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arXiv 2023年

作者： Scott, James M. Du, Qiang Department of Applied Physics and Applied Mathematics the Data Science Institute Columbia University New YorkNY10027 United States

We study nonlocal integral equations on bounded domains with finite-range nonlocal interactions that are localized at the boundary. We establish a Green’s identity for the nonlocal operator that recovers the classical boundary integral, which, along with the variational analysis established previously, leads to the well-posedness of these nonlocal problems with various types of classical local boundary conditions. We continue our analysis via boundary-localized convolutions, using them to analyze the Euler-Lagrange equations, which permits us to establish global regularity properties and classical Sobolev convergence to their classical local *** Codes 45K05, 35J20, 46E35 Copyright © 2023, The Authors. All rights reserved.

关键词： Sobolev spaces

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ASYMPTOTICALLY COMPATIBILITY OF A CLASS OF NUMERICAL SCHEMES FOR A NONLOCAL TRAFFIC FLOW MODEL

arXiv

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arXiv 2023年

作者： Huang, Kuang Du, Qiang Department of Applied Physics and Applied Mathematics Data Science Institute Columbia University New YorkNY10027 United States

This paper considers numerical discretization of a nonlocal conservation law modeling vehicular traffic flows involving nonlocal inter-vehicle interactions. The nonlocal model involves an integral over the range measured by a horizon parameter and it recovers the local Lighthill-Richards-Whitham model as the nonlocal horizon parameter goes to zero. Good numerical schemes for simulating these parameterized nonlocal traffic flow models should be robust with respect to the change of the model parameters but this has not been systematically investigated in the literature. We fill this gap through a careful study of a class of finite volume numerical schemes with suitable discretizations of the nonlocal integral, which include several schemes proposed in the literature and their variants. Our main contributions are to demonstrate the asymptotically compatibility of the schemes, which includes both the uniform convergence of the numerical solutions to the unique solution of nonlocal continuum model for a given positive horizon parameter and the convergence to the unique entropy solution of the local model as the mesh size and the nonlocal horizon parameter go to zero simultaneously. It is shown that with the asymptotically compatibility, the schemes can provide robust numerical computation under the changes of the nonlocal horizon *** Codes 65M08, 35L65, 76A30, 35R09, 65R20, 65D30 Copyright © 2023, The Authors. All rights reserved.

关键词： Continuum mechanics

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NONLOCAL PROBLEMS WITH LOCAL BOUNDARY CONDITIONS I: FUNCTION SPACES AND VARIATIONAL PRINCIPLES

arXiv

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arXiv 2023年

作者： Scott, James M. Du, Qiang Department of Applied Physics and Applied Mathematics The Data Science Institute Columbia University New YorkNY10027 United States

We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences weighted by a position-dependent function, which leads to heterogeneous localization on the domain boundary. We show the existence of minimizers for nonlocal variational problems with classically-defined, local boundary constraints, together with the variational convergence of these functionals to classical counterparts in the localization limit. This program necessitates a thorough study of the nonlocal space;we demonstrate properties such as a Meyers-Serrin theorem, trace inequalities, and compact embeddings, which are facilitated by new studies of boundary-localized convolution operators. Copyright © 2023, The Authors. All rights reserved.

关键词： Sobolev spaces

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Electronic structures and strengthening mechanisms of superhard high-entropy diborides

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Rare Metals 2023年第2期42卷 614-628页

作者： Gang Yao William-Yi Wang Pei-Xuan Li Ke Ren Jia-Qi Lu Xing-Yu Gao De-Ye Lin Jun Wang Yi-Guang Wang Hai-Feng Song Zi-Kui Liu Jin-Shan Li State Key Laboratory of Solidification Processing Northwestern Polytechnical UniversityXi’an710072China Innovation Center NPU ChongqingChongqing401135China Laboratory of Computational Physics Institute of Applied Physics and Computational MathematicsBeijing100088China Institute of Advanced Structure Technology Beijing Institute of TechnologyBeijing100081China Department of Materials Science and Engineering The Pennsylvania State UniversityUniversity ParkPA16802USA

High-entropy diborides(HEBs)have attracted extensive research due to their potential ultra-high *** the present work,the effects of transition metals(TM)on lattice parameters,electron work function(EWF),bonding charge density,and hardness of HEBs are comprehensively investigated by the first-principles calculations,including(TiZrHfNbTa)B_(2),(TiZrHfNbMo)B_(2),(TiZrHfTaMo)B_(2),(TiZrNbTaMo)B_(2),and(TiHfNbTaMo)B_(2).It is revealed that the disordered TM atoms result in a severe local lattice distortion and the formation of weak *** view of bonding charge density,it is understood that the degree of electron contribution of TM atoms directly affects the bonding strength of the metallic layer,contributing to the optimized hardness of ***,the proposed power-law-scaled relationship integrating the EWF and the grain size yields an excellent agreement between our predicted results and those reported experimental *** is found that the HEBs exhibit relatively high hardness which is higher than those of single transition metal *** particular,the hardness of(TiZrNbTaMo)B_(2)and(TiHfNbTaMo)B_(2)can be as high as29.15 and 28.02 GPa,*** work provides a rapid strategy to discover/design advanced HEBs efficiently,supported by the coupling hardening mechanisms of solid solution and grain refinement based on the atomic and electronic interactions.

关键词： High-entropy diborides(HEBs) Hardness Electronic structure Lattice distortion Power-law

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Novel Scheme for Robust Confusion Component Selection Based on Pythagorean Fuzzy Set

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Computers, Materials & Continua 2023年第3期74卷 6523-6534页

作者： Nabilah Abughazalah Mohsin Iqbal Majid Khan Iqtadar Hussain Department of Mathematical Sciences College of SciencePrincess Nourah bint Abdulrahman UniversityP.O.Box 84428Riyadh11671Saudi Arabia Department of Mathematics&Statistics Riphah International UniversityIslamabadPakistan Department of Applied Mathematics&Statistics Institute of Space TechnologyIslamabadPakistan Mathematics Program Department of MathematicsStatistics and PhysicsCollege of Arts and SciencesQatar University2713DohaQatar Statistical Consulting Unit College of Arts and ScienceQatar UniversityDohaQatar

The substitution box,often known as an S-box,is a nonlinear component that is a part of several block *** purpose is to protect cryptographic algorithms from a variety of cryptanalytic assaults.A Multi-Criteria Decision Making(MCDM)problem has a complex selection procedure because of having many options and criteria to choose *** of this,statistical methods are necessary to assess the performance score of each S-box and decide which option is the best one available based on this *** the Pythagorean Fuzzy-based Technique for Order of Preference by Similarity to Ideal Solution(TOPSIS)method,the major objective of this investigation is to select the optimal S-box to be implemented from a pool of twelve key *** the help of the Pythagorean fuzzy set(PFS),the purpose of this article is to evaluate whether this nonlinear component is suitable for use in a variety of encryption *** this article,we have considered various characteristics of S-boxes,including nonlinearity,algebraic degree,strict avalanche criterion(SAC),absolute indicator,bit independent criterion(BIC),sum of square indicator,algebraic immunity,transparency order,robustness to differential cryptanalysis,composite algebraic immunity,signal to noise ratio-differential power attack(SNR-DPA),and confusion coefficient variance on some standard S-boxes that are Advanced Encryption Following this,the findings of the investigation are changed into Pythagorean fuzzy numbers in the shape of a *** matrix is then subjected to an analysis using the TOPSIS method,which is dependent on the Pythagorean fuzzy set,to rank the most suitable S-box for use in encryption applications.

关键词： Decision making substitution box TOPSIS multi-criterion decision making fuzzy set Pythagorean fuzzy set

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Findings of the Second Shared Task on Multilingual Coreference Resolution 6

Findings of the Second Shared Task on Multilingual Coreferen...

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CRAC Shared Task on Multilingual Coreference Resolution at 6th Workshop on Computational Models of Reference, Anaphora and Coreference, CRAC 2023

作者： Žabokrtský, Zdeněk Konopík, Miloslav Nedoluzhko, Anna Novák, Michal Ogrodniczuk, Maciej Popel, Martin Pražák, Ondřej Sido, Jakub Zeman, Daniel Charles University Faculty of Mathematics and Physics Institute of Formal and Applied Linguistics Prague Czech Republic University of West Bohemia Faculty of Applied Sciences Department of Computer Science and Engineering Pilsen Czech Republic Institute of Computer Science Polish Academy of Sciences Warsaw Poland

ISBN: (纸本)9781955917025

This paper summarizes the second edition of the shared task on multilingual coreference resolution, held with the CRAC 2023 workshop. Just like last year, participants of the shared task were to create trainable systems that detect mentions and group them based on identity coreference;however, this year’s edition uses a slightly different primary evaluation score, and is also broader in terms of covered languages: version 1.1 of the multilingual collection of harmonized coreference resources CorefUD was used as the source of training and evaluation data this time, with 17 datasets for 12 languages. 7 systems competed in this shared task. © CRAC 2023. All Rights Reserved.

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Versatile techniques based on the Thermionic Vacuum Arc(TVA)and laser-induced TVA methods for Mg/Mg:X thin films deposition-A review

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Journal of Magnesium and Alloys 2024年第8期12卷 3115-3134页

作者： R.Vladoiu A.Mandes V.Dinca M.Tichy P.Kudrna C.C.Ciobotaru S.Polosan Ovidius University of Constanta Faculty of Applied Sciences and EngineeringDept of PhysicsMamaia Av.no 124Constanta900527Romania Charles University Faculty of Mathematics and PhysicsDepartment of Surface and Plasma ScienceV Holesovickach 218000 Praha 8Czech Republic National Institute of Materials Physics P.O.Box MG-7Bucharest-Magurele 077125Romania Academy of Romanian Scientists Ilfov no 3Bucharest 050094Romania

Magnesium and magnesium thin alloy films were deposited using a thermionic vacuum arc(TVA),which has multiple applications in the field of metallic electrodes for diodes and batteries or active corrosion *** improved laser-induced TVA(LTVA)method favors the crystallization processes of the deposited magnesium-based films because the interaction between laser and plasma discharge changes the thermal energy during photonic processes due to the local temperature *** diagnosis based on current discharge measurements suggests an inelastic collision between the laser beam and the atoms from the plasma *** morphology and surface properties of the obtained thin films differ between these two *** the amorphous character is dominant for TVA thin films,enabling a smooth surface,the LTVA method produces rough surfaces with prominent crystallinity,less hydrophobic character and lower surface *** smooth surfaces obtained by the TVA methods produce metallic electrodes with good electrical contact,ensuring better diodes and battery charge *** methods allow uniform magnesium alloys to be obtained,but the laser used in the LTVA on the discharge plasma controls the added metal or element ratio.

关键词： Magnesium Magnesium alloys Thermionic vacuum arc Laser induced Thin films

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HIGH-DIMENSIONAL SGD ALIGNS WITH EMERGING OUTLIER EIGENSPACES 12

HIGH-DIMENSIONAL SGD ALIGNS WITH EMERGING OUTLIER EIGENSPACE...

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12th International Conference on Learning Representations, ICLR 2024

作者： Arous, Gérard Ben Gheissari, Reza Huang, Jiaoyang Jagannath, Aukosh Courant Institute New York University New YorkNY United States Department of Mathematics Northwestern University EvanstonIL United States Department of Statistics and Data Science University of Pennsylvania PhiladelphiaPA United States Department of Statistics and Actuarial Science Department of Applied Mathematics Cheriton School of Computer Science University of Waterloo WaterlooON Canada

We rigorously study the joint evolution of training dynamics via stochastic gradient descent (SGD) and the spectra of empirical Hessian and gradient matrices. We prove that in two canonical classification tasks for multi-class high-dimensional mixtures and either 1 or 2-layer neural networks, the SGD trajectory rapidly aligns with emerging low-rank outlier eigenspaces of the Hessian and gradient matrices. Moreover, in multi-layer settings this alignment occurs per layer, with the final layer's outlier eigenspace evolving over the course of training, and exhibiting rank deficiency when the SGD converges to sub-optimal classifiers. This establishes some of the rich predictions that have arisen from extensive numerical studies in the last decade about the spectra of Hessian and information matrices over the course of training in overparametrized networks. © 2024 12th International Conference on Learning Representations, ICLR 2024. All rights reserved.

关键词： Statistics

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Fine-tune chiroptical activity in discrete chiral Au nanorods

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Nano Research 2022年第7期15卷 6574-6581页

作者： Guangchao Zheng Sulin Jiao Wei Zhang Shenli Wang Qinghua Zhang Lin Gu Weixiang Ye Junjun Li Xiaochen Ren Zhicheng Zhang Kwok-yin Wong School of Physics and Microelectronics Zhengzhou UniversityZhengzhou 450001China State Key Laboratory of Chemical Biology and Drug Discovery Department of Applied Biology and Chemical TechnologyThe Hong Kong Polytechnic UniversityKowloonHong KongChina Institute of Applied Physics and Computational Mathematics Beijing 100088China School of Food Science and Engineering Henan University of TechnologyZhengzhou 450001China Beijing National Laboratory for Condensed Matter Physics Institute of PhysicsChinese Academy of SciencesBeijing 100190China Department of Applied Physics School of ScienceHainan UniversityHaikou 570228China Tianjin Key Laboratory of Molecular Optoelectronic Sciences Department of ChemistrySchool of ScienceTianjin University&Collaborative Innovation Center of Chemical Science and EngineeringTianjin 300072China

Accurate researches on the surface plasmon resonance(SPR)-based applications of chiral plasmonic metal nanoparticles(NPs)still remain a great ***,a series of chiral plasmonic metal NPs,e.g.,chiral Au nanorods(c-Au NRs),c-Au@Ag core–shell,and c-Au@TiO_(2) core–shell NRs,with different chiroptical activities have been *** circular dichroism(PCD)bands of c-Au NRs can be precisely tailored by tuning the longitudinal SPR(LSPR)and amount of Au NRs as ***,a shift of PCD bands within ultraviolet–visible–near infrared ray(UV–vis–NIR)region can also be achieved through the functionalization of a shell of another metal or ***,chirality transfer from c-Au core to Ag shell leads to new PCD bands at the near-UV *** tuning of PCD bands and chirality transfer are confirmed by our developed theoretical *** chiral Au NRs-based chiral plasmonic nanomaterials with tunable chiroptical activities will be helpful to understand the structure-direct PCD and to extend circularly polarized-based applications.

关键词： chiral Au nanorods(c-Au NRs) surface plasmon resonance optical activity chirality transfer

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NONLOCAL BOUNDARY-VALUE PROBLEMS WITH LOCAL BOUNDARY CONDITIONS

arXiv

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arXiv 2023年

作者： Scott, James M. Du, Qiang Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Department of Applied Physics and Applied Mathematics The Data Science Institute Columbia University New YorkNY10027 United States

We describe and analyze nonlocal integro-differential equations with classical local boundary conditions. The interaction kernel of the nonlocal operator has horizon parameter dependent on position in the domain, and vanishes as the boundary of the domain is approached. This heterogeneous localization allows for boundary values to be captured in the trace sense. We state and prove a nonlocal Green’s identity for these nonlocal operators that involve local boundary terms. We use this identity to state and establish the well-posedness of variational formulations of the nonlocal problems with several types of classical boundary conditions. We show the consistency of these nonlocal boundary-value problems with their classical local counterparts in the vanishing horizon limit via the convergence of solutions. The Poisson data for the local boundary-value problem is permitted to be quite irregular, belonging to the dual of the classical Sobolev space. Heterogeneously mollifying this Poisson data for the local problem on the same length scale as the horizon and using the regularity of the interaction kernel, we show that the solutions to the nonlocal boundary-value problem with the mollified Poisson data actually belong to the classical Sobolev space, and converge weakly to the unique variational solution of the classical Poisson problem with original Poisson data. Copyright © 2023, The Authors. All rights reserved.

关键词： Sobolev spaces

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