Jacobian of meromorphic curves

The contact structure of two meromorphic curves gives a factorization of their jacobian.Comment: 41 pages, amstex, to be published in the Proceedings of the Indian Academy of Science

Interferometer for measurement of optical polarization

Standard two-beam interferometer with polarizers in each beam and an analyzer at the recombined focal point provides greater accuracy and higher resolution than any other known method for measuring variation of polarization within a spectral line and in the surrounding continuum

Singularities in positive characteristic, stratification and simplification of the singular locus

We introduce an upper semi-continuous function that stratifies the highest multiplicity locus of a hypersurface in arbitrary characteristic (over a perfect field). The blow-up along the maximum stratum defined by this function leads to a form of simplification of the singularities, also known as a reduction to the monomial case.Comment: Several typos corrected. Minor improvements on the presentation of the published pape

Absolute dimensions of TT hydrae

The photometric elements of the Algol type binary TT Hydrae derived by the authors from their UBV observations during 1973-77 have been combined with the spectroscopic elements given by Sanford (1937) and Sahade and Cesco (1946) to obtain the absolute dimensions of the system. It is found that the spectroscopic orbital elements given by Sanford represent the evolutionary status of the secondary component better than those of Sahade and Cesco. The primary appears to be an Al v main sequence star of mass ~ 3 to 4m⊙ and radius ~2.3R⊙. The secondary fills its Roche lobe; it can be represented by a K0III star of mass ~0.8m⊙ and radius ~6.0Rm⊙. Better spectroscopic data are needed for confirmation of these results

Equivalent widths of atomic lines in sunspot spectra

Equivalent widths of 82 Cr I lines, 70 Fe 1 lines, and 74 Ti I lines are measured in the spectra of four sunspots of average area 55 millionths of the visible hemisphere of the sun. Separate curves of growth for Cr I, Fe t, and Ti I are constructed. Excitation temperatures of 4030° ± 80° , 4200° ± 150° , and 3800° ± 100° are obtained for Cr I, Fe I, and Ti I, respectively

A model of the Algol type close binary TT Hydrae

UBV photometric observations and elements of TT Hydrae obtained by Kulkarni and Abhyankar (1980) are combined with the radial velocity curve of Popper (1979, personal communication) to derive the absolute dimensions and a model of this important Algol system. While the photometric ratios of radii in V and B are in agreement giving k = 0.3812 for a limb darkening coefficient of x = 0.6, application of Irwin's (1947) method gives x = 0.4 for U. The primary is found to be a main sequence A1 V star of mass 2.61M⊙ and radius 2.01 R⊙, and the secondary is classified as a K1 III star of mass 0.70 M⊙ and radius 5.33 R⊙. The observed Fourier coefficients for the light outside the eclipse agree with those calculated from theory for the reflection and ellipticity effects. The system shows an ultraviolet excess of 0.5 to 0.6 magnitudes during primary eclipse, which is attributed to an asymmetric circumstellar distribution of matter around the primary. The evolutionary status of the secondary, which does not appear to fill its Roche lobe completely, is discussed

Techniques for the study of singularities with applications to resolution of 2-dimensional schemes

We give an overview of invariants of algebraic singularities over perfect fields. We then show how they lead to a synthetic proof of embedded resolution of singularities of 2-dimensional schemes.Comment: 26 pages; minor changes have been adde

Modeling, system identification, and control of ASTREX

The modeling, system identification and controller design aspects of the ASTREX precision space structure are presented in this work. Modeling of ASTREX is performed using NASTRAN, TREETOPS and I-DEAS. The models generated range from simple linear time-invariant models to nonlinear models used for large angle simulations. Identification in both the time and frequency domains are presented. The experimental set up and the results from the identification experiments are included. Finally, controller design for ASTREX is presented. Simulation results using this optimal controller demonstrate the controller performance. Finally the future directions and plans for the facility are addressed