An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.Comment: 15 pages and 4 figures. to appear in American Journal of Physic

Scanner observations of selected cool stars

Photoelectric spectral scans at 30-A resolution of 9 dwarfs, 10 giants and 6 supergiants with spectral types GO to M5 were presented. All stars were observed every 4 A from wavelength 3300 to wavelength 7000. Absorption features at this resolution coincide with: strong atomic lines of Fe 1,11, Ca 1,11, Mg 1, and Na 1; vibrational bands of the electronic transitions of TiO, MgH, CaH, SiH, AlH, Cn, Ch, C2, OH, and NH. The dependence of the wavelength 3740 Fe 1 blend and the wavelength 3440 depression on temperature is discussed

Bivariant long exact sequences II

Given a pair of short exact sequences 1) 0 → X → Y → Z → 0, 0 → A → B → C → 0 in an abelian category A, with sufficiently many projectives and injectives, and given an additive bifunctor T we show that T applied to the pair (1) gives rise to a diagram of a type described by C. T. C. Wall that contains 15 interlocking long exact sequences involving the derived functors of T at (A, X), (A, Y), etc. and also involving the derived functors of Tp and Tq which are two functors with domain A2 that arise through the failure of T to preserve pullbacks and pushouts. In the case of Hom (respectively ø) in the category of G-modules for a group G the derived functors of Tp (respectively Tq) are expressed in terms of group cohomology (respectively homology)

Harmonic Maa{\ss}-Jacobi forms of degree 1 with higher rank indices

We define and investigate real analytic weak Jacobi forms of degree 1 and arbitrary rank. En route we calculate the Casimir operator associated to the maximal central extension of the real Jacobi group, which for rank exceeding 1 is of order 4. In ranks exceeding 1, the notions of H-harmonicity and semi-holomorphicity are the same.Comment: 28 page

La velocidad del sistema δ Librae

In order to resolve the problem of the difference in the system of δ Librae as found when comparing observations made at Allegheny and at Michigan, all the available material, including the Mount Wilson material secured a few years ago and analyzed by two of the authors (J. Sahade and A .Hernández), was measured with the Grant line spectrum comparator of the Department of Astronomy of the Indiana University. When the measurements were reduced (they were made on only one direction of the carriage) it was found that there were systematic differences between the velocities from diffuse and from sharp lines. The latter are in keeping with the velocities obtained with the conventional type of comparators. The preliminary analysis of the results that are consistent suggest that the announced difference in the system velocity at two epochs has no significance and resulted only from the original method of measurement and reduction.Asociación Argentina de Astronomí

La velocidad del sistema δ Librae

In order to resolve the problem of the difference in the system of δ Librae as found when comparing observations made at Allegheny and at Michigan, all the available material, including the Mount Wilson material secured a few years ago and analyzed by two of the authors (J. Sahade and A .Hernández), was measured with the Grant line spectrum comparator of the Department of Astronomy of the Indiana University. When the measurements were reduced (they were made on only one direction of the carriage) it was found that there were systematic differences between the velocities from diffuse and from sharp lines. The latter are in keeping with the velocities obtained with the conventional type of comparators. The preliminary analysis of the results that are consistent suggest that the announced difference in the system velocity at two epochs has no significance and resulted only from the original method of measurement and reduction.Asociación Argentina de Astronomí

The two-square lemma

A new proof is given of the connecting homomorphism

La velocidad del sistema δ Librae

In order to resolve the problem of the difference in the system of δ Librae as found when comparing observations made at Allegheny and at Michigan, all the available material, including the Mount Wilson material secured a few years ago and analyzed by two of the authors (J. Sahade and A .Hernández), was measured with the Grant line spectrum comparator of the Department of Astronomy of the Indiana University. When the measurements were reduced (they were made on only one direction of the carriage) it was found that there were systematic differences between the velocities from diffuse and from sharp lines. The latter are in keeping with the velocities obtained with the conventional type of comparators. The preliminary analysis of the results that are consistent suggest that the announced difference in the system velocity at two epochs has no significance and resulted only from the original method of measurement and reduction.Asociación Argentina de Astronomí

Tribute

Tribute - In Memory of the Honorable Charles Clar

Response of Solid He-4 to External Stress: Interdigital Capacitor Solid Level Detector and Optical Interferometer

Two experiments are being conducted to observe the liquid/solid interface of He-4 near 1 K. Interesting instabilities are expected to occur when the solid is non-hydrostatically stressed. (1)A compact interdigital capacitor is used as a level detector to observe solid He-4 to which stresses are applied externally. The capacitor consists of 38 interlaced 50 m wide and 3.8 mm long gold films separated by 50 m and deposited onto a 5 mm by 5 mm sapphire substrate. The capacitor is placed on one flat end wall of a cylindrical chamber (xx mm diameter and xx mm long). The solid is grown to a known height and a stress is applied by a tubular PZT along the cylindrical axis. The observed small change in height of the solid at the wall is linearly proportional to the applied stress. The solid height decreases under compressive stress but does not change under tensile stress. The response of the solid on compressive stress is consistent with the expected quadratic dependence on strain. (2)Interferometric techniques are being developed for observing the solid He-4 surface profile. A laser light source is brought into the low temperature region via single mode optical fiber. The interference pattern is transmitted back out of the low temperature apparatus via optical fiber bundle. The solid He-4 growth chamber will be equipped with two PZT's such that stress can be applied from orthogonal directions. Orthogonally applied stress is expected to induce surface instability with island-like deformation on a grid pattern. Apparatus design and progress of its construction are described