Numerical Range and Radii Scientists, Journals, Countries, Grants

Numerical Range and Radii Scientists, Journals, Countries, Grants

Numerical Range and Radii Scientists, Journals, Countries, Grants and some open problems Some researchers with Numerical Range & Numerical Radii interest Natlia Bebiano (University of Coimbra) D. R. Farenick; (Universite de Montral) Marvin Marcus ; Ivan Filippenko; (University of California) Che-Man Cheng (University of Macau) Chi-Kwong Li;

(College of William & Mary) Chi Fai Chan; (University of Hong Kong) Michael E. Lundquist; (Brigham Young University Provo) Man-Duen Choi; University of Toronto Tin-Yau Tam; (Auburn University) Nam-Kiu Tsing; The University of Hong Kong Karl E. Gustafson; University of Colorado at Boulder J.L.M. van Dorsselaer;

University of Utrecht" Yiu Tung Poon; Iowa State University Nung-Sing Sze; University of Connecticut The Hong Kong Polytechnic University Duggirala K.M. Rao; Colegio Bolivar at Cali Karol yczkowski; (Uniwersytet Jagielloski) Edward Poon; Embry-Riddle Aeronautical University (Polska Akademia Nauk) Eugene Gutkin; (Center for Theoretical Physics) (Nicolaus Copernicus University) (Polish Academy of Sciences) Wai-Shun Cheung;

University of Hong Kong Nam-Kiu Tsing; The University of Hong Kong Xuhua (Roy) Liu; The University of Tennessee at Chattanooga Mao-Ting Chien; Soochow University Ilya M. Spitkovsky; College of William and Mary Chandler Davis ; University of Toronto Michael Karow; echnical University of Berlin Hiroshi Nakazato;

Hirosaki University Leiba Rodman; Edmond A. Jonckheere; College of William and Mary University of Southern California Naum Yakovlevich Krupnik; University of Toronto Hwa-Long Gau; ational Central University Taiwan Panayiotis J. Psarrakos; National Technical University of Athens Pei-Yuan Wu; National Chiao Tung University Taiwan Kuo-Zhong Wang; National Chiao Tung University

Aikaterini Aretaki; National Technical University of Athens Chi-Tung Chang; Feng Chia University John Maroulas; National Technical University of Athens Hiroyuki Tomita; Iowa State University Peter Lancaster; University of Calgary Charles F. Dunkl; University of Virginia John A R Holbrook; University of Guelph Sean A. Clark;

The College of William and Mary Mikio Nakahara; Kinki University Jennifer Mahle; The College of William and Mary David W. Kribs; University of Guelph Hugo J. Woerdeman; Drexel University, Michael Giesinger; University of Guelph Roman Drnovek; University of Ljubljana Vladimr Mller;

Academy of Sciences of the Czech Repu blic Miguel Martn Surez; Universidad de Granada Charles A. Akemann; University of California, Santa Barbara Javier Mer de la Maza; Universidad de Granada Sever Silvestru Dragomir; Victoria University Melbourne ngel Rodrguez-Palacios; Universidad de Granada Piotr Gawron;

Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences Zbigniew Puchaa; Jagiellonian University Alexander Litvak; University of Alberta Anne Greenbaum; University of Washington ukasz Skowronek; Jagiellonian University Although, Scopus is not completely reliable search engine(for example, you may find some typos in its work, by concentrating on the following slides!), we want to present some statistics using it!

Scopus results of numerical range or numerical radii in their abstract title, abstract or keywords Article(873) Conference Paper(104) Article in Press(24) Review(10) Conference Review(1) Editorial(1) Erratum(1)

Letter(1) Note(1) Report(1) Undefined(16) In the following slides, you see that in United States and other top universities which publish manuscripts in the field of numerical range, there exist a few researchers which play a key role; in the other hand, they rely on a few scientists! And team work cycles in that little group. Author Name (Number of Scopus results which have numerical range or numerical radii in their abstract title, abstract or keywords) Li, C.K.(71) Chien, M.T.(44) Nakazato, H.(39) Wu, P.Y.(30) Gau, H.L. (28) Rodman, L.(22) Bebiano, N.(22) Poon, Y.T.(20) Psarrakos, P.(17) Sze, N.S. (17) Spitkovsky, I.M.(17) Martin, M.(15) Cheung, W.S.(13) Tam, T.Y.(13) Li, C.K.(12) Dragomir, S.S.(12) Psarrakos, P.J.(12) Maroulas, J.(11) Goldberg, M. (10) Zyczkowski, K.(9) Kittaneh, F.(9) Crouzeix, M.(9) Meri, J.(9) Tsatsomeros,

M.J.(9) Tretter, C.(9) Da Providencia, J.(9) Wang, K.Z.(8) Adam, M.(8) Choi, M.D.(8) Hou, J.(8) Acosta, M.D.(7) Woerdeman, H.J.(7) Salemi, A.(7) Liu, X. (7) Tsing, N.K.(7) Verma, R.U.(7) Kim, S.G.(7) Li, H.(6) da Providencia, J. (6) Marcus, M.(6) Soares, G.(6) Abdollahi, A.(6) Spitkovsky, I.(6) Okubo, K. (6) Straus, E.G.(5) Tsai, M.C.(5) Tam, T.Y.(5) Ando, T.(5) Gawron, P.(5) Garcia, D.(5) Afshin, H.R.(5) Lemos, R.(5) Choi, Y.S.(5) Agure, J.O.(5) Karaev, M.T. (5) Maestre, M.(5) Aksoy, A.G.(5) Markus, A.(5) Mirman, B.(5) Poon, E. (5) Puchala, Z.(5) Schneider, H.(5) Shebrawi, K.(5) Owens, D.H.(4) Kribs, D.W.(4) Drury, S.W.(4) Palazoglu, A.(4) Langer, H.(4) Johnson, C.R. (4) Mehrjoofard, M.A.(4) Du, H.K.(4) Nata, A.(4) Ren, F.G.(4) Langer, M.(4) Gorkin, P. (4) Paul, K.(4) Paya, R.(4) Heydari, M.T.(4) Miszczak, J.A.(4) Seddik, A.(4) Dritschel, M.A. (4) Holbrook, J.A.(4) Tadmor, E.(4) Tam, B.S.(4) Timoney, R.M.(4) Boumazgour, M. (4) Wimmer, H.K.(4) Bekiroglu, H.(3) Cui, J.(3) Friedland, S.(3) Fabiano, R.H.(3) Gutkin, E. (3) Khambanonda, T.(3) Matache, V.(3) Huang, Y.(3) Jonckheere, E.A.(3) Palacios, A.R. (3) Patton, L.J.(3) Barraa, M.(3) Elomaa, T.(3) Dunkl, C.F.(3) Al-Hawari, M.(3) Da Providencia, J.(3) Rousu, J.(3) Ruiz Galan, M.(3) Drnovsek, R.(3) Sano, T.(3) Hou, J.C. (3) Lins, B.(3) Schulte-Herbruggen, T.(3) Lancaster, P.(3) Fixman, U.(3) Semrl, P.(3) Farid, F.O.(3) Bonyo, J.O.(3) Spain, P.G.(3) Dou, Y.N.(3) Hochstenbach, M.E.(3) He, K.(3) Hirzallah, O.(3) Delyon, B.(3) Lewicki, G.(3) Glasser, L.A.(3) Fan, Y.(3) Tibken, B.(3) Helmke, U.(3) Dirr, G.(3) Bag, S.(3) Guerrero, J.B.(3) Akemann, C.A.(3) Uhlig, F.(3) Chorianopoulos, C.

(3) Williams, J.P.(3) Beckermann, B.(3) Higham, N.J.(3) Glaser, S.J.(3) Yeh, L.(3) Zaharia, A. (3) Zhang, S.(3) Finet, C.(3) Gregory, R.(2) Cassier, G.(2) Agrillo, C.(2) Ahmad, F. (2) Henningson, D.S.(2) Ai, W.(2) Li, Y.C.(2) Chalendar, I.(2) Liu, L.Y.(2) Kamp, Y.(2) Liu, X. (2) Alizadeh, R.(2) Chan, J.T.(2) Alshorman, A.A.(2) Markus, A.S.(2) Marletta, M. (2) Anderson, J.(2) Deutsch, E.(2) Chang, C.T.(2) Undefined(1) Affiliation Country (Number of Scopus results of numerical range or numerical radii in their abstract title, abstract or keywords) United States(314), China(95), Taiwan(90), Japan(67), Germany(50), Canada(48), United Kingdom(46), France(39), Hong Kong(38), Spain(38), Greece(34), Portugal(26), Iran(24), Australia(23), Poland(18), Israel(17), Jordan(17), India(15), South Korea(14), Italy(13), Netherlands(12), Russian Federation(12), Finland(11), Slovenia(10), Austria(8), Morocco(8), Saudi Arabia(8), Switzerland(8), Mexico(7), Belgium(6), Czech Republic(6) South Africa(6), Ukraine(6), Kenya(5), Romania(5), Azerbaijan(4), Ireland(4), Turkey(3), Lithuania(2), Algeria(2), Armenia(2), Singapore(2), Croatia(2), Bulgaria(2), United Arab Emirates(2), Mongolia(2), New Zealand(2), ,Yemen(2), Macao(1), Brazil(1), Denmark(1), Russia(1), Chile(1), Sweden(1), Egypt(1), Yugoslavia(1)

Universities (Number of Affiliation results indexed in Scopus) The College of William and Mary(105) Soochow University, Taipei(44)

Hirosaki University(38) National Chiao Tung University Taiwan(36) Ethniko Metsovio Polytechnico(31) (=National Technical University of Athens) National Central University Taiwan(28) The University of Hong Kong(26) Universidade de Coimbra(22) Iowa State University(20) Auburn University(20) Universidad de Granada, Facultad de Ciencias(20) University of Toronto(15) University of California, Santa Barbara(15) Victoria University Melbourne(14) Uniwersytet Jagiellonski w Krakowie(14) Shaanxi Normal University(13)

Hong Kong Polytechnic University(11) Shandong University of Technology(11) University of Guelph(10) Universidad de Granada(10) The University of Jordan(10) Shanxi Normal University(9) Shanxi University(8) Center for Theoretical Physics of the Polish Academy of Sciences(8) Julius-Maximilians-Universitt Wrzburg(8)

Kyungpook National University(8) Taiyuan Li Gong Daxue(8) Washington State University Pullman(8) Massachusetts Institute of Technology(8) University of California, Los Angeles(8) University of Ljubljana(8) Universit des Sciences et Technologies de Lille(7) Technische Universitat Wien(7) Indiana University(7) Technion - Israel Institute of Technology(7) University of Connecticut(7) Ben-Gurion University of the Negev(7) Daneshgahe Shahid Bahonar-e-Kerman(7)

Al-Balqa Applied University(7) University of Waterloo(6) Universidade de Tras-os-Montes e Alto Douro(6) Hokkaido University of Education(6) Universidade de Aveiro(6) Shiraz University(6) California Institute of Technology(6) University of Wisconsin Madison(6) Aalto University(6)

University of Calgary(5) McGill University(5) Claremont McKenna College(5) Technische Universitt Berlin(5) UC Davis(5) University of Maryland(5) Universitt Bern(5) Institute of Theoretical and Applied Informatics of the Polish Academy of Sciences(5)

Universite Claude Bernard Lyon 1(5) University of Strathclyde(5) Embry Riddle Aeronautical University, Prescott Campus(5) University of Regina(5) Vali-e-Asr University of Rafsanjan(5) University of Glasgow(4) Universitat de Valencia(4) Chinese University of Hong Kong(4) Indian Institute of Technology, Kharagpur(4)

Universitt Bremen(4) Duke University(4) Trinity College Dublin(4) University of Leeds(4) Polish Academy of Sciences(4) Queen's University, Kingston(4) Instituto Politcnico de Tomar(4) Xi'an Jiaotong University(4) Tamkang University(4) University of Nebraska at Omaha(4)

Technische Universitt Mnchen(4) Bucknell University(4) Texas A and M University(4) Jadavpur University(4) University of Central Florida(4)

University of New South Wales(4) University of Southern California(4) Universite de Rennes 1(4) Universidad Nacional Autnoma de Mxico(4) Hashemite University(4) Maseno University(4) Tongji University(4) University of Central Greece(4) Sleyman Demirel niversitesi(3) Case Western Reserve University(3) Ewha Womans University(3) Universite Pierre et Marie Curie(3) Helsingin Yliopisto(3) University of Victoria(3) Princeton University(3) Ohio State University(3)

University of Manchester(3) Arizona State University(3) Rice University(3) Hampden-Sydney College(3) University of Primorska(3) Kanagawa University(3)

Suffolk University(3) Wayne State University(3) Universite de Mons-Hainaut(3) CalPoly(3) Hokkaido University(3) University of Kansas Lawrence(3) University of Washington Seattle(3) Yamagata University(3) University of Witwatersrand(3) National Tsing Hua University(3)

University of Virginia(3) University of Macau(3) Rensselaer Polytechnic Institute(3) Tianjin University of Technology(3) Ludwig-Maximilians-Universitt Mnchen(3) Chung Yuan Christian University(3) Facult des Sciences Semlalia(3) University of Cambridge(3) Pohang University of Science and Technology(3) Hunan University(3) Technische Universiteit Eindhoven(3) State Engineering University of Armenia(3) Taiyuan Normal University(2) Chiba University(2)

Swarthmore College(2) China Earthquake Administration(2) Northwestern Polytechnical University(2)

Swansea University(2) King Abdulaziz University(2) Tel Aviv University(2) Hong Kong University of Science and Technology(2) University of Dundee(2) INP Grenoble(2) Purdue University(2) Washington University in St. Louis(2) Politecnico di Torino(2) Nara University of Education(2) University of Florida(2) City University of Hong Kong(2) Indian Institute of Science(2) State University of New York Geneseo(2) University of Kentucky(2)

Consiglio Nazionale delle Ricerche(2) North China Electric Power University(2) Uniwersytet Mikolaja Kopernika w Toruniu(2) Bergische Universitat Wuppertal(2) Beijing Normal University(2) Washington and Lee University(2) Cardiff University(2) Southern Illinois University(2)

National University of Defense Technology(2) Universite Paris-Sud XI(2) Benemrita Universidad Autnoma de Puebla(2) Tokyo University of Science(2) University of Cincinnati(2) Sam Houston State University(2) University of Tokyo(2) University of Alabama(2) Huazhong University of Science and Technology(2) Journal(Number of Scopus results) (2012IF;5yrsIF)(ISSN)(MCQ2012)(MCQ rank) Linear Algebra and Its Applications(209) (2012 IF: 0.968; 5Yrs IF: 1.032) (ISSN: 0024-3795) Linear and Multilinear Algebra (98) (2012 IF: 0.677; 5yrs IF: 0.696) (ISSN: 0308-1087) Journal of Mathematical Analysis and Applications (46) (2012 IF: 1.050; 5Yrs IF: 1.259)(ISSN: 0022-247X) Proceedings of the American Mathematical Society (25) (2012 IF: 0.609; 5Yrs IF: 0.649) (ISSN: 0002-9939) Integral Equations and Operator Theory (22) (2012 IF: 0.713; 5Yrs IF: 0.688) (ISSN: 0378-620X) Electronic Journal of Linear Algebra (19) (2012IF: 0.667; 5Yrs IF:0.779) (ISSN:1537-9582) Journal of Functional Analysis (17) (2012IF: 1.252; 5Yrs IF: 1.333) (ISSN: 0022-1236) Studia Mathematica (16) (2012IF: 0.549; 5Yrs IF: 0.672) (ISSN: 0039-3223) Operators and Matrices (13) (2012IF: 0.529; 5Yrs IF: 0.598) (ISSN: 1846-3886)

SIAM Journal on Matrix Analysis and Applications (12) (2012IF: 1.342; 5Yrs IF: 2.203) (ISSN: 0895-4798) (MCQ2012: 1.45)(MCQ rank: 47) Applied Mathematics Letters (11) (2012IF: 1.501; 5Yrs IF: 1.374) (ISSN: 0893-9659) Journal of Operator Theory (11) (2012IF: 0.565; 5Yrs IF: 0.615) (ISSN: 0379-4024) International Journal of Mathematical Analysis (9) () Applied Mathematics and Computation (8) (2012IF: 1.349; 5Yrs IF: 1.454) (ISSN: 0096-3003) Rocky Mountain Journal of Mathematics (8) (2012IF: 0.389; 5Yrs IF: 0.334) (ISSN:0035-7596) Canadian Mathematical Bulletin(7) (2012IF: 0.217; 5YrsIF:0.346) (ISSN: 0008-4395) Taiwanese Journal of Mathematics(7) (2012IF: 0.670; 5YrsIF:0.654) (ISSN: 1027-5487) Fangzhi Gaoxiao Jichukexue Xuebao (6) Numerical Functional Analysis and Optimization (6) (2012IF: 0.500; 5YrsIF:0.671) (ISSN: 0163-0563) SIAM Journal on Numerical Analysis (6) (2012IF: 1.484; 5YrsIF:2.157) (ISSN: 0036-1429) Journal of Computational and Applied Mathematics (5) (2012IF: 0.989; 5YrsIF:1.193) (ISSN:0377-0427) Abstract and Applied Analysis (5) (2012IF: 1.102; 5YrsIF:1.183) (ISSN:1085-3375) Archiv Der Mathematik (5) (2012IF: 0.376; 5YrsIF:0.443) (ISSN:0003-889X) Journal of Inequalities and Applications (5) (2012IF: 0.822; 5YrsIF:0.866) (ISSN:1029-242X) Rendiconti Del Circolo Matematico Di Palermo (5) International Journal of Mathematics and Mathematical Sciences (4) Journal of the Australian Mathematical Society (4) (2012IF: 0.445; 5YrsIF:0.486) (ISSN:1446-7887) Positivity(4) (2012IF: 0.295; 5YrsIF:0.431) (ISSN:1385-1292)

Aequationes Mathematicae (4) (2012IF: 0.422; 5YrsIF:-) (ISSN:0001-9054) Israel Journal of Mathematics (4) (2012IF: 0.646; 5YrsIF:0.750) (ISSN:0021-2172) SIAM Journal on Scientific Computing (4) (2012IF: 1.949; 5YrsIF:2.233) (ISSN:1064-8275) Journal of Physics A Mathematical and Theoretical (3) (2012IF: 1.766; 5YrsIF:1.514) (ISSN:1751-8113) Journal of Soviet Mathematics (3) (ISSN:0090-4104) Journal of the Korean Mathematical Society (3) (2012IF: 0.323; 5YrsIF:0.372) (ISSN:0304-9914) Lecture Notes in Computer Science Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics(3) Manuscripta Mathematica(3) Glasgow Mathematical Journal(3) Mathematical Inequalities and Applications(3) Numerische Mathematik(3) Proceedings IEEE International Symposium on Circuits and Systems(3) Bulletin of the Australian Mathematical Society(3) Proceedings of SPIE the International Society for Optical Engineering(3) Proceedings of the Edinburgh Mathematical Society(3) Publications of the Research Institute for Mathematical Sciences(3) IMA Journal of Numerical Analysis(3) Canadian Journal of Mathematics(3) SAE Technical Papers(3)

Transactions of the American Mathematical Society(3) World Academy of Science Engineering and Technology(3) Indiana University Mathematics Journal(3) Applied Numerical Mathematics(3) Complex Analysis and Operator Theory(3) Journal D Analyse Mathematique(3) International Journal of Pure and Applied Mathematics(3) Journal of Mathematical Physics(3) Zeitschrift Fur Analysis Und Ihre Anwendung(3) 2009 Etp Iita World Congress in Applied Computing Computer Science and Computer Engineering ACC 2009(2) Functional Analysis and Its Applications(2) IEEE Transactions on Information Theory(2) International Journal of Control(2) Czechoslovak Mathematical Journal(2) Acta Mathematica(2) (2012IF:2.714 5YrsIF:3.650)(ISSN: 0001-5962) (MCQ:3.55, MCQ rank: 1) Acta Mathematica Hungarica(2) Acta Mathematica Scientia(2) Guangzi Xuebao Acta Photonica Sinica(2) Acta Polytechnica Scandinavica Electrical Engineering(2)

Acta Scientiarum Mathematicarum(2) Advanced Materials Research(2) Journal of Approximation Theory(2) Central European Journal of Mathematics(2) Mathematische Annalen(2) Memoirs of the American Mathematical Society(2) Nonlinear Analysis Theory Methods and Applications(2) International Journal of Systems Science(2) Computers and Mathematics with Applications(2) Open Systems and Information Dynamics(2) Computers and Chemical Engineering(2) Pacific Journal of Mathematics(2) Physical Review B Condensed Matter and Materials Physics(2) Zhongbei Daxue Xuebao Ziran Kexue Ban Journal of North University of China Natural Science Edition(2) IEEE Transactions on Automatic Control(2) Proceedings 2009 2nd IEEE International Conference on Computer Science and Information Technology Iccsit 2009(2) Proceedings 2009 Asia Pacific Conference on Information Processing Apcip 2009(2) Asian European Journal of Mathematics(2) Banach Journal of Mathematical Analysis(2)

Lithuanian Mathematical Journal(2) Comptes Rendus Mathematique(2) Journal of the London Mathematical Society(2) Proceedings of the IEEE Conference on Decision and Control(2) Proceedings of the IEEE International Conference on Control Applications(2) Proyecciones(2) IEEE Transactions on Circuits and Systems(2) Quantum Information Processing(2) Quantum Information and Computation(2) (2012IF: 1.646; 5YrsIF:2.027) (ISSN:1533-7146) Quarterly Journal of Mathematics(2) Electronic Transactions on Numerical Analysis(2) Journal of Physics A Mathematical and General(2) Mathematical Notes(2) SIAM Journal on Control and Optimization(2) Communications on Pure and Applied Mathematics (2) (2012IF: 3.337; 5YrsIF:3.253) (ISSN:0010-3640) (MCQ2012: 2.57)(MCQ rank: 6) International Geoscience and Remote Sensing Symposium IGARSS(2) Chinese Science Bulletin(2) Science of the Total Environment(2) Atti Della Accademia Nazionale Dei Lincei Classe Di Scienze Fisiche Matematiche E Naturali Rendiconti

Lincei Matematica E Applicazioni(2) Systems and Control Letters(2) Aip Conference Proceedings(2) Mathematical Physics Analysis and Geometry(2) Water Environment Research(2) Mathematics of Operations Research(2) Proceedings IEEE International Conference on Data Mining Icdm(2) Conference Record International Conference on Communications(1) Conference Record of the Asilomar Conference on Signals Systems and Computers(1) Cybernetics(1) Data Mining and Knowledge Discovery(1) Dianli Xitong Zidonghua Automation of Electric Power Systems(1) Dianzi Yu Xinxi Xuebao Journal of Electronics and Information Technology(1) Digest of Technical Papers IEEE International Solid State Circuits Conference(1) Doboku Gakkai Ronbun Hokokushu(1) Doklady Akademii Nauk(1) Doklady Mathematics(1) Earth Science Reviews(1) Earthquake(1) Educational Studies in Mathematics(1)

Electric Power Systems Research(1) Electronic Products Garden City New York(1) Engineering Applications of Artificial Intelligence(1) Environmental Science and Technology(1) Environmental Toxicology and Chemistry(1) European Journal of Oncology Nursing(1) European Journal of Scientific Research(1) Gaodianya Jishu High Voltage Engineering(1) General Relativity and Gravitation(1) Gongcheng Lixue Engineering Mechanics(1) Guofang Keji Daxue Xuebao Journal of National University of Defense Technology(1) Hospital and Community Psychiatry(1) Huagong Xuebao Ciesc Journal(1) ICASSP IEEE International Conference on Acoustics Speech and Signal Processing Proceedings(1) IEE Conference Publication(1) IEE Proceedings Circuits Devices and Systems(1) IEE Proceedings D Control Theory and Applications(1) IEE Proceedings Part F Communications Radar and Signal Processing(1) IEEE Engineering in Medicine and Biology Society Annual Conference(1) IEEE International Conference on Fuzzy Systems(1)

IEEE International Symposium on Information Theory Proceedings(1) IEEE Transactions on Biomedical Engineering(1) IEEE Transactions on Neural Networks(1) Icctd 2009 2009 International Conference on Computer Technology and Development(1) Informatik Aktuell(1) Intelligent Engineering Systems Through Artificial Neural Networks(1) International Journal of Acoustics and Vibrations(1) International Journal of Applied Mathematics and Statistics(1) International Journal of Cancer Research and Prevention(1) International Journal of Computational and Mathematical Sciences(1) International Journal of Computer Mathematics(1) International Journal of Industrial and Systems Engineering(1) International Journal of Mathematics(1) International Journal of Multiphase Flow(1) International Journal of Nonlinear Sciences and Numerical Simulation(1) Iranian Journal of Mathematical Sciences and Informatics(1) Undefined(2) In the following slides, we try to present some grants

National Science Foundation Collaborative Research: Mathematical Aspects of Quantum Information Science Start Date: September 15, 2010 Expires:August 31, 2014 (Estimated) Awarded Amount to Date: $149,999.00 Investigator(s):Chi-Kwong Li [email protected] (Principal Investigator) Sponsor: College of William and Mary Office of Sponsored Programs Williamsburg, VA 23187-8795 (757)221-3966 National Science Foundation CSUMS: Theory, techniques, and research in computational mathematics Start Date: September 15, 2007 Expires:August 31, 2013 (Estimated) Awarded Amount to Date: $848,882.00

Investigator(s):Chi-Kwong Li [email protected]th.wm.edu (Principal Investigator) Junping Shi (Co-Principal Investigator) Robert Lewis (Co-Principal Investigator) Virginia Torczon (Former Co-Principal Investigator) Andreas Stathopoulos (Former Co-Principal Investigator) Sponsor: College of William and Mary Office of Sponsored Programs Williamsburg, VA 23187-8795 (757)221-3966 Natural Sciences and Engineering R esearch Council of Canada 2013 Research Grants Competition - Results by Evaluation Group Mathematics and Statistics Applicant Name Kribs, David DW Department Mathematics and Statistics

Institution Guelph Program RGPIN Title Operator Structures and Methods in Quantum Information Term Awarded Amount 5 $23, 000.00 Discovery Accelerator Supplements Program 2008 Competition Results Researcher Research Title Department

Institution Mathematical synthesis of Department of Kribs, David application and Mathematics and University of Guelph theory in quantum Statistics error correction Ontario Early Researcher Award Experimental prototypes of the quantum mechanical computer have already been built, and it is only a matter of time before they will process billions of calculations simultaneously. These amazing possibilities face challenges including errors that disrupt quantum systems as they evolve in time. Dr. David W. Kribs and a team at the University of Guelph will use a mathematical approach to find new techniques for error correction. Since their work is interdisciplinary, it

will offer opportunities to apply tools from physics and computer science to the problems. Total Project Costs: $190,000 Numerical range W A x* Ax : x C n , x* x 1 , Joint numerical range W A1 , , Am x* A1 x, , x* Am x : x* x 1, x C n . Polynomial numerical hull V k

A a : a, , a k conv W A aI ,, A aI k Rank-k numerical range k A a : U M n ,k , s.t., U *U I k ,U * AU aI k Joint rank-k numerical range k A1 , , Am *

* a , , a : U M j 1, , m , s .

t ., U U I , U A jU a j I k 1 m n,k k Open problems 1. Compute the joint higher-rank numerical range for an arbitrary Pauli channel. Kr 09

2. Compute the joint higher-rank numerical range for the class of randomized unitary channels, which are channels with noise operators Ai given by scalar multiples of unitary operators. Kr 09 3. Compute the joint higher-rank numerical ranges for channels with mutually commuting normal noise operators Ai . Kr 09 4. If A1 , A2 , A3 mutually commute and n 5, then 2 A1 , A2 , A3 is non-empty. for general A1 , A2 , A3 H n , we only know that 2 A1 , A2 , A3 is non-empty if n 7. How about n 5, 6? Kinki13 5. It would be interesting to determine the minimum n (depending on m and k ) for which k A1 , , Am is nonempty, star-shaped, or convex. Kinki13

Refrences [Kinki13], CHI-KWONG. MATRIX TECHNIQUES IN QUANTUM INFORMATION SCIENCE, Diversities in Quantum Computation and Quantum Information, Kinki University Series on Quantum Computing - Vol. 5, 2013 [Kr09] Kribs, David W., et al. "Research problems on numerical ranges in quantum computing." Linear and Multilinear Algebra 57.5 (2009): 491-502.

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