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Least Squares Regression (LSR) is a powerful machine learning method for image classification and feature selection. In this study, a framework approach is introduced for the multi-classification problem based on the $L_{2,p}$ -norm, utilizing more general loss functions and regularization terms, which is a robust sparse kernel-free quadratic surface least squares regression (RSQSLSR). The nonlinear relationship between features is addressed using a quadratic kernel-free technique combined with $\epsilon $ -dragging technology and manifold regularization to learn soft labels, which can achieve the goal of feature selection and classification, simultaneously. This model utilizes K quadratic surfaces mapping samples from the input space to the label space, preserving the local structure of the samples. To enhance practical applications, such as image classification, a simplified version of the method is proposed. An iterative algorithm for RSQSLSR is designed and its convergence is proved theoretically. The salient features and theoretical analysis of our proposed method are comprehensively discussed in this paper. Extensive experiments on synthetic and real datasets validate the effectiveness of our method, surpassing other state-of-the-art methods in terms of classification accuracy and feature selection performance.

Abstract $$\nu$$ -one-class support vector classification ( $$\nu$$ -OCSVC) has garnered significant attention for its remarkable performance in handling single-class classification and anomaly detection. Nonetheless, the model does not yield a unique decision boundary, and potentially compromises learning performance when the training data is contaminated by some outliers or mislabeled observations. This paper presents a novel C-parameter version of bounded one-class support vector classification (C-BOCSVC) to determine a unique decision boundary. The distance from the origin to decision boundary is the geometrical margin in the space $$\hat{\mathcal {H}}$$ (higher 1-dimension than feature space), and its maximization corresponds to the structural risk minimization (SRM) principle inscribed by an $$L_2$$ -norm regularization term both on the normal direction and bias of the decision boundary. To enhance the anti-noise and anti-outlier abilities of C-BOCSVC, the alternative robust version (C-RBOCSVC) is also developed, which incorporates the k-nearest neighbor relative density to assign varying weights to observations and mitigate the negative impact of outliers on the optimal decision boundary. The theoretical properties of the proposed method are successively derived, including the relationship between the solutions to the primal and dual problems, the connections between our C-BOCSVC and $$\nu$$ -OCSVC and the computational complexity. Experimental results over massive datasets demonstrate the feasibility and reliability of our C-BOCSVC, and highlight the superior performance of C-RBOCSVC compared to other state-of-the-art one-class classifiers when data is contaminated. The demo code of this work is publicly available at https://github.com/Zhangmath1122/C-RBOCSVC .

This paper introduces a novel phenolic resin-coated silica stationary phase grafted from the surface of amino-functionalized porous silica microspheres through copolymerization of 1,5-dihydroxynaphthalene and 1,3,5-trioxane in the dispersed state, followed by low-temperature calcination at 200 °C. The new material was identified by scanning electron microscopy, elemental analysis, thermogravimetric analysis and Fourier-transform infrared spectroscopy. The new column has the capability to separate different types of compounds. When utilizing hydrophilic interaction liquid chromatography, sulfonamide drugs and nucleosides/nucleobases could be separated with good resolution even if there were no buffer salts in the eluent. In reversed-phase liquid chromatography, the column indicated satisfactory separation abilities for positional isomers, alkylbenzenes as well as polycyclic aromatic hydrocarbons (PAHs). The selectivity and retention of the new column for PAHs were higher than those for alkylbenzene, which may be affected by the π–π forces between the PAH analytes and naphthalene ring from the surface of the silica. Depending on the retention mode, the elution order can be reversed using this column. Thus, the stationary phase was intended as a novel mixed-mode column. Meanwhile, the retention and selectivity can be adjusted very flexibly by changing the chromatographic conditions.

Chiral glutamide-derived lipids form self-assembled fibrous molecular gels that can be used as HPLC organic phases. In this study, HPLC separation efficiency was improved through the addition of branched amphiphilic glutamide lipids to the side chains of a terminally immobilized flexible polymer backbone. Poly(4-vinylpyridine) with a trimethoxysilyl group at one end was grafted onto the surface of porous silica particles (Sil−VP15, polymerization degree = 15), and the pyridyl side chains were quaternized with a glutamide lipid having a bromide group (BrG). Elemental analysis indicated that the total amount of the organic phase of the prepared stationary phase (Sil−VPG15) was 38.0 wt%, and the quaternization degree of the pyridyl groups was determined to be 32.5%. Differential scanning calorimetric analysis of a methanol suspension of Sil−VPG15 indicated that the G moieties formed a highly ordered structure below the phase transition temperature even on the silica surface, and the ordered G moieties exhibited a gel-to-liquid crystalline phase transition. Compared with a commercially available octadecylated silica column, the Sil−VPG15 stationary phase showed high selectivity toward polycyclic aromatic hydrocarbons, and particularly excellent separations were obtained for geometrical and positional isomers. Sil−VPG15 also showed highly selective separation for phenol derivatives, and bio-related molecules containing phenolic groups such as steroids were successfully separated. These separation abilities are probably due to multiple interactions between the elutes and the highly ordered functional groups, such as the pyridinium and amide groups, on the highly ordered molecular gel having self-assembling G moieties.

Fe-Cr-C-B wear-resistant steels are widely used as wear-resistant alloys in harsh environments. The M3X (M = Fe, Cr; X = C, B) cementite-type material is a commonly used strengthening phase in these alloys. This study investigated the mechanical properties of cementite (Fe, Cr)3(C, B) using the first-principle density functional theory. We constructed crystal structures of (Fe, Cr)3(C, B) with different concentrations of Cr and B. The bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and hardness of the material were calculated, and a comprehensive mechanical property database based on CALPHAD modeling of the full composition was established. The optimal concentrations of the (Fe, Cr)3(C, B) phase were systematically evaluated across its entire composition range. The material exhibited the highest hardness, shear modulus, and Young’s modulus at Cr and B concentrations in the range of 70–95 at% and 40 at%, respectively, rendering it difficult to compress and relatively poor in machinability. When the B content exceeded 90 at%, and the Cr content was zero, the shear modulus and hardness were low, resulting in poor resistance to deformation, reduced stiffness, and ease of plastic processing. This study provides an effective alloying strategy for balancing the brittleness and toughness of (Fe, Cr)3(C, B) phases.

Along with the development of the world of science, it is getting faster ICT in education. The objectives to be achieved in this study are to find out how the student's response to the utilization of the Hawgent Dynamic Mathematics application on the material of the curved side of the learning room in the teaching and learning process took place in the classroom. The main object in this study was the 9th-grade junior high school student who was 96 students at Gusui Middle School in Guangxi Zhuang Autonomous Region. Data collection in this study was a questionnaire containing indicators that have to measure the student's response to the use of learning media using Hawgent Dynamic Mathematics and the primary tool processing research data, namely Ms. Excel and SPSS statistical. The study results were related to the student's response that students agreed, were happy, and were assisted by the Hawgent Dynamic application. The perception or student response results concluded that learning using Hawgent Dynamic software could help in mathematics. It was easier and satisfying for students to understand the material about building a curved side space. However, the use of Hawgent software was only limited to trials, so it was recommended that it be able to use and utilize this software for other discussions on mathematics lessons.

Understanding the concept is one aspect that is needed and must be owned by students in learning mathematics. This research aims to make learning media assisted by hawgent dynamic mathematics software on understanding the absolute value in grade 10 Senior high school to help teachers explain the concepts and assist students in finding and understanding the basic concepts of absolute value topic. The development model used in this research is ADDIE development model. ADDIE is an abridgment of Analyze, Design, Develop and Evaluation. Researchers the learning media Hawgent can help students to understand and find the concept of absolute value. Based on several aspects, clearly and attractively with an average of 78.9% in the excellent category. It is concluded that the development of learning media Hawgent dynamic mathematics software can be used on the subject of understanding the concept of absolute value and with the help of this software it can help teachers explain the concept of absolute value and the students are also very interested in this ICT-based learning media. This conclusion is related to the validation results of media experts and material experts, where the validation results from media experts on the use of learning media are in good categories.