexamples for two unique solvability conditions that appeared in the published paper by Wu et al. (J Optim Theory Appl 169:705–712, 2016). [ABSTRACT FROM AUTHOR]

The letter is a response to comments made on a recently published paper about thrombocytopenia in the intensive care unit (ICU). The authors acknowledge that thrombocytopenia is a complex condition with various contributing factors and that its impact on prognosis may vary between different patient populations. The study focused on defining thrombocytopenia and its association with outcomes, rather than investigating its causes or management. The authors suggest that further research is needed to explore the association between thrombocytopenia and mortality in a broader ICU population and to gather randomized data on the use of platelet transfusions in ICU patients. [Extracted from the article]

Rapidly populating renewable energy sources and storage units at the distribution system, made it crucial to monitor the system in real-time. This necessity brings new challenges and business opportunities for the distribution system operator (DSO). DSO requires situational awareness on the system via several analyses, most of which rely on correct system topology. However, switch statuses of the distribution system may not be telemetered or transferred correctly to the DSO, despite having several switching actions daily. This paper proposes a state estimation based method for distribution systems with limited number of measurements to detect and identify topology error. The method is applicable with both conventional SCADA and/or PMU measurements. Weighted Least Absolute Values (WLAV) state estimator is employed because of its robustness against inaccurate measurements or bad data. The computational performance of the proposed method is comparable with that of the WLAV state estimator, and hence applicable in practical applications. • High performance algorithm for distribution system topology error detection. • Performing in the presence of limited number of field measurements. • Reduced uncertainty using the Weighted Least Absolute Value (WLAV) state estimator. [ABSTRACT FROM AUTHOR]

• A disturbance simulation model of tooth-flexible body residual film-soil based on DEM-MBD was established. • The flow characteristics of film-soil was studied using DEM-MBD simulation methods. • A film picking test bench was established to verify the reliability of the simulation model. • The cross-sectional shape of soil was used to verify the accuracy of DEM simulation models. • The mechanical properties and tensile performance of the residual film were analyzed. The residual film in the cotton cultivation layer will seriously affect cotton cultivation, and mechanized recycling of residual film is currently the best way to solve this problem. To improve the recovery effect of the chain tooth tillage layer residual film recovery machine, a bionic elastic tooth was designed in this paper. Furthermore, DEM-MBD coupling multibody dynamics was used as the research method to study the bionic elastic tooth-residual film-soil interactive disturbance. A DEM-MBD simulation model for predicting the film lifting effect of a film lifting device has been established. And the DEM-MBD simulation model was used to optimize the design parameters of the film lifting device by studying the film lifting effect of the elastic teeth. The absolute value of the maximum curvature at the tip of the elastic tooth (A), the angle between the midline of the power wheel and the ground plane (B), and the spacing of the elastic teeth (C) were used as the influencing factors. The optimal solution parameters (A = 0.03, B = 54°, C = 83 mm) were obtained. The field test's film picking and disturbance rate was 91.27 %, the error with the simulation results (89.69 %) was 1.8 %, which verified the accuracy of the simulation results and the superiority of the optimized parameters. The recovery rates of residual film under soil compaction conditions of 600 kPa, 800 kPa, and 1000 kPa were 91.25 %, 90.94 %, and 90.89 % (Verified the strong adaptability of the device). This study can provide a theoretical research basis and test methods for the design optimization of touching parts. [ABSTRACT FROM AUTHOR]

• A composite fringe pattern based on a spatial orthogonal frequency multiplexing is meticulously crafted, incorporating ample spatial and temporal information and providing neural network with the theoretical basis for learning the required mapping correspondence. • An end-to-end network is designed to achieve pixel-wise prediction of absolute phase values, utilizing a nested strategy and the concept of centralized information interaction. • A diverse dataset comprising numerous scenes is collected, wherein high-precision ground truths are computed using standard N -step phase-shifting and multi-frequency temporal phase unwrapping methods. • A seven-map training loss calculation strategy is adopted to instruct training process. • The first qualitative experiment proves the superiority of our method over alternative four methods. The second quantitative evaluation and respectively validates its capability in high dynamic range 3D measurement and in precise 3D measurement. The pursuit of precise and efficient 3D shape measurement has long been a focal point within the fringe projection profilometry (FPP) domain. However, achieving precise 3D reconstruction for isolated objects from a single fringe image remains a challenging task in the field. In this paper, a deep learning-based frequency-multiplexing (FM) composite-fringe projection profilometry (DFCP) is proposed, where an end-to-end absolute phase retrieval network (APR-Net) is trained to directly recover the absolute phase map from a FM composite fringe pattern. The obtained absolute phase map exhibits exceptional precision and is devoid of spectrum crosstalk or leakage disturbance typically encountered in traditional FM techniques. APR-Net is intricately crafted, incorporating a nested strategy along with the concept of centralized information interaction. A diverse dataset encompassing various scenarios and free from spectrum aliasing is assembled to guide the training process. A seven-map loss calculation scheme is employed to guide the training process, of which the efficacy is proved through ablation experiments. In the first qualitative experiment, DFCP demonstrates comparable phase accuracy to ground truths with 47 fewer projected images, outperforming other three methods with mean absolute phase errors of 0.0052 rad, 0.1761 rad, 0.0169 rad, and 0.0139 rad. The second qualitative experiment and the quantitative evaluation respectively prove DFCP's capability in high dynamic range 3D measurement and in precise 3D measurement, with sphere diameter errors of 0.0780 mm and 0.0726 mm, and a spherical centroid distance error of 0.0555 mm. [ABSTRACT FROM AUTHOR]

In order to enhance the texture and particle retention capabilities of the anti-abrasive seal layer, this paper focuses on the interlocking pattern between the seal and the particles of the pavement, and for the first time considers the base pavement texture, the particle size of the seal, and the amount of seal particles as design variables. The study investigates the relationship between these factor variables and response variables such as texture loss and mass loss. An optimization of the plan design was conducted using the I-optimization method in the mixture design of Design Expert software. The study involved a long-term wear test of 20,000 wear cycles on anti-abrasive seals. The response surfaces corresponding to each response variable were calculated using RSM (response surface method), thereby providing design solutions with high wear-resistant performance. Finally, the rationality and scientific nature of the optimized solutions were verified using three-dimensional texture indices, preliminarily elucidating the texture characteristics of the high wear-resistant performance. The results indicate that combinations of 0.7 kg/m² aggregate usage, 0.8 mm-1.0 mm texture depth, 0.6 mm-1.18 mm aggregate particle size, and 0.75 kg/m² aggregate usage, 1.2 mm-1.3 mm texture depth, 0.3 mm-0.6 mm aggregate particle size experienced the least quality and TD loss. The general texture characteristics of high wear-resistant seal layers include a small Sq value (Sq less than 1.8), a moderate Ssk value (Ssk approximately 0), and a slightly higher Sku value (Sku greater than 3). However, if Ssk is not close to zero (and the absolute value of Ssk is too large), even higher Sku values can result in increased large losses. • The durability of the seal layer is enhanced by improving the interlock between particles and aggregates. • RSM is used to optimize the design of sealing parameters such as aggregate size, aggregate amount, and base texture. • The height distribution of particles is assessed through the kurtosis and skewness measurements in three-dimensional texture analysis. • Recommendations are made regarding the appropriate matching of the base texture with the particle size and quantity. [ABSTRACT FROM AUTHOR]

Many problems in scientific computing and engineering fields lead to the solution of generalized absolute value equations (GAVE). In this paper, by simultaneously splitting both coefficient matrices in the differential and non-differential parts of the GAVE, a modified Newton-based matrix splitting (MNMS) iteration method is proposed. The MNMS iteration method not only covers the well-known generalized Newton iteration method as well as the recent proposed modified Newton-based iteration method and the Newton-based matrix splitting iteration method for solving the GAVE, but also results in a series of relaxation versions that are very flexible in real applications. Convergence properties of the MNMS iteration method are studied in detail when the coefficient matrices are positive definite matrices and H + -matrices. Finally, three numerical examples are presented to show the feasibility and effectiveness of the proposed MNMS iteration method. [ABSTRACT FROM AUTHOR]

In the paper, the mechanical properties of uniaxial tensile sintered nano-silver components were investigated by molecular dynamics method, and the effects of sintering pressure and temperature on them were analyzed. The sintered body was obtained by sintering three adjacent cubes, and the sintered nano-silver component under uniaxial tension was cut from the existing sintered body. The results show that the potential energy decreases while the kinetic energy has a jump. The higher the sintering pressure, the earlier the nano-silver sintering begins. Temperature has little effect on sintering time. When sintered nano-silver components are uniaxial tensile, the greater the sintering pressure, the greater the rising absolute value of the potential energy, and the greater the yield stress. When the sintering temperature is 250 °C, the variation of potential energy is large and the yield stress is high. The paper aims to supplement and guide the mechanical properties of sintered nano-silver. • The mechanical properties of sintered nano-silver components were simulated. • Uniaxial tension rather than sintering process is analyzed. • The influence of sintering pressure and temperature on it was investigated. • The greater the sintering pressure, the greater the yield stress. • When the sintering temperature is 250 °C, the yield stress is high. [ABSTRACT FROM AUTHOR]

The current standard in China does not specify the standard test method for determining Poisson's ratio, and the Poisson's ratio used in pavement design is often roughly fixed, which can result in large errors in the calculations and analysis of road structure. In this paper, the research on different test methods for Poisson's ratio is carried out and the non-linear characteristics of tensile and compressive Poisson's ratio on pavement materials under different influencing factors are analyzed. The results indicate that the absolute value of the ratio between transverse rebound strain and longitudinal rebound strain under 50% of the maximum destructive load can objectively characterize the mechanical properties of Poisson's ratio, and it is the optimal measurement method for Poisson's ratio in asphalt pavement materials. The Poisson's ratio of two pavement materials both decreases with the increase of loading rate and gradually tends to a constant value. Cement dosage and temperature are the most significant factors affecting the tensile and compressive Poisson's ratio of cement stabilized crushed stone and asphalt mixture, respectively. Specifically, when cement dosage increases by 1%, the Poisson's ratio of cement stabilized crushed stone decreases by approximately 10%, and the temperature has a significant influence on the difference in tension and compression for Poisson's ratio of asphalt mixture (up to 40%). The asphalt content corresponding to the minimum Poisson's ratio is basically consistent with the optimal asphalt content obtained by the Marshall volume method. Based on these, a quantification value-taking model is established of the tensile and compressive Poisson's ratios of typical asphalt pavement materials varying with multiple factors. The research results can serve as a reference for the scientific value-taking of pavement structural design parameters considering the different mechanical characteristics of materials in tension and compression. • The scientific and reasonable measuring method of Poisson's ratio was established. • The quantitative model of Poisson's ratio affected by many factors was established. • The Poisson's ratio increases with loading speed and gradually tends to stabilize. • The optimum asphalt content mixture by Marshall method has minimum Poisson's ratio [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]

Precision current detection is essential in smart power switches. In this paper, a current-sensing amplifier with symmetric topology is presented, which adopts the chopping technique to improve sensing accuracy. This design offers four advantages at the same time. Firstly, the rail-to-rail complementary differential pairs are achieved to obtain a full input voltage swing, and the Class AB output stage is incorporated to increase the slew rate. Secondly, symmetric topology with the current shunt source provides moderate gain enhancement without extra power consumption and further increases the gain bandwidth product. Thirdly, the chopping technique is applied to achieve a significant reduction in the amplifier's input offset without an extra low pass filter. Fourthly, the constant G M -C biasing circuit is introduced to improve the robustness of system response and current sensing accuracy under process variations. The four advantages can be substantiated through the application of a 0.5-μm BCD technology process, with multiple simulation results, including frequency responses and current sensing accuracy in process corners and temperature variations. The mismatch Monte-Carlo and noise analyses are also conducted with the chopper on or off. Chip experimental results show that the current sensing error is within ±1.6 % from 0.01 A to 3 A load current. Furthermore, multiple tests have been conducted to determine the absolute values of the input offset voltages, ranging between 20 μV and 50 μV, which is a relatively small amount to vastly improve the sensing accuracy. [ABSTRACT FROM AUTHOR]

For layered models with a low-velocity half-space, Rayleigh waves can exhibit inversely dispersive patterns and thus are advantageous for providing useful information on the seismic properties of such structures. However, the calculation of dispersion curves usually encounters some difficulties such as root skipping or numerical instability due to the presence of leaky modes. The full-wavefield method and spectral element method can offer better solutions but at the cost of a significant computational effort. For practical applications, most researchers treat the zeros of the real part of the secular function as an approximation to the leaky modes, which may lead to relatively large errors that cannot be ignored. Instead, in this paper, we propose a simple and efficient method to approximate the leaky mode based on the local minima of the absolute value of the secular function. Compared with the dispersion curve generated from the real part of the secular function, the proposed method can provide a more accurate approximation. We further apply a new efficient Monte Carlo search technique to two synthetic datasets and a permafrost example. Results show that our forward and inverse methods are effective, efficient, and robust. Moreover, our numerical experiments indicate that the modified Thomson-Haskell method is more suitable for calculating leaky modes compared with the fast delta method and the generalized reflection/transmission method, and that the inversion results are less sensitive to the effect of the limited spread length on the measured dispersion curves. The present study emphasizes the high efficiency of the proposed method in imaging permafrost structures and foundation features of buildings or roads. • A fast solver for calculating the apparent modes due to a low-velocity half-space. • The modified Thomson-Haskell method is more suitable for calculating the leaky modes. • Application for imaging permafrost structures. [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]

Let Γ = (G , σ) be a signed graph. The spectral radius of Γ is the largest absolute value of its adjacency eigenvalues. In this paper we identify the real numbers which are limit points of spectral radii of signed graphs. This is one of the two aspects of a problem in spectral graph theory known as the Hoffman program, implemented here for signed graphs. [ABSTRACT FROM AUTHOR]