Features of the ionospheric E-region drifts during daytime hours at Sibizmir (dip 72 deg N) are d... more Features of the ionospheric E-region drifts during daytime hours at Sibizmir (dip 72 deg N) are described on the basis of the spaced receiver data for the year 1970-75 published by the Academy of Sciences, USSR. The drift pattern is highly seasonal, dependent on westward drift during winter and eastward drift during summer. The magnitude of the drift velocity decreases with increasing sunspot number but increases with increasing magnetic activity (Kp). Small changes due to lunar tidal effects have also been isolated.
Fixed point theory for set-valued maps was initiated by Nadler and has developed in different dir... more Fixed point theory for set-valued maps was initiated by Nadler and has developed in different directions. In the present paper we extend the theorem due to D. Klim and D.Wardowski [6]in a more general setting of complete symmetric spaces. Further, we introduce a more general definition of contraction of set -valued maps in symmetric spaces. In this setting we prove a fixed point theorem for generalised contractions under certain restrictive conditions on the semi-metric.This leads to generalisation of a result of Driss El Moutawakil .
Functional Analysis Approximation and Computation, Feb 17, 2015
In this paper, we discuss the decomposability of weighted composition operator uC ϕ on L p (X)(1 ... more In this paper, we discuss the decomposability of weighted composition operator uC ϕ on L p (X)(1 ≤ p < ∞) of a σ-finite atomic measure space (X, S, µ) with the assumption that u ∈ L ∞ (X) and |u| has positive ess inf. We prove that if the analytic core of uC ϕ is zero and uC ϕ is not quasinilpotent, then it is not decomposable. We also show that if ϕ is either injective almost everywhere or surjective almost everywhere but not both, then uC ϕ is not decomposable. Finally, we give a necessary condition for decomposability of uC ϕ .
RH-560 rockets instrumented with Langmuir probes were launched from SHAR, India (dip 11 deg N) fo... more RH-560 rockets instrumented with Langmuir probes were launched from SHAR, India (dip 11 deg N) for in situ studies of electron density irregularities associated with equatorial spread-F (ESF) when the F-region plasma was drifting down and strong range spread-F was observed with an ionosonde at SHAR. A high variability was observed in the steepness of the base of the F-region. The bases were found to be steeper during the periods when the F-region plasma was drifting down. On one of the flights irregularities were observed in the region around 280 km where the gradients in electron density were downwards, indicating that the gradient drift instability is the main mechanism for their generation.
In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible m... more In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible maps in probabilistic semi -metric space. These results are extensions of the results which we have obtained on symmetric spaces .
Journal of Atmospheric and Solar Terrestrial Physics, Jun 30, 2015
Long term ionospheric trends estimated over Indian low latitudes.Decreasing trend in the F2 layer... more Long term ionospheric trends estimated over Indian low latitudes.Decreasing trend in the F2 layer critical frequencies is found.Height of the F2-region of the ionosphere shows decreasing trend.Increased concentration of greenhouse gases due to anthropogenic activities warm the troposphere and have a cooling effect in the middle and upper atmosphere. Ionospheric densities and heights are affected due to cooling. Carbon dioxide is one of the most dominant gases for the cause of long term ionospheric trends along with other radiatively active greenhouse gases. Regular ionospheric soundings are made over Ahmedabad (23.1°N, 72.7°E), since 1953. Long term changes in the ionosphere as a consequence of the cooling of the mesosphere and thermosphere due to the increased concentration of greenhouse gases have been studied. Ionospheric observations over Ahmedabad, a low latitude station in the anomaly crest region, for the years 1955–2003 are examined to study the long term changes in the critical frequencies of the various ionospheric layers and the height of the maximum ionization as characterized by hPF2. A decrease in foF2 (1.9 MHz for midday, 1.4 MHz for midnight) and hPF2 (18 km for midday, 17 km for midnight) during about five decades are noted. An increase is noted in foF1 (0.4 MHz). The foF2 data are also examined over an equatorial station Kodaikanal (10.2°N, 77.5°E), situated near the magnetic equator for the years 1960–1995 and a decrease of 0.5 MHz for midday and 0.7 MHz for midnight are noted in ~35 years.
Indian Journal of Radio and Space Physics, Aug 1, 1990
A review is presented of recent developments in understanding the phenomenon of equatorial spread... more A review is presented of recent developments in understanding the phenomenon of equatorial spread-F. Particular emphasis is placed on the rocket-borne in situ studies of the last ten years, a number of which were made from SHAR in India. A wide range of scale sizes in plasma density irregularities extending from a few hundred kilometers down to a fraction of a meter are connected with equatorial spread-F and produce various phenomena such as radio wave oscillations and radar backscatter. Power spectral features of the electron density irregularities in different scale sizes and their causative mechanisms are discussed. Also described are some recent developments in ground-based optical techniques.
Solar Eclipses are one of the most fascinating celestial events These events do provide a unique ... more Solar Eclipses are one of the most fascinating celestial events These events do provide a unique opportunity to study variety of geophysical phenomenon in the terrestrial atmosphere Since last five decades regular Ionospheric observations are being made by operating an Ionosonde at Ahmedabad 23 1 oN 72 6 oE which is an important station near the northern crest of equatorial
Indian Journal of Radio and Space Physics, Feb 1, 1978
The continuous and extended measurements of E-region drifts at Ahmedabad during the period 1970-7... more The continuous and extended measurements of E-region drifts at Ahmedabad during the period 1970-75 show a marked seasonal variation with zonal component towards west during winter and towards east during summer for the daytime hours (transition occurring in March-April and again in September). Meridional component of the drift is generally equatorward, strongest during equinoxes, except for the period June-July when it is poleward. There is no significant variation of the drift speed with sunspot activity; however, drift speeds during summer are consistently lower as compared to the speeds observed during winter or equinoxes.
The effect of instrument errors on the determination of ionospheric drift velocities by full corr... more The effect of instrument errors on the determination of ionospheric drift velocities by full correlation analysis of data obtained with three spaced receivers is investigated theoretically. The analysis reveals that small errors in the evaluation of the correlation functions could lead to a decrease in true drift velocity if the receiver separation is too small in comparison to the pattern scale. It is shown that the errors could be due to differences between the receiver channels, digitizing limitations, or the human operator (if records are digitized manually from films or paper charts). It is concluded that proper receiver separation must be achieved so that the correlation values will not be too high. Limits of 0.8 for the maximum cross-correlation value and 0.60 for zero time lag are suggested.
Indian Academy of Sciences Proceedings Section, Nov 1, 1979
Partial reflection drift measurements in the range 80-100 km made during the year 1972 at a midla... more Partial reflection drift measurements in the range 80-100 km made during the year 1972 at a midlatitude station Buckland Park near Adelaide (35 deg S) are examined for the storm-time behavior. Changes in the zonal wind pattern are associated with magnetic storms. A decrease in the eastward component is associated with increase in foF2 whereas an increase in the eastward component is associated with a decrease in foF2. Day-to-day variability in the prevailing and tidal components of winds in mesosphere reported earlier may be due to the changes in the circulation pattern caused by the energy deposition during storm times.
In this paper we obtain common fixed point theorems of weakly compatible maps on symmetric spaces... more In this paper we obtain common fixed point theorems of weakly compatible maps on symmetric spaces. We prove that if S and T are weakly compatible maps satisfying property (E-A) along with strict contractive conditions, then they have common fixed points. Since these results are obtained without using full force of metric, they are improved generalization of results obtained by Pant ([10], ).
In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in... more In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.[A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182].
Indian Journal of Radio and Space Physics, Feb 1, 1978
Drift motion of ionization irregularities has been studied by making measurements from first and ... more Drift motion of ionization irregularities has been studied by making measurements from first and second multiples. The results are found to be in agreement with earlier observations from the spaced receiver technique.
Indian Journal of Radio and Space Physics, Apr 1, 1979
Several spaced fading records obtained in South Australia are analyzed by the cross-spectrum meth... more Several spaced fading records obtained in South Australia are analyzed by the cross-spectrum method and by the full correlation method with the use of raw as well as filtered data. The apparent and true drift speeds determined by correlating normal amplitude data are found not to be related to the velocity spread obtained by the cross-spectrum method. It is shown that the cross-spectrum method yields a positive dispersion even when the filtering method indicates constant velocity.
Partial reflection drift observations of the 80-100 km altitude region made at Adelaide, Australi... more Partial reflection drift observations of the 80-100 km altitude region made at Adelaide, Australia, are examined for the irregular component due to internal gravity waves. The fluctuations have a mean period of 3 hr and the rms amplitudes show a large day-to-day variability. No correlation was found between the rms amplitude fluctuations and the geomagnetic disturbance parameter; the mean rms values of these fluctuations increase with altitude, with the vertical wave length of the order of 10 km. The energy densities of gravity wave motions decrease with increasing altitude; the energy and momentum deposition and the eddy diffusion coefficient are estimated and discussed.
Features of the ionospheric E-region drifts during daytime hours at Sibizmir (dip 72 deg N) are d... more Features of the ionospheric E-region drifts during daytime hours at Sibizmir (dip 72 deg N) are described on the basis of the spaced receiver data for the year 1970-75 published by the Academy of Sciences, USSR. The drift pattern is highly seasonal, dependent on westward drift during winter and eastward drift during summer. The magnitude of the drift velocity decreases with increasing sunspot number but increases with increasing magnetic activity (Kp). Small changes due to lunar tidal effects have also been isolated.
Fixed point theory for set-valued maps was initiated by Nadler and has developed in different dir... more Fixed point theory for set-valued maps was initiated by Nadler and has developed in different directions. In the present paper we extend the theorem due to D. Klim and D.Wardowski [6]in a more general setting of complete symmetric spaces. Further, we introduce a more general definition of contraction of set -valued maps in symmetric spaces. In this setting we prove a fixed point theorem for generalised contractions under certain restrictive conditions on the semi-metric.This leads to generalisation of a result of Driss El Moutawakil .
Functional Analysis Approximation and Computation, Feb 17, 2015
In this paper, we discuss the decomposability of weighted composition operator uC ϕ on L p (X)(1 ... more In this paper, we discuss the decomposability of weighted composition operator uC ϕ on L p (X)(1 ≤ p < ∞) of a σ-finite atomic measure space (X, S, µ) with the assumption that u ∈ L ∞ (X) and |u| has positive ess inf. We prove that if the analytic core of uC ϕ is zero and uC ϕ is not quasinilpotent, then it is not decomposable. We also show that if ϕ is either injective almost everywhere or surjective almost everywhere but not both, then uC ϕ is not decomposable. Finally, we give a necessary condition for decomposability of uC ϕ .
RH-560 rockets instrumented with Langmuir probes were launched from SHAR, India (dip 11 deg N) fo... more RH-560 rockets instrumented with Langmuir probes were launched from SHAR, India (dip 11 deg N) for in situ studies of electron density irregularities associated with equatorial spread-F (ESF) when the F-region plasma was drifting down and strong range spread-F was observed with an ionosonde at SHAR. A high variability was observed in the steepness of the base of the F-region. The bases were found to be steeper during the periods when the F-region plasma was drifting down. On one of the flights irregularities were observed in the region around 280 km where the gradients in electron density were downwards, indicating that the gradient drift instability is the main mechanism for their generation.
In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible m... more In this paper we prove common fixed point theorems for a pair of occasionally weakly compatible maps in probabilistic semi -metric space. These results are extensions of the results which we have obtained on symmetric spaces .
Journal of Atmospheric and Solar Terrestrial Physics, Jun 30, 2015
Long term ionospheric trends estimated over Indian low latitudes.Decreasing trend in the F2 layer... more Long term ionospheric trends estimated over Indian low latitudes.Decreasing trend in the F2 layer critical frequencies is found.Height of the F2-region of the ionosphere shows decreasing trend.Increased concentration of greenhouse gases due to anthropogenic activities warm the troposphere and have a cooling effect in the middle and upper atmosphere. Ionospheric densities and heights are affected due to cooling. Carbon dioxide is one of the most dominant gases for the cause of long term ionospheric trends along with other radiatively active greenhouse gases. Regular ionospheric soundings are made over Ahmedabad (23.1°N, 72.7°E), since 1953. Long term changes in the ionosphere as a consequence of the cooling of the mesosphere and thermosphere due to the increased concentration of greenhouse gases have been studied. Ionospheric observations over Ahmedabad, a low latitude station in the anomaly crest region, for the years 1955–2003 are examined to study the long term changes in the critical frequencies of the various ionospheric layers and the height of the maximum ionization as characterized by hPF2. A decrease in foF2 (1.9 MHz for midday, 1.4 MHz for midnight) and hPF2 (18 km for midday, 17 km for midnight) during about five decades are noted. An increase is noted in foF1 (0.4 MHz). The foF2 data are also examined over an equatorial station Kodaikanal (10.2°N, 77.5°E), situated near the magnetic equator for the years 1960–1995 and a decrease of 0.5 MHz for midday and 0.7 MHz for midnight are noted in ~35 years.
Indian Journal of Radio and Space Physics, Aug 1, 1990
A review is presented of recent developments in understanding the phenomenon of equatorial spread... more A review is presented of recent developments in understanding the phenomenon of equatorial spread-F. Particular emphasis is placed on the rocket-borne in situ studies of the last ten years, a number of which were made from SHAR in India. A wide range of scale sizes in plasma density irregularities extending from a few hundred kilometers down to a fraction of a meter are connected with equatorial spread-F and produce various phenomena such as radio wave oscillations and radar backscatter. Power spectral features of the electron density irregularities in different scale sizes and their causative mechanisms are discussed. Also described are some recent developments in ground-based optical techniques.
Solar Eclipses are one of the most fascinating celestial events These events do provide a unique ... more Solar Eclipses are one of the most fascinating celestial events These events do provide a unique opportunity to study variety of geophysical phenomenon in the terrestrial atmosphere Since last five decades regular Ionospheric observations are being made by operating an Ionosonde at Ahmedabad 23 1 oN 72 6 oE which is an important station near the northern crest of equatorial
Indian Journal of Radio and Space Physics, Feb 1, 1978
The continuous and extended measurements of E-region drifts at Ahmedabad during the period 1970-7... more The continuous and extended measurements of E-region drifts at Ahmedabad during the period 1970-75 show a marked seasonal variation with zonal component towards west during winter and towards east during summer for the daytime hours (transition occurring in March-April and again in September). Meridional component of the drift is generally equatorward, strongest during equinoxes, except for the period June-July when it is poleward. There is no significant variation of the drift speed with sunspot activity; however, drift speeds during summer are consistently lower as compared to the speeds observed during winter or equinoxes.
The effect of instrument errors on the determination of ionospheric drift velocities by full corr... more The effect of instrument errors on the determination of ionospheric drift velocities by full correlation analysis of data obtained with three spaced receivers is investigated theoretically. The analysis reveals that small errors in the evaluation of the correlation functions could lead to a decrease in true drift velocity if the receiver separation is too small in comparison to the pattern scale. It is shown that the errors could be due to differences between the receiver channels, digitizing limitations, or the human operator (if records are digitized manually from films or paper charts). It is concluded that proper receiver separation must be achieved so that the correlation values will not be too high. Limits of 0.8 for the maximum cross-correlation value and 0.60 for zero time lag are suggested.
Indian Academy of Sciences Proceedings Section, Nov 1, 1979
Partial reflection drift measurements in the range 80-100 km made during the year 1972 at a midla... more Partial reflection drift measurements in the range 80-100 km made during the year 1972 at a midlatitude station Buckland Park near Adelaide (35 deg S) are examined for the storm-time behavior. Changes in the zonal wind pattern are associated with magnetic storms. A decrease in the eastward component is associated with increase in foF2 whereas an increase in the eastward component is associated with a decrease in foF2. Day-to-day variability in the prevailing and tidal components of winds in mesosphere reported earlier may be due to the changes in the circulation pattern caused by the energy deposition during storm times.
In this paper we obtain common fixed point theorems of weakly compatible maps on symmetric spaces... more In this paper we obtain common fixed point theorems of weakly compatible maps on symmetric spaces. We prove that if S and T are weakly compatible maps satisfying property (E-A) along with strict contractive conditions, then they have common fixed points. Since these results are obtained without using full force of metric, they are improved generalization of results obtained by Pant ([10], ).
In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in... more In this paper, we obtain some fixed point theorems for occasionally weakly compatible mappings in cone metric space. Our results extends the result of A.Bhatt, et al.[A. Bhatt, et al., Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Nonlinear Anal., 73(2010) 176-182].
Indian Journal of Radio and Space Physics, Feb 1, 1978
Drift motion of ionization irregularities has been studied by making measurements from first and ... more Drift motion of ionization irregularities has been studied by making measurements from first and second multiples. The results are found to be in agreement with earlier observations from the spaced receiver technique.
Indian Journal of Radio and Space Physics, Apr 1, 1979
Several spaced fading records obtained in South Australia are analyzed by the cross-spectrum meth... more Several spaced fading records obtained in South Australia are analyzed by the cross-spectrum method and by the full correlation method with the use of raw as well as filtered data. The apparent and true drift speeds determined by correlating normal amplitude data are found not to be related to the velocity spread obtained by the cross-spectrum method. It is shown that the cross-spectrum method yields a positive dispersion even when the filtering method indicates constant velocity.
Partial reflection drift observations of the 80-100 km altitude region made at Adelaide, Australi... more Partial reflection drift observations of the 80-100 km altitude region made at Adelaide, Australia, are examined for the irregular component due to internal gravity waves. The fluctuations have a mean period of 3 hr and the rms amplitudes show a large day-to-day variability. No correlation was found between the rms amplitude fluctuations and the geomagnetic disturbance parameter; the mean rms values of these fluctuations increase with altitude, with the vertical wave length of the order of 10 km. The energy densities of gravity wave motions decrease with increasing altitude; the energy and momentum deposition and the eddy diffusion coefficient are estimated and discussed.
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