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Abstracts of Conference Papers
C82: Generalization of Principle of EquivalenceWork done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270,
Pakistan Kamal SA, the
Fifth Symposium on Computational Complexities, Innovations and Solutions,
COMSATS Institute of Information Technology, Abbotabad, KP, Pakistan, 2010, abstract # 2, p 11 (Prof. Dr.
Q. K. Ghori memorial lecture) — |
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nominated by Vice
Chancellor, University of Karachi
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This lecture discussed the mathematics, the physics and the philosophy of principle of equivalence to understand its nature and scope itself as a fundamental principle. The weak version states that it is possible to choose a locally inertial coördinate system, at every spacetime point in an arbitrary gravitational field, such that, within a sufficiently small region of the point in question, “the laws of motion of freely-falling bodies” take the same form as in unaccelerated-cartesian-coördinate systems in the absence of gravitation. In the strong version “the laws of motion of freely-falling bodies” are replaced by “the laws of nature”. The medium-strong principle applies to all phenomena except gravitation itself, whereas very-strong principle applies to all phenomena. Einstein’s general theory of relativity is based on the strong version. The equivalence principle appears to hold only locally, but not globally. The speaker introduced possible approaches to generalization of principle of equivalence to inhomogeneous, anisotropic and time-varying gravitational fields and, hence, write a generalized-Robertson-Walker lineelement, using local-perturbation formulation. It was assumed that the gravitational field was homogeneous and stationary in an infinitesimal volume during a short span of time. Connection coefficients might, then, be used to write appropriate expressions of the generalized principle of equivalence. This lecture was dedicated to the memory of our beloved colleague, Prof. Dr. Q. K. Ghori (1932-2009), who passed away last year on May 17. Prof. Ghori got his MSc from University of Karachi in 1952 and PhD from University of British Columbia, Vancouver, Canada in 1961. During 1952-55, he taught at DJ Government Science, College, Karachi, affiliated with his alma mater (University of Karachi), where he had the honor to teach Dr. Abdul Qadeer Khan, NI (Bar), the renowned nuclear scientist of Pakistan. In 1955, he joined University of Sindh, Jamshoro. Upon his return from Canada (1961), he joined the Quaid-é-Azam University, Islamabad, as Associate Professor, becoming Full Professor in 1966 and held the posts of Acting Director of National Institute of Modern languages (1970-72), Professor-in-Charge of Computer Center (1968-73) and Dean, Faculty of Natural Sciences (1973-75). Other universities, which benefited from his vast experience and scholarship, are Garyounis University, Libya (1979-82, 1983-84), the King Fahad University of Petroleum and Minerals (FUFPM), Dhahran, Saudi Arabia (1988-94) and the Ghulam Ishaq Khan (GIK) Institute of Engineering Sciences and Technologies, Topi, KP (1994-2000). At GIK he served as Dean, Faculty of Engineering Sciences (1996-98) and Pro-Rector (1999-2000). At the time of his sad demise, he was serving as Advisor, the COMSATS Institute of Information Technology, concurrently serving as Treasurer, the Pakistan Academy of Sciences, the institution, which elected him Fellow in 1974. In 1975, he was awarded the Sir Shah Suleiman Memorial Prize. His professional memberships included the All Pakistan Mathematical Association (Past President), the Karachi Mathematical Association, the Pakistan Association for Advancement of Science, the Pakistan Association for History and Philosophy of Science, the Pakistan Scientific Society and the Punjab Mathematical Association. He supervised MPhil thesis of Mrs. Rashida Fahim, who taught at my university for more than two decades. Almost, every student of mathematics in the entire country has benefited from his classic book on mechanics (taught in BSc). Prof. Ghori has left behind 2 sons and 3 daughters. Mathematics community cannot recover back from this great loss. Some of the very last pictures of Prof. Ghori (taken on May 12, 2009) were shown during the lecture. Abstract PDF
C81: An Airport-Passenger-Screening
System based on Emitted IR and thermal Radiation
Work done
at: UNIVERSITY OF
KARACHI, University Road, Karachi 75270, Pakistan
Kamal SA, the Fifth Symposium on Computational Complexities,
Innovations and Solutions, COMSATS Institute of
Information Technology, Abbotabad, KP, Pakistan, 2010, abstract # 24, p 21
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This paper discussed health issues related to
passenger-screening-full-body scan (backscatter-X-ray scan), currently
implemented at selected airports in Europe and North America, and propose a
safer system. In the full-body scan, X rays penetrate through clothes and
Compton scattered to produce an unclothed image (which
could be stored,
although not stored during test runs) of the person being screened.
Modern-image-processing systems can display this image as negative (looking
like a body pattern) or positive (depicting the actual shape of face and body).
In this process, it sets off millions of electrons on or near the skin. The
scientific concerns arise from the fact that Compton scattering of X rays
(ionizing radiation), sets of a very large number of scattered electrons. They
could disturb fluid-electrolyte balance of the body. Backscatter-X rays, not
only, expose passengers, but also, security guards, who have to stand exposed
for a whole shift of passengers. Depending on the geometry of the source
producing them, they may fall off as inverse square (spherical symmetry) or
inverse (cylindrical symmetry). These X rays are stated to be of low intensity
and medium energy (the cross section of Compton scattering is maximum at medium
energy). The nature of damage depends
on the energy of the photons interacting with the surface. The extent of damage depends on the number
of photons (intensity) interacting with the surface. The operational
requirements of the process (detection of weapons concealed anywhere on the body
surface) demand that private body parts of the image not be blurred using
filters, because that would defeat the very purpose of scanning. For this very reason, there is no provision of shielding of gonads in the backscatter-X-ray-screening system, which is a standard safety requirement in the clinical-X-ray procedures. Further, at
some stage, the authorities managing the system would like to store the images
for follow-up, investigation and evaluation of any security lapses discovered
at a later stage as well as research purposes. Hence, the statement that the
images are destroyed after processing seems not to be compatible with standard
security and surveillance procedures. Presently, data are not available on
false positives. However, it seems that these would be almost as many as for
security gates, because many things, which are harmless, may look like
potential threat on screen (a pen may be mistaken as a pen pistol). It has been
pointed out that application of talcum powder on the skin may, also, produce
false positives. As regards missed cases, the system would not be able to
detect material, which has the same reflective properties as human skin. Also,
since it is a surface-analysis technique (like moiré fringe topography and
rasterstereography), it would not detect explosives contained inside the body
and in the body folds (radiation dose is kept low enough to skim the body
surface) as well as other contraband. This type of screening poses highest risk to infants, children, elderly people and pregnant women (the first three have weak immune systems; as for the last group, radiation may inflict permanent damage to the unborn child). An airport-passenger-screening system was
proposed based on recording and display of IR (infra-red) and thermal radiation
emitted by a prospective traveler. It was stated that this system had the
potential to detect explosives and controlled substances hidden in clothes, on
the person or inside the body (surgically-implanted bombs), if IR and thermal imaging were combined with
advanced signal- and image-processing techniques, canine teams and pat downs.
Since there was no radiation, which was given
to body (only the radiation given out
by the body was examined), there seemed to be no significant health concern
arising from this procedure. Security systems would become more efficient and
highly effective if explosive-trace detection was coupled, not only, with
passenger-identification systems based on previously proposed (by the speaker) static- and dynamic-3-D-face-recognition
systems,
gait recognition, biometric identifiers, but also, the study
of psychological traits. These might include face reading (people have employed
statistical methods to study temperature distribution of face) and checking
whether a person was heavily influenced by persuasive individuals or ideologies
(using, say, NN graphs).
Abstract PDF
C80: Air-Spacecraft of
the Third Millennium
Work
done at: UNIVERSITY OF
KARACHI, University Road, Karachi 75270, Pakistan
Kamal SA, the
Fifth Symposium on Computational Complexities, Innovations and Solutions, COMSATS Institute of
Information Technology, Abbotabad, KP, Pakistan, 2010, abstract # 25, p 21
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This paper described
the salient features of Air-Spacecraft of
the Third Millennium (ASTM), which should travel, partly, in space in the ballistic orbits; this technology,
already, being used in targeted spacecrafts. The
product satisfied most of the requirements of green engineering. Technological
benefits included:
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a) |
Decrease in travel time — comfort |
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b) |
Minimization of fuel consumption (most of the flight
in the ballistic phase, consuming no fuel), which could be passed on to
customer as reduced ticket price — economical/environmentally friendly |
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c) |
Reduction in average engine noise during the flight (most
of the flight in the ballistic phase, during which the engines shut down) —
comfort |
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d) |
Absence of turbulence (most of the flight in the
ballistic phase in space) — comfort |
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e) |
Reduction of engine-failure risk (engines are not
required in the ballistic phase) — safety |
ASTM should have its payload as passengers and cargo, and could reach New York
from Karachi in less than an hour; the fare charged might be comparable to what
was, currently, being charged by airlines for a trip from Karachi to Dubai.
ASTM could have its own Inertial Navigation System (INS), in addition to Global
Positioning System (GPS). These systems would generate navigational
information, whereas the desired trajectory, drawn-up in the
elliptic-astrodynamical-coördinate mesh (the ballistic orbit
being ellipse), should be computed by a combination of the multi-stage Lambert
scheme (incorporating cross-range error) and the multi-stage-Q system. Corrections to be
achieved by applying control laws — the
extended-cross-product steering and the ellipse-orientation
steering. Final check, ascertaining that the corrections had been
achieved, was made possible by employing the dot-product steering. For cargo transport,
this seemed to be an ideal solution. Even before the necessary database was
established for human travel, ASTM could be used to transport checked baggage
of passengers (earlier than their own arrival at destination), leaving more
space in conventional aircrafts for passengers, thus reducing
fuel-per-passenger ratio. The real challenge, on the other hand, lay in
modeling the effects of enhanced and reduced gravity on physiological systems, e.
g., functions of brain, heart and spinal column as well as flow of blood, etc., in particular, for the
pediatric and the geriatric populations. Some theoretical
estimates had, already, been made. During reduced gravity, there would
be increased blood flow to upper torso and brain. Moiré fringe topography and
rasterstereography could be used to study and model changes in shapes and
curvatures of upper torso during altered-gravity situations. In conclusion,
ASTM had the potential to take over the travel market, after it passed through
the designing and the development phase. Abstract PDF
C79: Mathematics in the Life Sciences
Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270,
Pakistan
Kamal
SA, the First National
Conference on Mathematical Sciences, Golden Jubilee Celebration, National
Center for Mathematics and Department of
Mathematics, University of Karachi, 2010, abstract # 10, p 19 (the Syed Firdous memorial lecture)
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This lecture introduced activities of the Mathematical Biology Group, with a bird’s eye view of mathematical models of brain (covariant, generalized coupling, covariant generalized coupling, mathematical definition of brain death), heart (standing wave), spinal column (static and dynamic), physical growth of children (statistical, ICP, KFA) and clinical examination (inverse problem, precedence and influence graphs used in the ordering of examination sequence). The spinal-column models generate 3-D profile of the human backbone using non-contact, non-invasive measurements obtained from moiré contours. Moiré fringe topography and rasterstereography are stereophotogrammetric techniques, which provide height and curvature maps of a surface, respectively. These techniques supplemented by edge-based moiré and edge-based raster have the potential to be applied to security technologies, gymnastic training, speech, posture and gait analyses of child, detect and quantify curvatures of spinal column (scoliosis, kyphosis and lordosis). The emphasis, then, shifted to the NGDS (National Growth and Developmental Standards for the Pakistani Children) Pilot Project as the speaker’s main sphere of interaction with (Late) Syed Firdous (SF), who was associated with this project from its inception in 1998 to his death on June 21, 2008. He was involved in planning, implementation, community outreach, data collection, modeling and analysis involving measurements of heights, weights and mid-upper-circumferences (MUAC) of primary-school children (co-authored 10 papers with the Project Director). He had, himself, measured over 2000 children on the school premises (Figure 1). This paper unveiled the next level of accuracy in height (Figure 2; to 0.01 cm using a vernier scale pasted on the set square used in the NGDS-height-measurement system, combined with spirit-level and plumb-line checks for horizontal and vertical alignments, respectively), mass (Figure 3; to 0.01 kg using a vernier scale pasted on the set square aligned with a beam scale, combined with spirit-level checks for floor and weighing scale) and MUAC (to 0.01 cm using a sliding vernier scale on a tailor’s tape) measurement techniques (the idea of using a vernier scale to go to the next level of accuracy was inspired by a physics laboratory session of Mr. Hussain Bilgirami conducted in 1972, when the author was studying in First year Science at Government College, Hyderabad, Sindh, Pakistan). In addition, the formula
could be used to compute net mass without asking the subject to disrobe
completely (m is net
mass, ma mass with one set of clothing worn, mb mass with the other set of clothing worn and ma+b mass with both sets of clothing worn). Mathematics of body sizes, forms, proportions and structures may be termed as anthromathematics.
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This lecture was dedicated to the memory of
our loving colleague (SF), born on September 4, 1952 in Jacobabbad, Sindh
(Pakistan), educated at University of Sindh. At the time of his death he was
serving as Associate Professor and Head, Department of Mathematics, SM
Government Science College, Karachi as well as Member, Board of Studies,
Department of Mathematics, University of Karachi. Abstract PDF
C78: A Minkowski-Type Metric
for Curved Spacetime
Work done at: UNIVERSITY OF KARACHI, University Road,
Karachi 75270, Pakistan
Kamal
SA, Conference on General Relativity and
Gravitation, Department of Mathematics, University of the Punjab, Lahore,
Pakistan, 2010, abstract # 15, p 12 (Prof. Dr. Khursheed Alam Khan memorial lecture) — nominated by Vice Chancellor, University of Karachi
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There has been a considerable interest among mathematicians and
theoretical physicists to construct a quantum theory as a possible approach
towards unification of all forces. Theory of general relativity and quantum
field theory are not in agreement with each other, which is the main problem in
making a mathematically consistent quantum theory of gravitation. Wigner
describes it as: “There is, hardly, any common ground between general theory of
relativity and quantum mechanics”. One encounters the problems of infinities in
the quantum theory of gravity. The theory is not renormalizable, because
Newton’s constant has dimensions of (energy)-2. The lagrangian for
Einstein’s gravity is a sum of curvature scalar Lgravity
(kinetic energy of the graviton) and Lmatter (all
the other fields and their interactions with the gravitational field). For a
physical theory to be valid it is not, always, necessary that the mathematical
formulation must be simple. There are examples, when theories with a complex
mathematical formulation, but simple ideas, worked. The lagrangian of
representation of Glashow, Weinberg and
Salam, when proposed for the first time, looked so complex that people thought it
would not work. Another example is, Einstein’s general theory of relativity. It
is based on a 10-dimensional tensorial field with complex mathematical
formulation. However, it is based on the simple ideas of equivalence of a
uniform gravitation field and uniform acceleration. Even special theory of
relativity, as presented by Einstein, did not seem elegant, mathematically. It
was Minkowski, who put the theory in spacetime-vector-field formulation. The
formulation of general relativity available to us is not adequate to unite gravity and quantum mechanics. General
relativity is a tensorial theory, while quantum mechanics is a linear theory
based on the principle of superposition, which is valid, only, for linear
systems. In this paper, an attempt was made to formulate general relativity by
writing curved-spacetime metric describing riemannian geometry, whose tensorial
components in a particular coördinate basis are given by gmn,
in a form similar to flat-spacetime metric describing minkowskian geometry, whose
components are given by hmn,
in extra dimensions. Curvature infinities may be avoided by writing a
linearized version of curved-spacetime-metric tensor. Transformation of
coördinates has, also, been used to avoid infinities from Lorentz
transformations and the Poincaré transformations. Use of extra dimensions to
describe physical systems has been a practice in theoretical physics. Some
well-known examples are Kaluza-Klein theories and superstring theories. This
lecture was dedicated to the memory of Prof. Dr. Khursheed Alam Khan (whose
contributions to theory of relativity cannot be overlooked), who passed away in
October 2009. A research student of Roger Penrose of University of Oxford, he
was associated with the Sir Syed University of Engineering and Technology at
the time of his death. Abstract PDF
Abstracts of Conference Papers (1970-1979) (1980-1989) (1990-1999) (2000-2009)
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