Lattice-point enumerators of ellipsoids

Minkowski's second theorem on successive minima asserts that the volume of a 0-symmetric convex body K over the covolume of a lattice \Lambda can be bounded above by a quantity involving all the successive minima of K with respect to \Lambda. We will prove here that the number of lattice points inside K can also accept an upper bound of roughly the same size, in the special case where K is an ellipsoid. Whether this is also true for all K unconditionally is an open problem, but there is reasonable hope that the inductive approach used for ellipsoids could be extended to all cases.Comment: 9 page

Audio vs. Video: Does Viewing Support Learning? A Comparision of an Audio-Visual with an Auditory Virtual Lecture

Häufig wird behauptet, dass audiovisuelle Informationen gegenüber auditiven lernwirksamer sind. Dies wird meist mit der kognitiv-anregenden Funktion begründet, die der audiovisuellen Darstellung zugeschrieben wird. Bisherige empirische Arbeiten konnten das auch tendenziell bestätigen; allerdings beziehen sich diese Befunde überwiegend auf das video- oder fernsehgestützte Lernen, bei dem den Lernenden keine zusätzlichen textbasierten Informationen zur Verfügung stehen. Für den Bereich der virtuellen Vorlesung wurde noch nicht untersucht, ob sich eine audiovisuelle Präsentation des Vortragenden gegenüber einer rein auditiven Präsentation positiv auf den Lernerfolg auswirkt. In einer empirischen Studie mit 61 Versuchspersonen wurde daher Lernenden ein Ausschnitt aus einer Online-Vorlesung in zwei Variationen präsentiert. Während die eine Gruppe eine Lerneinheit bearbeitete, in der sie neben textbasierten Informationen eine Videosequenz (Aufnahme des Dozenten) präsentiert bekam, bearbeitete die zweite Gruppe die gleiche Lerneinheit; hier war jedoch nur die Stimme des Dozenten hörbar. In einem direkt anschließenden Wissens- und späteren Behaltenstest zeigten sich keine signifikanten Leistungsunterschiede zwischen den beiden Gruppen. Jedoch berichtete die Mehrheit der Versuchspersonen, dass sie die Videovariante für affektiv-unterstützender hält als die Tonvariante. (ZPID

Cavity Heating Experiments Supporting Shuttle Columbia Accident Investigation

The two-color thermographic phosphor method has been used to map the local heating augmentation of scaled idealized cavities at conditions simulating the windward surface of the Shuttle Orbiter Columbia during flight STS-107. Two experiments initiated in support of the Columbia Accident Investigation were conducted in the Langley 20-Inch Mach 6 Tunnel. Generally, the first test series evaluated open (length-to-depth less than 10) rectangular cavity geometries proposed as possible damage scenarios resulting from foam and ice impact during launch at several discrete locations on the vehicle windward surface, though some closed (length-to-depth greater than 13) geometries were briefly examined. The second test series was designed to parametrically evaluate heating augmentation in closed rectangular cavities. The tests were conducted under laminar cavity entry conditions over a range of local boundary layer edge-flow parameters typical of re-entry. Cavity design parameters were developed using laminar computational predictions, while the experimental boundary layer state conditions were inferred from the heating measurements. An analysis of the aeroheating caused by cavities allowed exclusion of non-breeching damage from the possible loss scenarios being considered during the investigation

Q-value of the superallowed beta decay of Ga-62

Masses of the radioactive isotopes 62Ga, 62Zn and 62Cu have been measured at the JYFLTRAP facility with a relative precision of better than 18 ppb. A Q_EC value of (9181.07 +- 0.54) keV for the superallowed decay of 62Ga is obtained from the measured cyclotron frequency ratios of 62Ga-62Zn, 62Ga-62Ni and 62Zn-62Ni ions. The resulting Ft-value supports the validity of the conserved vector current hypothesis (CVC). The mass excess values measured were (-51986.5 +-1.0) keV for 62Ga, (-61167.9 +- 0.9) keV for 62Zn and (-62787.2 +- 0.9) keV for 62Cu.Comment: 12 pages, 3 figures, 2 tables, submitted to Phys. Lett. B. v2: added acknowledgement

Recent direct reaction experimental studies with radioactive tin beams

Direct reaction techniques are powerful tools to study the single-particle nature of nuclei. Performing direct reactions on short-lived nuclei requires radioactive ion beams produced either via fragmentation or the Isotope Separation OnLine (ISOL) method. Some of the most interesting regions to study with direct reactions are close to the magic numbers where changes in shell structure can be tracked. These changes can impact the final abundances of explosive nucleosynthesis. The structure of the chain of tin isotopes is strongly influenced by the Z=50 proton shell closure, as well as the neutron shell closures lying in the neutron-rich, N=82, and neutron-deficient, N=50, regions. Here we present two examples of direct reactions on exotic tin isotopes. The first uses a one-neutron transfer reaction and a low-energy reaccelerated ISOL beam to study states in 131Sn from across the N=82 shell closure. The second example utilizes a one-neutron knockout reaction on fragmentation beams of neutron-deficient 106,108Sn. In both cases, measurements of gamma rays in coincidence with charged particles proved to be invaluable.Comment: 11 pages, 5 figures, Zakopane Conference on Nuclear Physics "Extremes of the Nuclear Landscape", Zakopane, Poland, August 31 - September 7, 201

Beta-decay branching ratios of 62Ga

Beta-decay branching ratios of 62Ga have been measured at the IGISOL facility of the Accelerator Laboratory of the University of Jyvaskyla. 62Ga is one of the heavier Tz = 0, 0+ -> 0+ beta-emitting nuclides used to determine the vector coupling constant of the weak interaction and the Vud quark-mixing matrix element. For part of the experimental studies presented here, the JYFLTRAP facility has been employed to prepare isotopically pure beams of 62Ga. The branching ratio obtained, BR= 99.893(24)%, for the super-allowed branch is in agreement with previous measurements and allows to determine the ft value and the universal Ft value for the super-allowed beta decay of 62Ga

Impact of the assimilation of ozone from the Tropospheric Emission Spectrometer on surface ozone across North America

We examine the impact of assimilating ozone observations from the Tropospheric Emission Spectrometer (TES) on North American surface ozone abundances in the GEOS-Chem model in August 2006. The assimilation reduces the negative bias in the modeled free tropospheric ozone, which enhances the ozone flux into the boundary layer. Surface ozone abundances increased by as much as 9 ppb in western North America and by less than 2 ppb in the southeast, resulting in a total background source of ozone of 20-40 ppb. The enhanced ozone in the model reduced the model bias with respect to surface ozone observations in the western USA, but exacerbated it in the east. This increase in the bias in the boundary layer in the east, despite the agreement between the assimilation and ozonesonde measurements in the free troposphere, suggests errors in the ozone sources or sinks or in boundary layer mixing in the model. © 2009

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

On positivity of Ehrhart polynomials

Ehrhart discovered that the function that counts the number of lattice points in dilations of an integral polytope is a polynomial. We call the coefficients of this polynomial Ehrhart coefficients, and say a polytope is Ehrhart positive if all Ehrhart coefficients are positive (which is not true for all integral polytopes). The main purpose of this article is to survey interesting families of polytopes that are known to be Ehrhart positive and discuss the reasons from which their Ehrhart positivity follows. We also include examples of polytopes that have negative Ehrhart coefficients and polytopes that are conjectured to be Ehrhart positive, as well as pose a few relevant questions.Comment: 40 pages, 7 figures. To appear in in Recent Trends in Algebraic Combinatorics, a volume of the Association for Women in Mathematics Series, Springer International Publishin

Reactions of a Be-10 beam on proton and deuteron targets

The extraction of detailed nuclear structure information from transfer reactions requires reliable, well-normalized data as well as optical potentials and a theoretical framework demonstrated to work well in the relevant mass and beam energy ranges. It is rare that the theoretical ingredients can be tested well for exotic nuclei owing to the paucity of data. The halo nucleus Be-11 has been examined through the 10Be(d,p) reaction in inverse kinematics at equivalent deuteron energies of 12,15,18, and 21.4 MeV. Elastic scattering of Be-10 on protons was used to select optical potentials for the analysis of the transfer data. Additionally, data from the elastic and inelastic scattering of Be-10 on deuterons was used to fit optical potentials at the four measured energies. Transfers to the two bound states and the first resonance in Be-11 were analyzed using the Finite Range ADiabatic Wave Approximation (FR-ADWA). Consistent values of the spectroscopic factor of both the ground and first excited states were extracted from the four measurements, with average values of 0.71(5) and 0.62(4) respectively. The calculations for transfer to the first resonance were found to be sensitive to the size of the energy bin used and therefore could not be used to extract a spectroscopic factor.Comment: 16 Pages, 10 figure