Dr. Sameen Ahmed Khan             ([email protected])       (Visiting Card, Picture, Pictures and the Biographical-Note)
Assistant Professor,
Department of Mathematics and Sciences
College of Arts and Applied Sciences (CAAS)
Dhofar University (Logo)
Post Box No. 2509, Postal Code 211
Salalah
Dhofar
Sultanate of Oman (National Emblem).

List of 38+ Articles from the Scopus
http://SameenAhmedKhan.webs.com/
http://www.imsc.res.in/~jagan/khan-cv.html
http://sites.google.com/site/rohelakhan/
http://rohelakhan.webs.com/
http://www.du.edu.om/





Research Summary
Resistor Networks


The set of equivalent resistances formed by any conceivable network (series/parallel or bridge, or non-planar configurations) of n equal resistors has over twenty Integer Sequences associated with it. Ten new Integer Sequences occurring in the following articles are listed below:





Technical Writings


  1. Sameen Ahmed Khan,
    The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel,
    37 pages, LANL E-Print Archive: http://arxiv.org/abs/1004.3346/.
    Bibliographic Code: 2010arXiv1004.3346K
    (Wednesday the 21 April 2010).
    * Cited in
    Scott B. Guthery,
    A Motif of Mathematics
    History and Applications of the Mediant and the Farey Sequence
    ,
    Section 4.7, Networks of Resistors, pp. 169-172,
    Docent Press (Logo, Boston, Massachusetts, USA, 11 September 2010).
    (ISBN-10: 1453810579 and ISBN-13: 9781453810576, Book Cover).
    (ISBN: International Standard Book Number System, Logo).

  2. Sameen Ahmed Khan,
    Farey Sequences and Resistor Networks,
    Mathematical Sciences - Proceedings of the Indian Academy of Sciences, Vol., 122, No. 2, pp, 153-162 (May 2012, Journal Front Cover and Journal Back Cover).
    (A Publication of IAS the Indian Academy of Sciences, Logo, Copublished with Springer, Logo).
    Also available from SpringerLink:
    Proceedings - Mathematical Sciences, Indian Academy of Sciences, Vol. 122, No. 2, p p. 153-162 (May 2012).
    Digital Object Identifier (DOI, Logo): http://dx.doi.org/10.1007/s12044-012-0066-7
    The MR Number in The Mathematical Reviews Database: MR2945087.
    Larger Version: 37 pages , LANL E-Print archive http://arxiv.org/abs/1004.3346/.

  3. Sameen Ahmed Khan,
    How many equivalent resistances?,
    Resonance Journal of Science Education, Vol. 17, No. 5 468-475 (May 2012, Journal Front Cover and Journal Back Cover).
    (A Monthly Publication of IAS the Indian Academy of Sciences, Logo, Copublished with Springer, Logo).
    Also available from SpringerLink:
    Resonance Journal of Science Education, Vol. 17, No. 5, p p. 468-475 (May 2012).
    Digital Object Identifier (DOI, Logo): http://dx.doi.org/10.1007/s12045-012-0050-7
    Larger Version: 37 pages , LANL E-Print archive http://arxiv.org/abs/1004.3346/.

  4. Sameen Ahmed KHAN,
    Number Theory and Resistor Networks,
    Chapter 5 in
    Resistors: Theory of Operation, Behavior and Safety Regulations,
    Editor: Roy Abi Zeid Daou,
    (Nova Science Publishers, Logo, New York, May 2013) pp. 99-154 (May 2013).
    (Hard Cover: pp. 99-154, ISBN-10: 1622577884 and ISBN-13: 978-1-62257-788-0, Book Cover).
    (ebook: pp. ???-???, ISBN-10: 1626187959 and ISBN-13: 978-1-62618-795-5, Book Cover).
    (ISBN: International Standard Book Number System, Logo).

  5. Sameen Ahmed Khan,
    Set Theoretic Approach to Resistor Networks,
    Physics Education, Volume 29, No. 4, Article Number: 5 (October-December 2013, Journal Cover).
    (Quarterly e-Journal devoted to Physics Pedagogy, by IAPT, Logo).
    (IAPT: Indian Association of Physics Teachers, Logo).

  6. Sameen Ahmed Khan,
    Beginning to count the Number of Equivalent Resistances,
    Indian Journal of Science and Technology (INDJST), Volume 9, No. 44, pp 1-7 (November 2016).
    Digital Object Identifier (DOI, Logo): http://dx.doi.org/10.17485/ijst/2016/v9i44/88086.
    Print ISSN: 0974-6846 and Online ISSN: 0974-5645.
    E-Print Archive: http://arxiv.org/abs/1004.3346/.

  7. Sameen Ahmed Khan,



List of 35+ Writeups from the INSPIRE HEP (Logo), Originally SLAC SPIRES (Logo). List of 20+ Writeups from the LANL E-Print archive (see the Atom Feeds).

Some Publications from the American Mathematical Society (AMS, Logo) MathSciNet (Logo). List of 230+ Writeups from the Google Scholar (Logo).


Integer Sequences


  1. Sameen Ahmed Khan,
    Sequence A174283: 1, 2, 4, 9, 23, 57, 151, 409, ...
    Number of distinct resistances that can be produced using n equal resistors in, series, parallel and/or bridge configurations,
    Sequence A174283 in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A174283.
    (Monday the 15 March 2010).

  2. Sameen Ahmed Khan,
    Sequence A174284: 1, 3, 7, 15, 35, 79, 193, 489, ...
    Number of distinct resistances that can be produced using at most n equal resistors (n or fewer resistors) in series, parallel and/or bridge configurations,
    Sequence A174284 in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A174284.
    (Monday the 15 March 2010).

  3. Sameen Ahmed Khan,
    Sequence A174285: 0, 0, 0, 0, 1, 3, 17, 53, ...
    Number of distinct resistances that can be produced using n equal resistors in, series and/or parallel,
    confined to the five arms (four arms and the diagonal) of a bridge configuration.
    ,
    Sequence A174285 in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A174285.
    (Monday the 15 March 2010).

  4. Sameen Ahmed Khan,
    Sequence A174286: 0, 0, 0, 0, 1, 3, 19, 67, ...
    Number of distinct resistances that can be produced using at most n equal resistors (n or fewer resistors) in, series and/or parallel,
    confined to the five arms (four arms and the diagonal) of a bridge configuration
    ,
    Sequence A174286 in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A174286.
    (Monday the 15 March 2010).

  5. Sameen Ahmed Khan,
    Sequence A176497: 0, 0, 0, 1, 4, 9, 25, 75, 195, 475, 1265, 3135, 7983, 19697, 50003, 126163, 317629, 802945, 2035619, 5158039, 13084381, 33240845, 84478199, ...,
    Order of the Cross Set which is the subset of the set of distinct resistances that can be produced using n equal resistors in series and/or parallel,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176497.
    (Wednesday the 21 April 2010).

  6. Sameen Ahmed Khan,
    Sequence A176498: 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 9, 24, 58, 124, 312, ...,
    Number of elements less than half in the Cross Set which is the subset of the set of distinct resistances that can be produced using n equal resistors in series and/or parallel,
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176498.
    (Wednesday the 21 April 2010).

  7. Sameen Ahmed Khan,
    Sequence A176499: 2, 3, 5, 11, 23, 59, 141, 361, 941, 2457, 6331, 16619, 43359, 113159, 296385, 775897, 2030103, 5315385, 13912615, 36421835, 95355147, 249635525, 653525857, 1710966825, 4479358275, 11726974249, 30701593527, 80377757397, 210431301141, ...,
    Haros-Farey Sequence whose argument is the Fibonacci Number; Farey(m) where m = Fibonacci (n + 1),
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176499.
    (Wednesday the 21 April 2010).

  8. Sameen Ahmed Khan,
    Sequence A176500: 1, 3, 7, 19, 43, 115, 279, 719, 1879, 4911, 12659, 33235, 86715, 226315, 592767, 1551791, 4060203, 10630767, 27825227, 72843667, 190710291, 499271047, 1307051711, 3421933647, 8958716547, 23453948495, 61403187051, 160755514791, 420862602279, ...,
    2Farey(m) - 3 where m = Fibonacci (n + 1),
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176500.
    (Wednesday the 21 April 2010).

  9. Sameen Ahmed Khan,
    Sequence A176501: 1, 2, 4, 9, 19, 50, 122, 317, 837, 2213, 5758, 15236, 40028, 105079, 276627, 727409, 1910685, 5020094, ...,
    Farey(m; I) where m = Fibonacci (n + 1) and I = [1/n, 1],
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176501.
    (Wednesday the 21 April 2010).

  10. Sameen Ahmed Khan,
    Sequence A176502: 1, 3, 7, 17, 37, 99, 243, 633, 1673, 4425, 11515, 30471, 80055, 210157, 553253, 1454817, 3821369, 10040187, ...,
    2Farey(m; I) - 1 where m = Fibonacci (n + 1) and I = [1/n, 1],
    in N. J. A. Sloane (Editor), The On-Line Encyclopedia of Integer Sequences,
    published electronically at
    http://oeis.org/A176502.
    (Wednesday the 21 April 2010).

  11. Sameen Ahmed Khan,

List of the 35 Integer Sequences from the http://oeis.org/ (Logo).

http://oeis.org/wiki/User:Sameen_Ahmed_Khan at OEIS Wiki (Logo).


Integer Sequences Occurring in the Resistor Networks

n

Sequence A000027
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

m =
Fibonacci(n+1)

Sequence A000045
1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 10946 17711 28657 46368 75025 121393 196418 317811 514229 832040

Farey (m)

Sequence A176499
2 3 5 11 23 59 141 361 941 2457 6331 16619 43359 113159 296385 775897 2030103 5315385 13912615 36421835 95355147 249635525 653525857 1710966825 4479358275 11726974249 30701593527 80377757397 210431301141

Farey(m; I)
where
I = [1/n, 1]

Sequence A176501
1 2 4 9 19 50 122 317 837 2213 5758 15236 40028 105079 276627 727409 1910685 5020094                      

2*Farey(m) - 3

Sequence A176500
1 3 7 19 43 115 279 719 1879 4911 12659 33235 86715 226315 592767 1551791 4060203 10630767 27825227 72843667 190710291 499271047 1307051711 3421933647 8958716547 23453948495 61403187051 160755514791 420862602279

2*Farey(m; I) - 1
where
I = [1/n, 1]

Sequence A176502
1 3 7 17 37 99 243 633 1673 4425 11515 30471 80055 210157 553253 1454817 3821369 10040187                      

G(n)

ROUNDED

- 0 3 10 30 84 229 614 1634 4333 11459 30252 79757 210051 552741 1453558 3820388 10036637 26357608 69196797 181613601 476551197 1250210313 3279292134 8600229222 22551775256 59128782742 155013801893 406349705279

Number of Configurations for A(n)

Sequence A000084
1 2 4 10 24 66 180 522 1532 4624 14136 43930 137908 437502 1399068 4507352 14611576 47633486 156047204 513477502 1696305728 5623993944 18706733128 62408176762 208769240140 700129713630 2353386723912 7927504004640 26757247573360

A(n)
(all n)

Sequence A048211
1 2 4 9 22 53 131 337 869 2213 5691 14517 37017 93731 237465 601093 1519815 3842575 9720769 24599577 62283535 157807915 400094029            

Number of Configurations for C(n)

Sequence A058351
1 3 7 17 41 107 287 809 2341 6965 21101 65031 202939 640441 2039509 6546861 21158437 68791923 224839127 738316629 2434622357 8058616301 26765349429 89173526191 297942766331 998072479961 3351459203873 11278963208513 38036210781873

C(n)
(n or fewer)

Sequence A153588
1 3 7 15 35 77 179 429 1039 2525 6235 15463 38513 96231 241519 607339                          

B(n)
(all n)

Sequence A174283
1 2 4 9 23 57 151 409                                          

D(n)
(n or fewer)

Sequence A174284
1 3 7 15 35 79 193 489                                          

Exclusive Bridge
(all n)

Sequence A174285
- - - - 1 3 17 53                                          

Exclusive Bridge
(n or fewer)

Sequence A174286
- - - - 1 3 19 67                                          

Cross Set

Sequence A176497
- 0 0 1 4 9 25 75 195 475 1265 3135 7983 19697 50003 126163 317629 802945 2035619 5158039 13084381 33240845 84478199            

Elemnets below Half in the Cross Set

Sequence A176498
0 0 0 0 1 6 9 24 58 124 312                                    

n Arbitrary Resistors


Sequence A005840
1 2 8 46 332 2874 29024 334982 4349492 62749906 995818760 17239953438 323335939292 6530652186218 141326092842416 3262247252671414 80009274870905732 2077721713464798210 56952857434896699992 1643312099715631960910 49786762554744011232812 1580196539672201518288282 52434059362544660900127488 1815512577984496899161437926 65480774823244278018634552532 2456188516887596642041913174834 95675336805658147904301565396904 3864849350457321165077279200462462 161698170758943550097720969839744892

n or Fewer Arbitrary Resistors


Sequences A123750
1 4 17 94 667 5752 58053 669970 8698991 125499820 1991637529 34479906886 646671878595 13061304372448 282652185684845 6524494505342842 160018549741811479 4155443426929596436                      

n Resistors with values 1, 2, 3, ...


Sequences A051045
1 2 8 44 298 2350 22774                                            

Integer Sequences
                                                         

n

Sequence A000027
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29

List of Integer Sequences for "Resistors" from the http://oeis.org/ (Logo).

http://oeis.org/wiki/User:Sameen_Ahmed_Khan at OEIS Wiki (Logo).


Research in Charged-Particle Beam Optics.

Research in Light Beam Optics.

Some Research Encounters:

  1. Number Theory.

  2. Crystallographic Studies of the 123-Superconductors (YBa2Cu3O7-x the Yttrium Barium Copper Oxide).

  3. SOC: Self-Organized Criticality (SandPiles).

  4. Resistor Networks.

  5. Quadratic Surfaces.

  6. Salt Solutions.


60+ Technical Writings

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200+ Non-Technical Writings (Popular Writings)

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In March 2005, I was appointed as the Regular Correspondent for the International Committee for Future Accelerators (ICFA, Logo) Beam Dynamics Panel Newsletters (Logo), for the region of Middle East & Africa. ICFA, the International Committee for Future Accelerators (Logo), provides a forum to discuss and implement plans for further promoting collaborative accelerator-based science. Its primary purpose is to strengthen collaboration in accelerator-based science, to encourage future projects, and to make recommendations to governments. See the International Committee for Future Accelerators (ICFA, Logo) Beam Dynamics Panel Newsletter (Logo), No. 36 (April 2005).
http://icfa-usa.jlab.org/archive/newsletter.shtml

Patents

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Integer Sequences

Click for a LaTeX/MiKTeX Derived DVI Version, PS Version or/and PDF Version of the Integer Sequences

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List of the 35 Integer Sequences from the http://oeis.org/ (Logo)

http://oeis.org/wiki/User:Sameen_Ahmed_Khan.


Curriculum Vitae

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Three Page Resume in MS WORD (view the PS and the PDF)

Eleven Page Resume in MS WORD (view the PS and the PDF)

Forty-one Page CV in MS WORD (view the PS and the PDF)

Versión en Español Octubre 2001 DVI Version, PS Version, O/Y PDF Version


MECIT Report (for the stay at the Middle East College of Information Technology, Logo)

SCOT Report (for the stay at the Salalah College of Technology, Logo)

The Oman Report: The Consolidated Report of my stay in the Sultanate of Oman (National Emblem); at the Middle East College of Information Technology (MECIT, Logo), Muscat and the Salalah College of Technology (SCOT, Logo), Salalah.
My Erdös Number and Einstein Number
My Academic Genealogy
Mathematics Genealogy Project (Logo, Entry No. 93310)

VIDWAN: EXPERT DATABASE
Online Profiles of Academic Community of Indian Universities
(Logo)
Persistent URL: https://vidwan.inflibnet.ac.in/profile/41991
View the Photographs, http://www.flickr.com/photos/rohelakhan/ at http://www.flickr.com/

For Copies of Preprints and Additional Information: [email protected]
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