A. Qadir - Profile on Academia.edu (original) (raw)

Papers by A. Qadir

Research paper thumbnail of Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

Pramana, Oct 2, 2015

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations b... more The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.

Research paper thumbnail of Virial clouds explaining the observed rotational asymmetry in the galactic halos

Physical Review D

Rotation of galactic objects has been seen in the CMB that could be ascribed to molecular hydroge... more Rotation of galactic objects has been seen in the CMB that could be ascribed to molecular hydrogen clouds with, or without, dust contamination and contamination from other sources. We model the clouds using the canonical ensemble for pure molecular hydrogen, a mixture of hydrogen helium and or dust, in order to constrain the physical parameters of these clouds. Since, the clouds are cold, we justify the use of the canonical ensemble by explicitly calculating the interaction between the hydrogen molecules and the CMB photons and determining the time required for thermal equilibrium to be reached, and show that there is enough time for the equilibrium to be attained.

Research paper thumbnail of On the rotational energy loss of pulsars

On the rotational energy loss of pulsars

Lettere al Nuovo Cimento, 1980

An alternative model for identifying pulsars with rotating neutron stars is proposed in order to ... more An alternative model for identifying pulsars with rotating neutron stars is proposed in order to explain the observed pulsar emission figures. Equations of a dimensionless quantity, independent of the neutron star parameters, are obtained with respect to the deceleration rate. It is noted that this rate is directly related to the energy generation processes of pulsars.

Research paper thumbnail of Dispersion characteristics of plasmonic waveguides for THz waves

SPIE Proceedings, 2013

Today there is an increasing surge in Surface Plasmon based research and recent studies have show... more Today there is an increasing surge in Surface Plasmon based research and recent studies have shown that a wide range of plasmon-based optical elements and techniques have led to the development of a variety of active switches, passive waveguides, biosensors, lithography masks, to name just a few. The Terahertz (THz) frequency region of the electromagnetic spectrum is located between the traditional microwave spectrum and the optical frequencies, and offers a significant scientific and technological potential in many fields, such as in sensing, in imaging and in spectroscopy. Waveguiding in this intermediate spectral region is a major challenge. Amongst the various THz waveguides suggested, the metal-clad waveguides supporting surface plasmon modes waves and specifically hollow core structures, coated with insulating material are showing the greatest promise as low-loss waveguides for their use in active components and as well as passive waveguides. The H-field finite element method (FEM) based full-vector formulation is used to study the vectorial modal field properties and the complex propagation characteristics of Surface Plasmon modes of a hollow-core dielectric coated rectangular waveguide structure. Additionally, the finite difference time domain (FDTD) method is used to estimate the dispersion parameters and the propagation loss of the rectangular waveguide.

Research paper thumbnail of Virial clouds evolution from the last scattering upto the formation of first stars

Noraiz Tahir, Asghar Qadir, Muhammad Sakhi, and Francesco De Paolis Department of Mathematics and... more Noraiz Tahir, Asghar Qadir, Muhammad Sakhi, and Francesco De Paolis Department of Mathematics and Physics “E. De Giorgi”, University of Salento, Via per Arnesano, I-73100 Lecce, Italy INFN, Sezione di Lecce, Via per Arnesano, I-73100 Lecce, Italy Abdus Salam School of Mathematics, G.C. University, Lahore, Pakistan Department of Physics, Quaid-e-Azam University, Islamabad, Pakistan noraiz.tahir@le.infn.it asgharqadir46@gmail.com sakhi.cosmos@gmail.com †††† francesco.depaolis@le.infn.it

Research paper thumbnail of Recent results and perspectives on cosmic backgrounds from radio to far-infrared

Recent results and perspectives on cosmic backgrounds from radio to far-infrared

Cosmological and astrophysical surveys from radio to far-infrared, in both temperature and polari... more Cosmological and astrophysical surveys from radio to far-infrared, in both temperature and polarization, offer a unique view of the universe properties and of the formation and evolution of its structures. The last release, close to be finalized, of the Planck mission results sets the scene for cosmological models and parameters, while the comparison with other types of data sets raises the issue of possible tensions about some parameters, first of all the Hubble constant. At the same time, on the extragalactic side, Planck carried out the deepest systematic all-sky survey of SZ galaxy clusters and detected thousands of dusty galaxies and many hundreds of extragalactic radio sources, also allowing us to investigate many specific topics, including molecular hydrogen clouds in galactic halos. The exploitation of future generation of CMB missions and the next radio facilities will allow us to deeply investigate several topics in cosmology and astrophysics, from the existence of primord...

Research paper thumbnail of Evolution of virial clouds-I: from surface of last scattering up to the formation of population-III stars

The European Physical Journal C

The analysis of WMAP and Planck CMB data has shown the presence of temperature asymmetries toward... more The analysis of WMAP and Planck CMB data has shown the presence of temperature asymmetries towards the halos of several galaxies, which is probably due to the rotation of clouds present in these halos about the rotational axis of the galaxies. It had been proposed that these are hydrogen clouds that should be in equilibrium with the CMB. However, standard theory did not allow equilibrium of such clouds at the very low CMB temperature, but it was recently shown that the equilibrium could be stable. This still does not prove that the cloud concentration and that the observed temperature asymmetry is due to clouds in equilibrium with the CMB. To investigate the matter further, it would be necessary to trace the evolution of such clouds, which we call “virial clouds”, from their formation epoch to the present, so as to confront the model with the observational data. The task is to be done in two steps: (1) from the cloud formation before the formation of first generation of stars; (2) f...

Research paper thumbnail of Observing molecular hydrogen clouds and dark massive objects in galactic halos

arXiv: Astrophysics, 1995

Molecular hydrogen clouds can contribute substantially to the galactic halo< dark matter and m... more Molecular hydrogen clouds can contribute substantially to the galactic halo< dark matter and may lead to the birth of massive halo objects (MHOs) observed indirectly by microlensing. We present a method to detect these molecular clouds in the halo of M31 using the Doppler shift effect. We also consider the possibility to directly observe MHOs in the halo of M31 via their infrared emission.

Research paper thumbnail of Observing molecular hydrogen clouds and dark massive objects in galactic halos

Arxiv preprint astro-ph/ …, 1995

Molecular hydrogen clouds can contribute substantially to the galactic halo dark matter and may l... more Molecular hydrogen clouds can contribute substantially to the galactic halo dark matter and may lead to the birth of Massive Halo Objects (MHOs) observed indirectly by microlensing. We present a method to detect these molecular clouds in the halo of M31 using the Doppler shift e ect. We also consider the possibility to directly observe MHOs in the halo of M31 via their infrared emission.

Research paper thumbnail of Messier 81’s Planck view vs its halo mapping

This paper is a follow-up of a previous paper about the M82 galaxy and its halo based on Planck o... more This paper is a follow-up of a previous paper about the M82 galaxy and its halo based on Planck observations. As in the case of M82, so also for the M81 galaxy a substantial North-South and East-West temperature asymmetry is found, extending up to galactocentric distances of about 1.5. The temperature asymmetry is almost frequency independent and can be interpreted as a Doppler-induced effect related to the M81 halo rotation and/or triggered by the gravitational interaction of the galaxies within the M81 Group. Along with the analogous study of several nearby edge-on spiral galaxies, the CMB temperature asymmetry method thus is shown to act as a direct tool to map the galactic haloes and/or the intergalactic bridges, invisible in other bands or by other methods.

Research paper thumbnail of Conditional Linearizability Criteria for Scalar Fourth Order Semi-Linear Ordinary Differential Equations

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary di... more Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not been discussed in the literature previously. It is shown that the procedure can be extended to higher order. Though the results for the higher orders are complicated, they are doable by algebraic computing. The standard Lie approach, as developed at present does not seem to be amenable to giving results that can be handled even by algebraic computing.

Research paper thumbnail of Planck view of the M82 galaxy

Astronomy and Astrophysics

Planck data towards the galaxy M82 are analyzed in the 70, 100 and 143 GHz bands. A substantial n... more Planck data towards the galaxy M82 are analyzed in the 70, 100 and 143 GHz bands. A substantial north-south and East-West temperature asymmetry is found, extending up to 1 0 from the galactic center. Being almost frequencyindependent, these temperature asymmetries are indicative of a Doppler-induced effect regarding the line-of-sight dynamics on the halo scale, the ejections from the galactic center and, possibly, even the tidal interaction with M81 galaxy. The temperature asymmetry thus acts as a model-independent tool to reveal the bulk dynamics in nearby edge-on spiral galaxies, like the Sunyaev-Zeldovich effect for clusters of galaxies.

Research paper thumbnail of Planck revealed bulk motion of Centaurus A lobes

Astronomy & Astrophysics, 2015

Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100 and 143 GHz bands. ... more Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100 and 143 GHz bands. We find a temperature asymmetry of the northern radio lobe with respect to the southern one that clearly extends at least up to 5 0 from the Cen A center and diminishes towards the outer regions of the lobes. That transparent parameter-the temperature asymmetry-thus has to carry a principal information, i.e. indication on the line-of-sight bulk motion of the lobes, while the increase of that asymmetry at smaller radii reveals the differential dynamics of the lobes as expected at ejections from the center.

Research paper thumbnail of Science Fiction and Popular Science from Ancient to Modern Times: Scientists Versus Laymen

While working on that review I tried to find out how others had found it. Despite being on the be... more While working on that review I tried to find out how others had found it. Despite being on the best seller list, it appeared that few people had actually read it, of whom few had read it cover to cover. Of those, even fewer had actually followed all of it. I had a head start, having been a student of Roger's. It is an odd fact fashion that has evolved to keep such books on the shelf-and even dip into it a bit-but seldom to actually try to follow it. This despite the fact that there is much more popular science available than ever before, and often written by the experts in the field. This was far from being the case earlier. There has been an increasing trend for practicing scientists to write science fiction (SF) and PS. For example, the famous astronomer and astrophysicist, Fred Hoyle, wrote some remarkable SF and the physics Nobel Laureate, Steve Weinberg, wrote a PS best seller. Stephen Hawking's "A Brief History of Time" is probably one of the most popular unread books. At one time such activities on the part of serious scientists would have been viewed askance. How much and why has this attitude changed over recent times? For that matter, why did they arise in the first place? I will be unable to address these questions in the depth they deserve, within the space limitations for this article, but will try to explore them somewhat. This abstractness of modern science becomes a problem for the non-scientist who wants to understand what the new theories are all about. A separate problem associated with science is that its practitioners tend to get "bogged down" with the details and lose sight of the "broad picture". The non-scientists, faced with the outpourings of such scientists, find themselves floundering in a sea of jargon whose relevance continues to elude them. Yet another problem is the tendency of some scientists to mystify their work in an attempt to make it seem more profound, rather than clarifying it to make it more intelligible. Unfortunately, many lay people like to praise such works, because they feel that they gain reflected glory by "comprehending the incomprehensible". All these problems are relevant for our later discussion of the attitude of scientists to their colleagues writing SF. Since the attitude of the practitioners of science to SF and PS depends on the nature of the scientific discussion in the work, it becomes necessary to categorise the science used in SF, or explained in PS. There can be various categorisations. I will choose only those relevant for my discussion here. 2. Categorization of Science There is the most common, currently accepted, division of sciences into natural and social. The former is what was regarded as "science" from the Renaissance to the first half of the twentieth century. (As with all historical statements of this type, it must be taken with caution. In this context dates cannot be exact and must be taken only as giving rough estimates.) It was assumed that there are "natural laws" (which can not be doubted) waiting to be "discovered". There is obviously no room in this view for social sciences. During Greek and Muslim times that was not the view of "science". Matters pertaining to human behaviour were very much part of "science". In the latter part of the twentieth century, the "science" dealing with collective human behaviour was developed along the lines of what had become accepted as "science" in modern times and again entered the purview of "science" under the title of "social sciences". Natural sciences can be further divided into the physical sciences and the life sciences. At the border between natural and social sciences lie medical science and psychology, which deal with individual human beings and groups of human beings. The former of these subjects deals with humans as biological organisms, which are studied more thoroughly because of our special interest in them. The latter is complicated by the fact that it deals with consciousness. This complication is fundamental because it changes our concept of scientific laws. The usual assumption that stating a scientific law cannot change the subject of that law, no longer applies. In this case, as with human laws, there will be changes in the behaviour of the subject of the "laws". To the extent that we deal with humans as living organisms, to be studied as such, these subjects can be regarded as branches of the natural sciences. To the extent that we have to take account of their ethical and moral aspects, they become branches of the social sciences. These aspects are obvious for psychology but are also relevant for medicine. For example, we can perform experiments on animals with only minor twinges of conscience, but would be stopped by law from doing so on human beings, even if our consciences were dormant 3. (Ethical problems can arise even with natural sciences where testing a theory may have serious consequences for people or for animals. There are some interesting SF stories that explore such possibilities.

Research paper thumbnail of Conditional Linearizability Criteria for Third Order Ordinary Differential Equations

Journal of Nonlinear Mathematical Physics, 2008

Using geometric methods for linearizing systems of second order cubically non-linear in the first... more Using geometric methods for linearizing systems of second order cubically non-linear in the first derivatives ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for conditional linearizability via point transformation with respect to a second order equation of classes of third order ordinary differential equations, which are distinct from the classes available in the literature. Some examples are given and discussed.

Research paper thumbnail of Symmetries of static, spherically symmetric space‐times

Symmetries of static, spherically symmetric space‐times

Journal of Mathematical Physics, 1987

ABSTRACT

Research paper thumbnail of Collineations of the Ricci tensor

Collineations of the Ricci tensor

Journal of mathematical physics, 1993

... conservation laws that may be admitted in the standard form of general relativity.&amp;am... more ... conservation laws that may be admitted in the standard form of general relativity.&amp;amp;amp;#x27; Some more rigorous work was done on the important role of Ricci collineations admitted by certain relativistic matter fields and the related conservation laws that may ... c3= -csc aA,+cot 8A2+A3(t,r,4 ...

Research paper thumbnail of Length and volume of the Qadir-Wheeler “suture model”

Physical Review D, 2001

It had been shown that the Qadir-Wheeler inhomogeneous cosmological model constructed by a ''cut-... more It had been shown that the Qadir-Wheeler inhomogeneous cosmological model constructed by a ''cut-andpaste'' procedure from two closed Friedmann models develops a corridor in the late stages of crunch. It had been argued that the proper length of the corridor tends to infinity with York time. However, it was not proved that it does so, and nor was it really clear how it would tend to infinity. Again, it was argued that the volume of the model would shrink to zero, but it was not apparent precisely how it would do so. The earlier conjecture for the first order behavior of the proper length and volume of the model is proved and the next order correction worked out so as to make clear at what York time the onset of the crunch occurs.

Research paper thumbnail of Perlurbative Invariance: A Proposal for a New Physical Principle

Perlurbative Invariance: A Proposal for a New Physical Principle

gravityresearchfoundation.org

Perlurbative Invariance: A Proposal for a New Physical Principle Asghar Qadir* Department of Math... more Perlurbative Invariance: A Proposal for a New Physical Principle Asghar Qadir* Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan and Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 3126], Saudi Arabia ...

Research paper thumbnail of Dimensional regularization and infra-red divergence

Dimensional regularization and infra-red divergence

Lettere Al Nuovo Cimento (1971–1985), 1974

... K. AHMED Department o] Physics, University o/ Islamabad - Islamabad ... Following BELLINI and... more ... K. AHMED Department o] Physics, University o/ Islamabad - Islamabad ... Following BELLINI and GIA~BIAGI (~) (hereafter referred to as BG), we have re-exaznined the problem of infra-red divergence in v-dimensional quantum electro-dynamics. ...

Research paper thumbnail of Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

Charged analogue of Vlasenko–Pronin superdense star with variable cosmological term

Pramana, Oct 2, 2015

The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations b... more The set of three static spherically symmetric solutions of the Einstein–Maxwell field equations by Maurya and Gupta, Astrophys. Space Sci.333, 149 (2011) are modified by introducing the variable cosmological term. Motivated by Tiwari et al, Indian J. Pure Appl. Math.31, 1017 (2000), some particular values of the cosmological term are taken to obtain well-behaved solutions of the Einstein–Maxwell field equations. All the results given by Maurya and Gupta can be obtained as particular cases of our solutions by choosing a cosmological term equal to zero.

Research paper thumbnail of Virial clouds explaining the observed rotational asymmetry in the galactic halos

Physical Review D

Rotation of galactic objects has been seen in the CMB that could be ascribed to molecular hydroge... more Rotation of galactic objects has been seen in the CMB that could be ascribed to molecular hydrogen clouds with, or without, dust contamination and contamination from other sources. We model the clouds using the canonical ensemble for pure molecular hydrogen, a mixture of hydrogen helium and or dust, in order to constrain the physical parameters of these clouds. Since, the clouds are cold, we justify the use of the canonical ensemble by explicitly calculating the interaction between the hydrogen molecules and the CMB photons and determining the time required for thermal equilibrium to be reached, and show that there is enough time for the equilibrium to be attained.

Research paper thumbnail of On the rotational energy loss of pulsars

On the rotational energy loss of pulsars

Lettere al Nuovo Cimento, 1980

An alternative model for identifying pulsars with rotating neutron stars is proposed in order to ... more An alternative model for identifying pulsars with rotating neutron stars is proposed in order to explain the observed pulsar emission figures. Equations of a dimensionless quantity, independent of the neutron star parameters, are obtained with respect to the deceleration rate. It is noted that this rate is directly related to the energy generation processes of pulsars.

Research paper thumbnail of Dispersion characteristics of plasmonic waveguides for THz waves

SPIE Proceedings, 2013

Today there is an increasing surge in Surface Plasmon based research and recent studies have show... more Today there is an increasing surge in Surface Plasmon based research and recent studies have shown that a wide range of plasmon-based optical elements and techniques have led to the development of a variety of active switches, passive waveguides, biosensors, lithography masks, to name just a few. The Terahertz (THz) frequency region of the electromagnetic spectrum is located between the traditional microwave spectrum and the optical frequencies, and offers a significant scientific and technological potential in many fields, such as in sensing, in imaging and in spectroscopy. Waveguiding in this intermediate spectral region is a major challenge. Amongst the various THz waveguides suggested, the metal-clad waveguides supporting surface plasmon modes waves and specifically hollow core structures, coated with insulating material are showing the greatest promise as low-loss waveguides for their use in active components and as well as passive waveguides. The H-field finite element method (FEM) based full-vector formulation is used to study the vectorial modal field properties and the complex propagation characteristics of Surface Plasmon modes of a hollow-core dielectric coated rectangular waveguide structure. Additionally, the finite difference time domain (FDTD) method is used to estimate the dispersion parameters and the propagation loss of the rectangular waveguide.

Research paper thumbnail of Virial clouds evolution from the last scattering upto the formation of first stars

Noraiz Tahir, Asghar Qadir, Muhammad Sakhi, and Francesco De Paolis Department of Mathematics and... more Noraiz Tahir, Asghar Qadir, Muhammad Sakhi, and Francesco De Paolis Department of Mathematics and Physics “E. De Giorgi”, University of Salento, Via per Arnesano, I-73100 Lecce, Italy INFN, Sezione di Lecce, Via per Arnesano, I-73100 Lecce, Italy Abdus Salam School of Mathematics, G.C. University, Lahore, Pakistan Department of Physics, Quaid-e-Azam University, Islamabad, Pakistan noraiz.tahir@le.infn.it asgharqadir46@gmail.com sakhi.cosmos@gmail.com †††† francesco.depaolis@le.infn.it

Research paper thumbnail of Recent results and perspectives on cosmic backgrounds from radio to far-infrared

Recent results and perspectives on cosmic backgrounds from radio to far-infrared

Cosmological and astrophysical surveys from radio to far-infrared, in both temperature and polari... more Cosmological and astrophysical surveys from radio to far-infrared, in both temperature and polarization, offer a unique view of the universe properties and of the formation and evolution of its structures. The last release, close to be finalized, of the Planck mission results sets the scene for cosmological models and parameters, while the comparison with other types of data sets raises the issue of possible tensions about some parameters, first of all the Hubble constant. At the same time, on the extragalactic side, Planck carried out the deepest systematic all-sky survey of SZ galaxy clusters and detected thousands of dusty galaxies and many hundreds of extragalactic radio sources, also allowing us to investigate many specific topics, including molecular hydrogen clouds in galactic halos. The exploitation of future generation of CMB missions and the next radio facilities will allow us to deeply investigate several topics in cosmology and astrophysics, from the existence of primord...

Research paper thumbnail of Evolution of virial clouds-I: from surface of last scattering up to the formation of population-III stars

The European Physical Journal C

The analysis of WMAP and Planck CMB data has shown the presence of temperature asymmetries toward... more The analysis of WMAP and Planck CMB data has shown the presence of temperature asymmetries towards the halos of several galaxies, which is probably due to the rotation of clouds present in these halos about the rotational axis of the galaxies. It had been proposed that these are hydrogen clouds that should be in equilibrium with the CMB. However, standard theory did not allow equilibrium of such clouds at the very low CMB temperature, but it was recently shown that the equilibrium could be stable. This still does not prove that the cloud concentration and that the observed temperature asymmetry is due to clouds in equilibrium with the CMB. To investigate the matter further, it would be necessary to trace the evolution of such clouds, which we call “virial clouds”, from their formation epoch to the present, so as to confront the model with the observational data. The task is to be done in two steps: (1) from the cloud formation before the formation of first generation of stars; (2) f...

Research paper thumbnail of Observing molecular hydrogen clouds and dark massive objects in galactic halos

arXiv: Astrophysics, 1995

Molecular hydrogen clouds can contribute substantially to the galactic halo< dark matter and m... more Molecular hydrogen clouds can contribute substantially to the galactic halo< dark matter and may lead to the birth of massive halo objects (MHOs) observed indirectly by microlensing. We present a method to detect these molecular clouds in the halo of M31 using the Doppler shift effect. We also consider the possibility to directly observe MHOs in the halo of M31 via their infrared emission.

Research paper thumbnail of Observing molecular hydrogen clouds and dark massive objects in galactic halos

Arxiv preprint astro-ph/ …, 1995

Molecular hydrogen clouds can contribute substantially to the galactic halo dark matter and may l... more Molecular hydrogen clouds can contribute substantially to the galactic halo dark matter and may lead to the birth of Massive Halo Objects (MHOs) observed indirectly by microlensing. We present a method to detect these molecular clouds in the halo of M31 using the Doppler shift e ect. We also consider the possibility to directly observe MHOs in the halo of M31 via their infrared emission.

Research paper thumbnail of Messier 81’s Planck view vs its halo mapping

This paper is a follow-up of a previous paper about the M82 galaxy and its halo based on Planck o... more This paper is a follow-up of a previous paper about the M82 galaxy and its halo based on Planck observations. As in the case of M82, so also for the M81 galaxy a substantial North-South and East-West temperature asymmetry is found, extending up to galactocentric distances of about 1.5. The temperature asymmetry is almost frequency independent and can be interpreted as a Doppler-induced effect related to the M81 halo rotation and/or triggered by the gravitational interaction of the galaxies within the M81 Group. Along with the analogous study of several nearby edge-on spiral galaxies, the CMB temperature asymmetry method thus is shown to act as a direct tool to map the galactic haloes and/or the intergalactic bridges, invisible in other bands or by other methods.

Research paper thumbnail of Conditional Linearizability Criteria for Scalar Fourth Order Semi-Linear Ordinary Differential Equations

Using geometric methods for linearizing systems of second order cubically semi-linear ordinary di... more Using geometric methods for linearizing systems of second order cubically semi-linear ordinary differential equations and third order quintically semi-linear ordinary differential equations, we extend to the fourth order by differentiating the third order equation. This yields criteria for linearizability of a class of fourth order semi-linear ordinary differential equations, which have not been discussed in the literature previously. It is shown that the procedure can be extended to higher order. Though the results for the higher orders are complicated, they are doable by algebraic computing. The standard Lie approach, as developed at present does not seem to be amenable to giving results that can be handled even by algebraic computing.

Research paper thumbnail of Planck view of the M82 galaxy

Astronomy and Astrophysics

Planck data towards the galaxy M82 are analyzed in the 70, 100 and 143 GHz bands. A substantial n... more Planck data towards the galaxy M82 are analyzed in the 70, 100 and 143 GHz bands. A substantial north-south and East-West temperature asymmetry is found, extending up to 1 0 from the galactic center. Being almost frequencyindependent, these temperature asymmetries are indicative of a Doppler-induced effect regarding the line-of-sight dynamics on the halo scale, the ejections from the galactic center and, possibly, even the tidal interaction with M81 galaxy. The temperature asymmetry thus acts as a model-independent tool to reveal the bulk dynamics in nearby edge-on spiral galaxies, like the Sunyaev-Zeldovich effect for clusters of galaxies.

Research paper thumbnail of Planck revealed bulk motion of Centaurus A lobes

Astronomy & Astrophysics, 2015

Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100 and 143 GHz bands. ... more Planck data towards the active galaxy Centaurus A are analyzed in the 70, 100 and 143 GHz bands. We find a temperature asymmetry of the northern radio lobe with respect to the southern one that clearly extends at least up to 5 0 from the Cen A center and diminishes towards the outer regions of the lobes. That transparent parameter-the temperature asymmetry-thus has to carry a principal information, i.e. indication on the line-of-sight bulk motion of the lobes, while the increase of that asymmetry at smaller radii reveals the differential dynamics of the lobes as expected at ejections from the center.

Research paper thumbnail of Science Fiction and Popular Science from Ancient to Modern Times: Scientists Versus Laymen

While working on that review I tried to find out how others had found it. Despite being on the be... more While working on that review I tried to find out how others had found it. Despite being on the best seller list, it appeared that few people had actually read it, of whom few had read it cover to cover. Of those, even fewer had actually followed all of it. I had a head start, having been a student of Roger's. It is an odd fact fashion that has evolved to keep such books on the shelf-and even dip into it a bit-but seldom to actually try to follow it. This despite the fact that there is much more popular science available than ever before, and often written by the experts in the field. This was far from being the case earlier. There has been an increasing trend for practicing scientists to write science fiction (SF) and PS. For example, the famous astronomer and astrophysicist, Fred Hoyle, wrote some remarkable SF and the physics Nobel Laureate, Steve Weinberg, wrote a PS best seller. Stephen Hawking's "A Brief History of Time" is probably one of the most popular unread books. At one time such activities on the part of serious scientists would have been viewed askance. How much and why has this attitude changed over recent times? For that matter, why did they arise in the first place? I will be unable to address these questions in the depth they deserve, within the space limitations for this article, but will try to explore them somewhat. This abstractness of modern science becomes a problem for the non-scientist who wants to understand what the new theories are all about. A separate problem associated with science is that its practitioners tend to get "bogged down" with the details and lose sight of the "broad picture". The non-scientists, faced with the outpourings of such scientists, find themselves floundering in a sea of jargon whose relevance continues to elude them. Yet another problem is the tendency of some scientists to mystify their work in an attempt to make it seem more profound, rather than clarifying it to make it more intelligible. Unfortunately, many lay people like to praise such works, because they feel that they gain reflected glory by "comprehending the incomprehensible". All these problems are relevant for our later discussion of the attitude of scientists to their colleagues writing SF. Since the attitude of the practitioners of science to SF and PS depends on the nature of the scientific discussion in the work, it becomes necessary to categorise the science used in SF, or explained in PS. There can be various categorisations. I will choose only those relevant for my discussion here. 2. Categorization of Science There is the most common, currently accepted, division of sciences into natural and social. The former is what was regarded as "science" from the Renaissance to the first half of the twentieth century. (As with all historical statements of this type, it must be taken with caution. In this context dates cannot be exact and must be taken only as giving rough estimates.) It was assumed that there are "natural laws" (which can not be doubted) waiting to be "discovered". There is obviously no room in this view for social sciences. During Greek and Muslim times that was not the view of "science". Matters pertaining to human behaviour were very much part of "science". In the latter part of the twentieth century, the "science" dealing with collective human behaviour was developed along the lines of what had become accepted as "science" in modern times and again entered the purview of "science" under the title of "social sciences". Natural sciences can be further divided into the physical sciences and the life sciences. At the border between natural and social sciences lie medical science and psychology, which deal with individual human beings and groups of human beings. The former of these subjects deals with humans as biological organisms, which are studied more thoroughly because of our special interest in them. The latter is complicated by the fact that it deals with consciousness. This complication is fundamental because it changes our concept of scientific laws. The usual assumption that stating a scientific law cannot change the subject of that law, no longer applies. In this case, as with human laws, there will be changes in the behaviour of the subject of the "laws". To the extent that we deal with humans as living organisms, to be studied as such, these subjects can be regarded as branches of the natural sciences. To the extent that we have to take account of their ethical and moral aspects, they become branches of the social sciences. These aspects are obvious for psychology but are also relevant for medicine. For example, we can perform experiments on animals with only minor twinges of conscience, but would be stopped by law from doing so on human beings, even if our consciences were dormant 3. (Ethical problems can arise even with natural sciences where testing a theory may have serious consequences for people or for animals. There are some interesting SF stories that explore such possibilities.

Research paper thumbnail of Conditional Linearizability Criteria for Third Order Ordinary Differential Equations

Journal of Nonlinear Mathematical Physics, 2008

Using geometric methods for linearizing systems of second order cubically non-linear in the first... more Using geometric methods for linearizing systems of second order cubically non-linear in the first derivatives ordinary differential equations, we extend to the third order by differentiating the second order equation. This yields criteria for conditional linearizability via point transformation with respect to a second order equation of classes of third order ordinary differential equations, which are distinct from the classes available in the literature. Some examples are given and discussed.

Research paper thumbnail of Symmetries of static, spherically symmetric space‐times

Symmetries of static, spherically symmetric space‐times

Journal of Mathematical Physics, 1987

ABSTRACT

Research paper thumbnail of Collineations of the Ricci tensor

Collineations of the Ricci tensor

Journal of mathematical physics, 1993

... conservation laws that may be admitted in the standard form of general relativity.&amp;am... more ... conservation laws that may be admitted in the standard form of general relativity.&amp;amp;amp;#x27; Some more rigorous work was done on the important role of Ricci collineations admitted by certain relativistic matter fields and the related conservation laws that may ... c3= -csc aA,+cot 8A2+A3(t,r,4 ...

Research paper thumbnail of Length and volume of the Qadir-Wheeler “suture model”

Physical Review D, 2001

It had been shown that the Qadir-Wheeler inhomogeneous cosmological model constructed by a ''cut-... more It had been shown that the Qadir-Wheeler inhomogeneous cosmological model constructed by a ''cut-andpaste'' procedure from two closed Friedmann models develops a corridor in the late stages of crunch. It had been argued that the proper length of the corridor tends to infinity with York time. However, it was not proved that it does so, and nor was it really clear how it would tend to infinity. Again, it was argued that the volume of the model would shrink to zero, but it was not apparent precisely how it would do so. The earlier conjecture for the first order behavior of the proper length and volume of the model is proved and the next order correction worked out so as to make clear at what York time the onset of the crunch occurs.

Research paper thumbnail of Perlurbative Invariance: A Proposal for a New Physical Principle

Perlurbative Invariance: A Proposal for a New Physical Principle

gravityresearchfoundation.org

Perlurbative Invariance: A Proposal for a New Physical Principle Asghar Qadir* Department of Math... more Perlurbative Invariance: A Proposal for a New Physical Principle Asghar Qadir* Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan and Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran 3126], Saudi Arabia ...

Research paper thumbnail of Dimensional regularization and infra-red divergence

Dimensional regularization and infra-red divergence

Lettere Al Nuovo Cimento (1971–1985), 1974

... K. AHMED Department o] Physics, University o/ Islamabad - Islamabad ... Following BELLINI and... more ... K. AHMED Department o] Physics, University o/ Islamabad - Islamabad ... Following BELLINI and GIA~BIAGI (~) (hereafter referred to as BG), we have re-exaznined the problem of infra-red divergence in v-dimensional quantum electro-dynamics. ...