Advanced turboprop vibratory characteristics

The assembly of SR5 advanced turboprop blades to develop a structural dynamic data base for swept props is reported. Steady state blade deformation under centrifugal loading and vibratory characteristics of the rotor assembly were measured. Vibration was induced through a system of piezoelectric crystals attached to the blades. Data reduction procedures are used to provide deformation, mode shape, and frequencies of the assembly at predetermined speeds

Monomial transformations of the projective space

We prove that, over any field, the dimension of the indeterminacy locus of a rational transformation $f$ of $P^n$ which is defined by monomials of the same degree $d$ with no common factors is at least $(n-2)/2$, provided that the degree of $f$ as a map is not divisible by $d$. This implies upper bounds on the multidegree of $f$

HAT-P-67b: An Extremely Low Density Saturn Transiting an F-subgiant Confirmed via Doppler Tomography

We report the discovery of HAT-P-67b, which is a hot-Saturn transiting a rapidly rotating F-subgiant. HAT-P-67b has a radius of R_p = 2.085^(+0.096)_(-0.071) R_J, and orbites a M* = 1.642^(+0.155)_(-0.072) M⊙, R* = 2.546^(+0.099)_(-0.084) R⊙ host star in a ~4.81 day period orbit. We place an upper limit on the mass of the planet via radial velocity measurements to be M_p 0.056 M_J by limitations on Roche lobe overflow. Despite being a subgiant, the host star still exhibits relatively rapid rotation, with a projected rotational velocity of ν sin I⋆ = 35.8 ± 1.1 km s^(-1), which makes it difficult to precisely determine the mass of the planet using radial velocities. We validated HAT-P-67b via two Doppler tomographic detections of the planetary transit, which eliminate potential eclipsing binary blend scenarios. The Doppler tomographic observations also confirm that HAT-P-67b has an orbit that is aligned to within 12°, in projection, with the spin of its host star. HAT-P-67b receives strong UV irradiation and is among one of the lowest density planets known, which makes it a good candidate for future UV transit observations in the search for an extended hydrogen exosphere

HATS-7b: A Hot Super Neptune Transiting a Quiet K Dwarf Star

We report the discovery by the HATSouth network of HATS-7b, a transiting Super-Neptune with a mass of 0.120 ± 0.012 M_J, a radius of 0.563_(-0.034)^(+0.046) R_J, and an orbital period of 3.1853 days. The host star is a moderately bright (V = 13.340 ± 0.010 mag, K_S = 10.976 ± 0.026 mag) K dwarf star with a mass of 0.849 ± 0.027 M_⊙, a radius of 0.815_(-0.035)^(+0.049) R_⊙, and a metallicity of [Fe/H] = + 0.250 ± 0.080. The star is photometrically quiet to within the precision of the HATSouth measurements, has low RV jitter, and shows no evidence for chromospheric activity in its spectrum. HATS-7b is the second smallest radius planet discovered by a wide-field ground-based transit survey, and one of only a handful of Neptune-size planets with mass and radius determined to 10% precision. Theoretical modeling of HATS-7b yields a hydrogen–helium fraction of 18 ± 4% (rock-iron core and H_2–He envelope), or 9 ± 4% (ice core and H_2–He envelope), i.e., it has a composition broadly similar to that of Uranus and Neptune, and very different from that of Saturn, which has 75% of its mass in H_2–He. Based on a sample of transiting exoplanets with accurately (<20%) determined parameters, we establish approximate power-law relations for the envelopes of the mass–density distribution of exoplanets. HATS-7b, which, together with the recently discovered HATS-8b, is one of the first two transiting super-Neptunes discovered in the Southern sky, is a prime target for additional follow-up observations with Southern hemisphere facilities to characterize the atmospheres of Super-Neptunes (which we define as objects with mass greater than that of Neptune, and smaller than halfway between that of Neptune and Saturn, i.e., 0.054 M_J < M_p < 0.18 M_J)

Implications of non-feasible transformations among icosahedral hh orbitals

The symmetric group $S_6$ that permutes the six five-fold axes of an icosahedron is introduced to go beyond the simple rotations that constitute the icosahedral group $I$. Owing to the correspondence $h\leftrightarrow d$, the calculation of the Coulomb energies for the icosahedral configurations $h^N$ based on the sequence $O(5) \supset S_6 \supset S_5 \supset I$ can be brought to bear on Racah's classic theory for the atomic d shell based on $SO(5) \supset SO_L(3) \supset I$. Among the elements of $S_6$ is the kaleidoscope operator ${\cal K}$ that rotates the weight space of SO(5) by $\pi/2$. Its use explains some puzzling degeneracies in d^3 involving the spectroscopic terms ^2P, ^2F, ^2G and ^2H.Comment: Tentatively scheduled to appear in Physical Preview Letters Apr 5, 99. Revtex, 1 ps figur

Grothendieck groups and a categorification of additive invariants

A topologically-invariant and additive homology class is mostly not a natural transformation as it is. In this paper we discuss turning such a homology class into a natural transformation; i.e., a "categorification" of it. In a general categorical set-up we introduce a generalized relative Grothendieck group from a cospan of functors of categories and also consider a categorification of additive invariants on objects. As an example, we obtain a general theory of characteristic homology classes of singular varieties.Comment: 27 pages, to appear in International J. Mathematic

Coulomb Blockade and Coherent Single-Cooper-Pair Tunneling in Single Josephson Junctions

We have measured the current-voltage characteristics of small-capacitance single Josephson junctions at low temperatures (T < 0.04 K), where the strength of the coupling between the single junction and the electromagnetic environment was controlled with one-dimensional arrays of dc SQUIDs. We have clearly observed Coulomb blockade of Cooper-pair tunneling and even a region of negative differential resistance, when the zero-bias resistance of the SQUID arrays is much higher than the quantum resistance h/e^2 = 26 kohm. The negative differential resistance is evidence of coherent single-Cooper-pair tunneling in the single Josephson junction.Comment: RevTeX, 4 pages with 6 embedded figure

HAT-P-67b: An Extremely Low Density Saturn Transiting an F-subgiant Confirmed via Doppler Tomography

We report the discovery of HAT-P-67b, which is a hot-Saturn transiting a rapidly rotating F-subgiant. HAT-P-67b has a radius of R_p = 2.085^(+0.096)_(-0.071) R_J, and orbites a M* = 1.642^(+0.155)_(-0.072) M⊙, R* = 2.546^(+0.099)_(-0.084) R⊙ host star in a ~4.81 day period orbit. We place an upper limit on the mass of the planet via radial velocity measurements to be M_p 0.056 M_J by limitations on Roche lobe overflow. Despite being a subgiant, the host star still exhibits relatively rapid rotation, with a projected rotational velocity of ν sin I⋆ = 35.8 ± 1.1 km s^(-1), which makes it difficult to precisely determine the mass of the planet using radial velocities. We validated HAT-P-67b via two Doppler tomographic detections of the planetary transit, which eliminate potential eclipsing binary blend scenarios. The Doppler tomographic observations also confirm that HAT-P-67b has an orbit that is aligned to within 12°, in projection, with the spin of its host star. HAT-P-67b receives strong UV irradiation and is among one of the lowest density planets known, which makes it a good candidate for future UV transit observations in the search for an extended hydrogen exosphere