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On the Rayleigh-Taylor Instability for Two Uniform Viscous Incompressible Flows

Chinese Annals of mathematics,Series B 2014年第6期35卷 907-940页

作者： Fei JIANG Song JIANG Weiwei WANG College of Mathematics and Computer Science Fuzhou University Institute of Applied Physics and Computational Mathematics

The authors study the Rayleigh-Taylor instability for two incompressible immiscible fluids with or without surface tension, evolving with a free interface in the presence of a uniform gravitational field in Eulerian coordinates. To deal with the free surface, instead of using the transformation to Lagrangian coordinates, the perturbed equations in Eulerian coordinates are transformed to an integral form and the two-fluid flow is formulated as a single-fluid flow in a fixed domain, thus offering an alternative approach to deal with the jump conditions at the free interface. First, the linearized problem around the steady state which describes a denser immiscible fluid lying above a light one with a free interface separating the two fluids, both fluids being in(unstable) equilibrium is analyzed. By a general method of studying a family of modes, the smooth(when restricted to each fluid domain) solutions to the linearized problem that grow exponentially fast in time in Sobolev spaces are constructed, thus leading to a global instability result for the linearized ***, by using these pathological solutions, the global instability for the corresponding nonlinear problem in an appropriate sense is demonstrated.

关键词： Rayleigh-Taylor instability Viscous incompressible flows Global insta-bility

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Estimates, trends, and drivers of the global burden of type 2 diabetes attributable to PM_2·5 air pollution, 1990–2019: an analysis of data from the Global Burden of Disease Study 2019

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The Lancet Planetary Health 2022年第7期6卷 e586-e600页

作者： Burkart, Katrin Causey, Kate Cohen, Aaron J Wozniak, Sarah S Salvi, Devashri Digvijay Abbafati, Cristiana Adekanmbi, Victor Adsuar, Jose C Ahmadi, Keivan Alahdab, Fares Al-Aly, Ziyad Alipour, Vahid Alvis-Guzman, Nelson Amegah, Adeladza Kofi Andrei, Catalina Liliana Andrei, Tudorel Ansari, Fereshteh Arabloo, Jalal Aremu, Olatunde Aripov, Timur Babaee, Ebrahim Banach, MacIej Barnett, Anthony Bärnighausen, Till Winfried Bedi, Neeraj Behzadifar, Masoud Béjot, Yannick Bennett, Derrick A Bensenor, Isabela M Bernstein, Robert S Bhattacharyya, Krittika Bijani, Ali Biondi, Antonio Bohlouli, Somayeh Breitner, Susanne Brenner, Hermann Butt, Zahid A Cámera, Luis Alberto Cantu-Brito, Carlos Carvalho, Felix Cerin, Ester Chattu, Vijay Kumar Chauhan, Bal Govind Choi, Jee-Young Jasmine Chu, Dinh-Toi Dai, Xiaochen Dandona, Lalit Dandona, Rakhi Daryani, Ahmad Davletov, Kairat De Courten, Barbora Demeke, Feleke Mekonnen Denova-Gutiérrez, Edgar Dharmaratne, Samath Dhamminda Dhimal, Meghnath Diaz, Daniel Djalalinia, Shirin Duncan, Bruce B El Sayed Zaki, Maysaa Eskandarieh, Sharareh Fareed, Mohammad Farzadfar, Farshad Fattahi, Nazir Fazlzadeh, Mehdi Fernandes, Eduarda Filip, Irina Fischer, Florian Foigt, Nataliya A Freitas, Marisa Ghashghaee, Ahmad Gill, Paramjit Singh Ginawi, Ibrahim Abdelmageed Gopalani, Sameer Vali Guo, Yuming Gupta, Rajat Das Habtewold, Tesfa Dejenie Hamadeh, Randah R Hamidi, Samer Hankey, Graeme J Hasanpoor, Edris Hassen, Hamid Yimam Hay, Simon I Heibati, Behzad Hole, Michael K Hossain, Naznin Househ, Mowafa Irvani, Seyed Sina Naghibi Jaafari, Jalil Jakovljevic, Mihajlo Jha, Ravi Prakash Jonas, Jost B Jozwiak, Jacek Jerzy Kasaeian, Amir Kaydi, Neda Khader, Yousef Saleh Khafaie, Morteza Abdullatif Khan, Ejaz Ahmad Khan, Junaid Khan, Md Nuruzzaman Khatab, Khaled Khater, Amir M Kim, Yun Jin Kimokoti, Ruth W Kisa, Adnan Kivimäki, Mika Knibbs, Luke D Kosen, Soewarta Koul, Parvaiz A Koyanagi, Ai Defo, Barthelemy Kuate Kugbey, Nuworza Lauriola, Paolo Lee, Paul H Leili, Mostafa Lewycka, Sonia Li, Shanshan Lim, Lee-Ling Li Institute for Health Metrics and Evaluation University of Washington Seattle WA United States Department of Health Metrics Sciences School of Medicine University of Washington Seattle WA United States Division of Plastic and Reconstructive Surgery University of Washington Seattle WA United States Research Insights and Innovation Seattle WA United States Health Effects Institute Boston MA United States School of Public Health Boston University Boston MA United States Department of Juridical and Economic Studies La Sapienza University Rome Italy Department of Population Medicine Cardiff University Cardiff United Kingdom Sport Science Department University of Extremadura Badajoz Spain School of Public Health Imperial College London London United Kingdom Department of Primary Care and Public Health Imperial College London London United Kingdom Mayo Evidence-based Practice Center Mayo Clinic Foundation for Medical Education and Research Rochester MN United States John T. Milliken Department of Internal Medicine Washington University in St. Louis St. Louis MO United States Clinical Epidemiology Center US Department of Veterans Affairs (VA) St Louis MO United States Health Management and Economics Research Center Iran University of Medical Sciences Tehran Iran Department of Health Economics Iran University of Medical Sciences Tehran Iran Preventive Medicine and Public Health Research Center Iran University of Medical Sciences Tehran Iran Pars Advanced and Minimally Invasive Medical Manners Research Center Iran University of Medical Sciences Tehran Iran Department of Community and Family Medicine Iran University of Medical Sciences Tehran Iran Research Group in Hospital Management and Health Policies Universidad de la Costa (University of the Coast) Barranquilla Colombia Research Group in Health Economics University of Cartagena Cartagena Colombia Department of Biomedical Science University of Cape Coast Cape Coast Ghana Cardiology Department Ca

Background: Experimental and epidemiological studies indicate an association between exposure to particulate matter (PM) air pollution and increased risk of type 2 diabetes. In view of the high and increasing prevalence of diabetes, we aimed to quantify the burden of type 2 diabetes attributable to PM_2·5 originating from ambient and household air pollution. Methods: We systematically compiled all relevant cohort and case-control studies assessing the effect of exposure to household and ambient fine particulate matter (PM_2·5) air pollution on type 2 diabetes incidence and mortality. We derived an exposure–response curve from the extracted relative risk estimates using the MR-BRT (meta-regression—Bayesian, regularised, trimmed) tool. The estimated curve was linked to ambient and household PM_2·5 exposures from the Global Burden of Diseases, Injuries, and Risk Factors Study 2019, and estimates of the attributable burden (population attributable fractions and rates per 100 000 population of deaths and disability-adjusted life-years) for 204 countries from 1990 to 2019 were calculated. We also assessed the role of changes in exposure, population size, age, and type 2 diabetes incidence in the observed trend in PM_2·5-attributable type 2 diabetes burden. All estimates are presented with 95% uncertainty intervals. Findings: In 2019, approximately a fifth of the global burden of type 2 diabetes was attributable to PM_2·5 exposure, with an estimated 3·78 (95% uncertainty interval 2·68–4·83) deaths per 100 000 population and 167 (117–223) disability-adjusted life-years (DALYs) per 100 000 population. Approximately 13·4% (9·49–17·5) of deaths and 13·6% (9·73–17·9) of DALYs due to type 2 diabetes were contributed by ambient PM2·5, and 6·50% (4·22–9·53) of deaths and 5·92% (3·81–8·64) of DALYs by household air pollution. High burdens, in terms of numbers as well as rates, were estimated in Asia, sub-Saharan Africa, and South Am

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations

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Physical Review E 2015年第2期92卷 022119-022119页

作者： G. Zhang F. H. Stillinger S. Torquato Department of Chemistry Department of Physics Princeton Institute for the Science and Technology of Materials and Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA

Systems of particles interacting with “stealthy” pair potentials have been shown to possess infinitely degenerate disordered hyperuniform classical ground states with novel physical properties. Previous attempts to sample the infinitely degenerate ground states used energy minimization techniques, introducing algorithmic dependence that is artificial in nature. Recently, an ensemble theory of stealthy hyperuniform ground states was formulated to predict the structure and thermodynamics that was shown to be in excellent agreement with corresponding computer simulation results in the canonical ensemble (in the zero-temperature limit). In this paper, we provide details and justifications of the simulation procedure, which involves performing molecular dynamics simulations at sufficiently low temperatures and minimizing the energy of the snapshots for both the high-density disordered regime, where the theory applies, as well as lower densities. We also use numerical simulations to extend our study to the lower-density regime. We report results for the pair correlation functions, structure factors, and Voronoi cell statistics. In the high-density regime, we verify the theoretical ansatz that stealthy disordered ground states behave like “pseudo” disordered equilibrium hard-sphere systems in Fourier space. The pair statistics obey certain exact integral conditions with very high accuracy. These results show that as the density decreases from the high-density limit, the disordered ground states in the canonical ensemble are characterized by an increasing degree of short-range order and eventually the system undergoes a phase transition to crystalline ground states. In the crystalline regime (low densities), there exist aperiodic structures that are part of the ground-state manifold but yet are not entropically favored. We also provide numerical evidence suggesting that different forms of stealthy pair potentials produce the same ground-state ensemble in the zero-temperatur

关键词： THERMODYNAMIC equilibrium PROBABILITY theory QUANTUM spin models MOLECULAR dynamics QUANTUM entropy

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Causes of blindness and vision impairment in 2020 and trends over 30 years, and prevalence of avoidable blindness in relation to VISION 2020: the Right to Sight: an analysis for the Global Burden of Disease Study (vol 2, pg 144, 2021)

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LANCET GLOBAL HEALTH 2021年第4期9卷 E408-E408页

作者： Steinmetz, Jaimie D. Vision and Eye Research Institute Anglia Ruskin University Cambridge United Kingdom Biomedical Informatics Seoul National University Hospital Seoul South Korea Institute for Health Metrics and Evaluation University of Washington Seattle WA United States Department of Health Metrics Sciences School of Medicine University of Washington Seattle WA United States Institute of Health Services Research Yonsei University Seoul South Korea Department of Ophthalmology University of Washington Seattle WA United States Department of Mathematics Imperial College London London United Kingdom WHO Collaborating Centre for Public Health Education and Training Imperial College London London United Kingdom Department of Primary Care and Public Health Imperial College London London United Kingdom School of Population and Global Health University of Melbourne Carlton VIC Australia School of Optometry and Vision Science UNSW Sydney NSW Australia Brien Holden Vision Institute Sydney Australia Department of Ophthalmology University of Adelaide Adelaide SA Australia Department of Parasitology and Mycology Jahrom University of Medical Sciences Jahrom Iran Department of Clinical Sciences University of Sharjah Sharjah United Arab Emirates Ophthalmic Research Center Shahid Beheshti University of Medical Sciences Tehran Iran Department of Ophthalmology Shahid Beheshti University of Medical Sciences Tehran Iran Research Institute for Endocrine Sciences Shahid Beheshti University of Medical Sciences Tehran Iran Ophthalmic Epidemiology Research Center Shahid Beheshti University of Medical Sciences Tehran Iran Health Services Management Department Qazvin University of Medical Sciences Qazvin Iran Department of Systems Populations and Leadership University of Michigan Ann Arbor MI United States Department of Medicine Sofia Ismail Memorial Medical Centre Bogura Bangladesh The Fred Hollows Foundation Sydney NSW Australia Berhan Public Health & Eye Care Consultancy Addis A

Hospital El Salvador: a novel paradigm of intensive care in response to COVID-19 in central America. Lancet Glob Health 2021;9: e241?42?In this Comment, the conflict of interest statement should have included the following: ?By virtue of their roles within a public hospital or the Ministry of Health, MB, LC, WH, and XS are government employees. The findings and conclusions in the Comment are only those of the authors.? This correction has been made as of Feb 26, 2021.

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A demonstration of improved constraints on primordial gravitational waves with delensing

arXiv

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arXiv 2020年

作者： Ade, P.A.R. Ahmed, Z. Amiri, M. Anderson, A.J. Austermann, J.E. Avva, J.S. Barkats, D. Thakur, R. Basu Beall, J.A. Bender, A.N. Benson, B.A. Bianchini, F. Bischoff, C.A. Bleem, L.E. Bock, J.J. Boenish, H. Bullock, E. Buza, V. Carlstrom, J.E. Chang, C.L. Cheshire, J.R. Chiang, H.C. Chou, T.-L. Citron, R. Connors, J. Moran, C. Corbett Cornelison, J. Crawford, T.M. Crites, A.T. Crumrine, M. Cukierman, A. de Haan, T. Dierickx, M. Dobbs, M.A. Duband, L. Everett, W. Fatigoni, S. Filippini, J.P. Fliescher, S. Gallicchio, J. George, E.M. Germaine, T.St. Goeckner-Wald, N. Goldfinger, D.C. Grayson, J. Gupta, N. Hall, G. Halpern, M. Halverson, N.W. Harrison, S. Henderson, S. Henning, J.W. Hildebrandt, S.R. Hilton, G.C. Holder, G.P. Holzapfel, W.L. Hrubes, J.D. Huang, N. Hubmayr, J. Hui, H. Irwin, K.D. Kang, J. Karkare, K.S. Karpel, E. Kefeli, S. Kernasovskiy, S.A. Knox, L. Kovac, J.M. Kuo, C.L. Lau, K. Lee, A.T. Leitch, E.M. Li, D. Lowitz, A. Manzotti, A. McMahon, J.J. Megerian, K.G. Meyer, S.S. Millea, M. Mocanu, L.M. Moncelsi, L. Montgomery, J. Nadolski, A. Namikawa, T. Natoli, T. Netterfield, C.B. Nguyen, H.T. Nibarger, J.P. Noble, G. Novosad, V. O’Brient, R. Ogburn, R.W. Omori, Y. Padin, S. Palladino, S. Patil, S. Prouve, T. Pryke, C. Racine, B. Reichardt, C.L. Reintsema, C.D. Richter, S. Ruhl, J.E. Saliwanchik, B.R. Schaffer, K.K. Schillaci, A. Schmitt, B.L. Schwarz, R. Sheehy, C.D. Sievers, C. Smecher, G. Soliman, A. Stark, A.A. Steinbach, B. Sudiwala, R.V. Teply, G.P. Thompson, K.L. Tolan, J.E. Tucker, C. Turner, A.D. Umiltà, C. Veach, T. Vieira, J.D. Vieregg, A.G. Wandui, A. Wang, G. Weber, A.C. Whitehorn, N. Wiebe, D.V. Willmert, J. Wong, C.L. Wu, W.L. Kimmy Yang, H. Yefremenko, V. Yoon, K.W. Young, E. Yu, C. Zeng, L. Zhang, C. Cardiff University CardiffCF10 3XQ United Kingdom SLAC National Accelerator Laboratory 2575 Sand Hill Road Menlo ParkCA94025 United States Kavli Institute for Particle Astrophysics and Cosmology Stanford University 452 Lomita Mall StanfordCA94305 United States Department of Physics and Astronomy University of British Columbia VancouverBCV6T 1Z1 Canada Fermi National Accelerator Laboratory MS209 P.O. Box 500 BataviaIL60510 United States NIST Quantum Devices Group 325 Broadway Mailcode 817.03 BoulderCO80305 United States Department of Physics University of Colorado BoulderCO80309 United States Department of Physics University of California BerkeleyCA94720 United States Harvard-Smithsonian Center for Astrophysics 60 Garden Street CambridgeMA02138 United States California Institute of Technology MS 249-17 1216 E. California Blvd. PasadenaCA91125 United States High Energy Physics Division Argonne National Laboratory 9700 S. Cass Avenue ArgonneIL60439 United States Kavli Institute for Cosmological Physics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States Department of Astronomy and Astrophysics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States School of Physics University of Melbourne ParkvilleVIC3010 Australia Department of Physics University of Cincinnati CincinnatiOH45221 United States Jet Propulsion Laboratory PasadenaCA91109 United States Department of Physics Harvard University CambridgeMA02138 United States Minnesota Institute for Astrophysics University of Minnesota MinneapolisMN55455 United States Department of Physics University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States Enrico Fermi Institute University of Chicago 5640 South Ellis Avenue ChicagoIL60637 United States Department of Physics McGill University 3600 Rue University MontrealQCH3A 2T8 Canada School of Mathematics Statistics & Computer Science University of KwaZulu-Natal

We present a constraint on the tensor-to-scalar ratio, r, derived from measurements of cosmic microwave background (CMB) polarization B-modes with "delensing," whereby the uncertainty on r contributed by the sample variance of the gravitational lensing B-modes is reduced by cross-correlating against a lensing B-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, Bicep/Keck, and Planck data. We expand the Bicep/Keck likelihood analysis framework to accept a lensing template and apply it to the Bicep/Keck data set collected through 2014 using the same parametric foreground modelling as in the previous analysis. From simulations, we find that the uncertainty on r is reduced by ∼ 10%, from σ(r)= 0.024 to 0.022, which can be compared with a ∼ 26% reduction obtained when using a perfect lensing template or if there were zero lensing B-modes. Applying the technique to the real data, the constraint on r is improved from r0.05 Copyright © 2020, The Authors. All rights reserved.

关键词： Cosmology

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26th Annual computational Neuroscience Meeting (CNS*2017): Part 3 Antwerp, Belgium. 15-20 July 2017 Abstracts

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BMC NEUROscience 2017年第SUPPL 1期18卷 95-176页

作者： [Anonymous] Department of Neuroscience Yale University New Haven CT 06520 USA Department Physiology & Pharmacology SUNY Downstate Brooklyn NY 11203 USA NYU School of Engineering 6 MetroTech Center Brooklyn NY 11201 USA Departament de Matemàtica Aplicada Universitat Politècnica de Catalunya Barcelona 08028 Spain Institut de Neurobiologie de la Méditerrannée (INMED) INSERM UMR901 Aix-Marseille Univ Marseille France Center of Neural Science New York University New York NY USA Aix-Marseille Univ INSERM INS Inst Neurosci Syst Marseille France Laboratoire de Physique Théorique et Modélisation CNRS UMR 8089 Université de Cergy-Pontoise 95300 Cergy-Pontoise Cedex France Department of Mathematics and Computer Science ENSAT Abdelmalek Essaadi’s University Tangier Morocco Laboratory of Natural Computation Department of Information and Electrical Engineering and Applied Mathematics University of Salerno 84084 Fisciano SA Italy Department of Medicine University of Salerno 84083 Lancusi SA Italy Dipartimento di Fisica Università degli Studi Aldo Moro Bari and INFN Sezione Di Bari Italy Data Analysis Department Ghent University Ghent Belgium Coma Science Group University of Liège Liège Belgium Cruces Hospital and Ikerbasque Research Center Bilbao Spain BIOtech Department of Industrial Engineering University of Trento and IRCS-PAT FBK 38010 Trento Italy Department of Data Analysis Ghent University Ghent 9000 Belgium The Wellcome Trust Centre for Neuroimaging University College London London WC1N 3BG UK Department of Electronic Engineering NED University of Engineering and Technology Karachi Pakistan Blue Brain Project École Polytechnique Fédérale de Lausanne Lausanne Switzerland Departement of Mathematics Swansea University Swansea Wales UK Laboratory for Topology and Neuroscience at the Brain Mind Institute École polytechnique fédérale de Lausanne Lausanne Switzerland Institute of Mathematics University of Aberdeen Aberdeen Scotland UK Department of Integrativ

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26th Annual computational Neuroscience Meeting (CNS*2017) of the Organization for computational Neuroscience Antwerp, Belgium, July 15-20, 2017

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BMC NEUROscience 2017年第SUPPL 1期18卷 59-59页

作者： [Anonymous] Indiana University Purdue University Indianapolis Indianapolis IN 46032 USA Stark Neurosciences Research Institute Indiana University School of Medicine Indianapolis IN 46032 USA Department of Mathematics East Carolina University Greenville NC 27858 USA Jülich Supercomputing Centre Forschungszentrum Jülich 52425 Jülich Germany Future Systems Swiss National Supercomputing Centre 8092 Zurich Switzerland User Engagement and Support Swiss National Supercomputing Centre 6900 Lugano Switzerland Institut de Neurosciences des Systèmes Aix Marseille Univ 13005 Marseille France Simulation Lab Neuroscience Forschungszentrum Jülich Jülich Germany Department of Experimental Psychology Ghent University 9000 Ghent Belgium Donders Center for Cognitive Neuroimaging Radboud University 6525HR Nijmegen The Netherlands Department of Electrical Computer and Energy Engineering University of Colorado Boulder CO 80309 USA Department of Neurosurgery Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Neurology Johns Hopkins School of Medicine Baltimore MD 21287 USA Department of Otolaryngology Johns Hopkins School of Medicine Baltimore MD 21287 USA INSERM U968 Paris France Sorbonne Universités UPMC University Paris 06 UMR_S 968 Institut de la Vision Paris France CNRS UMR_7210 Paris France Department of Computer Architecture and Technology University of Granada (CITIC) Granada Spain Sorbonne Universités UPMC Univ Paris 06 INSERM CNRS Institut de la Vision Paris France Department of Adaptive Machine Systems Osaka University Osaka Japan Department of Computer Science University of Cergy-Pontoise Cergy-Pontoise France Department of Physics and Astronomy College of Charleston Charleston SC 29424 USA School of Physics Faculty of Science University of Sydney Sydney NSW 2006 Australia Center of Excellence for Integrative Brain Function Australian Research Council Sydney Australia Max Planck Institute for Human Cognitive and Brain Sciences Saxony Lei

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Absolute change pivot rule for the simplex algorithm

Absolute change pivot rule for the simplex algorithm

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International MultiConference of Engineers and computer Scientists, IMECS 2014

作者： Chankong, Kittiphong Intiyot, Boonyarit Sinapiromsaran, Krung Applied Mathematics and Computational Science Program Department of Mathematics and Computer Science Faculty of Science Chulalongkorn University Bangkok Thailand

ISBN: (纸本)9789881925336

The simplex algorithm is a widely used method for solving a linear programming problem (LP) which is first presented by George B. Dantzig. One of the important steps of the simplex algorithm is applying an appropriate pivot rule, the rule to select the entering variable. An effective pivot rule can lead to the optimal solution of LP with the small number of iterations. In a minimization problem, Dantzig's pivot rule selects an entering variable corresponding to the most negative reduced cost. The concept is to have the maximum improvement in the objective value per unit step of the entering variable. However, in some problems, Dantzig's rule may visit a large number of extreme points before reaching the optimal solution. In this paper, we propose a pivot rule that could reduce the number of such iterations over the Dantzig's pivot rule. The idea is to have the maximum improvement in the objective value function by trying to block a leaving variable that makes a little change in the objective function value as much as possible. Then we test and compare the efficacy of this rule with Dantzig' original rule.

关键词： Linear programming

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The cluster heritage project with XMM-Newton: Mass assembly and thermodynamics at the endpoint of structure formation I. programme overview

arXiv

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arXiv 2020年

作者： Arnaud, M. Ettori, S. Pratt, Gabriel W. Rossetti, M. Eckert, D. Gastaldello, F. Gavazzi, R. Kay, S.T. Lovisari, L. Maughan, B.J. Pointecouteau, E. Sereno, M. Bartalucci, I. Bonafede, A. Bourdin, H. Cassano, R. Duffy, R.T. Iqbal, A. Maurogordato, S. Rasia, E. Sayers, J. Andrade-Santos, F. Aussel, H. Barnes, D.J. Barrena, R. Borgani, S. Burkutean, S. Clerc, N. Corasaniti, P.-S. Cuillandre, J.-C. de Grandi, S. de Petris, M. Dolag, K. Donahue, M. Ferragamo, A. Gaspari, M. Ghizzardi, S. Gitti, M. Haines, C.P. Jauzac, M. Johnston-Hollitt, M. Jones, C. Kéruzoré, F. LeBrun, A.M.C. Mayet, F. Mazzotta, P. Melin, J.-B. Molendi, S. Nonino, M. Okabe, N. Paltani, S. Perotto, L. Pires, S. Radovich, M. Rubino-Martin, J.-A. Salvati, L. Saro, A. Sartoris, B. Schellenberger, G. Streblyanska, A. Tarrío, P. Tozzi, P. Umetsu, K. van der Burg, R.F.J. Vazza, F. Venturi, T. Yepes, G. Zarattini, S. AIM CEA CNRS Université Paris-Saclay Université Paris Diderot Sorbonne Paris Cité Gif-sur-YvetteF-91191 France INAF Osservatorio di Astrofisica e Scienza dello Spazio via Pietro Gobetti 93/3 Bologna40129 Italy INFN Sezione di Bologna viale Berti Pichat 6/2 BolognaI-40127 Italy INAF IASF-Milano via A. Corti 12 MilanoI-20133 Italy Department of Astronomy University of Geneva ch. d'Écogia 16 VersoixCH-1290 Switzerland CNRS Sorbonne Université UMR 7095 Institut d'Astrophysique de Paris 98 bis Boulevard Arago Paris75014 France Jodrell Bank Centre for Astrophysics Department of Physics and Astronomy School of Natural Sciences The University of Manchester ManchesterM13 9PL United Kingdom Center for Astrophysics | Harvard & Smithsonian 60 Garden Street CambridgeMA02138 United States HH Wills Physics Laboratory University of Bristol Tyndall Ave BristolBS8 1TL United Kingdom IRAP Université de Toulouse CNRS CNES UPS 9 av du colonel Roche BP44346 Toulouse Cedex 431028 France Dipartimento di Fisica e Astronomia Universitá di Bologna Via Gobetti 92/3 Bologna40121 Italy INAF Istituto di Radio Astronomia Via Gobetti 101 Bologna40129 Italy Hamburger Sternwarte Gojenbergsweg 112 Hamburg21029 Germany Università degli studi di Roma Tor Vergata via della ricerca scientifica 1 Roma00133 Italy Université Côte d'Azur Observatoire de la Côte d'Azur CNRS Laboratoire Lagrange Nice France INAF - Osservatorio Astronomico di Trieste via Tiepolo 11 TriesteI-34131 Italy IFPU - Institute for Fundamental Physics of the Universe via Beirut 2 Trieste34151 Italy California Institute of Technology PasadenaCA91125 United States Department of Physics Kavli Institute for Astrophysics and Space Research Massachusetts Institute of Technology CambridgeMA02139 United States C/ Vía Láctea s/n La Laguna TenerifeE-38205 Spain Universidad de La Laguna Departamento de Astrofísica C/ Astrofísico Francisco Sánchez s/n La Laguna TenerifeE-38206 Spain D

The Cluster HEritage project with XMM-Newton - Mass Assembly and Thermodynamics at the Endpoint of structure formation (CHEX-MATE) is a three-mega-second Multi-Year Heritage programme to obtain X-ray observations of a minimally-biased, signal-to-noise-limited sample of 118 galaxy clusters detected by Planck through the Sunyaev-Zeldovich effect. The programme, described in detail in this paper, aims to study the ultimate products of structure formation in time and mass. It is composed of a census of the most recent objects to have formed (Tier-1: 0.05 14 M 500 14 M), together with a sample of the highest mass objects in the Universe (Tier-2: z 500 > 7.25 × 1014 M). The programme will yield an accurate vision of the statistical properties of the underlying population, measure how the gas properties are shaped by collapse into the dark matter halo, uncover the provenance of non-gravitational heating, and resolve the major uncertainties in mass determination that limit the use of clusters for cosmological parameter estimation. We will acquire X-ray exposures of uniform depth, designed to obtain individual mass measurements accurate to 15 − 20% under the hydrostatic assumption. We present the project motivations, describe the programme definition, and detail the ongoing multi-wavelength observational (lensing, SZ, radio) and theoretical effort that is being deployed in support of the project. Copyright © 2020, The Authors. All rights reserved.

关键词： Thermodynamics

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