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
Charged-Particle Beam Optics
The quantum theory of charged-particle beam dynamics is being
developed essentially using an algebraic approach. On the basis of this
theory, optics of the transport of nonrelativistic and relativistic
charged-particle beams through electromagnetic systems (of importance
for charged-particle beam devices, like electron microscopy,
microelectron-beam lithography, etc ., and accelerator design) is
being analyzed systematically. The machinery of Lie algebraic methods
is used primarily and this facilitates an easy passage from the quantum
theory to the traditional classical theory (geometrical optics). Our
results include the modifications of the paraxial properties and the
aberration coefficients, with hbar -dependent contributions, for
the various optical elements, like the magnetic round lenses,
quadrupoles, etc., using the Schrödinger (nonrelativistic),
Klein-Gordon and Dirac equations. For charged spin-half particles, the
Dirac equation leads to spinor contributions to the beam dynamics. We
do hope that these quantum corrections, albeit small, would be of some
practical significance in certain situations; it should, however, be
emphasized that, in any case, it is certainly satisfying to understand
the working of the traditional classical theory as an approximation of
a proper quantum theory since after all any physical system is quantum
mechanical at the fundamental level.
The application of the Wigner phase-space distribution for
studying the quantum mechanics of charged-particle beam transport
through electromagnetic optical systems provides a natural link between
the classical and the quantum descriptions. In this context, the
relation between the transformation of the Wigner function of a
charged-particle optical system, corresponding to the associated scalar
wave function, and the transformation of the classical phase-space of
the system has been studied.
The application of the spinor beam optical formalism has been shown to
lead to a fully quantum mechanical understanding of the dynamics of a
spin-half particle with anomalous magnetic moment, including the spin
evolution, at the level of single-particle dynamics. The general
theory, developed for any magnetic optical element with straight axis,
describes the the quantum mechanics of the orbital dynamics, the
Stern-Gerlach kicks and the Thomas-Bargmann-Michel-Telegdi
(Thomas-BMT) spin evolution.
The corrections to the traditional descriptions rigorously derived in the
above articles have a significant bearing on the celebrated Scherzer Theorem
in the wavelength-dependent regime in electron microscopy and the algebraically
equivalent system of fiber optics.
An application for a patent shall be made in the near future!
Technical Writings
A. Books
Sameen Ahmed Khan ,
International Year of Light and Light-based Technologies
(IYL ,
Logo ),
LAP LAMBERT Academic Publishing ,
Logo ,
Germany , 96 pages (Thursday the 30 July 2015).
(ISBN-10 :
3659764825 and
ISBN-13 :
9783659764820 ,
Book Cover ),
(ISBN :
International Standard Book Number System ,
Logo ).
Link to the Publisher .
B. Articles
S. A. Khan and
R. Jagannathan ,
Theory of relativistic electron beam transport based on the
Dirac equation ,
Preprint:IMSc /93/53
Presented at
The 3rd National Seminar on Physics and Technology of Particle
Accelerators and their Applications, PATPAA-93,
IUC-DAEF
Kolkata (Calcutta) Centre ,
India ,
25-27 November 1993
Editor : S. N. Chintalapudi,
IUC-DAEF
Kolkata (Calcutta) , 102-107.
http://cds.cern.ch/record/263573 .
S. A. Khan and
R. Jagannathan ,
Quantum mechanics of charged particle beam optics: An operator
approach ,
Preprint:IMSc /94/11
Presented at the
JSPS -
KEK
International Spring School on High Energy Ion Beams-Novel Beam
Techniques and their Applications,
Japan ,
17-29 March 1994.
(JSPS :
Japan Society for the Promotion of Science
Logo ).
(KEK :
High Energy Accelerator Research Organization ,
Logo ).
http://cds.cern.ch/record/263576 .
S.
A.
Khan and
R. Jagannathan ,
Quantum mechanics of charged particle beam transport through magnetic lenses ,
Preprint:IMSc /94/41,
Physical Review
E
51 ,
Issue 3 ,
2510 -
2515
(March
1995 ,
Journal Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1103/PhysRevE.51.2510
R.
Jagannathan and
S. A. Khan ,
Quantum theory of the optics of charged particles ,
Preprint:IMSc /95/31
Chapter
4 in
Invited article for :
Advances
in
Imaging and Electron Physics ,
Editors : Peter W. Hawkes, B. Kazan and
T. Mulvey ,
(Academic Press ,
Logo ,
San Diego , 1996),
Vol .
97 ,
257-358 (1996).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1016/S1076-5670(08)70096-X
(ISBN :
0-12-014739-4 ,
ISBN-10 :
0120147394 and
ISBN-13 :
978-0120147397 ,
Book Cover ).
(ISBN :
International Standard Book Number System ,
Logo ).
Also available from:
ScienceDirect
(Logo ).
* See the
Preface .
R. Jagannathan and
S. A. Khan ,
Wigner functions in charged particle optics ,
Preprint:IMSc /94/53
In : Selected Topics in Mathematical Physics-Professor R. Vasudevan Memorial Volume,
Editors :
R. Sridhar ,
K. Srinivasa Rao
(Picture ) and
V.
Lakshminarayanan
(Picture ),
(Allied Publishers ,
Logo ,
Delhi ,
India , 1995), 308-321.
(ISBN-10 :
8170234883 and
ISBN-13 :
978-8170234883 ,
Book Cover ).
(ISBN :
International Standard Book Number System ,
Logo ).
* See the Obituary,
Ramabhadra Vasudevan (1929-1993) , by
K. Srinivasa Rao and
R. Sridhar , in
Obituary Notices ,
Physics
Today ,
Vol.
47 ,
No.11 ,
pp.
106
(November
1994 ,
Journal Cover ).
Digital Object Identifier
(DOI ,
Logo ):
DOI:10.1063/1.2808716 .
M. Conte ,
R. Jagannathan ,
S.
A.
Khan and
M.
Pusterla ,
Beam optics of the Dirac particle with anomalous magnetic moment ,
Preprint:IMSc /96/07,
INFN /AE-96/08
Particle Accelerators
56 (2) , 99-126 (1996).
http://cds.cern.ch/record/307931/files/p99.pdf .
S. A. Khan ,
Transport of Dirac-particle beams through magnetic quadrupoles ,
Preprint:IMSc /96/33.
Sameen Ahmed Khan ,
Quantum theory of charged-particle beam optics
(Thesis Cover ),
PhD Thesis ,
The Institute of Mathematical Sciences
(MATSCIENCE /IMSc ,
Logo ,
January 1997).
(Details with the Complete Thesis ).
*
Thesis Supervisor :
Professor Ramaswamy
JAGANNATHAN
(Picture )
*
Description of Ph.D Research :
Development of quantum mechanical treatment for the study of
transport of charged-particle beams through electromagnetic systems.
*
Complete Thesis Available from :
IMSc Library Digital Repository
(Logo )
S. A. Khan ,
Quantum theory of charged-particle beam optics
(Thesis Cover ),
Theses
in Physics ,
Complete Thesis: 181 pages
(1997 ).
*
Click here for the
Long Thesis-Abstract
(DVI Version ,
PS Format or/and
PDF Format ).
*
Click here for the
Short Thesis Abstract which appeared in the
International Committee for Future Accelerators
(ICFA ,
Logo )
Beam Dynamics Panel
Newsletter
(Logo ),
No. 15 ,
pp. 44-45
(December 1997 ).
* See the IMSc
Annual Report
1997 ,
pp .
83
for the Thesis Submission
and
IMSc
Annual Report
1998 ,
pp .
80
for the Award of PhD Degree .
R. Jagannathan and
S. A. Khan ,
Quantum mechanics of accelerator optics ,
International Committee for Future Accelerators
(ICFA ,
Logo )
Beam Dynamics Panel
Newsletter
(Logo ),
No. 13 ,
pp. 21-27
(April 1997 ).
Editors :
Kohji Hirata ,
John M Jowett and
Shyh-Yuan Lee .
S. A. Khan ,
Quantum theory of magnetic quadrupole lenses for spin-1/2 particles ,
In :
Proceedings
of the
15th
Advanced
International Committee for Future Accelerators
(ICFA ,
Logo )
Beam Dynamics
Workshop on
Quantum Aspects of Beam Physics (QABP)
(Logo )
(04-09 January 1998,
Monterey ,
California ,
USA)
Editor :
Pisin Chen
(World Scientific ,
Logo ,
Singapore , 1999), pp. 682-694.
(ISBN-10 :
9810235518 and
ISBN-13 :
978-9810235512 ,
Book Cover ).
Table of Contents
(ISBN :
International Standard Book Number System ,
Logo ).
LANL
E-Print archive
http://arXiv.org/abs/physics/9809032/ .
Sameen A. Khan ,
Quantum aspects of accelerator optics ,
In :
Proceedings of
the
1999 Particle Accelerator Conference
(PAC99 ,
Logo )
(29 March - 02 April 1999,
New York City ,
NY ,
USA )
Editors :
A.
Luccio and
W. MacKay ,
Vol. 4 ,
pp. 2817-2819
(IEEE
Catalog Number : 99-CH36366).
PAC99 Archive
THA98.pdf
Proceedings
at the
IEEE Website :
Abstract
in
Vol. 4 .
(ISBN-10 :
0780355733 and
ISBN-13 :
978-0780355736 ,
Book Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1109/PAC.1999.792948
LANL
E-Print archive
http://arXiv.org/abs/physics/9904063/ .
(ISBN :
International Standard Book Number System ,
Logo ).
(IEEE :
Institute of Electrical and Electronics Engineers ,
Logo ).
* Link to
JACoW
(Logo ):
Joint Accelerator Conference Website for the Particle Accelerator
Conferences .
Sameen A. Khan and
Modesto Pusterla ,
Quantum mechanical aspects of the halo puzzle ,
In :
Proceedings of the
1999 Particle Accelerator Conference
(PAC99 ,
Logo )
(29 March - 02 April 1999,
New York City ,
NY )
Editors :
A.
Luccio and
W. MacKay ,
Vol. 5 ,
pp. 3280-3281
(IEEE
Catalog Number : 99-CH36366).
PAC99 Archive
THP136.pdf
Proceedings
at the
IEEE Website :
Abstract
in
Vol. 5 .
(ISBN-10 :
0780355733 and
ISBN-13 :
978-0780355736 ,
Book Cover ).
(IEEE :
Institute of Electrical and Electronics Engineers ,
Logo ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1109/PAC.1999.792276
LANL
E-Print archive
http://arXiv.org/abs/physics/9904064/ .
(ISBN :
International Standard Book Number System ,
Logo ).
Sameen A. Khan and
Modesto Pusterla ,
Quantum-like approaches to the beam halo problem ,
in :
Proceedings
of the
6th
International Conference on Squeezed States and Uncertainty Relations
(ICSSUR'99 ,
Logo ),
(24-29 May 1999, Napoli ,
Italy )
Editors :
D Han ,
Y S Kim ,
and
S Solimeno ,
(NASA Conference Publication No.
2000-209899 )
pp. 438-441 (July 2000).
Book Cover ,
Complete Proceedings
from the
NASA Technical Report Server
(Logo )
(NASA :
National Aeronautics and Space Administration ,
Logo ).
LANL
E-Print archive
http://arXiv.org/abs/physics/9905034/ .
Sameen Ahmed Khan and
Modesto Pusterla ,
On the form of Lorentz-Stern-Gerlach force ,
10 pages, LANL
E-Print archive
http://arXiv.org/abs/physics/9910034/
(communicated ).
S. A. Khan and
M. Pusterla ,
Quantum-like approach to the transversal and longitudinal beam
dynamics. The halo problem ,
The
European
Physical
Journal
A ,
Vol.
7 ,
No.
4 ,
p
p
583-587
(2000,
Journal Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1007/s100500050430
LANL
E-Print archive
http://arXiv.org/abs/physics/9910026/ .
*
Also available from EDP Sciences
(Logo )
The
European
Physical
Journal
A ,
Vol.
7 ,
No.
4 ,
p
p
583-
587
(2000 ).
Sameen Ahmed Khan and
Modesto Pusterla ,
Quantum approach to the halo formation in high current beams ,
Nuclear Instruments and Methods in Physics Research (NIMS)
A ,
Vol. 464, Issue 1-3 ,
pp. 461-464
(21 May
2001 ,
Journal Cover ).
(Refereed
Proceedings of the
13th International
Symposium on Heavy Ion Inertial Fusion (HIF2000)
(13-17 March 2000,
San Diego ,
USA ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1016/S0168-9002(01)00108-5
LANL
E-Print archive
http://arXiv.org/abs/physics/0112082/ .
Sameen
Ahmed
Khan ,
Quantum mechanical formalism of particle beam optics ,
in :
Proceedings
of the
18th
Advanced
International Committee for Future Accelerators
(ICFA ,
Logo )
Beam Dynamics
Workshop on
Quantum Aspects of Beam Physics (QABP)
(15-20 October 2000,
Capri ,
ITALY )
Editor :
Pisin Chen
(World Scientific ,
Logo ,
Singapore , May 2002), pp. 517-526.
(ISBN-10 :
9810249500 and
ISBN-13 :
9789810249502 ,
Book Cover ).
(ISBN :
International Standard Book Number System ,
Logo ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1142/9789812777447_0042
LANL
E-Print archive
http://arXiv.org/abs/physics/0112085/ .
Sameen Ahmed Khan ,
The
World of Synchrotrons ,
Resonance Journal of Science Education ,
Vol. 6, No. 11
77-84
(November
2001 ,
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. 6, No. 11
p
p.
77-86
(November
2001 ,
Journal Front Cover and
Journal Back Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1007/BF02868247
Larger Version : 11 pages,
LANL
E-Print archive
http://arXiv.org/abs/physics/0112086/ .
*
Cited in the
Accelerators Section
and the
Synchrotrons Section
of
THE
NET ADVANCE OF PHYSICS .
(Review Articles and Tutorials in an Encyclopaedic Format).
Sameen Ahmed Khan ,
Introduction to Synchrotron Radiation ,
Bulletin of the
IAPT ,
19 (5), 149-153 (May 2002).
(IAPT :
Indian Association of Physics Teachers ,
Logo ).
Sameen Ahmed Khan ,
Electron Beams for Radiation ,
Kiran ,
13 (3), 40-42 (July 2002).
(Kiran : the
Bulletin
of the
Indian Laser Association ,
Logo ).
Sameen
Ahmed
Khan ,
Analogies between light optics and charged-particle optics ,
International Committee for Future Accelerators
(ICFA ,
Logo )
Beam Dynamics Panel
Newsletter
(Logo ),
No. 27 ,
pp.
42-48
(June
2002 ).
Editors :
W. Chou ,
John M Jowett ,
C. Biscari,
S.
Chattopadhyay ,
S. Ivanov,
H. Mais ,
J. Wei ,
and
C. Zhang .
LANL
E-Print archive
http://arXiv.org/abs/physics/0210028/ .
*
Cited in the
Optics Section
of
THE
NET ADVANCE OF PHYSICS .
(Review Articles and Tutorials in an Encyclopaedic Format).
Sameen Ahmed Khan ,
Synchrotron Radiation (in Asia) ,
ATIP
Report ,
No.
ATIP02.034 ,
28
pages
(21 August
2002 ).
(ATIP :
The Asian Technology Information Program ,
Logo ,
Tokyo ,
Japan ,
2002 ).
Azher
Majid
Siddiqui
and
Sameen Ahmed Khan ,
Ion Beam Channeling and Accelerator Programmes in India ,
MRSI
Newsletter ,
Vol. B 02, Number 4 , pp. 3-5
(October
2002 ).
(MRSI :
Materials Research Society of India ,
Logo ).
Sameen Ahmed Khan ,
The Foldy-Wouthuysen Transformation Technique in Optics ,
Optik -
International Journal for Light and Electron Optics ,
Volume 117 ,
Issue 10 ,
pp. 481-488
(October 2006 ,
Journal Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1016/j.ijleo.2005.11.010
(Elsevier ,
Logo , 2006).
(Available online since Friday the 17 February 2006 ).
Sameen
Ahmed
Khan ,
The Foldy-Wouthuysen Transformation Technique in Optics ,
Chapter
2 in
Invited article for :
Advances in Imaging and Electron Physics ,
Editor : Peter W. Hawkes,
Vol .
152 ,
49-78
(Elsevier ,
Logo , August 2008).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1016/S1076-5670(08)00602-2
(ISBN :
0-12-374219-6 ,
ISBN-10 :
0123742196 and
ISBN-13 :
978-0-12-374219-3 ,
Book Cover ).
Table of Contents .
(ISBN :
International Standard Book Number System ,
Logo ).
Also available from:
ScienceDirect
(Logo ).
* See the
Preface
Sameen Ahmed Khan ,
Quantum Aspects of Charged-Particle Beam Optics ,
in : Proceedings of the
Fifth Saudi International Meeting on Frontiers of Physics 2016
(SIMFP 2016 ),
(16-18 February 2016,
Department of Physics ,
Jazan University ,
Gizan ,
Saudi
Arabia ).
Editors: Ali Al-Kamli ,
Nurdogan Can ,
Galib Omar Souadi ,
Mohamed Fadhali ,
Abdelrahman Mahdy and
Mahmoud Mahgoub ,
AIP Conference Proceedings ,
1742 ,
030008-1–030008-4 (10 June 2016,
Book Cover ).
(American Institute of Physics ,
Logo );
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1063/1.4953129 .
Sameen Ahmed Khan ,
Linearization of Wave Equations ,
Optik -
International Journal for Light and Electron Optics ,
Volume 131 ,
C ,
pp. 350-363
(February 2017 ,
Journal Cover ).
Digital Object Identifier
(DOI ,
Logo ):
http://dx.doi.org/10.1016/j.ijleo.2016.11.073 .
(Elsevier ,
Logo , 2017).
(Available online since Wednesday the 16 November 2016 ).
Sameen Ahmed Khan ,
Quantum Methods in Light-Beam Optics ,
Optics & Photonics News
(OPN ,
Logo ),
Vol.
27 ,
No. 12 ,
pp.
47
(December
2016 ,
Journal Cover ).
(A publication of the OSA :
Optical Society of America ,
Logo ).
*
One of the thirty papers selected under the theme,
Optics in 2016 ,
highlighting the most exciting peer-reviewed optics research to have emerged over the past 12 months.
*
This work was strongly influenced by the
Quantum theory of charged-particle beam optics .
(See the Doctoral Thesis on this topic)
resulting in a Unified Treatment of Light Beam Optics and Light Polarization
(initial results available in Research in Light Beam Optics ).
C. Articles in Preparation
Ramaswamy Jagannathan and
Sameen Ahmed Khan ,
Quantum Mechanics of Charged Particle Beam Optics ,
(in preparation ).
Sameen Ahmed Khan and
Ramaswamy Jagannathan ,
Quantum Methodology Approach to Light Beam Optics ,
(in preparation ).
Sameen Ahmed Khan ,
Hamilton's Optical-Mechanical Analogy in the Wavelength-dependent Regime .
Sameen Ahmed Khan ,
Why is the Foldy-Wouthuysen transform so little known in optics? .
LANL
E-Print archive
http://arXiv.org/abs/physics/0510???
S. A. Khan ,
Beam Optics of the Dirac particle .
M. Conte,
R. Jagannathan ,
S. A. Khan and
M. Pusterla ,
A quantum mechanical formalism for studying the transport of
Dirac-particle beams through magnetic optical elements in accelerators .
S. A. Khan ,
Anomalous moments... Thomas-BMT... .
S. A. Khan and
R. Jagannathan ,
Quantum theory of aberrations in charged-particle beam optics .
Sameen A. Khan and
Modesto Pusterla ,
A diffraction model for the beam halo problem .
Azher
Majid
Siddiqui
and
Sameen
Ahmed
Khan ,
Introduction to Ion Beam Channeling ,
(in preparation ).
Azher
Majid
Siddiqui and
Sameen Ahmed Khan ,
Accelerator-Based Techniques and Applications in
Research and Industry ,
(in preparation ).
Sameen Ahmed Khan ,
And others...
Research in Light Beam Optics .
Some Research Encounters:
Number Theory .
Crystallographic Studies of the 123-Superconductors
(YBa_{2} Cu_{3} O_{7-x} the Yttrium Barium Copper Oxide) .
SOC: Self-Organized Criticality (SandPiles) .
Integer Sequences in Resistor Networks .
Quadratic Surfaces .
Salt Solutions .
60+
Technical
Writings
Click here for a
LaTeX /MiKTeX
Derived
DVI Version ,
PS Version or/and
PDF Version of the Technical Writings
MS WORD Version
200+
Non-Technical Writings (Popular Writings)
Click here for a
LaTeX /MiKTeX
Derived
DVI Version ,
PS Version or/and
PDF Version of the
Non-Technical Writings (Popular Writings)
MS WORD Version
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
Click for a
LaTeX /MiKTeX
Derived
DVI Version ,
PS Version or/and
PDF Version of
the Patents
MS Word Version of the
Patents
Sameen Ahmed Khan ,
Quadricmeter ,
Official Journal of the Patent Office ,
Issue No.
43/2008 ,
Part-I ,
pp .
25296
(24 October
2008 ).
Application No.:
2126/MUM/2008 A ,
International Classification: B69G1/36 ,
Controller General of Patents Designs and Trade Marks, Government of India
(Logo ).
http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/patent_journal_2008.htm
http://ipindia.nic.in/ipr/patent/journal_archieve/journal_2008/pat_arch_102008/official_journal_24102008_part_i.pdf
http://www.patentoffice.nic.in/ ,
http://www.ipindia.nic.in/
(Logo ) .
(patent in process , see the Quadricmeter ).
(Click for a
MS Word Version ,
DVI Version ,
PS Version or/and
PDF Version of the
Quadricmeter ).
Quadricmeter is the instrument devised to identify (distinguish) and measure the various
parameters (axis, foci, latera recta, directrix, etc.,) completely characterizing the important
class of surfaces known as the quadratic surfaces. Quadratic surfaces (also known as quadrics)
include a wide range of commonly encountered surfaces including, cone, cylinder, ellipsoid,
elliptic cone, elliptic cylinder, elliptic hyperboloid, elliptic paraboloid, hyperbolic cylinder,
hyperbolic paraboloid, paraboloid, sphere, and spheroid. Quadricmeter is a generalized form of
the conventional spherometer and the lesser known cylindrometer (also known as the “Cylindro-Spherometer”
and "Sphero-Cylindrometer").
With a conventional spherometer it was possible only to measure the radii of spherical surfaces.
Cylindrometer can measure the radii of curvature of a cylindrical surface in addition to the spherical
surface. In both the spherometer and the cylindrometer one assumes the surface to be either spherical
or cylindrical respectively. In the case of the quadricmeter, there are no such assumptions.
Click for a
LaTeX /MiKTeX
Derived
DVI Version ,
PS Version or/and
PDF Version of
the Integer Sequences
MS WORD Version of the Integer Sequences
MS EXCEL Version of the Integer Sequences
Click here for a
LaTeX /MiKTeX
Derived
DVI Version ,
PS Version or/and
PDF Version of
the Curriculum Vitae
Fifty-eight Page MS Word Version of the Curriculum Vitae
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
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