Abstracts of Conference Papers

Abstracts of Conference Papers
(1970-1979) (1980-1989) (1990-1999)

2011 2010



C87: 3-D-Optical Imaging in Diabetic Foot Care of Children

Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270, Pakistan

Kamal SA, Rajput MK, Khan SA, Sympo-sium on Diabetic Foot Care, Department of Orthopedic Surgery, Jinnah Post graduate Medical Center, Najmuddin Auditorium, JPMC, Karachi, 2011, p 1

Diabetes in children presents additional problems in terms of their feet care as they are

 by nature robust and active, indulging in play and activities involving climbing, jumping,

running and walking. Polished, properly-fitting-pure-leather shoes (shoes with damaged

internal surface should be, immediately, discarded) and clean, pure-cotton socks (disinfectant powder should be applied before putting on socks) should be worn for school, replacing dress shoes with sport shoes/trainers for sport participation. Whenever children go out in the garden, backyard or playground, they should be mandated to put on socks and sport shoes. Too loose (foot support may be used to adjust such shoes) or too tight shoes should not be used. The former increase the chances of accidents and injuries and the later may block circulation. Parents should inspect feet of diabetic children upon arrival from school or sport events for blisters, cuts, sores or warts. If any such condition is suspected, a podiatrist should monitor the feet using visual, photographic and video recording in the anatomical position (posture study — cf. Fig. 1a) as well as during walking and running (gait studycf. Fig. 2). The soles and the upper surfaces of feet must, also, be studied using moiré fringe topography (providing 3-D surface map) and rasterstereography (providing 3-D curvature map) — sterophotogrammetric, non-contact, non-invasive, non-infecting, non-destructive techniques providing permanent digital record. Edge-based moiré and edge-based raster could be employed to quantify infinitesimal movements during a gait cycle. Study of soles of feet on sand would provide clues to vascular-system disorders trigged by diabetes. Facilities available in the SF Laboratory include anthropometry (heights to accuracies of 0.01 cm and masses to 0.01 kg, respectively), growth-and-obesity profile software, moiré fringe topography, rasterstereopgraphy and video analysis. In order to prevent diabetes in children, it is recommended to keep track of their growth-and-obesity profiles from 3 years onward. The children should, also, be monitored if they are under excessive pressure to excel (by teachers, parents, sports coaches). Any form of abuse (neglect, bullying, physical, sexual) may, also, contribute to diabetes. In case a child is diagnosed with diabetes, it should be treated with a proper combination of diet, exercise and lifestyle adjustment. Abstract PDF



Fig. 1. Study of feet of child in
(a) anatomical position and
(b) during normal gait


C86: Curbing Corruption in Pre-University Education
Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270, Pakistan
Kamal SA
, Seminar on Curbing Corruption in the Education Sector, the Education Committee, Transparency International Pakistan, Ambassador III, Hotel Marriott Karachi, 2011, p 1

Corruption in a society is a dissipative force, which tends to slow
down the pace of progress (in the presence of dissipative force,
the system dissipates energy to the surroundings, the force law
being function of generalized velocities in addition to generalized
coördinates; opposed to conservative force, which is characterized
by the property that total work done along a closed path vanishes,
the force law being function of generalized coördinates, only). It
cannot be eliminated, but it can be quantified, and, possibly, mini-
mized. Corruption can be understood by looking at the second law
of thermodynamics
. Just like
flow of heat is the basis of all physical
processes, flow of money is the basis of all economic activities.
When there is money involved, there appears corruption.
essence of s
econd law of thermodynamics may be summarized in
the statement that heat from a hot body is partially converted into
work and partially wasted in a heat sink.
Money allocated for a
project (equivalent to heat extracted from a hot reservoir — heat source) ends up partially in infrastructure (equivalent to increase in internal energy, in the context of first law of thermodynamics) and services/products (equivalent to work done by the system — first law of thermodynamics) and partially goes into corrupt hands (equivalent to heat absorbed by a cold reservoir — heat sink).
The measures for curbing corruption may be broadly classified as pre-assignment phase (identification of soft areas/conflict of interest), implementation phase (follow through— monitoring) and commissioning phase (follow up — evaluation). Public must be made aware that they have a right-to-know and a right-to-question. There should be a website/a hotline to receive complaints, with proper filter to screen out false accusations.  A system of reward and recognition should be established to encourage honest practices.  The paper, then, focused on the fee structure of private schools. It was suggested that the fee structure should be according to the services provided. In addition, teachers should be compensated in line with the fee charged from the students. It was, further, observed that hidden charges pose a big burden to parents’ pockets. Hence, it is need of the hour to streamline the fee structure of such institutions with strict enforcement of locally applicable laws. The other issue discussed was that of ghost schools. Besides causing wastage of funds, the unoccupied buildings become sources of garbage dump as well as hub of antisocial activities, e. g., hideouts for criminals and drug addicts. There is a need to keep track of all func

tional and non-functional schools. As regards religious schools, it was observed that the different philosophies, the different contents and the different pedagogical techniques are creating a divide between religious and secular schools, widening with the passage of time. The mindset of students is shaped by teachers’ perception of religion and driven by sources of support. “A teacher has the power to make a student tolerant in one minute and a terrorist in another minute, not only, in the religious schools, but also, in the secular schools”. The role of a teacher should be to promote tolerance, empathy for emotions/points-of-view of others (discouraging hate towards any community, religion or sect) and use of non-violent means to achieve objectives. Today’s religious schools should prepare students to resolve conflicts, not generate new controversies as well as face challenges of modern-day social order (internet, cable TV). It is a wrong assumption that terrorism breeds only in impoverished neighborhoods or when children are exposed to domestic or street violence (gang war, civil war due to political unrest, economic meltdown or natural disasters, war imposed by a foreign power) or any form of abuse (neglect, peer pressure/bullying, verbal, physical, sexual abuse). It has been observed that suicidal tendencies may be present in students, who excel in academics and co-curricular activities. The proposed solutions include (a) continuous monitoring of emotional intelligence of students, (b) integrating secular and religious education in the form of an Integrated Educational System, (c) requiring teachers (in particular, the ones entrusted to impart religious education) to declare their religion, school of thought and sphere of influence in writing (cross checked through NN graphs) and (d) ascertaining the sources of support of an institution. It was concluded that SMART (specific-measurable-attainable-realistic-time bound) targets should be set for reducing corruption. This might be achieved by modeling money flow as a substance-like quantity to obtain an optimal solution using tools of operational research. Abstract PDF


C85: Anthromathematics: A New Branch of Mathematics

Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270, Pakistan

Kamal SA, the Sixth Symposium on Computational Complexities, Innovations and Solutions(CCIS 2011),
COMSATS Institute of Information Technology, Abbotabad, KP, Pakistan, 2011, abstract # 1, pp 13, 14 (keynote lecture)

This lecture introduced activities of the Mathematical Biology Group, with a brief introduction to mathematical models of brain (covariant, generalized coupling, covariant-generalized coupling, mathematical definition of brain death), heart (standing wave), spinal column (static and dynamic) and physical growth of children (ICP, KFA, KJK; last two developed during the course of the NGDS Pilot Project). Anthromathematics was defined as the mathematics of human body sizes, forms, proportions and structures. The term was first used on March 22, 2010 by the author during the First Conference on Mathematical Sciences held at University of Karachi. Third millennium challenges required that the sciences of anthropology (study of human being) and anthropometry (measurement of human being) be transformed to anthromathematics through ideas from mathematics, e. g., mathematical equations employed to approximate human body form (analysis — formulae for surface area and volume of human body), discrete structures recognized in the anatomy and the physiology of human body (algebra — brain death defined, mathematically, through study of group structure), invariance under deformations discovered (topology — spinal column deformed because of scoliosis, kyphosis or lordosis, studied by static and dynamic models), properties of numbers studied (number theory — numbers giving height, weight and other anthropometric measures) as well as inferences analyzed (logic — upper limits of optimal weight-for-height). To elaborate the point further, an anthropometrist is supposed to take heights, but an anthromathematician, not only, must measure heights, but also, determine accuracy, precision and reproducibility of the techniques used, while planning the session, align the scale, ascertain that the surface is level, check the equipment against agreed-upon standards at the start of each session and, finally, estimate consistency of collected data at the end of every session. Measurement of height was used to teach the mathematical concepts of serial measurements, graph plotting, slope computation, height function as time series, estimation of adult height and comparison with cut-off height for armed-forces careers. A situation, in which engineering tape was mounted in a tilted position by mistake, was used to teach the following concepts: (a) Computation of hypotenuse from perpendicular (trigonometry); (b) A line parallel to base intersects the sides of triangle such that the line segments are proportional (geometry).   Similarly, measurement of weight offered opportunities to teach concepts in mathematics (estimated-adult weight, net-weight computation from clothed weight, optimal weight-for-height). The focus, then, shifted towards mathematical model of physical examination. Mathematical concepts used in the physical examination were elaborated: (i) symmetry (left-right) in the body shape, size, number of limbs (fingers, toes), anatomical landmarks (scapulae, body triangles, spinal dimples, shoulder/neck line, knee joints, in the context of scoliosis indicators) — asymmetry as the first indicator of breast cancer, (ii) inverse problem — determining properties of source from the properties of field (e. g., auscultation using stethoscope; the sound recorded from heart, lungs or stomach comes through the body tissue and skin, which must be accounted for), radiative-transfer equation was used to compute intensity, when source function was known (proper interpretation of X-ray intensity in CT scan using radiative transfer equation brought Nobel Prize in medicine, basis of clinical thermograms), (iii) precedence graph — some checks have to be performed before the others, overlooking this might  effect, adversely, on patient’s health (e. g., examination of resting heart to be performed before treadmill testing, or hernia check must precede cardiac function testing in the squatting position), (iv) influence graph — some procedures influence certain portions of the examination (e. g., running influenced blood pressure and heart rate). There is, therefore, a need a devise protocols of examination in such a way that interacting procedures are performed in a laid-down sequence, or during separate sessions. These protocols must indicate which procedures must precede the others and which ones could be performed concurrently (e. g., cardiac function in the standing position and check for undescended testicles). The techniques used in physical examination by a medical professional consist of auscultation, percussion and olfaction (all three employ inverse problem), inspection (employs symmetry) and palpation (employs properties of material, body temperature). Facilities available in SF Growth and Imaging Laboratory operated by Mathematical Biology Group, University of Karachi include stereophotogrammtery (moiré fringe topography, rasterstereography), video analysis, height and weight measurements to accuracies of 0.01 cm and 0.01 kg, respectively as well as software to generate growth-and-obesity profiles of children.  Abstract PDF

C84: Intelligent Ledger Balance using Theory of Matrices

Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270, Pakistan

Kamal SA, the Sixth Symposium on Computational Complexities, Innovations and Solutions(CCIS 2011), COMSATS Institute of Information Technology, Abbotabad, KP, Pakistan, 2011, abstract # 2, pp 14, 15 (the Islamuddin memorial lecture) — nominated by Vice Chancellor, University of Karachi
his lecture introduced intelligent ledger balance using theory of matrices. The methods presented here could, also, be used in computation of attendance and similar applications. The ledger entries might be visualized as the elements of ledger matrix ₤, represented as £ij, where i is the number of rows and j the number of columns. Let x be a 1 by i row vector, and y be a j by 1 column vector, each entry of these vectors consists of unity. The product of row vector and ledger matrix, represented in Einstein convention as xi£ij, generates a 1 by j row vector, each entry of which was the sum of entries of respective ledger column. Similarly, the product of column vector and ledger matrix, represented in Einstein convention as £ijyj, generates a i by 1 column vector, each entry of which was the sum of entries of respective ledger row. The triple product xi£ijyj, therefore, represented the grand sum of ledger, which could be obtained in 2 ways: (a) summation of the entries of the i by 1 column vector, £ijyj, or (b) summation of the entries of the 1 by j row vector, xi£ij. The two methods generated identical results. A difference in the sums obtained using method (a) and method (b) was the first indicator that errors had crept in the summation process. Often, it was tedious and time-consuming job to detect the fault. In the attendance register, with rows representing attendance of a particular student during the entire course and columns representing attendance of students in a particular lecture, the same procedure generated a row sum (indicating if a particular student has attended the required minimum of classes and qualified to sit in the final examination) and a column sum (indicating the class attendance in a particular lecture). A method was proposed to isolate the area, which contained the errors. To do so, the ledger matrix was partitioned into 4 or more matrices, and each matrix was considered a sub-ledger. In this way, one was quickly able to identify the sub-ledger containing the error and rectify it. The grand row-sum was easily obtained by adding the respective row-sums of sub-ledgers. Similarly, grand column-sum was readily available from the total of respective column-sums of sub-ledgers. Practical examples were worked out during the lecture. This lecture was dedicated to the loving memory of Islamuddin, who served as Chairman, Department of Mathematics, University of Karachi during 1997-2000. The speaker had a chance to work on many projects/ activities during his chairmanship, in particular preparing proposal for the Institute of Mathematical Science (1998), launching of the NGDS Pilot Project (1998; run successfully since its inception to date with the speaker as Project Director — anthromathematics talk focused, mainly, on this project), approval of Program of Industrial and Business Mathematics from Board of Faculty of Science, the Last-Total-Solar-Eclipse Expedition of the Second Millennium (August 11, 1999  — violation of Kepler’s second law of planetary motion confirmed during this scientific activity), display of stall of Department of Mathematics at the University of Karachi Alumni Reunion (February 28 & March 1, 1998). There was a vibrant academic atmosphere during the tenure of Islamuddin: the speaker was awarded Dean’s Research Grant to model planetary orbits, gave 4 seminars at different institutions including the parent university, the Aga Khan University and Hamdard University, wrote 5 general-interest articles, presented 3 conference papers, published 5 journal papers and prepared one manual. The Former Chairman was, also, conscious of the need of recognition and reward for faculty members. Senior posts were announced during his tenure, although he, himself, did not apply for one (this showed his integrity and honesty — he retired in 2001 as Associate Professor). The speaker, however, got a chance to apply for the post of Professor. Born in 1941, Islamuddin did his MSc in 1962 from the department he was supposed to lead in 1997. The same year he was appointed Lecturer in his alma meter. In the early seventies, he was promoted as Assistant Professor and in 1995 as Associate Professor. He, also, got a chance to earn postgraduate diploma from England. His interests included numerical analysis and statistics. In the first week of August 2010, he bid farewell to this world for his heavenly abode. Mathematicians all over the country are going to remember Islamuddin for his dedication, sincerity, truthfulness and selfless service for a long time. May Allah rest his soul in eternal peace!  Sample Calculations PDF Abstract PDF

C83: The Fourth Law of Thermodynamics

Work done at: UNIVERSITY OF KARACHI, University Road, Karachi 75270, Pakistan

Kamal SA, the Pakistan Institute of Physics Conference (PIPC 2011), University of Engineering and Technology, Lahore, Pakistan, 2011, paper # PIPC-11-25, p 4 (the Salim Ahmed memorial lecture) — nominated by Vice Chancellor, University of Karachi
This paper discusses differences between equilibrium, steady state and non-equilibrium both in terms of energy transfer as well as probability of occupation. Steady state is the optimal solution in information processing, traffic management, electric transmission, heat exchangers and international politics. Next, the paper reviews the zeroth, the first, the second and the third laws of thermodynamics. The existence of negative temperatures in small, isolated subsystems does pose a question whether the first law would remain valid if one is able to construct a heat engine, which uses these states as sink. Such processes may be discovered in future, which make operation of such an engine possible. In order to avoid logical inconsistencies, the fourth law of thermodynamics is presented, which states that it is not possible to run a Carnot Engine or any other physical heat engine between a source having a positive (absolute) temperature and a sink having a negative (absolute) temperature. This lecture was dedicated to the loving memory of the speaker’s teacher and inspirer, (Late) Salim Ahmed, who taught him courses entitled Theory of Relativity and Methods of Mathematical Physics as faculty member of Department of Physics, University of Karachi. He, then, proceeded to USA for his graduate studies. At the time of his death he was associated with Hamdard University. The motivation of this paper was a question by BS First Year Student of Mathematics (Evening Program — Class of 2013), Syed Ghulam Murtaza, regarding the possibility of using negative-temperature-isolated subsystems as heat sink. Paper PDF



  C82: Generalization of Principle of Equivalence

  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 # 2, p 11 (Prof. Dr. Q. K. Ghori memorial lecture) —nominated by Vice Chancellor, University of Karachi                                                 

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 line element, 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

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


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 proposed 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 stated not to be 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), generates 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 (or even more), because many things, which are harmless, may look like potential threat on screen (a pen may be mistaken as a pen pistol; an implant or an artificial body part may prompt the screener to conduct an intrusive search). 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, as well as objects hidden under thick clothes (cf. Minority Communities). In order to test the effectiveness of full-body-X-ray-backscatter-scanning system, a simulated-plastic explosive (a baggy with powdery substance) and a syringe were strapped to the body of a person, and had him go through the scanner. The scanner showed nothing except the needle and the unclothed figure of that person. The airline employee performing the blind screening missed both. Only metal shows white or very light gray. Hence, there seems to be no significant improvement over conventional security gates. 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, cancer patients and pregnant women (cf. Health Concerns) (the first four have weak immune systems; as for the last group, radiation may inflict permanent damage to the unborn child) as well as frequent travelers and flight crews (the unnecessary radiation exposure of eyes and neck region — nobody covers eyes; it seems, extremely, strange to bombard the traveler’s eyes with millions of vibrating electrons; similarly, interaction of radiation in the neck region may increase risk of thyroid cancer). Active-millimeter-wave scanners (Types of Scanners), look like not to be posing so many health hazards, although they can not be ruled out because of interaction of high-frequency radiowaves with human body. The privacy issues are same as those in backscatter-X-ray scanners. An airport-passenger-screening system was proposed based on recording and display of IR (infra-red) and thermal radiation emitted by a prospective traveler (similar to passive-millimeter-wave scanners developed elsewhere). 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. Being a passive scanner, the probability of damage to human body is, almost, negligible in case of malfunction. Such is not the case with active scanners (mainly, cheap systems bought by corrupt-third-world officials), e. g., malfunctioning-iris-scanning system or defected-full-body-scanning (both backscatter and millimeter wave) can, permanently, damage eyes. Such full-body systems have the potential to burn skin and other organs, too. The un-researched health hazards of active-scanning systems and their potential to be converted into devices invading body privacy of a traveler are the prime reasons cited for the airline passengers to demand from screening authorities the model numbers, the specifications and the samples of outputs of such devices, so that they can record and document radiation exposure through security-screening devices, which use active-scanning processes (note that radiation doses add up from exposure-to-exposure, increasing cancer risk). Further, the prospective air travelers may be given the option to select non-electronic systems for security screening, if they so desire. The safe radiation limits must be declared clearly (medical exposure — no limit; occupational exposure — approximately, 20 millisievert per year; general public — approximately, 1 millisievert per year) in all public places. Passive exposure of general public through flying in an aircraft, etc., must, also be accounted for. When there is a doubt that authorities are not providing proper information, public must exercise constitutional right to self-monitor possible overexposure. Of course, it is against law, ethics and commonsense to hide such information from the tax-paying consumer. It, also, violates all norms of accountability and transparency. 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

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


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:



Decrease in travel time — comfort


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


Reduction in average engine noise during the flight (most of the flight in the ballistic phase, during which the engines shut down) — comfort


Absence of turbulence (most of the flight in the ballistic phase in space) — comfort


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. The processes involved in the proposed product are efficient (economical, time saving) as well as effective (safe, environmentally friendly). 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)

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 (Fig. 3). This paper unveiled the next level of accuracy in height (Fig. 4; 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 (Fig. 5; 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 (mass with zero clothing) 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.


Fig. 3. An 8-year old boy being weighed by SF in Growth-and-Imaging Laboratory

Fig. 4. Vernier scale mounted on set square to record height (least count of 0.01 cm using the NGDS system)

Fig. 5.  Vernier scale mounted on set square to record mass (least count of 0.01 kg aligned with a beam scale)





, (Depart- ment of Mathematics, UOK



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


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 h mn, 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

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