World's Best Scientists 2026 revealed!
VIEW LIST
Vincenzo Mainieri

D-Index & Metrics

Discipline name D-Index World Ranking Current World Ranking National Ranking Current National Ranking Publications Citations
Physics 136 456 439 37 35 486 59751

Vincenzo Mainieri publications per year

The chart shows the history of publications by Vincenzo Mainieri between 2001 and 2025, highlighting the no. of papers published in each year and offering an overview of the publication velocity of this scholar. Vincenzo Mainieri published across 25 years, from 2001 to 2025, averaging 21 papers a year. Output peaked at 55 publications in 2009. 19 of the 524 publications appeared in the last two years.

No. of publications
10 20 30 40 50
Bar chart. Horizontal axis: year, 2001 to 2025. Vertical axis: number of publications, 0 to 55. Peak 55 publications in 2009. 2001: 3 publications 2002: 10 publications 2003: 7 publications 2004: 18 publications 2005: 17 publications 2006: 17 publications 2007: 27 publications 2008: 29 publications 2009: 55 publications 2010: 46 publications 2011: 37 publications 2012: 34 publications 2013: 29 publications 2014: 15 publications 2015: 23 publications 2016: 13 publications 2017: 20 publications 2018: 21 publications 2019: 20 publications 2020: 14 publications 2021: 17 publications 2022: 15 publications 2023: 18 publications 2024: 11 publications 2025: 8 publications
2001 2025

524 publications in total across all disciplines

View publications per year as a table
Vincenzo Mainieri: publications per year, 2001 to 2025
Year Publications
2001 3
2002 10
2003 7
2004 18
2005 17
2006 17
2007 27
2008 29
2009 55
2010 46
2011 37
2012 34
2013 29
2014 15
2015 23
2016 13
2017 20
2018 21
2019 20
2020 14
2021 17
2022 15
2023 18
2024 11
2025 8
Total 524
Download as CSV

Vincenzo Mainieri publication distribution in Physics in 2026

The chart shows the distribution of publications by all Research.com ranked scientists in the field of Physics in 2026. The highlighted bar marks where Vincenzo Mainieri sits on this spectrum.

No. of scientists
50 100 150
Bar chart with 70 bars. Horizontal axis: publications, 103–122 to 1,469+. Vertical axis: number of scientists, 0 to 162. Most scientists, 162, have 323–342 publications. The last bar groups every scientist with 1,469 publications or more. The highlighted bar, 483–502 publications, is where this scientist sits. 103–122 publications: 7 scientists 123–142 publications: 10 scientists 143–162 publications: 31 scientists 163–182 publications: 35 scientists 183–202 publications: 53 scientists 203–222 publications: 81 scientists 223–242 publications: 85 scientists 243–262 publications: 112 scientists 263–282 publications: 114 scientists 283–302 publications: 126 scientists 303–322 publications: 136 scientists 323–342 publications: 162 scientists 343–362 publications: 155 scientists 363–382 publications: 156 scientists 383–402 publications: 134 scientists 403–422 publications: 145 scientists 423–442 publications: 147 scientists 443–462 publications: 131 scientists 463–482 publications: 131 scientists 483–502 publications: 116 scientists 503–522 publications: 106 scientists 523–542 publications: 103 scientists 543–562 publications: 87 scientists 563–582 publications: 84 scientists 583–602 publications: 94 scientists 603–622 publications: 70 scientists 623–642 publications: 76 scientists 643–662 publications: 60 scientists 663–682 publications: 54 scientists 683–702 publications: 60 scientists 703–722 publications: 48 scientists 723–742 publications: 64 scientists 743–762 publications: 48 scientists 763–782 publications: 37 scientists 783–802 publications: 43 scientists 803–822 publications: 34 scientists 823–842 publications: 36 scientists 843–862 publications: 32 scientists 863–882 publications: 32 scientists 883–902 publications: 31 scientists 903–922 publications: 25 scientists 923–942 publications: 15 scientists 943–962 publications: 24 scientists 963–982 publications: 13 scientists 983–1,002 publications: 21 scientists 1,003–1,022 publications: 21 scientists 1,023–1,042 publications: 16 scientists 1,043–1,062 publications: 9 scientists 1,063–1,082 publications: 19 scientists 1,083–1,102 publications: 11 scientists 1,103–1,122 publications: 17 scientists 1,123–1,142 publications: 11 scientists 1,143–1,162 publications: 7 scientists 1,163–1,182 publications: 4 scientists 1,183–1,202 publications: 10 scientists 1,203–1,222 publications: 8 scientists 1,223–1,242 publications: 16 scientists 1,243–1,262 publications: 4 scientists 1,263–1,282 publications: 10 scientists 1,283–1,302 publications: 5 scientists 1,303–1,322 publications: 7 scientists 1,323–1,342 publications: 4 scientists 1,343–1,362 publications: 8 scientists 1,363–1,382 publications: 6 scientists 1,383–1,402 publications: 7 scientists 1,403–1,422 publications: 3 scientists 1,423–1,442 publications: 4 scientists 1,443–1,462 publications: 4 scientists 1,463–1,468 publications: 3 scientists 1,469+ publications: 100 scientists
103–122 publications 1,469+

This scientist: 486 publications — 54th percentile

54% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 1,469 publications or more.

View publications distribution as a table
Number of Physics scientists by publication count, Research.com 2026 ranking edition. Based on 3,678 ranked scientists.
Publications Scientists This scientist
103–122 7
123–142 10
143–162 31
163–182 35
183–202 53
203–222 81
223–242 85
243–262 112
263–282 114
283–302 126
303–322 136
323–342 162
343–362 155
363–382 156
383–402 134
403–422 145
423–442 147
443–462 131
463–482 131
483–502 116 486
503–522 106
523–542 103
543–562 87
563–582 84
583–602 94
603–622 70
623–642 76
643–662 60
663–682 54
683–702 60
703–722 48
723–742 64
743–762 48
763–782 37
783–802 43
803–822 34
823–842 36
843–862 32
863–882 32
883–902 31
903–922 25
923–942 15
943–962 24
963–982 13
983–1,002 21
1,003–1,022 21
1,023–1,042 16
1,043–1,062 9
1,063–1,082 19
1,083–1,102 11
1,103–1,122 17
1,123–1,142 11
1,143–1,162 7
1,163–1,182 4
1,183–1,202 10
1,203–1,222 8
1,223–1,242 16
1,243–1,262 4
1,263–1,282 10
1,283–1,302 5
1,303–1,322 7
1,323–1,342 4
1,343–1,362 8
1,363–1,382 6
1,383–1,402 7
1,403–1,422 3
1,423–1,442 4
1,443–1,462 4
1,463–1,468 3
1,469+ 100
Download as CSV

Vincenzo Mainieri D-index placement in Physics in 2026

The chart shows the D-index (discipline H-index) distribution of Physics scientists ranked by Research.com in 2026. The highlighted bar marks where Vincenzo Mainieri sits on this spectrum.

No. of scientists
50 100 150
Bar chart with 59 bars. Horizontal axis: D-Index, 70–71 to 185+. Vertical axis: number of scientists, 0 to 167. Most scientists, 167, have 80–81 D-Index. The last bar groups every scientist with 185 D-Index or more. The highlighted bar, 136–137 D-Index, is where this scientist sits. 70–71 D-Index: 76 scientists 72–73 D-Index: 110 scientists 74–75 D-Index: 143 scientists 76–77 D-Index: 153 scientists 78–79 D-Index: 144 scientists 80–81 D-Index: 167 scientists 82–83 D-Index: 167 scientists 84–85 D-Index: 166 scientists 86–87 D-Index: 132 scientists 88–89 D-Index: 155 scientists 90–91 D-Index: 134 scientists 92–93 D-Index: 137 scientists 94–95 D-Index: 102 scientists 96–97 D-Index: 112 scientists 98–99 D-Index: 110 scientists 100–101 D-Index: 116 scientists 102–103 D-Index: 97 scientists 104–105 D-Index: 103 scientists 106–107 D-Index: 87 scientists 108–109 D-Index: 90 scientists 110–111 D-Index: 67 scientists 112–113 D-Index: 78 scientists 114–115 D-Index: 75 scientists 116–117 D-Index: 67 scientists 118–119 D-Index: 69 scientists 120–121 D-Index: 60 scientists 122–123 D-Index: 59 scientists 124–125 D-Index: 53 scientists 126–127 D-Index: 42 scientists 128–129 D-Index: 41 scientists 130–131 D-Index: 33 scientists 132–133 D-Index: 32 scientists 134–135 D-Index: 45 scientists 136–137 D-Index: 19 scientists 138–139 D-Index: 24 scientists 140–141 D-Index: 28 scientists 142–143 D-Index: 31 scientists 144–145 D-Index: 22 scientists 146–147 D-Index: 20 scientists 148–149 D-Index: 12 scientists 150–151 D-Index: 16 scientists 152–153 D-Index: 24 scientists 154–155 D-Index: 23 scientists 156–157 D-Index: 15 scientists 158–159 D-Index: 15 scientists 160–161 D-Index: 11 scientists 162–163 D-Index: 17 scientists 164–165 D-Index: 12 scientists 166–167 D-Index: 11 scientists 168–169 D-Index: 9 scientists 170–171 D-Index: 9 scientists 172–173 D-Index: 11 scientists 174–175 D-Index: 4 scientists 176–177 D-Index: 8 scientists 178–179 D-Index: 5 scientists 180–181 D-Index: 3 scientists 182–183 D-Index: 4 scientists 184 D-Index: 4 scientists 185+ D-Index: 99 scientists
70–71 D-Index 185+

This scientist: 136 D-Index — 88th percentile

88% of scientists in this discipline score the same or lower.

The last bar groups every scientist with 185 D-Index or more.

View D-Index distribution as a table
Number of Physics scientists by D-index, Research.com 2026 ranking edition. Based on 3,678 ranked scientists.
D-Index Scientists This scientist
70–71 76
72–73 110
74–75 143
76–77 153
78–79 144
80–81 167
82–83 167
84–85 166
86–87 132
88–89 155
90–91 134
92–93 137
94–95 102
96–97 112
98–99 110
100–101 116
102–103 97
104–105 103
106–107 87
108–109 90
110–111 67
112–113 78
114–115 75
116–117 67
118–119 69
120–121 60
122–123 59
124–125 53
126–127 42
128–129 41
130–131 33
132–133 32
134–135 45
136–137 19 136
138–139 24
140–141 28
142–143 31
144–145 22
146–147 20
148–149 12
150–151 16
152–153 24
154–155 23
156–157 15
158–159 15
160–161 11
162–163 17
164–165 12
166–167 11
168–169 9
170–171 9
172–173 11
174–175 4
176–177 8
178–179 5
180–181 3
182–183 4
184 4
185+ 99
Download as CSV

Overview

Vincenzo Mainieri is affiliated with the European Southern Observatory in Germany and has a significant presence in the field of Physics and Astronomy, contributing extensively to Astronomy and Astrophysics. Their work encompasses an array of topics including galaxies formation, evolution, and phenomena; astrophysical phenomena and observations; astrophysics and star formation studies; and gamma-ray bursts and supernovae.

Mainieri has published scholarly articles primarily in several venues known for astrophysical research. These include:

  • arXiv (Cornell University)
  • Monthly Notices of the Royal Astronomical Society
  • Astronomy and Astrophysics
  • The Astrophysical Journal
  • The Astrophysical Journal Letters

Their research interests branch into subfields such as instrumentation, nuclear and high energy physics, and atomic and molecular physics alongside the dominant focus in astronomy and astrophysics.

Among recent papers associated with Mainieri's research are:

  • COSMOS-Web: An Overview of the JWST Cosmic Origins Survey (2023, The Astrophysical Journal)
  • Quasar feedback survey: multiphase outflows, turbulence, and evidence for feedback caused by low power radio jets inclined into the galaxy disc (2022, Monthly Notices of the Royal Astronomical Society)
  • High molecular gas content and star formation rates in local galaxies that host quasars, outflows, and jets (2020, Monthly Notices of the Royal Astronomical Society)
  • First Results from the JWST Early Release Science Program Q3D: Turbulent Times in the Life of a z ∼ 3 Extremely Red Quasar Revealed by NIRSpec IFU (2022, The Astrophysical Journal Letters)
  • KASHz: No evidence for ionised outflows instantaneously suppressing star formation in moderate luminosity AGN at z ∼ 1.4-2.6 (2020, Monthly Notices of the Royal Astronomical Society)

Their collaborative network features frequent co-authors such as C. M. Harrison, Darshan Kakkad, Chiara Circosta, Nadia L. Zakamska, and A. Marconi, highlighting a pattern of sustained partnerships in the field.

Mainieri's academic contributions are mainly concentrated in research on galaxies and cosmic phenomena, with publications examining the intricacies of AGN feedback, molecular gas content in galaxies, and quasar outflows. These topics reflect a broader engagement with astrophysical phenomena and cosmic star formation processes.

Best Publications

  • Mass and environment as drivers of galaxy evolution in SDSS and zCOSMOS and the origin of the Schechter function

    Y. Peng;S. J. Lilly;K. Kovac;M. Bolzonella

  • Mass and environment as drivers of galaxy evolution in SDSS and zCOSMOS and the origin of the Schechter function

    Ying-jie Peng;Simon J. Lilly;Katarina Kovač;Micol Bolzonella

  • zCOSMOS: A Large VLT/VIMOS redshift survey covering 0 < z < 3 in the COSMOS field

    S.J. Lilly;O. Le Fevre;A. Renzini;G. Zamorani

  • COSMOS Photometric Redshifts with 30-bands for 2-deg2

    O. Ilbert;P. Capak;M. Salvato;H. Aussel

  • zCOSMOS: A Large VLT/VIMOS Redshift Survey Covering 0 < z < 3 in the COSMOS Field*

    S. J. Lilly;O. Le Fèvre;A. Renzini;G. Zamorani

  • X-shooter, the new wide band intermediate resolution spectrograph at the ESO Very Large Telescope

    Joel Vernet;H. Dekker;S. D'Odorico;L. Kaper

  • The Chandra Deep Field South: the 1 Million Second

    P. Rosati;P. Tozzi;R. Giacconi;R. Gilli

  • Chandra Deep Field South: The 1 Ms Catalog

    Riccardo Giacconi;Riccardo Giacconi;Andrew Zirm;JunXian Wang;Piero Rosati

  • The Chandra Deep Field-South: Optical Spectroscopy. I.*

    G. P. Szokoly;J. Bergeron;G. Hasinger;I. Lehmann

  • The zCOSMOS 10k-Bright Spectroscopic Sample

    Simon J. Lilly;Vincent Le Brun;Christian Maier;Vincenzo Mainieri

  • THE CHANDRA DEEP FIELD-SOUTH SURVEY: 4 Ms SOURCE CATALOGS

    Yongquan Xue;Bin Luo;William Nielsen Brandt;Franz E. Bauer;Franz E. Bauer

  • zCOSMOS - 10k-bright spectroscopic sample. The bimodality in the Galaxy Stellar Mass Function: exploring its evolution with redshift

    L. Pozzetti;M. Bolzonella;E. Zucca;G. Zamorani

  • Improved constraints on the expansion rate of the Universe up to z ∼ 1.1 from the spectroscopic evolution of cosmic chronometers

    M. Moresco;A. Cimatti;R. Jimenez;L. Pozzetti

  • Active galactic nuclei: what’s in a name?

    P. Padovani;D. M. Alexander;R. J. Assef;B. De Marco

  • X-ray spectral properties of AGN in the Chandra Deep Field South

    P. Tozzi;R. Gilli;V. Mainieri;C. Norman

  • The Chandra COSMOS Survey. I. Overview and Point Source Catalog

    Martin Elvis;Francesca Civano;Cristian Vignali;Simonetta Puccetti

  • The Great Observatories Origins Deep Survey VLT/FORS2 spectroscopy in the GOODS-South Field

    P. Popesso;M. Dickinson;M. Nonino;E. Vanzella;E. Vanzella

  • The Herschel* PEP/HerMES luminosity function - I. Probing the evolution of PACS selected Galaxies to z ≃ 4

    C. Gruppioni;F. Pozzi;G. Rodighiero;I. Delvecchio

  • The XMM-Newton Wide-Field Survey in the COSMOS field (XMM-COSMOS): demography and multiwavelength properties of obscured and unobscured luminous AGN

    M. Brusa;F. Civano;A. Comastri;T. Miyaji

  • AGN wind scaling relations and the co-evolution of black holes and galaxies

    F. Fiore;C. Feruglio;F. Shankar;M. Bischetti

Frequent Co-Authors

Marcella Brusa
Marcella Brusa University of Bologna
Andrea Comastri
Andrea Comastri National Institute for Astrophysics
Roberto Gilli
Roberto Gilli National Institute for Astrophysics
Anton M. Koekemoer
Anton M. Koekemoer Space Telescope Science Institute
John D. Silverman
John D. Silverman University of Tokyo
G. Zamorani
G. Zamorani National Institute for Astrophysics
Paolo Tozzi
Paolo Tozzi National Institute for Astrophysics
S. Bardelli
S. Bardelli National Institute for Astrophysics
A. Iovino
A. Iovino National Institute for Astrophysics
Alvio Renzini
Alvio Renzini National Institute for Astrophysics

External Links

Personal website of Vincenzo Mainieri

If you think any of the details on this page are incorrect, let us know.

Report an issue

We appreciate your kind effort to assist us to improve this page, it would be helpful providing us with as much detail as possible in the text box below:

Best Scientists Citing Vincenzo Mainieri

Franz E. Bauer

Franz E. Bauer

Pontificia Universidad Católica de Chile

Publications: 407

Anton M. Koekemoer

Anton M. Koekemoer

Space Telescope Science Institute

Publications: 396

Mara Salvato

Mara Salvato

Max Planck Society

Publications: 318

Cristian Vignali

Cristian Vignali

University of Bologna

Publications: 277

Peter Capak

Peter Capak

California Institute of Technology

Publications: 270

Rob Ivison

Rob Ivison

European Southern Observatory

Publications: 254

Marcella Brusa

Marcella Brusa

University of Bologna

Publications: 250

Andrea Comastri

Andrea Comastri

National Institute for Astrophysics

Publications: 237

David M. Alexander

David M. Alexander

Durham University

Publications: 232

Emanuele Daddi

Emanuele Daddi

University of Paris-Saclay

Publications: 220

Alvio Renzini

Alvio Renzini

National Institute for Astrophysics

Publications: 212

H. J. McCracken

H. J. McCracken

Institut d'Astrophysique de Paris

Publications: 201

Alexis Finoguenov

Alexis Finoguenov

University of Helsinki

Publications: 198

Roberto Maiolino

Roberto Maiolino

University of Cambridge

Publications: 188

Francesca Civano

Francesca Civano

Harvard University

Publications: 183

Roberto Gilli

Roberto Gilli

National Institute for Astrophysics

Publications: 176

Trending Scientists

Jun Su

Jun Su

Huazhong University of Science and Technology

Paul C. Bethke

Paul C. Bethke

University of Wisconsin–Madison

Yilmaz Sozer

Yilmaz Sozer

University of Akron

David M. Janicke

David M. Janicke

University of Florida

Barbara A. Morrongiello

Barbara A. Morrongiello

University of Guelph

Boris B. Quednow

Boris B. Quednow

University of Zurich

Neal J. Evans

Neal J. Evans

The University of Texas at Austin

José Antunes-Rodrigues

José Antunes-Rodrigues

Universidade de São Paulo

Charles B. Niwagaba

Charles B. Niwagaba

Makerere University

Michael R. Rosen

Michael R. Rosen

United States Geological Survey

Masaru Katoh

Masaru Katoh

University of Pennsylvania

Kevin B. McGrattan

Kevin B. McGrattan

National Institute of Standards and Technology

Hayder Radha

Hayder Radha

Michigan State University

Serge Akoka

Serge Akoka

University of Nantes

Lawrence E. Armstrong

Lawrence E. Armstrong

University of Connecticut

Qingyi Wei

Qingyi Wei

Duke University

Related Physics Rankings & Guides

2027 Fastest Online Urban Planning Degree Programs You Can Finish in Under 2 Years

2027 Fastest Online Urban Planning Degree Programs You Can Finish in Under 2 Years
2027 Most Affordable Online Physics Degree Programs

2027 Most Affordable Online Physics Degree Programs
2027 How To Become a Paleontologist? Salary & Career Paths

2027 How To Become a Paleontologist? Salary & Career Paths
2027 Admission Requirements for Physics Degree Programs

2027 Admission Requirements for Physics Degree Programs
2027 Online Photography Degree Programs for Veterans: GI Bill Benefits, Costs & Top Considerations

2027 Online Photography Degree Programs for Veterans: GI Bill Benefits, Costs & Top Considerations
2027 Most Affordable Online Space Studies Degree Programs

2027 Most Affordable Online Space Studies Degree Programs
2027 Best Online Space Studies Degree Programs

2027 Best Online Space Studies Degree Programs
2027 Online Photography Degree Programs Costs: Tuition & Fees

2027 Online Photography Degree Programs Costs: Tuition & Fees
2027 Best Online Physics Degree Programs

2027 Best Online Physics Degree Programs

Recently Published Articles

2027 Online Project Management Doctorate Programs That Give Credit for Prior Graduate Work

2027 Online Project Management Doctorate Programs That Give Credit for Prior Graduate Work
2027 Patient Safety & Quality Degree Levels Explained: Bachelor's vs Master's vs Doctorate

2027 Patient Safety & Quality Degree Levels Explained: Bachelor's vs Master's vs Doctorate
2027 Entry-Level Jobs With a Biotechnology Master's Degree

2027 Entry-Level Jobs With a Biotechnology Master's Degree
2027 Job Placement Rates for Clinical Mental Health Counseling Master's Graduates: Employment Outcomes

2027 Job Placement Rates for Clinical Mental Health Counseling Master's Graduates: Employment Outcomes
2027 Online Pediatric Nurse Practitioner Doctorate Programs for Experienced Professionals Without Research Backgrounds

2027 Online Pediatric Nurse Practitioner Doctorate Programs for Experienced Professionals Without Research Backgrounds
2027 Self-Paced Online Physical Education Bachelor's Degree Programs

2027 Self-Paced Online Physical Education Bachelor's Degree Programs
2027 Highest-Paying Jobs with a Nonprofit Management Master's Degree

2027 Highest-Paying Jobs with a Nonprofit Management Master's Degree
2027 Shortest Online Substance Abuse Counseling Bachelor's Degree Programs That Pay Well: Cost, Time to Completion, and Salary Outlook

2027 Shortest Online Substance Abuse Counseling Bachelor's Degree Programs That Pay Well: Cost, Time to Completion, and Salary Outlook
2027 How to Become a Cybercrime Investigator

2027 How to Become a Cybercrime Investigator
2027 Online Educational Technology Doctorate Programs with Specializations: Concentrations, Tracks, and Career Paths

2027 Online Educational Technology Doctorate Programs with Specializations: Concentrations, Tracks, and Career Paths
2027 Mental Health Counseling Degree Careers Ranked by Stress Level, Salary, and Job Stability

2027 Mental Health Counseling Degree Careers Ranked by Stress Level, Salary, and Job Stability
2027 How to Become a Licensed Counselor (LPC) in Texas

2027 How to Become a Licensed Counselor (LPC) in Texas
2027 MBA in Healthcare Management Careers: Guide to Career Paths, Options & Salary

2027 MBA in Healthcare Management Careers: Guide to Career Paths, Options & Salary
2027 Best Marriage and Family Therapy (MFT) Programs in Montana: Online & Campus

2027 Best Marriage and Family Therapy (MFT) Programs in Montana: Online & Campus
2027 Human Resources Degree Coursework Explained: What Classes Can You Expect to Take?

2027 Human Resources Degree Coursework Explained: What Classes Can You Expect to Take?
2027 How to Become a Nurse Practitioner in San Jose, CA: Requirements & Salary

2027 How to Become a Nurse Practitioner in San Jose, CA: Requirements & Salary
2027 LMFT vs LMFTA: Explaining The Difference

2027 LMFT vs LMFTA: Explaining The Difference
2027 Easiest Online Social Psychology Master's Degree Programs That Pay Well: High-Salary Degrees with Simple Admissions

2027 Easiest Online Social Psychology Master's Degree Programs That Pay Well: High-Salary Degrees with Simple Admissions
2027 Online Educational Technology Doctorate Programs for Experienced Professionals Without Research Backgrounds

2027 Online Educational Technology Doctorate Programs for Experienced Professionals Without Research Backgrounds
2027 Best Health Information Management Degrees for Working Adults

2027 Best Health Information Management Degrees for Working Adults
2027 What Prerequisites Do You Need for an Interior Design Master's Degree? Entry Requirements, Credits & Eligibility Rules

2027 What Prerequisites Do You Need for an Interior Design Master's Degree? Entry Requirements, Credits & Eligibility Rules