Radon concentration of air over the Eastern Arabian Sea

The radon concentrations of air samples collected during the South West monsoon period at altitudes up to 4 km over the Arabian Sea at two locations,i.e., 0–50 km and 300–400 km west of Bombay, are reported. Radon was extracted from air, using a simple single stage apparatus. The concentration of radon in the monsoon air mass was found to range around 80–100 dpm/m³ STP, indicative of its recent continental origin. The results suggest that the coastal monsoon air mass, up to 400 km west of Bombay coast, is generally homogeneous and vertically well mixed. During the post-monsoon condition, a strong gradient in the radon concentration in the vertical is observed. The concentration of radon decreases from 157 dpm/m³ at sea level to 35 dpm/m³ at about 3·7 km altitude, suggesting a vertical turbulent diffusion coefficient of ～6×10⁴ cm²/sec. In contrast, the near absence of vertical gradient of radon in the monsoon air mass indicates that the vertical turbulence is much stronger during the monsoon period.     

The south-west monsoon

A review has been made of the ideas about the south-west monsoon upto 1963 and the modifications necessary in the same in the light of the results of the International Indian Ocean Expedition (IIOE) during 1963–64. Important papers on the IIOE results published in India and elsewhere have been discussed in brief from the point of their usefulness in forecasting, indicating in what respects the interpretations are against weather, climatic and topographical features of the Indo-Pakistan subcontinent. Taking into account the presence of the Western Ghats, changes which occur within about 500 km. of the west coast of the Peninsula regarding clouds and weather and depth of the moist current brought to light by the IIOE results, become intelligible. There are no cyclonic circulations in the north-east Arabian Sea and Bombay area and in the South Bay of Bengal of the type of ‘subtropical cyclone’ in the eastern Pacific; existence of the same has been postulated due to inadequate appreciation of the Indian conditions by the workers concerned.     

Measurements of total electron content over Ahmedabad and Bombay from Beacon satellite data

The paper outlines the method used at Ahmedabad for determining the total electron content in the ionosphere from differential Faraday rotations of plane polarised radio waves on 40.010 and 41.010 Mc./s. transmitted by NASA satellite 64-64A. The observations made during the period October 1964 to April 1965 are utilised to determine the diurnal variation of the total electron content up to the satellite height which was about 1,000 km. over Ahmedabad and Bombay latitudes. The curve of total electron content up to the satellite height shows similarity to the curve of maximum electron density at the F2 peak. The total electron contents over Bombay are in general higher than those over Ahmedabad.     

Features of electron density and temperature in the 500–3500 km region of the plasmasphere—(1) Dawn and dusk sectors

Dawn-dusk features of the plasmasphere are examined for intervals in February and September 1969, using electrostatic probe data ofN _e andT _e from the ISIS-I satellite. Clear plasmatrough formation is seen in the vicinity of 70° geomagnetic latitude in both dawn and dusk sectors in the 1500–3500 km region, but the plasmatrough is absent in the altitude range 500–1500 km. The plasmatrough minimum near 70°φ exhibits no asymmetry between dawn and dusk sectors in its latitudinal position. TheT _e peak associated with the plasmatrough is more pronounced in the dawn sector. DawnN _e is less than duskN _e, but dawnT _e exceeds duskT _e. The influence of processes in the magnetosphere in causing these features is examined.     

Variation with lunar phase of midday critical frequencies and heights of the F2 layer over Ahmedabad and other low latitude stations

The paper contains an analysis of the variation of the midday values of foF₂, h′F₂ and hpF₂ with lunar phase at Ahmedabad during the years 1954 and 1955 and of foF₂ alone at Bombay, Madras and Tiruchirapalli during 1954. It is found that while the semidiurnal lunar tidal variations at Ahmedabad and Bombay agree in phase with those observed at middle latitudes, the phase reverses in direction between Bombay and Madras. The results are compared with those relating to Huancayo and Singapore.     

Cantorian-fractal space-time and particles in a generalized magnetic field

In the fractal space-time theory the generalized precession, the generalized Stern–Gerlach experiment, the generalized Zeeman effect, the generalized Landau's levels and the generalized fractional quantum Hall effect are analyzed. The Cantorian structure of space-time implies the supplemental decreasing rate of the Ecliptic tilt, the “global” quantization in units of 36 km s⁻¹ and the filling factor ν=1/2n+1.     

The effect of polar magnetic sub-storms on the equatorial sporadic E

It is known that equatorial sporadic E disappears at night when dynamo field is east to west. During some DP₂ type magnetic sub-storms, which cause a depression of the geomagnetic horizontal field at the equator, theq type of sporadic E is found to disappear at the equatorial stations Huancayo and Kodaikanal. This suggests that one of the mechanisms causing the temporary disappearance of E _s —q during daytime in equatorial ionograms is the replacement of the east to west dynamo electric field by a west to east electric field due to the imposition of an electric field opposing the normal daytime S _q field.     

Study of aerosols in the atmosphere by twilight scattering

Photometric measurements of the light scattered from the twilight sky in the direction of the sun’s vertical at an angle of 70° from the zenith, were made during IGY-IGC (1957–59) at Mt. Abu with a photometer the telescope of which covered a circular field of about 1 degree. Observations showed that there were changes in the slopes of the curves of intensity against the depression θ of the sun below the horizon, when θ was 5–6°. This could be explained by assuming the existence of an aerosol layer at 20–25 km. The height of the layer could however vary from 15 to 30 km. The lowest heights of the stratospheric aerosol layer at Abu were found to occur in June and the highest in November–December. A second feebler maximum corresponding to a scattering layer at a height of 45–50 km. was also found on a number of occasions.     

Air-mass dynamics or subsidence processes in the Arabian Sea monsoon

Soundings over the Arabian Sea during the International Indian Ocean Expedition period and climatological data over the west coast of India have been discussed to determine the cause of the low-level inversion and the influence of the Western Ghats on the inversion and precipitation. There does not appear relation between maximum divergence and lowest height of base of inversion as presumed by Flohnet al. The pattern of precipitation frequency on the west coast as seen from Fig. 2 of Ramage does not show the same trend either as the number of rainy days or rainfall at the coastal observatories. The depth of the moist layer and the height of base of inversion increase as the Western Ghats are approached, such changes not occurring off west Kathiawar-Kutch-Sind where there are no orographic barriers on the coast. The air-mass considerations to explain the low-level inversion over the Arabian Sea, would appear substantially valid even now.     

Properties of the density for a three-dimensional stochastic wave equation

We consider a stochastic wave equation in space dimension three driven by a noise white in time and with an absolutely continuous correlation measure given by the product of a smooth function and a Riesz kernel. Let pt,x(y) be the density of the law of the solution u(t,x) of such an equation at points (t,x)∈]0,T]×R³. We prove that the mapping (t,x)?pt,x(y) owns the same regularity as the sample paths of the process {u(t,x),(t,x)∈]0,T]×R³} established in [R.C. Dalang, M. Sanz-Solé, Hölder-Sobolev regularity of the solution to the stochastic wave equation in dimension three, Mem. Amer. Math. Soc., in press]. The proof relies on Malliavin calculus and more explicitly, the integration by parts formula of [S. Watanabe, Lectures on Stochastic Differential Equations and Malliavin Calculus, Tata Inst. Fund. Res./Springer-Verlag, Bombay, 1984] and estimates derived from it.     

Nuclear power plant optimal control by successive linear programming

An attempt to find optimal controls for an extremely load-following nuclear power plant during large load pick-ups is reported in this paper. The choice of the numerical method to solve this highly constrained dynamic optimization problem is discussed. The results reported demonstrate the efficacy of the successive linear programming method in tackling this problem without recourse to model linearization.The first author wishes to express his gratitude for many helpful discussions with Prof. S. L. Mehndiratta, Indian Institute of Technology, Bombay and Mr. B. F. Chamany, Bhabha Atomic Research Centre, Bombay, India.     

Lectures on the ekeland variational principle with applications and detours

Book Review

Lectures on the ekeland variational principle with applications and detoursD. G. de Figueiredo Tata Institute of Fundamental Research, Bombay, Lectures on Mathematics and Physics-Mathematics 81, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1989, 96 pp., Softcover DM20,-, ISBN 3-540-51179-2     

The brightness of the zenith sky during twilight

A visual photometer is described for measuring the brightness of the zenith sky during twilight. The results of measurements made with it at Bombay on a large number of clear moonless evenings during the period December 1937 to March 1938 are discussed. A red filter RG₁ (Schott and Gen.) and a green filter VG₁ (Schott and Gen.) were used. With the latter, it was possible to continue observations even when twilight conditions had completely ceased. The variations in brightness agree with a relation proposed by Link, namely,dI/I=β sin θ sec² θdθ, where I is the brightness of the zenith sky, θ the angular depression of the sun below the horizon and β a constant. If the brightness is due only to primary scattering from the atmosphere illuminated by sunlight, it is possible to connect β with the temperature of the atmospheric layer responsible for the scattering. The difficulty however is to ascertain to what extent secondary scattering is important.     

Numerical modelling of continuous concrete box girder bridges considering construction stages

The aim of this study is to analyse the concrete continuous box girder bridges by considering segmentally construction stages through balanced cantilever method. Time-dependent material properties of concrete and steel are also taken into account. Budan Bridge is selected as a numerical example. The Bridge constructed with balanced cantilever method and located on Artvin–Erzurum highway, Turkey, at 55 + 729.00–56 + 079.00 km is modelled using SAP2000 program. Geometric nonlinearities are taken into consideration in the analysis using P-Delta and large displacement criterion. Time-dependent material properties are considered as compressive strength, aging, shrinkage and creep for concrete, and relaxation for steel. The structural behaviour of the bridge at different construction stages is examined. Variation of internal forces such as bending moment, shear forces and axial forces, and displacements for bridge deck and pier are given with detail.Analyses show that, to obtain real behaviour of concrete bridges, segmentally construction stage analysis using time dependent material properties and geometric nonlinearity should be considered, because construction period continue along time and loads may change during this period and after.     

Longest increasing subsequences,Plancherel-type measure and the Hecke insertion algorithm

We define and study the Plancherel–Hecke probability measure on Young diagrams; the Hecke algorithm of Buch–Kresch–Shimozono–Tamvakis–Yong is interpreted as a polynomial-time exact sampling algorithm for this measure. Using the results of Thomas–Yong on jeu de taquin for increasing tableaux, a symmetry property of the Hecke algorithm is proved, in terms of longest strictly increasing/decreasing subsequences of words. This parallels classical theorems of Schensted and of Knuth, respectively, on the Schensted and Robinson–Schensted–Knuth algorithms. We investigate, and conjecture about, the limit typical shape of the measure, in analogy with work of Vershik–Kerov, Logan–Shepp and others on the “longest increasing subsequence problem” for permutations. We also include a related extension of Aldous–Diaconis on patience sorting. Together, these results provide a new rationale for the study of increasing tableau combinatorics, distinct from the original algebraic-geometric ones concerning K-theoretic Schubert calculus.     

Arch model with Box–Cox transformed dependent variable

Box–Cox power transformation has been used traditionally to linearise otherwise nonlinear models. In this paper, Engle's linear ARCH specification is considered for a regression model in which the dependent variable is Box–Cox transformed. The consequent issues arising in both testing and estimation of the model are investigated. A Lagrange multiplier test is also developed to test Engle's linear ARCH model against this wider class of models. The usefulness of this generalisation is examined by applying it to the daily closing prices on the Bombay Stock Exchange Sensitive Index, and the findings strongly favour the proposed model.     

On the simultaneous existence of eastward and westward flowing equatorial electrojet currents

The counter-electrojet currents are evidenced by the disappearance of theq type ofEs layer (Es-q) or the appearance of the blanketing type ofEs (Es-b) at Kodaikanal, associated with the depression of the geomagneticH field and the reveisal of ionospheric drift at Thumba. The necessary condition for such an event is not the decrease of theH field below the night level but that the difference of theH field between an equatorial and a non-equatorial station should decrease below its night level. The different kinds of association between the disappearance ofEs-q and the depression in theH field are suggested due to superimposition over theSq current system (at about 107 km) of a separate westward current system at a lower level (about 100 km). The source of the reversed current over the dip equator during the daytime hours is sought in the current system generated by the lunar tides or in various magnetospheric processes generating the polar substorms. Large day-to-day variations of the solar daily range ofH at the equator independent ofSq variation at tropical latitudes are suggested to be due to superimposition at the equator of the two rather independent current systems.     

Moments of escape times of random walk

Extending an idea of Spitzer [2], a way to compute the moments of the time of escape from (−N,L) by a symmetric simple random walk is exhibited. It is shown that all these moments depend polynomially onL andN. The research of this author was supported by the National Board of Higher Mathematics, Bombay, India     

Molecular lines and continuum from W51A (I) —CO and NH3 spectra and 3 mm continuum

As for the 5′ × 4′(～llpc × 9pc) region centered at W51 lRSl the observations of the 3.4 mm continuum, CO (J = 1-0) line and simultaneous NH₃(1,1), (2,2), (3,3), (4,4) inverse lines were made for studying the massive star formation region located in the main spiral arms of the Galaxy. In the directions of W51 IRS1, IRS2 and el/e2 in 3.4 mm continuum, analyses of the line profiles show that the absorption lines of ammonia, which arise from the gas in front of the HII region, are red-shifted with respect to the emission lines, which arise from the surrounding cloud. Furthermore, a radiation transfer and statistical equilibrium calculation of ammonia molecules show that the densities increase by 3–10 times from the eastern border to the center. These points hint that the collapse is happening in the molecular cloud core obscured in optical wavelengths. The effects of the radiation fields from radio, infrared and UCHII sources is non-negligible on the excitation of various molecules (e.g. NH₃) within the circle of radius 40″ centered at IRS1. The profiles of the COJ = 1–0 line in the circle change from double peaks ( ～ 60, ～ 68 km. s^-1) to triple peaks, i.e. the component ～53 km·s^?1, which associates with UCHII, also appears in the spectra. There are indications that the circle of radius 40″ centered at IRSI is a region of massive star forming activity     

A construction of Spin(7)-instantons

Joyce constructed examples of compact eight-manifolds with holonomy Spin(7), starting with a Calabi–Yau four-orbifold with isolated singular points of a special kind. That construction can be seen as the gluing of ALE Spin(7)-manifolds to each singular point of the Calabi–Yau four-orbifold divided by an anti-holomorphic involution fixing only the singular points. On the other hand, there are higher-dimensional analogues of anti-self-dual instantons in four dimensions on Spin(7)-manifolds, which are called Spin(7)-instantons. They are minimizers of the Yang–Mills action, and the Spin(7)-instanton equation together with a gauge fixing condition forms an elliptic system. In this article, we construct Spin(7)-instantons on the examples of compact Spin(7)-manifolds above, starting with Hermitian–Einstein connections on the Calabi–Yau four-orbifolds and ALE spaces. Under some assumptions on the Hermitian–Einstein connections, we glue them together to obtain Spin(7)-instantons on the compact Spin(7)-manifolds. We also give a simple example of our construction.