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Journal of Physics B: Atomic, Molecular and Optical Physics 2020年第21期53卷

作者： Xiao-Kang Li Dian-Cheng Zhang Shuang-Fei Lv Jin-Yun Liu Feng-Dong Jia Yong Wu Xiao-He Lin Rui Li Xiang-Yuan Xu Ping Xue Xiao-Jing Liu Zhi-Ping Zhong School of Physical Sciences University of Chinese Academy of Sciences PO Box 4588 Beijing 100049 People's Republic of China Institute of Applied Physics and Computational Mathematics Beijing 100088 People's Republic of China Department of Physics Capital Normal University Beijing 100037 People's Republic of China State Key Laboratory of Low-Dimensional Quantum Physics Department of Physics Tsinghua University and Collaborative Innovation Center of Quantum Matter Beijing 100084 People's Republic of China School Physical Science and Technology ShanghaiTech University Shanghai 201210 People's Republic of China CAS Center for Excellence in Topological Quantum Computation University of Chinese Academy of Sciences Beijing 100190 People's Republic of China

Internal and external potential-field estimation from regional vector data at varying satellite altitude

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arXiv 2017年

作者： Plattner, Alain Simons, Frederik J. Department of Earth and Environmental Sciences California State University Fresno FresnoCA93740 United States Department of Geosciences Princeton University PrincetonNJ08544 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States

When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are available, or when data quality varies strongly with geographic location, the inversion problem becomes severely ill-posed. In those cases, adopting explicitly local methods is to be preferred over adapting global ones (e.g., by regularization). Here, we develop the theory behind a procedure to invert for planetary potential fields from vector observations collected within a spatially bounded region at varying satellite altitude. Our method relies on the construction of spatiospectrally localized bases of functions that mitigate the noise amplification caused by downward continuation (from the satellite altitude to the planetary surface) while balancing the conflicting demands for spatial concentration and spectral limitation. The 'altitude-cognizant' gradient vector Slepian functions (AC-GVSF) were first employed in a preceding paper. They enjoy a noise tolerance under downward continuation that is much improved relative to the 'classical' gradient vector Slepian functions (CL-GVSF), which do not factor satellite altitude into their construction. Furthermore, venturing beyond the realm of their first application, in the present article we extend the theory to being able to handle both internal and external potential-field estimation. Solving simultaneously for internal and external fields in the same setting of regional data availability reduces internal-field artifacts introduced by downward-continuing unmodeled external fields, as we show with numerical examples. We explain our solution strategies on the basis of analytic expressions for the behavior of the estimation bias and variance of models for which signal and noise are uncorrelated, (essentially) spaceand bandlimited, and spectrally (almost) white. The AC-GVSF are optimal linea

关键词： Harmonic analysis

First Measurement of Antideuteron Number Fluctuations at Energies Available at the Large Hadron Collider

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Physical Review Letters 2023年第4期131卷 041901-041901页

作者： S. Acharya D. Adamová A. Adler G. Aglieri Rinella M. Agnello N. Agrawal Z. Ahammed S. Ahmad S. U. Ahn I. Ahuja A. Akindinov M. Al-Turany D. Aleksandrov B. Alessandro H. M. Alfanda R. Alfaro Molina B. Ali Y. Ali A. Alici N. Alizadehvandchali A. Alkin J. Alme G. Alocco T. Alt I. Altsybeev M. N. Anaam C. Andrei A. Andronic V. Anguelov F. Antinori P. Antonioli C. Anuj N. Apadula L. Aphecetche H. Appelshäuser S. Arcelli R. Arnaldi I. C. Arsene M. Arslandok A. Augustinus R. Averbeck S. Aziz M. D. Azmi A. Badalà Y. W. Baek X. Bai R. Bailhache Y. Bailung R. Bala A. Balbino A. Baldisseri B. Balis D. Banerjee Z. Banoo R. Barbera L. Barioglio M. Barlou G. G. Barnaföldi L. S. Barnby V. Barret L. Barreto C. Bartels K. Barth E. Bartsch F. Baruffaldi N. Bastid S. Basu G. Batigne D. Battistini B. Batyunya D. Bauri J. L. Bazo Alba I. G. Bearden C. Beattie P. Becht D. Behera I. Belikov A. D. C. Bell Hechavarria R. Bellwied S. Belokurova V. Belyaev G. Bencedi S. Beole A. Bercuci Y. Berdnikov A. Berdnikova L. Bergmann M. G. Besoiu L. Betev P. P. Bhaduri A. Bhasin I. R. Bhat M. A. Bhat B. Bhattacharjee L. Bianchi N. Bianchi J. Bielčík J. Bielčíková J. Biernat A. Bilandzic G. Biro S. Biswas J. T. Blair D. Blau M. B. Blidaru N. Bluhme C. Blume G. Boca F. Bock T. Bodova A. Bogdanov S. Boi J. Bok L. Boldizsár A. Bolozdynya M. Bombara P. M. Bond G. Bonomi H. Borel A. Borissov H. Bossi E. Botta L. Bratrud P. Braun-Munzinger M. Bregant M. Broz G. E. Bruno M. D. Buckland D. Budnikov H. Buesching S. Bufalino O. Bugnon P. Buhler Z. Buthelezi J. B. Butt A. Bylinkin S. A. Bysiak M. Cai H. Caines A. Caliva E. Calvo Villar J. M. M. Camacho R. S. Camacho P. Camerini F. D. M. Canedo M. Carabas F. Carnesecchi R. Caron J. Castillo Castellanos F. Catalano C. Ceballos Sanchez I. Chakaberia P. Chakraborty S. Chandra S. Chapeland M. Chartier S. Chattopadhyay T. G. Chavez T. Cheng C. Cheshkov B. Cheynis V. Chibante Barroso D. D. Chinellato E. S. Chizzali S. Cho P. Chochula P. Christakoglou C. H. Christensen P. Christiansen T. Chujo M. Ciacco C. Cicalo L. C Université Clermont Auvergne CNRS/IN2P3 LPC Clermont-Ferrand France Variable Energy Cyclotron Centre Homi Bhabha National Institute Kolkata India Nuclear Physics Institute of the Czech Academy of Sciences Husinec-Řež Czech Republic Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik Fachbereich Informatik und Mathematik Frankfurt Germany European Organization for Nuclear Research (CERN) Geneva Switzerland Dipartimento DISAT del Politecnico and Sezione INFN Turin Italy INFN Sezione di Bologna Bologna Italy Department of Physics Aligarh Muslim University Aligarh India Korea Institute of Science and Technology Information Daejeon Republic of Korea Faculty of Science P.J. Šafárik University Košice Slovak Republic Affiliated with an institute covered by a cooperation agreement with CERN Research Division and ExtreMe Matter Institute EMMI GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Germany INFN Sezione di Torino Turin Italy Central China Normal University Wuhan China Instituto de Física Universidad Nacional Autónoma de México Mexico City Mexico COMSATS University Islamabad Islamabad Pakistan Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN Bologna Italy University of Houston Houston Texas USA Department of Physics and Technology University of Bergen Bergen Norway INFN Sezione di Cagliari Cagliari Italy Institut für Kernphysik Johann Wolfgang Goethe-Universität Frankfurt Frankfurt Germany Horia Hulubei National Institute of Physics and Nuclear Engineering Bucharest Romania Westfälische Wilhelms-Universität Münster Institut für Kernphysik Münster Germany Physikalisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany INFN Sezione di Padova Padova Italy Lawrence Berkeley National Laboratory Berkeley California USA SUBATECH IMT Atlantique Nantes Université CNRS-IN2P3 Nantes France Department of Physics University of Oslo Oslo Norway Yale University New Haven Connecticut USA L

The first measurement of event-by-event antideuteron number fluctuations in high energy heavy-ion collisions is presented. The measurements are carried out at midrapidity (|η|<0.8) as a function of collision centrality in Pb-Pb collisions at sNN=5.02 TeV using the ALICE detector. A significant negative correlation between the produced antiprotons and antideuterons is observed in all collision centralities. The results are compared with a state-of-the-art coalescence calculation. While it describes the ratio of higher order cumulants of the antideuteron multiplicity distribution, it fails to describe quantitatively the magnitude of the correlation between antiproton and antideuteron production. On the other hand, thermal-statistical model calculations describe all the measured observables within uncertainties only for correlation volumes that are different with respect to those describing proton yields and a similar measurement of net-proton number fluctuations.

关键词： Hadron-hadron interactions

Convex Inversion of the Entrywise Product of Real Signals with Known Signs

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Convex Inversion of the Entrywise Product of Real Signals wi...

Asilomar Conference on Signals, Systems, and Computers

作者： Alireza Aghasi Ali Ahmed Paul Hand School of Business Georgia State University Atlanta School of Electrical and Computer Engineering Information Technology University Lahore Pakistan Department of Computational and Applied Mathematics Rice University Houston TX

We consider the bilinear inverse problem of recovering two vectors, x and w, in R~L from their entrywise product. For the case where the vectors have known signs and belong to known subspaces, we introduce the convex program BranchHull, which is posed in the natural parameter space and does not require an approximate solution or initialization in order to be stated or solved. Under the structural assumptions that x and w are the members of known K and N dimensional random subspaces, we prove that BranchHull recovers x and w up to the inherent scaling ambiguity with high probability, whenever L {approx.>} K + N. This problem is motivated by applications in the sweep distortion removal task in dielectric imaging, where one of the signals is a nonnegative reflectivity, and the other signal lives in a known wavelet subspace. Additional potential applications are blind deconvolution and self-calibration.

关键词： Deconvolution Electronic mail Signal processing Calibration Task analysis Imaging

Scientific Data Interpolation with Low Dimensional Manifold ModelI

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arXiv 2017年

作者： Zhu, Wei Wang, Bao Barnard, Richard Hauck, Cory D. Jenko, Frank Osher, Stanley Department of Mathematics University of California Los Angeles Los AngelesCA90095 United States Computational and Applied Mathematics Group Oak Ridge National Laboratory Oak RidgeTN37831 United States Department of Mathematics University of Tennessee KnoxvilleTN37996-1320 United States Department of Physics and Astronomy University of California Los AngelesCA90095 United States

We propose to apply a low dimensional manifold model to scientific data interpolation from regular and irregular samplings with a significant amount of missing information. The low dimensionality of the patch manifold for general scientific data sets has been used as a regularizer in a variational formulation. The problem is solved via alternating minimization with respect to the manifold and the data set, and the Laplace-Beltrami operator in the Euler-Lagrange equation is discretized using the weighted graph Laplacian. Various scientific data sets from different fields of study are used to illustrate the performance of the proposed algorithm on data compression and interpolation from both regular and irregular samplings. Copyright © 2017, The Authors. All rights reserved.

关键词： Interpolation

An elementary and unified proof of grothendieck's inequality

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arXiv 2017年

作者： Friedland, Shmuel Lim, Lek-Heng Zhang, Jinjie Department of Mathematics Statistics and Computer Science University of Illinois ChicagoIL60607-7045 United States Computational and Applied Mathematics Initiative Department of Statistics University of Chicago ChicagoIL60637-1514 United States Department of Statistics University of Chicago ChicagoIL60637-1514 United States Department of Mathematics University of California San DiegoCA92093-0112 United States

We present an elementary, self-contained proof of Grothendieck's inequality that unifies the real and complex cases and yields both the Krivine and Haagerup bounds, the current bestknown explicit bounds for the real and complex Grothendieck constants respectively. This article is intended to be pedagogical, combining and streamlining known ideas of Lindenstrauss-Pe lczyński, Krivine, and Haagerup into a proof that need only univariate calculus, basic complex variables, and a modicum of linear algebra as prerequisites.47A07, 46B28, 46B85, 81P40, 81P45, 03D15, 97K30, 47N10, 90C27 Copyright © 2017, The Authors. All rights reserved.

关键词： Linear algebra

Measurement of ω meson production in pp collisions at = 13 TeV

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Journal of High Energy Physics 2025年第4期2025卷 1-30页

作者： Acharya, S. Adamová, D. Agarwal, A. Aglieri Rinella, G. Aglietta, L. Agnello, M. Agrawal, N. Ahammed, Z. Ahmad, S. Ahn, S. U. Ahuja, I. Akindinov, A. Akishina, V. Al-Turany, M. Aleksandrov, D. Alessandro, B. Alfanda, H. M. Alfaro Molina, R. Ali, B. Alici, A. Alizadehvandchali, N. Alkin, A. Alme, J. Alocco, G. Alt, T. Altamura, A. R. Altsybeev, I. Alvarado, J. R. Anaam, M. N. Andrei, C. Andreou, N. Andronic, A. Andronov, E. Anguelov, V. Antinori, F. Antonioli, P. Apadula, N. Aphecetche, L. Appelshäuser, H. Arata, C. Arcelli, S. Aresti, M. Arnaldi, R. Arneiro, J. G. M. C. A. Arsene, I. C. Arslandok, M. Augustinus, A. Averbeck, R. Azmi, M. D. Baba, H. Badalà, A. Bae, J. Baek, Y. W. Bai, X. Bailhache, R. Bailung, Y. Bala, R. Balbino, A. Baldisseri, A. Balis, B. Banerjee, D. Banoo, Z. Barbasova, V. Barile, F. Barioglio, L. Barlou, M. Barman, B. Barnaföldi, G. G. Barnby, L. S. Barreau, E. Barret, V. Barreto, L. Bartels, C. Barth, K. Bartsch, E. Bastid, N. Basu, S. Batigne, G. Battistini, D. Batyunya, B. Bauri, D. Bazo Alba, J. L. Bearden, I. G. Beattie, C. Becht, P. Behera, D. Belikov, I. Bell Hechavarria, A. D. C. Bellini, F. Bellwied, R. Belokurova, S. Beltran, L. G. E. Beltran, Y. A. V. Bencedi, G. Bensaoula, A. Beole, S. Berdnikov, Y. Berdnikova, A. Bergmann, L. Besoiu, M. G. Betev, L. Bhaduri, P. P. Bhasin, A. Bhat, M. A. Bhattacharjee, B. Bianchi, L. Bianchi, N. Bielčík, J. Bielčíková, J. Bigot, A. P. Bilandzic, A. Biro, G. Biswas, S. Bize, N. Blair, J. T. Blau, D. Blidaru, M. B. Bluhme, N. Blume, C. Boca, G. Bock, F. Bodova, T. Bok, J. Boldizsár, L. Bombara, M. Bond, P. M. Bonomi, G. Borel, H. Borissov, A. Borquez Carcamo, A. G. Bossi, H. Botta, E. Bouziani, Y. E. M. Bratrud, L. Braun-Munzinger, P. Bregant, M. Broz, M. Bruno, G. E. Buckland, M. D. Budnikov, D. Buesching, H. Bufalino, S. Buhler, P. Burmasov, N. Buthelezi, Z. Bylinkin, A. Bysiak, S. A. Cabanillas Noris, J. C. Cabrera, M. F. T. Cai, M. Caines, H. Caliva, A. Calvo Villar, E. Camacho, J. M. M. Camerini, P. Canedo, F. D. M. Cantway, S. L. Carabas, M. Université Clermont Auvergne CNRS/IN2P3 LPC Clermont-Ferrand France Nuclear Physics Institute of the Czech Academy of Sciences Husinec-Řež Czech Republic Variable Energy Cyclotron Centre Homi Bhabha National Institute Kolkata India European Organization for Nuclear Research (CERN) Geneva Switzerland Dipartimento di Fisica dell’Università and Sezione INFN Turin Italy Dipartimento DISAT del Politecnico and Sezione INFN Turin Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN Bologna Italy Department of Physics Aligarh Muslim University Aligarh India Korea Institute of Science and Technology Information Daejeon Republic of Korea Faculty of Science P.J. Šafárik University Košice Slovak Republic Frankfurt Institute for Advanced Studies Johann Wolfgang Goethe-Universität Frankfurt Frankfurt Germany Research Division and ExtreMe Matter Institute EMMI GSI Helmholtzzentrum für Schwerionenforschung GmbH Darmstadt Germany INFN Sezione di Torino Turin Italy Central China Normal University Wuhan China Instituto de Física Universidad Nacional Autónoma de México Mexico City Mexico University of Houston Houston United States Sungkyunkwan University Suwon City Republic of Korea Department of Physics and Technology University of Bergen Bergen Norway INFN Sezione di Cagliari Cagliari Italy Institut für Kernphysik Johann Wolfgang Goethe-Universität Frankfurt Frankfurt Germany INFN Sezione di Bari Bari Italy Physik Department Technische Universität München Munich Germany High Energy Physics Group Universidad Autónoma de Puebla Puebla Mexico Horia Hulubei National Institute of Physics and Nuclear Engineering Bucharest Romania University of Derby Derby United Kingdom Universität Münster Institut für Kernphysik Münster Germany Physikalisches Institut Ruprecht-Karls-Universität Heidelberg Heidelberg Germany INFN Sezione di Padova Padova Italy INFN Sezione di Bologna Bologna Italy Lawrence Berkeley National Laboratory Berkeley United Sta

The pT-differential cross section of ω meson production in pp collisions at $$ \sqrt{s} $$ = 13 TeV at midrapidity (|y| < 0.5) was measured with the ALICE detector at the LHC, covering an unprecedented transverse-momentum range of 1.6 < pT < 50 GeV/c. The meson is reconstructed via the ω → π+π−π0 decay channel. The results are compared with various theoretical calculations: PYTHIA8.2 with the Monash 2013 tune overestimates the data by up to 50%, whereas good agreement is observed with Next-to-Leading Order (NLO) calculations incorporating ω fragmentation using a broken SU(3) model. The ω/π0 ratio is presented and compared with theoretical calculations and the available measurements at lower collision energies. The presented data triples the pT ranges of previously available measurements. A constant ratio of Cω/π0 = 0.578 ± 0.006 (stat.) ± 0.013 (syst.) is found above a transverse momentum of 4 GeV/c, which is in agreement with previous findings at lower collision energies within the systematic and statistical uncertainties.

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Clinical response to azacitidine in MDS is associated with distinct DNA methylation changes in HSPCs

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Nature Communications 2025年第1期16卷 1-20页

作者： Thoms, Julie A. I. Yan, Feng Hampton, Henry R. Davidson, Sarah Joshi, Swapna Saw, Jesslyn Sarowar, Chowdhury H. Lim, Xin Ying Nunez, Andrea C. Kakadia, Purvi M. Bhuyan, Golam Sarower Zou, Xiaoheng Nguyen, Mary Ghodousi, Elaheh S. Koch, Forrest C. Vafaee, Fatemeh Thompson, I. Richard Karimi, Mohammad M. Pickford, Russell Raftery, Mark J. Hough, Sally Buckland, Griselda Bailey, Michelle Ghodke, Yuvaraj Absar, Noorul Vaughan, Lachlin Pasalic, Leonardo Fong, Chun Y. Kenealy, Melita Hiwase, Devendra K. Stoddart, Rohanna I. Mohammed, Soma Lee, Linda Passam, Freda H. Larsen, Stephen R. Spring, Kevin J. Skarratt, Kristen K. Rebeiro, Patricia Presgrave, Peter Stevenson, William S. Ling, Silvia Tiley, Campbell Fuller, Stephen J. Roncolato, Fernando Enjeti, Anoop K. Hoenemann, Dirk Lemech, Charlotte Jolly, Christopher J. Bohlander, Stefan K. Curtis, David J. Wong, Jason W. H. Unnikrishnan, Ashwin Hertzberg, Mark Olivier, Jake Polizzotto, Mark N. Pimanda, John E. School of Biomedical Sciences University of New South Wales Sydney NSW Australia Bioinformatics Division Walter and Eliza Hall Institute of Medical Research Parkville VIC Australia ANU Clinical Hub for Interventional Research (CHOIR) John Curtin School of Medical Research Canberra ACT Australia Kirby Institute University of New South Wales Sydney NSW Australia School of Clinical Medicine University of New South Wales Sydney NSW Australia Australian Centre for Blood Diseases Monash University Melbourne VIC Australia Leukaemia & Blood Cancer Research Unit Department of Molecular Medicine and Pathology Faculty of Medical and Health Sciences The University of Auckland Auckland New Zealand School of Biotechnology and Biomolecular Sciences University of New South Wales Sydney NSW Australia UNSW Data Science Hub University of New South Wales Sydney NSW Australia Comprehensive Cancer Centre School of Cancer and Pharmaceutical Sciences King’s College London London United Kingdom Bioanalytical Mass Spectrometry Facility University of New South Wales Sydney NSW Australia Westmead Hospital Sydney NSW Australia ICPMR Department of Haematology Westmead Hospital Sydney NSW Australia Department of Haematology Austin Health Melbourne VIC Australia Cabrini Hospital Melbourne VIC Australia Department of Haematology Royal Adelaide Hospital Adelaide SA Australia University of New South Wales Sydney NSW Australia Royal North Shore Hospital Sydney NSW Australia Haematology Research Group Heart Research Institute Sydney NSW Australia Institute of Haematology Royal Prince Alfred Hospital Sydney NSW Australia Medical Oncology Group Liverpool Clinical School School of Medicine Western Sydney University and Ingham Institute for Applied Medical Research Liverpool NSW Australia South-West Sydney Clinical Campuses UNSW Medicine & Health Sydney NSW Australia Sydney Medical School Nepean Clinical School Faculty of Medicine and Health University of Sydney

Hypomethylating agents are frontline therapies for myelodysplastic neoplasms (MDS), yet clinical responses remain unpredictable. We conducted a phase 2 trial comparing injectable and oral azacitidine (AZA) administered over one or three weeks per four-week cycle, with the primary objective of investigating whether response is linked to in vivo drug incorporation or DNA hypomethylation. Our findings show that injection results in higher drug incorporation, but lower DNA demethylation per cycle, while global DNA methylation levels in mononuclear cells are comparable between responders and non-responders. However, hematopoietic stem and progenitor cells (HSPCs) from responders exhibit distinct baseline and early treatment-induced CpG methylation changes at regulatory regions linked to tissue patterning, cell migration, and myeloid differentiation. By cycle six—when clinical responses typically emerge—further differential hypomethylation in responder HSPCs suggests marrow adaptation as a driver of improved hematopoiesis. These findings indicate that intrinsic baseline and early drug-induced epigenetic differences in HSPCs may underlie the variable clinical response to AZA in MDS. © The Author(s) 2025.

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Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

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arXiv 2017年

作者： Hubmer, Simon Sherina, Ekaterina Neubauer, Andreas Scherzer, Otmar Johannes Kepler University Linz Doctoral Program Computational Mathematics Altenbergerstraße 69 LinzA-4040 Austria Technical University of Denmark Department of Applied Mathematics and Computer Science Asmussens Allé Kongens Lyngby 2800 Denmark Johannes Kepler University Linz Industrial Mathematics Institute Altenbergerstraße 69 LinzA-4040 Austria University of Vienna Computational Science Center Oskar Morgenstern-Platz 1 Vienna1090 Austria Johann Radon Institute Linz Altenbergerstraße 69 LinzA-4040 Austria

We consider a problem of quantitative static elastography, the estimation of the Lamé parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically. The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lamé parameters from displacement data simulating a static elastography experiment are *** Codes 65J22, 65J15, 74G75 Copyright © 2017, The Authors. All rights reserved.

关键词： Inverse problems

Numerically testing generically reduced projective schemes for the arithmetic gorenstein property 6th

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Numerically testing generically reduced projective schemes f...

6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015

作者： Daleo, Noah S. Hauenstein, Jonathan D. Department of Mathematics Worcester State University WorcesterMA01602 United States Department of Applied and Computational Mathematics and Statistics University of Notre Dame Notre DameIN46556 United States

ISBN: (纸本)9783319328584

Let X ⊂ n be a generically reduced projective scheme. A fundamental goal in computational algebraic geometry is to compute information about X even when defining equations for X are not known. We use numerical algebraic geometry to develop a test for deciding if X is arithmetically Gorenstein and apply it to three secant varieties. © Springer International Publishing Switzerland 2016.

关键词： Algebra