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In order to scientifically and rationally evaluate the susceptibility to landslide hazards in Tekes County, Yili State. This paper takes Tekes County in Xinjiang as an example, on the basis of a comprehensive analysis of the regional geological environment conditions and the distribution pattern and formation conditions of geological disasters, using the data of geological disaster points (landslide center points), and through the correlation matrix calculation of the evaluation factors, the nine evaluation factors with larger absolute values of correlation coefficients were determined to construct the evaluation system of the susceptibility to landslide geological hazards in Tekesi County. Combining the information quantity method and the entropy value method, using the weights determined by the entropy value method, the information quantity method is used to calculate the information quantity value of each factor within the factor, calculate the susceptibility index of landslide geological disasters within the territory of Tekes County, and then carry out the landslide susceptibility evaluation. The susceptibility of landslide disasters was evaluated by ArcGIS. The results show that the landslide disaster susceptibility level in Tekes County can be divided into four levels: high susceptibility, medium susceptibility, low susceptibility, and not susceptible, with areas of 491.3276 km2, 1181.5171 km2, 1674.7609 km2 and 5295.2976 km2 accounting for 5.68%, 13.67%, 19.38% and 61.27% of the total area of Tex County, respectively. The AUC number obtained by the success curve method (ROC) is 0.8736, reflecting the evaluation accuracy of 87.36%, indicating that the model method used in this paper is effective. The results are expected to provide practical data support for landslide disaster control in Tekes County and provide a reference for geological disaster monitoring, early warning and engineering prevention and control deployment in Yili Valley. [ABSTRACT FROM AUTHOR]

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 calculation of satellite orbit involves some very complex formula derivations and expansions, which are very difficult to manually derive and prone to errors. And the efficiency of manual derivation is not high. We can use computer algebra systems to derive complex formulas related to satellite orbits. This can avoid some of the drawbacks of manual derivation and significantly improve computational efficiency and accuracy. In the past, the relationship among three anomalies was generally represented in the form of a trigonometric series with the first eccentricity e as the parameter. In this paper, the trigonometric series with the parameter m = 1 − 1 − e 2 e is used, as determined by the Lagrange conjugate series. We can use the formula of the Lagrange conjugate series to derive the relationship between the true anomaly and elliptic anomaly. And the relationship between the elliptic anomaly and the mean anomaly is derived by using the symbolic iteration method. In this research paper, we calculated the accuracy of the trigonometric series expansion among three types of anomalies at the first eccentricity e equal to values of 0.01, 0.1, and 0.2. The calculation results indicate that the accuracy of the trigonometric series expansion with m as the parameter is better than 10−5. Moreover, in some cases, the trigonometric series expansion among the three anomalies with m as a parameter is simpler in form than the expansion expressed with parameter e. This paper also derived and calculated the symbolic expressions and extreme values of the difference among three anomalies and expressed the extreme values of the difference in the form of a power series of e. It can be seen that the extreme value increases with the increase in eccentricity e. And the absolute values of the extreme value of the difference between the elliptic anomaly and the mean anomaly, the true anomaly and the elliptic anomaly, and the true anomaly and the mean anomaly increase in this order. When the eccentricity is small, the absolute value of the extreme value of the difference between the true anomaly and the mean anomaly is about twice as large as the elliptic anomaly and the mean anomaly and the true anomaly and the mean anomaly. [ABSTRACT FROM AUTHOR]

INTRODCTION: Listening strategy analysis and assessment not only need objective and fair sound listening strategy analysis, but also need high-precision and high real-time assessment model, and even more need in-depth analysis and feature extraction of the influencing factors of listening assessment. OBJECTIVES: To address the problems of current automatic assessment methods, such as non-specific application, poor generalization, low assessment accuracy, and poor real-time performance. METHODS: This paper proposes an automatic assessment method based on a deep confidence network based on crawfish optimization algorithm. First, the multi-dimensional listening strategy evaluation system is constructed by analyzing the listening improvement strategy; then, the depth confidence network is improved by the crayfish optimization algorithm to construct the automatic evaluation model; finally, through the analysis of simulation experiments. RESLUTS: The proposed method improves the evaluation accuracy, robustness, and real-time performance. The absolute value of the relative error of the automatic evaluation value of the proposed method is controlled in the range of 0.011, and the evaluation time is less than 0.005 s. The method is based on a deep confidence network based on the crayfish optimization algorithm. CONCLUSION: The problems of non-specific application of automated assessment methods, poor generalization, low assessment accuracy, and poor real-time performance are addressed. [ABSTRACT FROM AUTHOR]

The discrete cosine transform is a commonly used technique in the field of signal processing that employs cosine basis functions for signal analysis. Traditionally, the regression coefficients of the cosine basis functions are solely based on frequency information. This paper extends the regression coefficients associated with the cosine basis functions to take into account both frequency and time information, not just frequency information alone. This modification results in an ill-posed linear system, which requires regularization to prevent overfitting. To address this, this paper uses shaping regularization, a technique used to stabilize ill-posed problems. By doing so, the absolute values of these extended coefficients, now exhibiting variations in both frequency and time domains, are defined as the time–frequency distribution of that input signal. The numerical experiments conducted to validate this approach demonstrate that the proposed method yields a commendable time–frequency resolution. Consequently, it proves valuable for interpreting seismic data, showcasing its potential for applications in this field. [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]

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]

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 order to investigate the deformation characteristics of interbedded weak expansive rocks in water immersion, the sandstone–mudstone interbedded structures were taken as the object of this study. A total of 27 sets of indoor immersion tests were designed with three influencing factors, namely, the layer thickness ratios of sandstone and mudstone (1:1, 2:1, 3:1), the occurrence of the rock layers (flat, oblique, and vertical), and the overburden loadings (0 kPa, 12.5 kPa, and 25 kPa). Tests were conducted to obtain the deformation time series data of the samples during the immersion loading process. Based on this, the influence pattern of each influencing factor on the sample deformation was analyzed individually. The results show that with the increase in overburden loading and rock inclination angle, the sample develops from expansion deformation to compression deformation. Changes in the layer thickness ratio will not change the deformation trend of the sample, and the decrease in the relative mudstone content will only reduce the absolute value of the sample's expansion and compression deformation. The deformation stability rate of the sample under load is 5~7 times that under no load. The increase in layer thickness ratio and rock inclination angle will lead to different degrees of attenuation of sample expansion force in the range of 8.91~38.68% and 51.00~58.83%, respectively. The research results of this paper can provide a meaningful reference for the design and maintenance of a high-speed railway subgrade in a weak expansive rock area with an interbedded structure. [ABSTRACT FROM AUTHOR]

In this paper, a signal model and a mathematical analysis of an efficient approach are derived to acquire the approximate magnitude of a complex signal by inducing a pre-biased or a pre-scaled factor in the design criteria. According to the deductive results, the pre-biased or pre-scaled factor can be 2∼3 dB, which is determined through its application. The numerical evaluations show that the mean square error (MSE) of the proposed efficient approach for the random signal is around −33 dB. Based on the design templates for the considered approaches, the occupied areas of the proposed type-1 and -2 approaches are merely 0.13 and 0.09 times the area of the direct-method, respectively. As a result, the proposed efficient approach is certainly a cost-efficient method for obtaining the approximate magnitude of a complex signal. [ABSTRACT FROM AUTHOR]

A double-volute centrifugal pump is a very important pump type; the internal flow field of a centrifugal pump will change drastically during the transition process of power failure, which will affect the safety and stability of the pump's operation. In this paper, the CFD numerical simulation method is used, and the UDF procedure is developed to realize the continuous update of the impeller speed at each time step. The working parameters, such as the torque and flow rate at the instantaneous moment, are obtained through the sequential iteration of each small step, and a numerical simulation of the power-off transient is carried out on a double-volute centrifugal pump; additionally, the changes in the external characteristic parameters and the internal flow field of the centrifugal pump are analyzed in detail. The results show that the double-volute centrifugal pump experienced four different modes after power failure, namely pump mode, braking mode, turbine mode, and runaway mode, and the absolute values of the runaway speed and runaway flow rate are 1.465 times and 1.21 times the initial values, respectively. Through the analysis of the flow field in different regions, the change processes of the generation, development, and disappearance of the vortex at each position of the centrifugal pump are obtained, and the change and development processes of the internal velocity gradient of the centrifugal pump are obtained. In addition, it is found that the high-speed area located in the second volute runner is larger than that of the first volute runner because the second volute runner is shorter and narrower than the first volute runner. [ABSTRACT FROM AUTHOR]

In this paper, an analytical exact form of the ramp function is presented. This seminal function constitutes a fundamental concept of the digital signal processing theory and is also involved in many other areas of applied sciences and engineering. In particular, the ramp function is performed in a simple manner as the pointwise limit of a sequence of real and continuous functions with pointwise convergence. This limit is zero for strictly negative values of the real variable x , whereas it coincides with the independent variable x for strictly positive values of the variable x . Here, one may elucidate beforehand that the pointwise limit of a sequence of continuous functions can constitute a discontinuous function, on the condition that the convergence is not uniform. The novelty of this work, when compared to other research studies concerning analytical expressions of the ramp function, is that the proposed formula is not exhibited in terms of miscellaneous special functions, e.g., gamma function, biexponential function, or any other special functions, such as error function, hyperbolic function, orthogonal polynomials, etc. Hence, this formula may be much more practical, flexible, and useful in the computational procedures, which are inserted into digital signal processing techniques and other engineering practices. [ABSTRACT FROM AUTHOR]

Vanadium redox flow batteries are promising energy storage devices and are already ahead of lead–acid batteries in terms of installed capacity in energy systems due to their long service life and possibility of recycling. One of the crucial tasks today is the development of models for assessing battery performance and its residual resource based on the battery's present state. A promising method for estimating battery capacity is based on analyzing present voltage and current values under various load conditions. This paper analyzes the discharge characteristics of a 10 kW all-vanadium redox flow battery at fixed load powers from 6 to 12 kW. A linear dependence of operating voltage and initial discharge voltage on load power is established. It is also determined that the slope of the discharge curve linear section does not increase linearly in absolute value, and the Box–Lucas model can be used to describe it. Models for predicting current VRFB capacity based on different curve fitting functions are proposed. These models can be used to roughly estimate battery capacity at different load powers. [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]

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]

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]

A porous anti-reflective coating (P-ARC) with average transmittance in the visible range of 97.9% was fabricated through the sol-gel method, followed by calcination at a relatively low temperature (220 °C) using the porogen of Laureth-5 carboxylic acid via a one-step approach. The results demonstrated the coating had an absolute value that was 7.5% higher than that of bare glass (92%). The prepared porous anti-reflective coating had a refractive index as low as 1.21. The coating remained undamaged during 3M tape stripping tests while maintaining excellent light transmittance. This work presents a film that has good thermal stability, chemical stability, and mechanical stability. [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]

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]

Codebooks with small maximum cross-correlation amplitudes are used to distinguish the signals from different users in multiple access communication systems in code division. Firstly, this paper studies the Jacobi sums over Galois rings of arbitrary characteristics and completely determines their absolute values. This extends the work by Li et al. (Sci China 56(7):1457–1465, 2013), where the Jacobi sums over some Galois rings with characteristics of a prime square were discussed. It is worth mentioning that the generalization is not trivial, as the Galois rings of arbitrary characteristics have a more complicated structure. Our deterministic construction of codebooks is based on Jacobi sums over Galois rings of arbitrary characteristics, producing asymptotically optimal codebooks for the Welch bound. Finally, compared to the literature, this article proposes for the first time design of codebooks based on Jacobi sums over Galois rings. In addition, the parameters of the presented codebooks are new. [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]

It is of great significance to explore the flow velocity characteristics of piped cars when they are started under different loads. In this paper, the flow velocity characteristics of the water flow around a piped car when it is started in the straight pipe section are studied through physical experiments. The masses of the piped cars are 1.5 kg, 1.9 kg, and 2.3 kg, respectively. The results show that, with the increase in the load of the pipeline car, the axial flow velocity in the front section increases, the absolute values of radial flow velocity and circumferential flow velocity increase, and the gradient of flow velocity increases. The positive radial flow velocity and negative circumferential flow velocity regions increase, and the distribution of positive and negative radial flow velocities and circumferential flow velocities is obvious. The gradients of axial, radial, and circumferential flow velocities in the annular section all increase, and the contour spacing becomes smaller and more densely distributed. The absolute values of the radial and circumferential flow velocities increase. The regional demarcation of axial flow velocity in the rear section is more obvious, and the average value of axial flow velocity in the high-flow-velocity area behind the vehicle increases. Additionally, the gradient of flow velocity increases. The absolute values of radial velocity and circumferential velocity increase, the gradient of velocity increases, and the velocity distribution is obviously regional. This study supplements and improves the theoretical study of a piped car when it is started and has certain reference value for the research and application of the hydraulic transport technology of the barrel-loading pipeline. [ABSTRACT FROM AUTHOR]

In this paper, we give several numerical radius inequalities for Hilbert space operators by using the Young-type inequalities and the generalization of the Buzano of the Schwarz inequality. These inequalities improve the classical numerical radius inequalities. We also give the upper bound of the numerical radius of 2x2 operator matrices. [ABSTRACT FROM AUTHOR]

Stochastic adaptive gradient decent algorithms, such as AdaGrad and Adam, are extensively used to train deep neural networks. However, randomly sampling gradient information introduces instability to the learning rates, leading to adaptive methods with poor generalization. To address this issue, the ABNGrad algorithm, which leverages the absolute value operation and the normalization technique, is proposed. More specifically, the absolute value function is first incorporated into the iteration of the second-order moment estimate to ensure that it monotonically increases. Then, the normalization technique is employed to prevent a rapid decrease in the learning rate. In particular, the techniques used in this paper can also be integrated into other existing adaptive algorithms, such as Adam, AdamW, AdaBound, and RAdam, yielding good performance. Additionally, it is shown that ABNGrad can attain the optimal regret bound for solving online convex optimization problems. Finally, many experimental results illustrate the effectiveness of ABNGrad. For a comprehensive exploration of the advantages of the proposed approach and the specifics of its detailed implementation, the readers are referred to the following https://github.com/Wenhan-Jiang/ABNGrad.git [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]

Micromixers play a crucial role as essential components in microfluidic analysis systems. This paper introduces a novel micromixer designed by harnessing electrokinetic vortices arising on the surface of a Janus droplet within a microchannel. The Janus droplet is characterized by different polarities of charges on its two sides (upstream part and downstream part). In the presence of a direct current electric field, the droplet's surface generates electroosmotic flows in opposite directions, resulting in the formation of vortices and facilitating solution mixing. Results from numerical simulations suggest that a better mixing performance of the micromixer is associated with both a higher absolute value of the zeta potential ratio between the downstream and upstream surfaces of the Janus droplet and a larger downstream surface area. Additionally, this study reveals that microchannel dimensions significantly influence the performance of the micromixer. Smaller microchannel widths and heights correspond to a larger mixing index for the micromixer. The micromixer presented in this study features a simple structure, easy fabrication, and holds promising application potential. [ABSTRACT FROM AUTHOR]

Deep learning is widely utilized to acquire predictive models for mobile crowdsensing systems (MCSs). These models significantly improve the availability and performance of MCSs in real-world scenarios. However, training these models requires substantial data resources, rendering them valuable to their owners. Numerous protection schemes have been proposed to mitigate potential economic loss arising from legal issues pertaining to model copyright. Although capable of providing copyright verification, these schemes either compromise the model utility or prove ineffective against adversarial attacks. Additionally, the privacy concern surrounding copyright verification is noteworthy, given the increasing privacy concerns among model owners. This paper introduces a privacy-preserving testing framework for copyright protection (PTFCP) comprising multiple protocols. Our protocols adhere to the two-cloud server model, where the owner and the suspect transmit their model output to non-colluding servers for evaluating model similarity through the public-key cryptosystem with distributed decryption (PCDD) and garbled circuits. Additionally, we have developed novel techniques to enable secure differentiation for absolute values. Our experiments in real-world datasets demonstrate that our protocols in the PTFCP successfully operate under numerous copyright violation scenarios, such as finetuning, pruning, and extraction. [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]

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]

The seismic stability analysis of a slope is a complex process influenced by earthquake action characteristics and soil mechanical properties. This paper presents a novel seismic slope stability analysis method using the relative residual displacement increment method in combination with the strength reduction method (SRM) and the actual deformation characteristics of the slope. By calculating the relative displacement of the key point inside the landslide mass and the reference point outside the landslide mass after each reduction, the safety factor of the slope is determined by the strength reduction factor (SRF) corresponding to the maximum absolute value of the relative residual displacement increment that appears after a continuous plastic penetration zone. The method eliminates interference caused by significant displacement fluctuations of key points under earthquake action and reduces the subjective error that can occur when manually identifying displacement mutation points. The proposed method is validated by dynamic calculations of homogeneous and layered soil slopes and compared with three other criteria: applicability, accuracy, and stability. [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]

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]

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 dynamic behaviour of different materials has been widely studied using the split Hopkinson pressure bar (SHPB) testing. The striker bar's velocity (SV) and the incident bar's impact surface are well known to have a significant impact on producing a clear signal in the compressive SHPB studies. Several times, the shape of the incident strain signal differs from an ideal state, and the reason is difficult to find. In this paper, a parametric investigation of such understudied instances is carried out utilising Abaqus software for finite element analysis (FEA). The numerically obtained incident strain pulse for a perfectly aligned SHPB setup with different SV was validated experimentally on compressive SHPB apparatus. The numerical output was found to have good agreement with experimental results. Further, plots of incident strain were evaluated numerically for Sv (10, 15, 20, 25 and 30 in m/s) which was used for polynomial fitting using MATLAB's curve fitting tool. A similar method was adopted for symmetrically plane non-parallel impact surface on the incident bar. The angles chosen for FEA calculations were 5°, 10°, 15° and 20°. Filleted impact surface with radius (r) 1.5, 3, 4.5 and 6 mm was also studied. The study of the variation of impact surface shape was done at a striker velocity of 25 m/s. It was observed from this study that when striker velocity increases, the absolute magnitude of incident strain at peak increases while rise time remained constant. In turn, when the symmetrically non-parallel plane surface angle and fillet radius grow, the absolute value of incident strain at peak almost stays the same but the rising time lengthens. This study can help understand the nature and discrepancy of the incident strain signal obtained in the compressive SHPB setup and find its root cause. [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]

Purpose: Patients with spinal metastases undergoing surgical treatment face challenges related to preoperative anemia, intraoperative blood loss, and frailty, emphasizing the significance of perioperative blood management. This retrospective analysis aimed to assess the correlation between hemoglobin-related parameters and outcomes, identifying key markers to aid in blood management. Methods: A retrospective review was performed to identify patients who underwent surgical treatment for spinal metastases. Hb-related parameters, including baseline Hb, postoperative nadir Hb, predischarge Hb, postoperative nadir Hb drift, and predischarge Hb drift (both in absolute values and percentages) were subjected to univariate and multivariate analyses. These analyses were conducted in conjunction with other established variables to identify independent markers predicting patient outcomes. The outcomes of interest were postoperative short-term (6-week) mortality, long-term (1-year) mortality, and postoperative 30-day morbidity. Results: A total of 289 patients were included. Our study demonstrated that predischarge Hb (OR 0.62, 95% CI 0.44–0.88, P = 0.007) was an independent prognostic factor of short-term mortality, while baseline Hb (OR 0.76, 95% CI 0.66–0.88, P < 0.001) was identified as an independent prognostic factor of long-term mortality. Additionally, nadir Hb drift (OR 0.82, 95% CI 0.70–0.97, P = 0.023) was found to be an independent prognostic factor for postoperative 30-day morbidity. Conclusions: This study demonstrated that predischarge Hb, baseline Hb, and nadir Hb drift are prognostic factors for outcomes. These findings provide a foundation for precise blood management strategies. It is crucial to consider Hb-related parameters appropriately, and prospective intervention studies addressing these markers should be conducted in the future. [ABSTRACT FROM AUTHOR]

The use of absolute value equations (AVEs) is widespread across a wide range of fields, including scientific computing, management science, and engineering. Our aim in this study is to introduce two new methods for solving AVEs and to explore their convergence characteristics. Furthermore, numerical experiments will be carried out to demonstrate their feasibility, robustness, and effcacy. [ABSTRACT FROM AUTHOR]

The Dunhuang murals, a significant part of Chinese heritage, have suffered deterioration primarily due to environmental and chemical factors, notably salt damage. This study proposes a sophisticated method that synergizes Fractional Order Differentiation (FOD) and Partial Least Squares Regression (PLSR) to accurately invert the phosphate content in the mural plaster of the Dunhuang paintings. The focal points of the research include: (1) To address the issue of information loss and reduced modeling precision caused by integer-order differentiation algorithms, the FOD method is employed for preprocessing spectral data. This approach ensures the fine spectral differences in the phosphate content of the mural plaster are precisely captured, (2) Utilizing PLSR, the study models the spectral bands identified at a significance level of 0.01 with measured conductivity values, thereby enabling the precise prediction of the phosphate content in the murals. The research outcomes reveal: (1) The FOD method can elucidate the nonlinear characteristics and variation patterns of the mural samples in the spectral data. As the order increases from zero to two, the number of spectral bands meeting the 0.01 significance test initially decreases and then increases. The highest absolute value of the positive correlation coefficient is observed at the 1.9 order, corresponding to the 2077 nm band, (2) For predicting the phosphate content in the murals, the model at the 1.9 order is most suitable for inversion. This model, after cross-validation, achieves a maximum R2 value of 0.861. This study created an efficient FOD-based model for estimating phosphate in mural plaster. [ABSTRACT FROM AUTHOR]

Advanced optical neuromonitoring of cerebral hemodynamics with hybrid diffuse optical spectroscopy (DOS) and diffuse correlation spectroscopy (DCS) methods holds promise for non-invasive characterization of brain health in critically ill patients. However, the methods' fiber-coupled patient interfaces (probes) are challenging to apply in emergent clinical scenarios that require rapid and reproducible attachment to the head. To address this challenge, we developed a novel chassis-based optical probe design for DOS/DCS measurements and validated its measurement accuracy and reproducibility against conventional, manually held measurements of cerebral hemodynamics in pediatric swine (n = 20). The chassis-based probe design comprises a detachable fiber housing which snaps into a 3D-printed, circumferential chassis piece that is secured to the skin. To validate its reproducibility, eight measurement repetitions of cerebral tissue blood flow index (BFI), oxygen saturation (StO2), and oxy-, deoxy- and total hemoglobin concentration were acquired at the same demarcated measurement location for each pig. The probe was detached after each measurement. Of the eight measurements, four were acquired by placing the probe into a secured chassis, and four were visually aligned and manually held. We compared the absolute value and intra-subject coefficient of variation (CV) of chassis versus manual measurements. No significant differences were observed in either absolute value or CV between chassis and manual measurements (p > 0.05). However, the CV for BFI (mean ± SD: manual, 19.5% ± 9.6; chassis, 19.0% ± 10.8) was significantly higher than StO2 (manual, 5.8% ± 6.7; chassis, 6.6% ± 7.1) regardless of measurement methodology (p<0.001). The chassis-based DOS/DCS probe design facilitated rapid probe attachment/re-attachment and demonstrated comparable accuracy and reproducibility to conventional, manual alignment. In the future, this design may be adapted for clinical applications to allow for non-invasive monitoring of cerebral health during pediatric critical care. [ABSTRACT FROM AUTHOR]

The aim of this study was to confirm if predictive regression algorithms can provide reliable results in missing geophysical logging data in the western and eastern parts of the Drava Super Basin, especially Gola Field, and to apply unsupervised machine learning methods for a better understanding of lithological subsurface relations. Numerous regression models have been used for the estimation of prediction accuracy, along with some clustering algorithms to support the estimation of lithology distribution estimations in well log datasets, consisting of 20 wells in total. Tree-based algorithms and the boosting algorithm have been optimized and proven valuable in predicting well log data when they are not measured or are unavailable at all depth intervals. For blind datasets, predictions become much less reliable. For this purpose, neural networks with at least one Long Short-Term Memory (LSTM) layer have significantly improved the accuracy and reliability of predictions, not in terms of absolute values but in the aspect of the trends in values that change with the depth and other well features, as well as in terms of the magnitudes. Trendlines can further be used for pattern recognition or as a newly engineered feature. Unsupervised learning has confirmed reliability in lithology recognition on validation sets and has proven to be a great asset in distinguishing variabilities in the petrophysical properties of sediments. [ABSTRACT FROM AUTHOR]

We propose the "Marshall–Olkin Bivariate Weibull Model with Modified Singularity MOBW- μ ", which focuses on bivariate distributions essential for reliability and survival analyses. Distributions such as the Marshall–Olkin bivariate exponential (MOBE) and the Marshall–Olkin bivariate Weibull (MOBW) are discussed. The MOBW- μ model is introduced, which incorporates a lag parameter μ in the singular part, and probabilistic properties such as the joint survival function, marginal density functions, and the bivariate hazard rate function are explored. In addition, aspects such as the correlation structure and survival copulation are addressed and we show that the correlation of the MOBW- μ is always lower than that of its copula, regardless of the parameters. The latter result implies that the MOBW- μ does not have the Lancaster's phenomenon that explains that any nonlinear transformation of variables decreases the correlation in absolute value. The article concludes by presenting a robust theoretical framework applicable to various disciplines. [ABSTRACT FROM AUTHOR]

The purpose of this study was to examine the validity of two wearable smartwatches (the Apple Watch 6 (AW) and the Galaxy Watch 4 (GW)) and smartphone applications (Apple Health for iPhone mobiles and Samsung Health for Android mobiles) for estimating step counts in daily life. A total of 104 healthy adults (36 AW, 25 GW, and 43 smartphone application users) were engaged in daily activities for 24 h while wearing an ActivPAL accelerometer on the thigh and a smartwatch on the wrist. The validities of the smartwatch and smartphone estimates of step counts were evaluated relative to criterion values obtained from an ActivPAL accelerometer. The strongest relationship between the ActivPAL accelerometer and the devices was found for the AW (r = 0.99, p < 0.001), followed by the GW (r = 0.82, p < 0.001), and the smartphone applications (r = 0.93, p < 0.001). For overall group comparisons, the MAPE (Mean Absolute Percentage Error) values (computed as the average absolute value of the group-level errors) were 6.4%, 10.5%, and 29.6% for the AW, GW, and smartphone applications, respectively. The results of the present study indicate that the AW and GW showed strong validity in measuring steps, while the smartphone applications did not provide reliable step counts in free-living conditions. [ABSTRACT FROM AUTHOR]

Spray droplet diameters play a key role in the field of liquid plant protection product (PPP) application technology. However, the availability of various measurement techniques, each with its unique operating principles for evaluating droplet size spectra, can lead to different interpretations of spray characteristics. Therefore, in this study, four measurement techniques—Liquid Immersion (LI), Laser Diffraction (LD), Phase Doppler Particle Analysis (PDPA), and Shadowgraphy (SG)—were utilized to evaluate the droplet size distribution of agricultural spray nozzles. Additionally, PDPA and SG were used to assess the average velocity of spray droplets. Experiments were conducted in three different laboratories with the main aim of comparing results obtained with various types of equipment utilized under ordinary practical conditions. Spraying tests were carried out using three flat fan nozzles and an air-induction flat fan nozzle. As a general trend, the lowest values for droplet diameters were measured using the Laser Diffraction technique, followed by Shadowgraphy. The PDPA technique provided the highest values for mean diameters (D10, D20, and D30) and the numeric median diameter (Dn0.5), whereas the Liquid Immersion method yielded the highest values for the Sauter mean diameter (D32) and volumetric diameters (Dv0.1, Dv0.5, and Dv0.9). Importantly, all measurement techniques were able to discriminate the four nozzles based on their Dv0.5 diameter. Average droplet velocities showed a similar pattern across the four nozzles with the PDPA and the SG measurement techniques. The differences in diameter values observed with the four measurement techniques underline the necessity of always including reference nozzles in spray quality assessments to base classifications on relative rather than absolute values. [ABSTRACT FROM AUTHOR]

In this study, a specific identity was derived for functions that possess two continuous derivatives. Through the utilization of this identity and Riemann-Liouville fractional integrals, several fractional Milne-type inequalities were established for functions whose second derivatives inside the absolute value are convex. Additionally, an example and a graphical representation are included to clarify the core findings of our research. [ABSTRACT FROM AUTHOR]

We study the problem of recovering a signal from magnitudes of its wavelet frame coefficients when the analyzing wavelet is real-valued. We show that every real-valued signal can be uniquely recovered, up to global sign, from its multiwavelet frame coefficients \[ \{\lvert \mathcal {W}_{\phi _i} f(\alpha ^{m}\beta n,\alpha ^{m}) \rvert : i\in \{1,2,3\}, m,n\in \mathbb {Z}\} \] for every \alpha >1,\beta >0 with \beta \ln (\alpha)\leq 4\pi /(1+4p), p>0, when the three wavelets \phi _i are suitable linear combinations of the Poisson wavelet P_p of order p and its Hilbert transform \mathscr {H}P_p. For complex-valued signals we find that this is not possible for any choice of the parameters \alpha >1,\beta >0, and for any window. In contrast to the existing literature on wavelet sign retrieval, our uniqueness results do not require any bandlimiting constraints or other a priori knowledge on the real-valued signals to guarantee their unique recovery from the absolute values of their wavelet coefficients. [ABSTRACT FROM AUTHOR]

In today's information era, collaborative filtering algorithms are widely used and their distinct knowledge discovery techniques can effectively address numerous issues. However, conventional collaborative filtering algorithms encounter cold-start and data sparsity issues, which restrict their performance and accuracy. The study selected the multi-feature method to improve the traditional collaborative filtering algorithm, and introduced gray correlation calculation and Bayesian probability for user preference analysis. A learning resource recommendation model based on collaborative filtering was developed by comparing the target user's characteristics with those of other users, calculating their similarity, selecting users with high similarity to the target user and forming a neighbor set. Using Bayesian probability and grey correlation to analyze user preferences in library systems can be well applied in book classification and recommendation problems in university libraries. The computing layer, which includes the collaborative filtering calculation stage and the group recommendation calculation stage, is the model's main functional component. The smaller the value of mean absolute error, the higher the prediction accuracy of the model. The mean absolute error value of the multi-feature collaborative filtering algorithm was inferior to the traditional collaborative filtering algorithm, indicating that the classification accuracy of the former is higher than that of the latter. When the training set to test set ratio steadily became bigger, the mean absolute error value reached the lowest and smoothest point at 80%. In dataset A, the minimum mean absolute error values of multi-feature collaborative filtering and collaborative filtering were 0.765 and 0.809. Compared with traditional filtering algorithms, the mean absolute error value has decreased by 0.044. In dataset B, the mean absolute error values of multi-feature collaborative filtering and collaborative filtering were 0.796 and 0.836. Compared with traditional filtering algorithms, the mean absolute error value has decreased by 0.040. In dataset C, the minimum mean absolute error values of multi-feature collaborative filtering and collaborative filtering were 0.815 and 0.848. Compared with traditional filtering algorithms, the mean absolute error value has decreased by 0.033. When the accuracy was the highest; the mean absolute error value was the smallest at the grey correlation, which means that the technique improves the reliability of the recommendations compared with other methods. This means that the method has a positive impact on the accuracy of the recommendations compared to other methods. Grey correlation degree can comprehensively consider the interrelationships between multiple factors, handle uncertain and incomplete information, and explore potential user needs and behavior patterns. The implementation of the grey correlation degree has transformed the collaborative filtering algorithm into a group filtering algorithm, thereby enhancing its precision. The research on book classification and recommendation in university libraries, which enhances the group filtering algorithm, can address a range of issues such as improving classification accuracy, augmenting recommendation diversity, enhancing library management efficiency among others. This, in turn, enables more precise book recommendations to users. [ABSTRACT FROM AUTHOR]