PUBLICATIONS - Professor J.D. Whitehead
Journal Articles -
1. The quasi-transverse (Q.T.) approximation to Appleton's magneto-ionic
equation. J. atmos. terr. Phys. 2, 361, 1952.
2. The focussing of short radio waves reflected from the ionosphere. J.
atmos. terr. Phys. 9, 269, 1956.
3. The absorption of radio waves in an ionospheric layer. J. atmos. terr.
Phys. 9, 276, 1956.
4. The absorption of short radio waves in the ionosphere. J. atmos. terr.
Phys. 10, 12, 1957.
5. The distance attenuation of radio waves reflected at vertical incidence
from the ionosphere. J. atmos. terr. Phys. 12, 150, 1958.
6. Sudden changes in the virtual height of radio waves reflected from the
E-region of the onosphere. J. atmos. terr. Phys. 16, 99, 1959.
7. The absorption of short radio waves in the D-, E- and F-regions of the
ionosphere. J. atmos. terr. Phys. 16, 283, 1959.
8. Measuring the mean square amplitude of fading signals using a selected
quantile output device (SQOD). Proc. I.R.E. 48, No.6, 1960 (with A.E. Adam).
9. The mesopause region of the ionosphere. Nature 186, 461, 1960.
10. F-region travelling disturbances and sporadic-E ionization. J. Geophys.
Res. 65, 2767, 1960 (with L.H. Heisler).
11. Focussing of radio waves reflected from a rough curved ionosphere.
Aust. J. Phys. 13, 621, 1960.
12. Longitude effect in temperate zone sporadic-E and the earth's magnetic
field. Nature 187, 676, 1960 (with L.H. Heisler).
13. Formation of the sporadic-E layer in the temperate zones. Nature 188,
567, 1960.
14. The formation of the sporadic-E layer in the temperate zones. J. atmos.
terr. Phys. 20, 49, 1961.
15. Group and phase velocities of a travelling disturbance in the F-region
of the ionosphere. Nature 191, 157, 1961 (with L.H. Heisler).
16. The interpretation of F2 critical frequency measurements. J. atmos.
terr.Phys. 22, 186, 1961 (with L.H. Heisler).
17. The phase speed of a travelling disturbance in the F-region of the
ionosphere and its comparison with group velocity. Aust. J. Phys. 14, 481,
1961 (with L.H. Heisler).
18. The absorption of radio waves in the ionosphere with respect to
geomagnetic current control and other proposed models - a critical survey.
Planet. Space Sci. 8, 151, 1961.
19. World maps of ionospheric characteristics. J. atmos. terr. Phys. 24,
407, 1962.
20. Distribution of echo amplitudes from an undulating surface. J. atmos.
terr. Phys. 24, 715, 1962.
21. The reflection characteristics of a patchy sporadic-E layer. J. atmos.
terr. Phys. 24, 681, 1962.
22. Rapid variations in the sporadic-E region. J. atmos. terr. Phys. 24,
753, 1963 (with L.H. Heisler).
23. Theory of equatorial sporadic-E. J. atmos. terr. Phys. 25, 167, 1963.
24. The density of the atmosphere in the E-region of the ionosphere.
Planet. Space Sci. 11, 513, 1963.
25. A suggested method of accurately measuring the virtual height of
reflection of radio waves from the ionosphere. J. atmos. terr. Phys. 25,
599, 1963 (with A. Malek).
26. Comments on "Generalization and critique of the wind-shear theory of
Sporadic-E" by D. Layzer. J. Geophys. Res. 69, No.23, 5091, 1964.
27. The correlation between the occurrence of sporadic-E and the horizontal
component of the earth's magnetic field. J. atmos. terr. Phys. 26, 437,
1964 (with L.H. Heisler).
28. Mixtures of ions in the wind-shear theory of sporadic-E. Radio Science
1, 198, 1966.
29. The enigma of the equatorial electro-jet. Planet. Space Sci. 14, 519, 1966.
30. Sporadic-E at night. Radio Science 1, 1111, 1966.
31. Sporadic-E in middle latitudes. Nature 214, 261, 1967.
32. Errors in the measurement of virtual height using a phase ionosonde. J.
atmos. terr. Phys. 29, 1483, 1967 (with E. Kantarizis).
33. Survey of sporadic-E processes. Space Research VII, p.90, 1967.
34. Ion layers in the E-region of the ionosphere with a linear attachment
law. Planet. Space Sci. 15, 1055, 1967.
35. Instabilities in a gradient of ionization and sporadic-E. J. atmos.
terr. Phys. 29, 1285, 1967.
36. Low frequency plasma instabilities in the ionosphere. J. atmos. terr.
Phys. 30, 1563, 1968.
37. A better ionosonde. News and Views. Nature 220, 959, 1968 (with E.
Kantarizis and D.W. Rickard).
38. Report on the production and prediction of sporadic-E. Reviews of
Geophysics and Space Physics 8, 65, 1970.
39. The gradient instability in bounded ionospheric layers. J. atmos. terr.
Phys. 32, 1283, 1970.
40. On the reflection of internal gravity waves. Can. J. Phys. 48, 1830, 1970.
41. Effect of windshear on the nighttime E-region and an estimate of the
rate of production of molecular ions. J. Geophys. Res. 75, 3919, 1970.
42. Some F-region parameters measurable in the Boulder heating experiment.
J. Geophys. Res. 75, 6417, 1970.
43. Radio-reflectivity detection of artificial modification of the
ionospheric F-layer. J. Geophys. Res. 75, 6439, 1970 (with R. Cohen).
44. Ionospheric Si+ and SiO+. J. Geophys. Res. 75, 4366, 1970 (with E.E.
Ferguson and F.C. Fehsenfeld).
45. Ionization disturbances caused by gravity waves in the presence of an
electrostatic field and background wind. J. Geophys. Res. 76, 238, 1971.
46. The equatorial electrojet and the gradient instability. J. Geophys.
Res. 76, 3116, 1971.
47. Divergence of ion velocity in the E-region due to vertical winds. J.
Geophys. Res. 76, 2523, 1971 (with W.H. Hooke).
48. Difficulty associated with wind-shear theory of sporadic-E. J. Geophys.
Res. 76, 3127, 1971.
49. An improved true-height reduction technique. Radio Science 7, 1045, 1971.
50. Some recent work on sporadic-E theory. Radio Science 7, 381, 1972.
51. The structure of sporadic-E from a radio experiment. Radio Science 7,
355, 1972.
52. Winds in the E-region (comments on Chimonas' theory). Radio Science 7,
403,1972.
53. The position of electron density maxima with vertical ionization
movements. Radio Science 7, 425, 1972.
54. The observation of chemical releases in the upper atmosphere. Planet.
Space Sci. 20, 1348, 1972.
55. The distance attenuation of radio waves reflected from the ionosphere.
J. atmos. terr. Phys. 34, 165, 1972 (with T.B. Jones).
56. The Q.T. approximation for Appleton's formula. J. atmos. terr. Phys.
34, 517, 1972.
57. The seasonal variation of the height and thickness of the E-region. J.
atmos. terr. Phys. 35, 183, 1973.
58. Experimental test of wind-shear theory: do rocket-borne magnetometers
measure B? Planet. Space Sci. 21, 1815, 1973.
59. Measurement of the velocity of waves in the ionosphere. J. atmos. terr.
Phys. 35, 2147, 1973 (with G.D. Brownlie and L.G. Dryburgh).
60. A pencil beam radar for ionospheric research. Nature 243, 11, 1973.
61. The dispersion of waves in the ionosphere. Nature 244, 123, 1973 (with
G.D. Brownlie and L.G. Dryburgh).
62. Phase and amplitude analysis of radio echoes from the ionosphere. J.
atmos. terr. Phys. 37, 1427, 1975 (with P.E. Monro).
63. Comparison of Arecibo E-region data and sporadic-E theory: a measurement
of the diffusion coefficient. Radio Science 10, 357, 1975 (with R.H. Harper
and R.H. Wand).
64. The partially-aligned gradient instability in the ionosphere. J.
Geophys. Res. 81, 1361, 1976.
65. A radio lens in the ionosphere. J. atmos. terr. Phys. 39, 383, 1976
(with K. Davies).
66. On the peculiar shape of sporadic-E clouds. J. atmos. terr. Phys. 40,
1025, 1978 (with W.R. From).
67. Interpretation of the short-period oscillations in ionospheric group
height. Nature 274, 511, 1978 (with P.E. Monro).
68. Continuous A to D converter. Wireless World 85, 59, 1979 (with J.E. Dahl).
69. The use of sunrise and sunset terminators to calibrate ionospheric
movement measurements. J. atmos. terr. Phys. 43, 1267, 1981 (with G.D.
Brownlie and W.R. From).
70. The use of phasor display in studying ionospheric radio echoes. J.
atmos.terr. Phys. 43, 1265, 1981 (with W.R. From).
71. Measurements of movements in the ionosphere. J. atmos. Terr. Phys. 45,
345, 1983 (with W.R. From., K.L. Jones and P.E. Monro).
72. Splitting and divergence of `Stare' auroral radar velocities. J.
Geophys. Res. 88, 2147, 1983 (with E. Nielsen and H.M. Jerkie).
73. A test of the cosine relationship using three-radar velocity
measurements. Radio Science 18, 230, 1983 (with E. Nielsen, L.A. Bedberg and
T.B. Jones).
74. Radar auroral observations and ionospheric electric fields. Advances in
Space Research 2, 131, 1983 (with E. Nielsen).
75. On reducing the inherent noise in the double-pulse Doppler technique.
Radio Science 18, 93, 1983.
76. The calibration of an H.F. radar used for ionospheric research. Radio
Science 19, 423, 1983 (with W.R. From).
77. The radio power reflected from rough and undulating ionospheric
surfaces. Radio Science 19, 1078, 1983 (with W.R. From and L.G. Smith).
78. Es structure using an H.F. radar. Radio Science 21, 309, 1986 (with
W.R. From).
79. Dynamo action in sporadic-E formation. J. atmos. terr. Phys. (accepted
for publication). 986 (with K.L. Jones).
80. Measuring ionospheric movements with totally reflected radio waves. J.
atmos. terr. Physics 50, 2. 1988 (with W.R. From & E.M. Sadler).
81. Comments on "A statistical study of auroral radar spectra obtained with
Sabre" by K. Schlegel, E.C. Thomas and D. Ridge. J. Geophys. Res. 93, 5985.
1988.
82. Opportunities for Post-Graduate Studies and Research in Physics. The
Australian Physicist, 25, 298. 1988.
83. Physics Research in Australian Universities. Asia-Pacific Physics News
3, 11. 1988.
84. Sporadic E Research in Brisbane, Australia. URSI News December 1988.
p.1. Ionosphere Irregularities. World Ionosphere/Thermosphere Study WITS
Handbook Ed. C.H. Liu and B. Edwards 1, 127. 1988.
85. A strange result in the measurement of the angles of arrival of the
first and second echoes off the ionosphere at high radio frequencies. J.
Atmos. Terr. Phys. 51, 3, 223-231, 1989 with W.R. From & J. MacGibbon).
86. Recent work on mid-latitude and equatorial sporadic E. J. Atmos. Terr.
Phys. 51, 401, 1989.
87. Sporadic E. layers. History and Recent Observations. (Accepted for
publication Space Research.) Now published.
88. Using the STARE double pulse system to obtain the mean velocity and the
velocity of longer{LS}lived irregularities. J. atmos. terr. Phys. 52, 723,
1990.
89. The future of auroral radars for investigation of the E region of the
ionosphere (Accepted for publication in Annales Geophysicae).
90. Opportunities for Post-Graduate Studies and Research in Physics,
Australian & New Zealand Physicist 28, 136, 1991.
BARNES, R.I. HF measurements of the structure of mid-latitude spread-Es.
Abstract. 10th National Congress, Australian Institute of Physics,
Melbourne, February 1992.
BARNES, R.I. Mid-latitude sporadic-E structure and its effects on radio
propagation. PhD thesis. Univ Queensl, 316pp, 1992.
Heron, M.L., WHITEHEAD, J.D., MAINSTONE, J.S. & Prytz, A. A high precision
system for measuring ocean wave directions. Abstract. 10th National
Congress, Australian Institute of Physics, Melbourne, February 1992.
PARKINSON, M.L. Bathymetric broadening of first order MF/lower HF surface
radar ocean echoes. Abstract. 10th National Congress, Australian Institute
of Physics, Melbourne, February, 1992.
WHITEHEAD, J.D. The future of coherent radars in the study of E-region
irregularities. Ann Geophysicae, 10, 278-280, 1992.
WHITEHEAD, J.D., MEEHAN, D.H. & BARNES, R.I. The structure of mid-latitude
spread-F and sporadic-E. Abstract. EOS, Transactions American Geophysical
Union, 73, 70, 1992.
WHITEHEAD, J.D. Opportunities for post-graduate studies and research in
Physics. Australian & New Zealand Physicist, 29, 149-166, 1992.
WHITEHEAD, J.D. Search for solutions of the gradient instability in a
realistic ionosphere. Abstract. 10th National Congress, Australian Institute
of Physics, Melbourne, February 1992.
WHITEHEAD, J.D. The dust theory of sporadic E. Abstract. 10th National
Congress, Australian Institute of Physics, Melbourne, February 1992.
WHITEHEAD, J.D. Search for solutions of the gradient instability in a
realistic ionosphere. In Essex, E.A. & Whitehead, J.D., eds, Proceedings
of South Pacific STEP Workshop, Melbourne, 1992, 230-32. Bundoora, La Trobe
Univ, 1992.
WHITEHEAD, J.D. The dust theory of sporadic E. In Essex, E.A. & Whitehead,
J.D., eds, Proceedings of South Pacific STEP Workshop, Melbourne, 1992,
233-34. Bundoora, La Trobe Univ, 1992.
WILSON, M.J. Medium scale TID analysis of Bribie Island radar data. In
Essex, E.A. & Whitehead, J.D., eds, Proceedings of South Pacific STEP
Workshop, Melbourne, 1992, 210-13. Bundoora, La Trobe Univ, 1992.
WILSON, M.J. Medium scale TID analysis of Bribie Island radar data.
Abstract. 10th National Congress, Australian Institute of Physics,
Melbourne, February 1992.
WILSON, M.J. Assessment of POLAN true height analysis using doppler shifts.
Abstract. 10th National Congress, Australian Institute of Physics,
Melbourne, February 1992.
WILSON, M.J. Assessment of POLAN true height analysis using doppler shifts.
In Essex, E.A. & Whitehead, J.D., eds, Proceedings of South Pacific STEP
Workshop, Melbourne, 1992, 296-99. Bundoora, La Trobe Univ, 1992.
Barnes, R.I. & WHITEHEAD, J.D. Observations of spread sporadic-E.
Committee on Space Research Colloquium on Low-Latitude Ionospheric Physics,
42. Abstract. Taipei, Natl Cent Univ Inst Space Sci, 1993.
Meehan, D.H. & WHITEHEAD, J.D. The structure of mid-latitude spread-F.
Committee on Space Research Colloquium on Low-Latitude Ionospheric Physics,
83. Abstract. Taipei, Natl Cent Univ Inst Space Sci, 1993.
PARKINSON, M. L. Multi-frequency MF/lower HF ocean radar studies of
wind-wave transients. PhD thesis. Univ Queensl, 454pp, 1993.
PARKINSON, M., WHITEHEAD, J.D. & WILSON, J. Crossed horizontal dipoles
configured as top-loaded vertical dipoles transmitting high-frequency
radiation in the ground plane. Rev Sci Instrum 64(2), 585-86, 1993.
WHITEHEAD, J.D. The gradient instability in sporadic-E layers. 2nd South
Pacific STEP Workshop, 39. Abstract. Newcastle, Univ Newcastle, 1993.
WHITEHEAD, J.D. Modelling of instabilities in mid-latitude sporadic-E.
Committee on Space Research Colloquium on Low-Latitude Ionospheric Physics,
42. Abstract. Taipei, Natl Cent Univ Inst Space Sci, 1993.
WHITEHEAD, J.D. STEP work in the University of Queensland. 2nd South
Pacific STEP Workshop, 49. Abstract. Newcastle, Univ Newcastle, 1993.
WHITEHEAD, J.D. & DUNCAN, A.R. Dust theory of sporadic-E. Committee on
Space Research Colloquium on Low-Latitude Ionospheric Physics, 65. Abstract.
Taipei, Natl Cent Univ Inst Space Sci, 1993.
WHITEHEAD, J.D. & DUNCAN, A.R. Modelling the dust theory of sporadic-E.
2nd South Pacific STEP Workshop, 53. Abstract. Newcastle, Univ Newcastle, 1993.
WILSON, M.J. & WHITEHEAD, J.D. Medium scale travelling ionospheric
disturbances: Analysis of Bribie Island radar data. Committee on Space
Research Colloquium on Low-Latitude Ionospheric Physics, 146. Abstract.
Taipei, Natl Cent Univ Inst Space Sci, 1993.
LINGARD, D.M. (1994). "A study of wind measurement in the D-region of the
ionosphere." J.D. Whitehead. The University of Queensland. ix+254.
WHITEHEAD, J.D. and DUNCAN R. (1994). "Modelling thre dust theory of
sporadic E." Brisbane. Australia Inst Phys & Assoc Pac Phys Soc. 533.
WHITEHEAD, J.D. (1994). "Modelling of instabilities in mid-latitude
sporadic-E." Low-latitude ionospheric physics. Pergamon p.162-166.
Reports -
1. Technical Review (of Sporadic-E). Proc. of the Second Seminar on the
Cause and Structure of Temperate Latitude Sporadic-E. 1968.
2. The phase ionosonde. Proc. of the Second Seminar on the Cause and
Structure of Temperate Latitude Sporadic-E. 1968.
3. Some remarks on the theories of Sporadic-E. Proc. of the Second Seminar
on the Cause and Structure of Temperate Latitude Sporadic-E. 1968.
4. Sporadic-E structure - radio measurements. Proc. of the Second Seminar
on the Cause and Structure of Temperate Latitude Sporadic-E. 1968.
5. Theoretical models of sporadic-E. Penn. State Conference on Theoretical
Models of the Ionosphere. 1971.
6. Electronic systems of the Bribie pencil beam array. Ionospheric Research
Section No.6 (University of Queensland). 1973 (with G.D. Brownlie).
7. Use of the Arecibo back-scatter facility. IRL Internal Report No.32
(Penn. State University). 1973.
8. Sporadic-E analysis. IRL Internal Report No.33 (Penn. State University).
1973.
9. Phase and amplitude analysis of radio echoes from the ionosphere. IRL
Internal Report No.36 (Penn. State University). 1973.
10. The present state of sporadic-E theory. IRL Internal Report No.38
(Penn. State University). 1974.
11. The effects of radio lenses in the ionosphere on the scintillation of
satellite-to-ground radio signals. AGARD-CPP-209. 1976 (with K.{LS}Davies).
12. The production of sporadic-E in the presence of self-generating electric
fields. Internal Report. 1977.
13. A programme to simulate Bribie angles-of-arrival data. Internal Report.
1977.
14. E and F region of the ionosphere. Discussion Meeting on
Solar-Terrestrial Physics, August 1980, La Trobe University, p.90. 1980.
15. The H.F. radar on Bribie Island. Radio Research Board, Array
Beamforming and Steering Seminar, March 1981, Adelaide University. 1981
(with W.R. From).
16. Data analysis for a phase coherent pencil beam ionospheric radar at 1.9
to 6 MHz. Radio Research Board, Array Beamforming and Steering Seminar,
March 1981, Adelaide University. 1981 (with W.R. From).
17. The height of auroral radar irregularities. Max-Planck-Institut fur
Aeronomie MPAE-P-04-82-04. 1983.
18. Irregularities in E-region. Sixth National Congress, Australian
Institute of Physics. Solar Terrestrial Physics Workshop. 1983. Abstract.
19. Medium scale travelling ionospheric disturbances. Sixth National
Congress, Australian Institute of Physics. Solar Terrestrial Physics
Workshop. 1983. Abstract.
20. Future H.F. measurements. URSI/IPS Conference on Ionospheric Physics
and Radio Wave Propagation. 1985.
21. TID's - do they move? URSI/IPS Conference on Ionospheric Physics and
Radio Wave Propagation. 1985.
22. Es structure using an H.F. radar. URSI/IPS Conference on Ionospheric
Physics and Radio Wave Propagation. 1985.
23. Predicting ionospheric tilts. URSI/IPS Conference on Ionospheric
Physics and Radio Wave Propagation. 1985.
24. Ionospheric Physics, A.I.P. Congress, Sydney, August 1976, Aust. Phys.
14, 103, 1977.
25. Radio Research. In The Australian Encyclopedia 5, 3rd Ed., p.167, Syd.
Grolier Soc. Aust., 1977.
26. The structure of spread-F using an H.F. radar. A.I.P. Seventh National
Congress, Solar Terrestrial and Space Physics Workshops, Adelaide,
Australia, August 1986. p.31. 1986 (with D.H. Meehan).
27. The concept of effective reflecting surface. A.I.P. Seventh National
Congress, Solar Terrestrial and Space Physics Workshops, Adelaide,
Australia, August 1986. p.39. 1986.
28. The angles of arrival of the first and second radio echoes from the
ionosphere. A.I.P. Seventh National Congress, Solar Terrestrial and Space
Physics Workshops, Adelaide, Australia, August 1986. p.42. 1986 (with J.H.
MacGibbon).
29. Mid-latitude sporadic-E forecasting. A.I.P. Seventh National Congress,
Solar Terrestrial and Space Physics Workshops, Adelaide, Australia, August
1986. p.22. 1986.
30. Report on mid-latitude and equatorial sporadic-E. Department of
Defence. 1986.
31. Thoughts on STARE. Max-Planck-Institute fur Aeronomie. Report
MPAE-T-04-87-31. 1987.
32. Sporadic E. Elizabeth & Frederick White Conference, Canberra (WITS
study), January 1988.
33. Auroral radar studies. Elizabeth & Frederick White Conference, Canberra
(WITS Study), January 1988 (with E. Nielsen).
34. The effects of non-linearities in type 1 (two-stream) irregularities in
the ionosphere. Australian Bicentenary Congress of Physicists, Sydney,
Australia, January 1988. p.481.
35. Auroral radar velocities - a comparison of mean velocity and that of
longer lived irregularities. Australian Bicentenary Congress of Physicists,
Sydney, Australia, January 1988. p.481 (with E. Nielsen).
36. Joint VHF coherent radar and directional ionosonde measurements of small
and large scale plasma waves in the mid-latitude E region ionosphere.
Australian Bicentenary Congress of Physicists, Sydney, Australia, January
1988. p.481 (with E. Nielsen).
37. Sporadic E-layers. History and Recent Observations. Invited paper.
Twenty-seventh Plenary Meeting of the Committee on Space Research, Espoo,
Finland, July 1988.
38. Non-linear types electrojet irregularities. International Conference on
Auroral Physics, Cambridge, England, July 1988.
39. The mean velocity and the Velocity of Long-lived irregularities using
Auroral Radars. International Conference on Auroral Physics, Cambridge,
England, July 1988.
40. Auroral Radar Velocities. International Conference on Auroral Physics,
Cambridge, England, July 1988.
41. The Design of Modern Ionosondes. Solar Terrestrial Prediction Workshop,
Leura, Australia. IUWDS. 1989. p.157.
42. Production and Prediction of Mid-Latitude Sporadic-E. Solar Terrestrial
Prediction Workshop, Leura, Australia. IUWDS. 1989. p.158.
43. Predicting Sporadic E, Spread F and Travelling Ionospheric Disturbances.
Conference on Solar Terrestrial and Space Physics and Workshop on
Ionospheric Modelling and Radio Wave Propagation. La Trobe University 5-9
Feb 1990, p.12.
44. An experiment to Investigate the stability of Sporadic E Layers.
Conference on Solar Terrestrial and Space Physics and Workshop on
Ionospheric Modelling and Radio Wave Propagation. La Trobe University 5-9
Feb 1990, p.48 (with E. Nielsen).
45. Angles of Arrival using Doppler Sorting of D Region Scattered Echoes.
Conference on Solar Terrestrial and Space Physics and Workshop on
Ionospheric Modelling and Radio Wave Propagation. La Trobe University 5-9
Feb 1990, p.61 (with D. Lingard).
46. The velocity of electron density irregularities having a long lifetime
using coherent radar. European Geophysical Society 16th General Assembly,
Weisbaden, April 1991, 204, 1991.
47. On checking the accuracy of time height reduction from ionograms.
European Geophysical Society 16th General Assembly, Weisbaden, April 1991,
315, 1991 (with M. Wilson).
48. Search for solutions of the gradient instability in a realistic
ionosphere. South Pacific STEP Workshop, Melbourne Feb 1992 p.8 (also
accepted for publication in the Proceedings).
49. The dust theory of sporadic E. South Pacific STEP Workshop, Melbourne
Feb 1992 p.8 (also accepted for publication in the Proceedings).
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