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ON CONvERGENCE PROPERTY OF THE LANCZOS METHOD FOR SOLvING A COMPLEX SHIFTED HERMITIAN LINEAR SYSTEM

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Journal of Computational Mathematics 2013年第3期31卷 326-334页

作者： Guiding Gu department of applied Mathematics Shanghai University of Finance and Economics Shanghai 200433 China

We discuss the convergence property of the Lanczos method for solving a complex shifted Hermitian linear system （αI ＋ H）x = f. By showing the colinear coefficient of two system＇s residuals, our convergence analysis reveals that under the condition Re（α）＋ λmin（H）〉 0, the method converges faster than that for the real shifted Hermitian linear system （Re（α）I ＋ H）x = f. Numerical experiments verify such convergence property.

关键词： Hermitian matrix Complex shifted linear system Lanczos method.

Maximization of the sum of the trace ratio on the Stiefel manifold, II: Computation

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Science China Mathematics 2015年第7期58卷 1549-1566页

作者： ZHANG LeiHong LI RenCang department of applied Mathematics Shanghai University of Finance and Economics department of Mathematics University of Texas at Arlington

The necessary condition established in Part I of this paper for the global maximizers of the maximization problem max v tr（vTAv）/tr（vTBv）＋tr（vTCv）over the Stiefel manifold{v∈Rm×l ｜vTv=Il}（l〈m）,naturally leads to a self-consistent-field（SCF）iteration for computing a *** this part,we analyze the global and local convergence of the SCF iteration,and show that the necessary condition for the global maximizers is fulfilled at any convergent point of the sequences of approximations generated by the SCF *** is one of the advantages of the SCF iteration over optimization-based *** numerical tests are reported and show that the SCF iteration is very efficient by comparing with some manifold-based optimization methods.

关键词： trace ratio Rayleigh quotient Stiefel manifold nonlinear eigenvalue problem optimality condi-tion self-consistent-field iteration eigenspace

Cyberbullying Sexism Harassment Identification by Metaheurustics-Tuned eXtreme Gradient Boosting

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Computers, Materials and Continua 2024年第3期80卷 4997-5027页

作者： Dobrojevic, Milos Jovanovic, Luka Babic, Lepa Cajic, Miroslav Zivkovic, Tamara Zivkovic, Miodrag Muthusamy, Suresh Antonijevic, Milos Bacanin, Nebojsa Technical Faculty Singidunum University Belgrade 11000 Serbia Informatics and Computing Singidunum University Belgrade 11000 Serbia Business economics Singidunum University Belgrade 11000 Serbia Computing and Informatics Sinergija University Bijeljina 76300 Bosnia and Herzegovina department for Information Systems and Technologies University "Union Nikola Tesla" Cara Dusana Belgrade 11080 Serbia department for Computer Science and Informatics School of Electrical Engineering University of Belgrade Belgrade 11000 Serbia department of Electrical and Electronics Engineering Kongu Engineering College (Autonomous) Perundurai Erode 638060 India department of Mathematics Saveetha School of Engineering (Deemed to be University) SIMATS Thandalam Chennai 602105 India MEU Research Unit Middle East University Amman 11831 Jordan

Cyberbullying is a form of harassment or bullying that takes place online or through digital devices like smart-phones, computers, or tablets. It can occur through various channels, such as social media, text messages, online forums, or gaming platforms. Cyberbullying involves using technology to intentionally harm, harass, or intimidate others and may take different forms, including exclusion, doxing, impersonation, harassment, and cyberstalking. Unfortunately, due to the rapid growth of malicious internet users, this social phenomenon is becoming more frequent, and there is a huge need to address this issue. Therefore, the main goal of the research proposed in this manuscript is to tackle this emerging challenge. A dataset of sexist harassment on Twitter, containing tweets about the harassment of people on a sexual basis, for natural language processing (NLP), is used for this purpose. Two algorithms are used to transform the text into a meaningful representation of numbers for machine learning (ML) input: Term frequency inverse document frequency (TF-IDF) and Bidirectional encoder representations from transformers (BERT). The well-known eXtreme gradient boosting (XGBoost) ML model is employed to classify whether certain tweets fall into the category of sexual-based harassment or not. Additionally, with the goal of reaching better performance, several XGBoost models were devised conducting hyperparameter tuning by metaheuristics. For this purpose, the recently emerging Coyote optimization algorithm (COA) was modified and adjusted to optimize the XGBoost model. Additionally, other cutting-edge metaheuristics approach for this challenge were also implemented, and rigid comparative analysis of the captured classification metrics (accuracy, Cohen kappa score, precision, recall, and F1-score) was performed. Finally, the best-generated model was interpreted by Shapley additive explanations (SHAP), and useful insights were gained about the behavioral patterns of people w

关键词： Smartphones

Metcalfe＇s Law and Network Quality： An Extension of Zhang et al.

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Journal of Computer Science & Technology 2016年第1期31卷 117-123页

作者： Leo van Hove department of applied economics (APEC) Vrije Universiteit Brussel (Free University of Brussels) Brussels 1050 Belgium

Zhang et al. exploited data on Facebook and Tencent to validate Metcalfe＇s law, which states that the aggregate value of a communications network is proportional to the square of the number of users. This note points out that the value of a social network may be driven not only by its size, but also by increases in the variety and quality of the services offered. I therefore extend Zhang et al.＇s approach by explicitly controlling for changes in network quality over time. For the case of Tencent, I also filter out revenues and costs that are unrelated to Tencent＇s core （social network） services. I find that these two extensions only strengthen Zhang et al.＇s conclusions： Metcalfe＇s law now outperforms the other laws even more clearlv.

关键词： Metcalfe's law network value Facebook Tencent quality cost of revenue

Demographics, societal aging, and meat consumption in China

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Journal of Integrative Agriculture 2015年第6期14卷 995-1007页

作者： MIN Shi BAI Jun-fei James Seale Jr. Thomas Wahl Institute of Development and Agricultural economics Leibniz University Hannover College of economics and Management China Agricultural University department of Food and Resource economics University of Florida department of Agribusiness and applied economics North Dakota State University

Drawn on the data collected by surveying 1 340 urban households from six cities in China, this paper estimates the impacts of demographic structure and population aging on household meat consumption, by jointly considering meat consumed at home and away from home. Based on the trajectories of population, a simple simulation on meat demand trend in China is conducted subsequently. The results suggest： 1） Meat consumed away from home averagely accounts for near 30% of household total meat consumption in terms of quantity, so that its omission likely leads to a significant underestimate of total meat consumption and misunderstanding the driving forces; 2） population aging significantly and negatively affects per capita meat consumption, suggesting that the expected meat demand in China without considering population aging will be overestimated. The findings from this study have important implications for better understanding the relative issues on China＇s meat consumption under the situation of population aging.

关键词： capita household consumed income demographic jointly likely surveying estimates proportion

Bulking Up the Bay-Position Substituents Enables Enhanced Selectivity of C_(s)‑Symmetric Boron Subphthalocyanine−Subnaphthalocyanine Hybrids

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Precision Chemistry 2024年第4期2卷 161-181页

作者： Nina F.Farac Alan J.Lough Timothy P.Bender department of Chemical Engineering and applied Chemistry University of TorontoTorontoOntario M5S 3E5Canada department of Chemistry University of TorontoTorontoOntario M5S 3H6Canada department of Materials Science and Engineering University of TorontoTorontoOntario M5S 3E4Canada department of Mechanical and Industrial Engineering University of TorontoTorontoOntario M5S 3G8Canada

The precise synthesis of subporphyrinoid hybrids withπ-expanded topologies and unique material properties plays a promising role in the design of functional ***,selective,and controllable routes to boron subphthalocyanine−subnaphthalocyanine hybrids,Bsub(Pc_(3‑p)-Nc_(p))s,are desirable for this purpose yet synthetically challenging due to random mixtures of C_(s-),C_(3v-),and,in some cases,C_(1)-symmetric compounds that form during traditional statistical mixed ***,we addressed this issue by developing a sterically driven mixed cyclotrimerization with enhanced selectivity for the targeted C_(s)-symmetric hybrid and complete suppression of sterically crowded macrocyclic *** process,coupled with a rationally designed precursor bearing bulky phenyl substituents,enabled the synthesis and characterization of bay-position phenylated Ph_(2)-(R_(p))_(8)Bsub(Pc_(2)-Nc_(1))hybrids with halogens(Rp=Cl or F)in their peripheral isoindole *** selectivity ranged between 59 and 72%with remarkable yields,significantly higher than that of conventional mixed *** findings were augmented by theoretical calculations on precursor Lewis basicity as guiding principles into hybrid macrocycle ***,the incorporation of unfused phenyl groups and halogen atoms into the hybrid framework resulted in fine-tuned optical,structural,electronic,and electrochemical *** straightforward approach achieved improved selectivity and controlled narrowing of the product distribution,affording the efficient synthesis of structurally sophisticated Bsub(Pc_(2)-Nc_(1))*** then expands the library of 3-dimensionalπ-extended macrocycles for use in a range of applications,such as in optoelectronic devices with precisely tailored optical properties.

关键词： subphthalocyanine hybrids low-symmetry aromatic macrocycle selective cyclotrimerization sterically driven chemistry broad absorption material properties

Wavelet estimations for density derivatives

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Science China Mathematics 2013年第3期56卷 483-495页

作者： LIU YouMing WANG HuiYing department of applied Mathematics Beijing University of Technology School of applied Mathematics Central University of Finance and Economics

Donoho et al. in 1996 have made almost perfect achievements in wavelet estimation for a density function f in Besov spaces Bsr,q(R). Motivated by their work, we define new linear and nonlinear wavelet estimators flin,nm, fnonn,m for density derivatives f(m). It turns out that the linear estimation E(‖flinn,m-f(m)‖p) for f(m) ∈ Bsr,q(R) attains the optimal when r≥ p, and the nonlinear one E(‖fnonn,m-f(m)‖p) does the same if r≤p/2(s+m)+1 . In addition, our method is applied to Sobolev spaces with non-negative integer exponents as well.

关键词： wavelet estimators optimality Besov spaces Sobolev spaces density derivative

Optimal Control of variational Inequalities with Delays in the Highest Order Spatial Derivatives

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Acta Mathematica Sinica,English Series 2006年第2期22卷 607-624页

作者： Shang Wei ZHU Institute of Mathematics Fudan University department of applied Mathematics Shanxi Finance & Economics University

In this paper, an optimal control problem for parabolic variational inequalities with delays in the highest order spatial derivatives is investigated. The well-posedness of such kinds of variational inequalities is established. The existence of optimal controls under a Cesari-type condition is proved, and the necessary conditions of Pontryagin type for optimal controls is derived.

关键词： variational inequalities Time-delay operator Optimal control. Maximum Drinciple

On the Number of Limit Cycles of a Z_4-equivariant Quintic Near-Hamiltonian System

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Acta Mathematica Sinica,English Series 2015年第11期31卷 1805-1824页

作者： Xian Bo SUN Mao An HAN department of applied Mathematics Guangxi University of Finance and Economics The Institute of Mathematics Shanghai Normal University

In this paper, we study the number of limit cycles of a near-Hamiltonian system having Za- equivariant quintic perturbations. Using the methods of Hopf and heteroclinic bifurcation theory, we find that the perturbed system can have 28 limit cycles, and its location is also given. The main result can be used to improve the lower bound of the maximal number of limit cycles for some polynomial systems in a previous work, which is the main motivation of the present paper.

关键词： Limit cycle near-Hamiltonian system heteroclinic loop Za-equivariance Hopf bifurca-tion