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Nonlinear phenomena occur in diverse fields such as science, engineering and business. Research within computational science is continuously advancing, characterized by the development of new numerical techniques or the refinement of existing ones. However, these numerical techniques may be computationally expensive, while demonstrating superior convergence rate. By considering these demanding features, this paper aimed to devise new fourth- and eight-order iterative methods for root finding. This will be accomplished by taking the linear combination of Newton–Steffensen's method and Yu and Xu's method to obtain fourth-order method. We employed weight function approach to achieve eighth-order method. The proposed methods supports the Kung and Traub conjecture and hence are optimal by utilizing three function evaluations for fourth-order method and four functional evaluations for eighth-order method per cycle. The convergence criteria of the proposed schemes are thoroughly covered in the two primary theorems. To demonstrate the usefulness, validity and accuracy, we explore some real-world applications in civil and chemical engineering fields. In terms of the number of iterations, absolute residual errors, errors in consecutive iterations, the preassigned tolerance, convergence speed, percentage of convergent points, mean value of iterations for methods to converge and CPU time (sec), the numerical results obtained from the test examples illustrates that our proposed methods perform better than other methods of same order. Finally, several forms of complex functions are taken into consideration under basins of attraction in order to observe the overall fractal behavior of the proposed technique and some existing methods. [ABSTRACT FROM AUTHOR]

Given a doubling weight ω on the unit disk D , let Aωp be the space of all the holomorphic functions f, where ∥ f ∥ A p := (∫ D ∣ f (z) ∣ p (z) d A (z)) 1 / p < ∞. We completely characterize the topological connectedness of the set of composition operators on Aωp. As an application, we construct an interesting example which reveals that two composition operators on Aαp in the same path component may fail to have a compact difference and give a negative answer to the Shapiro-Sundberg question in the (standard) weighted Bergman space. In addition, we completely describe the central compactness of any finite linear combinations of composition operators on Aωp in three terms: a Julia-Carathéodory-type function-theoretic characterization, a power-type characterization, and a Carleson-type measure-theoretic characterization. [ABSTRACT FROM AUTHOR]

With the development of cloud computing and internet of things technology, verifiable computing has been widely used as a new computing technology. While verifiable computing brings convenience to users, there are also security challenges: data privacy, verifiability of results, and efficiency. At present, the sparse matrix multiplication encryption method is used to protect the privacy of data in the matrix multiplication verifiable calculation scheme. After analyzing the sparse matrix encryption algorithm, it is found that there are two challenges. The one is that the row or column common factor leaks the row or column data of the original matrix. The other is that the zero element leaks the statistic information of the zero element of the original matrix. Meanwhile,the existing scheme is also not ideal for the verification efficiency of cloud server computing results.Aiming at the challenge of data privacy protection, the designed batch matrix multiplication verifiable computation scheme uses triple perturbation encryption algorithm to achieve stronger privacy protection without increasing the computational complexity of encryption and decryption. Specifically, a special upper or lower triangular sparse matrix is constructed to add double perturbation (multiplicative perturbation and additive perturbation) to protect row or column data, and a special additive sparse matrix is constructed to add a single perturbation (additive perturbation) to protect zero element information. Aiming at the challenge of verification efficiency of cloud server computing results, the scheme uses matrix linear combination technology to realize batch verification of calculation results. The verification efficiency is increased by about 50 times and increases with the increase of the number of matrices. Performance analysis shows that this scheme does not increase the client encryption and decryption overhead and improves the efficiency of result verification.

With the development of cloud computing and internet of things technology, verifiable computing has been widely used as a new computing technology. While verifiable computing brings convenience to users, there are also security challenges: data privacy, verifiability of results, and efficiency. At present, the sparse matrix multiplication encryption method is used to protect the privacy of data in the matrix multiplication verifiable calculation scheme. After analyzing the sparse matrix encryption algorithm, it is found that there are two challenges. The one is that the row or column common factor leaks the row or column data of the original matrix. The other is that the zero element leaks the statistic information of the zero element of the original matrix. Meanwhile,the existing scheme is also not ideal for the verification efficiency of cloud server computing results.Aiming at the challenge of data privacy protection, the designed batch matrix multiplication verifiable computation scheme uses triple perturbation encryption algorithm to achieve stronger privacy protection without increasing the computational complexity of encryption and decryption. Specifically, a special upper or lower triangular sparse matrix is constructed to add double perturbation (multiplicative perturbation and additive perturbation) to protect row or column data, and a special additive sparse matrix is constructed to add a single perturbation (additive perturbation) to protect zero element information. Aiming at the challenge of verification efficiency of cloud server computing results, the scheme uses matrix linear combination technology to realize batch verification of calculation results. The verification efficiency is increased by about 50 times and increases with the increase of the number of matrices. Performance analysis shows that this scheme does not increase the client encryption and decryption overhead and improves the efficiency of result verification.

It is shown that the expression as A2=αA+βP{A}^{2}=\alpha A+\beta P for generalized quadratic matrices is not unique by numerical examples. Then it is proven that the uniqueness of expression for generalized quadratic matrices is concerned not only with the properties of AA but also with the rank of PP. Furthermore, the sufficient and necessary conditions for the uniqueness of generalized quadratic matrices’expression are obtained. Finally, some related discussions about generalized quadratic matrices are also given.

Copyright of Chinese Journal of Network & Information Security is the property of Beijing Xintong Media Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In the article taking suitable harmonic mappings f 1 , f 2 and f 3 , f 4 such that their convolution F 1 = f 1 ∗ f 2 and F 2 = f 3 ∗ f 4 be also harmonic univalent mappings then we construct a new harmonic mapping F 3 = t F 1 + (1 - t) F 2 = t (h 1 ∗ h 2) + (1 - t) (h 3 ∗ h 4) + t ( g 1 ∗ g 2 ¯) + (1 - t) ( g 3 ∗ g 4 ¯) = H 3 + G 3 ¯ and prove that under certain condition F 3 = t F 1 + (1 - t) F 2 , t ∈ 0 , 1 is univalent and convex in one direction. [ABSTRACT FROM AUTHOR]

It is given a characterization of being a matrix Q g (a 3 , b 3) (k) of linear combination of a matrix Q g (a 1 , b 1) (n) and a matrix Q g (a 2 , b 2) (m) , where a i , b i ∈ R ∗ , i = 1 , 2 , 3 , m , n , k ∈ Z , and Q g (a , b) (l) denotes an (a, b)-generalized Fibonacci Q-matrix with l ∈ Z . In addition, some examples are presented illustrating the main result. Finally, some applications of the main result obtained are given. [ABSTRACT FROM AUTHOR]

It is well-known that the research of linear combination of composition operators has become a topic of increasing interest. Recently, Choe, Koo and Wang proved that the compactness of combinations composition operators induced by the symbols satisfying the condition (CNC) implies that each difference is compact on the weighted Bergman space. Motivated by that work, in this paper, we discuss which difference is compact on the weighted Bergman space when the coefficients do not satisfy the condition (CNC). [ABSTRACT FROM AUTHOR]

To obtain reliable channel state information (CSI) in a full dimensional large-scale multiple input multiple output (MIMO) downlink system, a precoding design method based on two-stage sequential codebook was proposed. In this method, the precoded codeword was composed of internal code and external code. The internal code was used to approximate each radiation path, and the external code was used to make the best linear combination of the selected internal code. This method can not only accurately approximate the real channel, but also reduce the feedback overhead in the system. In addition, based on the assumed channel model, a scheme to determine the feedback overhead and a method to construct the rotated codebook were proposed. The accuracy and effectiveness of the design method were verified by experimental simulation. [ABSTRACT FROM AUTHOR]

The scale yield function has a great influence on the study of cross-border logistics platform building and rural agricultural products e-commerce selling. This paper analyzes the main factors affecting the effect of cross-border logistics platform construction through factor analysis. Among them, platform content construction, platform service level, platform user management, platform supply chain construction, and platform development potential are the most important factors of cross-border logistics platform construction. The linear combination is used to construct a cross-border logistics platform integrating content, service, management, supply, and development. The regression method is applied to calculate the factor scores, and the assumed return to scale is applied to calculate the relevant data after the construction of the cross-border logistics platform. Seeking the maximum scale return rate is greater than 80%, the return is higher. The experiment proves that the construction of a cross-border logistics platform can expand the rural agricultural products e-commerce sales market from mainly China to parallel sales in China and European and American countries, etc., and improve the scale gain. Relying on the construction of a cross-border logistics platform, the total sales of rural agricultural products and e-commerce sales in foreign countries increased by more than 10 million, and the revenue was higher than 4.5 times of previous years. Thus, the construction of a cross-border logistics platform is conducive to expanding the market of rural agricultural products e-commerce sales and increasing rural agricultural products e-commerce sales.

Principal component analysis is usually a linear combination of all variables, which is very detrimental to the interpretation of the results. Therefore, this paper proposes sparse principal component analysis for analyzing the impact of the Xinguang epidemic on tourism, which can find linear combinations containing only a few input variables, effectively filter out sparse principal components, and achieve the purpose of explaining a high percentage of changes with sparse linear combinations. By observing the trend of accommodation, food and beverage, and tourism turnover data in Guizhou Qiannan region before and after the epidemic from 2015 to 2021, it was confirmed that the data of 2020 was mainly used as the dataset. For sparse principal component analysis, four data sets were selected, each with 14 indicators and 32 samples. The findings revealed that the tourism topics of interest during the epidemic were more spread out and had a lower concentration of links among each other. In the accommodation industry, the 1st principal component is turnover, which has a common factor variance of 0.995 and an eigenvalue of 13.408. In the catering industry, the 2 principal components can be interpreted as the major category of operating costs and the major category of turnover, with component matrix values of (0.997, -0.073) and (0.996, 0.064), respectively.

The dimensional statistics approach of principal component analysis is utilized in this paper to transform a set of variable observations using orthogonal transformation to convert the data to a new coordinate. The original observations data are summed linearly by selecting appropriate values through cross-validation and calculating the spatial data of works with literary elements. Determine a sufficient number of basis functions selected mainly based on the fluctuation of time variables. The number of students who believe that reading classic works enhances scientific literacy was 92.56%, with the highest contribution of linguistic and literary elements found to be 92.56%. The uniqueness and richness of children's literature can enhance character-building and overall core literacy of students, as indicated by this.

An alternative new method for solving an epistemic uncertainty such as fuzzy-based linear programming problem with equality constraints has been proposed here. In this approach, the optimal solution of the considered fuzzy problem has been achieved by solving a related crisp problem. Moreover, the objective function of the crisp problem has been obtained by taking the linear combination of the fuzzified version of the original uncertain objective function. The coefficients of the linear combination are considered as strictly positive real numbers. And the constraints of the crisp problem are obtained equivalently from the equality constraints of the fuzzy problem. Triangular fuzzy numbers are considered for this analysis. Comparisons have been made with the results of Kumar et al. (Appl Math Model 35:817–823, 2011), Najafi and Edalatpanah (Appl Math Model 37:7865–7867, 2013), Ezzati et al. (Appl Math Model 39:3183-3193, 2015) and Ghoushchi et al. (Mathematics 9:2937, 2021. https://doi.org/10.3390/math9222937). [ABSTRACT FROM AUTHOR]

This paper focuses on the quasi-orthogonality between sequences of d -orthogonal polynomials and their characterization in terms of linear combinations as well as the left product of vector of linear forms by matrix polynomial. Therefore, structure relations for Hahn-classical d -orthogonal polynomials are provided. [ABSTRACT FROM AUTHOR]

In the present note we construct a linear combination $ L_{kn} $ of two Bernstein polynomials $ B_n $ and $ B_{kn} $, for natural number $ k\geq 2 $. The new operator $ L_{kn} $ reproduces all algebraic polynomials of degree $ \leq 2 $. A direct pointwise estimate is proved which shows that the rate of approximation of $ f\in C[0, 1] $ such that $ \|\varphi f^{(3)}\|_{C[0, 1]}<\infty $ by $ L_{kn} $ is $ O\left(\frac{1}{n^{\frac{5}{2}}} \right) $, when $ x $ is close to the ends of the interval $ [0, 1] $. [ABSTRACT FROM AUTHOR]

Sparse multiobjective optimization problems are common in practical applications. Such problems are characterized by large-scale decision variables and sparse optimal solutions. General large-scale multiobjective optimization problems (LSMOPs) have been extensively studied for many years. They can be well solved by many excellent custom algorithms. However, when these algorithms are used to deal with sparse LSMOPs, they often encounter difficulties because the sparse nature of the problem is not considered. Therefore, aiming at sparse LSMOPs, an algorithm based on multiple sparse detection is proposed in this paper. The algorithm applies an adaptive sparse genetic operator that can generate sparse solutions by detecting the sparsity of individuals. To improve the deficiency of sparse detection caused by local detection, an enhanced sparse detection (ESD) strategy is proposed in this paper. The strategy uses binary coefficient vectors to integrate the masks of nondominated solutions. Essentially, the mask is globally and deeply optimized by coefficient vectors to enhance the sparsity of the solutions. In addition, the algorithm adopts an improved weighted optimization strategy to fully optimize the key nonzero variables to balance exploration and optimization. Finally, the proposed algorithm is named MOEA-ESD and is compared to the current state-of-the-art algorithm to verify its effectiveness. [ABSTRACT FROM AUTHOR]

Abstract Sparse multiobjective optimization problems are common in practical applications. Such problems are characterized by large-scale decision variables and sparse optimal solutions. General large-scale multiobjective optimization problems (LSMOPs) have been extensively studied for many years. They can be well solved by many excellent custom algorithms. However, when these algorithms are used to deal with sparse LSMOPs, they often encounter difficulties because the sparse nature of the problem is not considered. Therefore, aiming at sparse LSMOPs, an algorithm based on multiple sparse detection is proposed in this paper. The algorithm applies an adaptive sparse genetic operator that can generate sparse solutions by detecting the sparsity of individuals. To improve the deficiency of sparse detection caused by local detection, an enhanced sparse detection (ESD) strategy is proposed in this paper. The strategy uses binary coefficient vectors to integrate the masks of nondominated solutions. Essentially, the mask is globally and deeply optimized by coefficient vectors to enhance the sparsity of the solutions. In addition, the algorithm adopts an improved weighted optimization strategy to fully optimize the key nonzero variables to balance exploration and optimization. Finally, the proposed algorithm is named MOEA-ESD and is compared to the current state-of-the-art algorithm to verify its effectiveness.

Although linearly combining multiple variables can provide adequate diagnostic performance, certain algorithms have the limitation of being computationally demanding when the number of variables is sufficiently high. Liu et al. proposed the min–max approach that linearly combines the minimum and maximum values of biomarkers, which is computationally tractable and has been shown to be optimal in certain scenarios. We developed the Min–Max–Median/IQR algorithm under Youden index optimisation which, although more computationally intensive, is still approachable and includes more information. The aim of this work is to compare the performance of these algorithms with well-known Machine Learning algorithms, namely logistic regression and XGBoost, which have proven to be efficient in various fields of applications, particularly in the health sector. This comparison is performed on a wide range of different scenarios of simulated symmetric or asymmetric data, as well as on real clinical diagnosis data sets. The results provide useful information for binary classification problems of better algorithms in terms of performance depending on the scenario. [ABSTRACT FROM AUTHOR]

We discuss a non-routine technique to solve some classes of integrals, which could enrich the syllabus of a first-year undergraduate calculus course. We begin with the class from which the inspiration originates: integrals of quotients of linear combinations of sines and cosines. Subsequently, we discuss a generalization, dealing with quotients formed by a linear combination of two arbitrary functions on the denominator and a linear combination of their derivatives on the numerator. Finally, for a variation, we consider integrals of quotients of linear combinations of three functions: exponentials, sines, and cosines. [ABSTRACT FROM AUTHOR]

Aim: Rapid intervention is required in patients with non-traumatic acute abdominal pain. It is very important to distinguish between surgical and non-surgical pathologies during this intervention. This study aimed to increase the diagnostic accuracy by combining the leukocyte count and D-dimer levels used in this evaluation with linear combination methods. Materials and Methods: Logistic regression, scoring, min-max, minimax, Su & Liu, Pepe & Thompson, Pepe, Cai & Langton, and Todor & Saplacan methods were used as linear combination methods. The data set was divided into 70% training set and 30% test set. Parameter optimization was performed on the training data by 5 fold cross-validation method using 10 repeats. The area under the ROC curve, sensitivity, selectivity, accuracy, positive and negative predictive value, and positive and negative likelihood ratio statistics were used in the performance evaluation. Results: The area under the ROC curve statistic for D-dimer level and log-transformed leukocyte count variable were obtained as 0.71 and 0.70, respectively. The accuracy rate was 0.69 for the D-dimer level and 0.73 for log-transformed leukocyte count. For the linear combination methods, the area under the ROC curve was between 0.77 and 0.81, and the accuracy statistics were between 0.72 and 0.79. The best performance was obtained with the min-max method. Conclusion: In patients with non-traumatic acute abdominal pain, leukocyte count and D-dimer levels can be evaluated together by using linear combination methods in differentiating surgical and non-surgical pathologies. The obtained results showed that the diagnostic performance of the combined results with the min-max procedure was higher than the leukocyte count and D-dimer levels. [ABSTRACT FROM AUTHOR]

Let A1 and A2 be an {α1, β1, γ1}-cubic matrix and an {α2, β2}-quadratic matrix, respectively, with α1 = β1, β1 = γ1, α1 = γ1 and α2 = β2 . In this work, we characterize all situations in which the linear combination A3 = a1A1 +a2A2 with the assumption A1A2 = A2A1 is an {α3, β3}-quadratic matrix, where a1 and a2 are unknown nonzero complex numbers. [ABSTRACT FROM AUTHOR]

It is shown that every self-adjoint operator in a σ -finite von Neumann factor of type III can be written as a real linear combination of 3 projections. This is in stark contrast to factors of type I ∞ , I I 1 and I I ∞ , where there are always operators that require at least 4 projections in such a representation. [ABSTRACT FROM AUTHOR]

In video surveillance, visual person attributes such as gender, backpack, type of clothing are crucial for person search or re-identification. For detecting and retrieving these attributes with high accuracy, the availability of high-quality videos is a necessity in general. However, this cannot be guaranteed in general surveillance videos or images; beside improving hardware technology, improving inference algorithms on low-resolution data is valuable. This paper attempts to propose two solutions in this direction: designing a combined neural network architecture from existing architectures, and a novel combination approach toward re-identification on low-resolution videos. The proposed architecture introduces a combined Neural Network architecture, called SRMAR, that jointly trains Super Resolution and Multi Attribute Recognition models for more effective recognition. Experiments on two benchmark datasets demonstrate the effectiveness and applicability of the proposed neural network architecture for low-resolution multi-attribute recognition. Furthermore, a higher-level linear combination scheme that optimally combines the proposed SRMAR architecture and multi-attribute recognition network is presented, yielding superior results in low-resolution person attribute recognition.

This study suggests a linearly combined ground motion model (GMM) optimized for the within-rock conditions of South Korea. Ground motions recorded by accelerometers positioned in within-rock layers are used as target intensity measures (IMs), and five local GMMs and four global GMMs are used as candidates for combination. Optimization, which seeks to find a weight vector minimizing the uncertainty of the combined model, is performed using the quadratic programming (QP) technique, which provides very fast and solid results for the linear combination problem. This study illustrates how to use the QP technique for the linear combination problems. Also, we suggest optimized weight vectors for GMM combinations for two conditions: 1) the IM prediction of a scenario event without observations and 2) the IM prediction of a past event with observations. Among the local and global GMMs considered, JB03, Eea15, JH21, and BSSA14 are selected as the best four GMMs for the first condition, and Jea02, JB03, JH21, and CB14 are selected as the best four GMMs for the second condition. The combined model reduces the standard deviation of residuals in natural logarithms by 10% and 8% for the first and second conditions, respectively, compared to the best individual GMM at each period. Among the GMMs considered, the prediction by Eea15 is only applicable for magnitudes less than 5. Hence, for large magnitude (Mw > 5) prediction, CB14 is recommended instead of Eea15 for the best four models for the first condition.

On the basis of previous studies, we explore the approximation of continuous functions with fractal structure. We first give the calculation of fractal dimension of the linear combination of continuous functions with different Hausdorff dimension. Fractal dimension estimation of the linear combination of continuous functions with the same Hausdorff dimension has also been discussed elementary. Then, based on Weierstrass Theorem and the related results of Weierstrass function, we give the conclusion that the linear combination of polynomials with the same Hausdorff dimension approximates the objective function. The corresponding results with noninteger and integer Hausdorff dimensions have been investigated. We also give the preliminary applications of the theory in the last section. [ABSTRACT FROM AUTHOR]

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Motivated by the recent work of Galindo et al. (J. Funct. Anal. 265, 629–643, 2013), in this paper, we give an elegant compactness criterion for any finite linear combination of composition operators on the weighted Bergman space in terms of power type characterization. More precisely, let T be any finite linear combination of composition operators, then T is compact on A α p (D) if and only if lim n → ∞ ∥ T z n ∥ A − γ ∥ z n ∥ A − γ = 0 , which reveals that the compactness of T on the weighted Bergman space A α p (D) and Korenblum space A−γ(D) are equivalent. [ABSTRACT FROM AUTHOR]

We study the linear combinations f(z) = f1(z) + (1 - 1)f2(z) of two univalent harmonic mappings f1 and f2 in the cases when is some complex number. We determine the radius of close-to-convexity of f and establish some sufficient conditions for f to be locally-univalent and sense-preserving. Some known results reduce to particular cases of our general results. [ABSTRACT FROM AUTHOR]

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Can every real matrix be expressed as a linear combination of a certain number of orthogonal matrices? What is the smallest number of these orthogonal matrices? These elegant and interesting questions were initially raised by Zhan [7]. Soon afterwards, Li and Poon [4] proved that kmin, the smallest number of these orthogonal matrices, is not greater than 4. These classic results inspire us to further explore the improvement or supplement of this theory. We investigate some fundamental properties of An(k), which is the set of all n×n real matrices that can be expressed as a linear combination of k orthogonal matrices. Furthermore, we characterize the singular value structure of matrices in set An(2) and the block structure of related orthogonal matrices. We obtain an equivalent condition and some sufficient or necessary conditions of A ∈ An(2). Based on these results, we demonstrate the existence of matrices that are not in set An(2), and prove that kmin > 2 (for n ≥ 3). [ABSTRACT FROM AUTHOR]

Copyright of Journal of Geodesy & Geodynamics (1671-5942) is the property of Editorial Board Journal of Geodesy & Geodynamics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This assay was performed to select chemical compounds and rheological parameters for the prediction of the bread volume and crumb firmness of breads made with a blend of wheat flour-fine bran, using multivariate analysis. Two main factors were used, the source of fine bran and the particle size of fine bran. The experiment consisted in a completely random design, in a 2 × 3 factorial arrangement, the statistical analysis shown that the particle size of fine bran influence almost all the analytical variables. In addition, discriminant analysis was performed to analyse which rheological parameters and chemical components show the greater influence on dough behaviour and bread quality. Biaxial extensional viscosity, farinograph consistency, dough development time and stability were the main rheological parameters that govern the specific volume and crumb firmness and, were both closely related to the fibre, protein and starch content in the flour-fine bran blends. Particle size-genotype interaction has a significant influence on gelatinisation enthalpy and biaxial extensional viscosity that change the bread volume and the crumb firmness. The simplicity of linear equation of five independent variables to predict bread quality with high levels of accuracy could be advantageous in both basic research and the routine quality control of wheat mills. [ABSTRACT FROM AUTHOR]