Families of spectral sets for Bernoulli convolutions

In this paper, we study the harmonic analysis of Bernoulli measures. We show a variety of orthonormal Fourier bases for the L^2 Hilbert spaces corresponding to certain Bernoulli measures, making use of contractive transfer operators. For other cases, we exhibit maximal Fourier families that are not orthonormal bases.Comment: 25 pages, same result

Additive spectra of the 1/4 Cantor measure

In this paper, we add to the characterization of the Fourier spectra for Bernoulli convolution measures. These measures are supported on Cantor subsets of the line. We prove that performing an odd additive translation to half the canonical spectrum for the 1/4 Cantor measure always yields an alternate spectrum. We call this set an additive spectrum. The proof works by connecting the additive set to a spectrum formed by odd multiplicative scaling.Comment: 9 pages, 1 figur

Laser radiation pressure slowing of a molecular beam

There is substantial interest in producing samples of ultracold molecules for possible applications in quantum computation, quantum simulation of condensed matter systems, precision measurements, controlled chemistry, and high precision spectroscopy. A crucial step to obtaining large samples of ultracold, trapped molecules is developing a means to bridge the gap between typical molecular source velocities (~150-600 m/s) and velocities for which trap loading or confinement is possible (~5-20 m/s). Here we show deceleration of a beam of neutral strontium monofluoride (SrF) molecules using radiative force. Under certain conditions, the deceleration results in a substantial flux of molecules with velocities <50 m/s. The observed slowing, from ~140 m/s, corresponds to scattering ~10000 photons. We also observe longitudinal velocity compression under different conditions. Combined with molecular laser cooling techniques, this lays the groundwork to create slow and cold molecular beams suitable for trap loading.Comment: 7 pages, 7 figures. Supplementary material updated

Scaling by 5 on a 1/4-Cantor Measure

Each Cantor measure (\mu) with scaling factor 1/(2n) has at least one associated orthonormal basis of exponential functions (ONB) for L^2(\mu). In the particular case where the scaling constant for the Cantor measure is 1/4 and two specific ONBs are selected for L^2(\mu), there is a unitary operator U defined by mapping one ONB to the other. This paper focuses on the case in which one ONB (\Gamma) is the original Jorgensen-Pedersen ONB for the Cantor measure (\mu) and the other ONB is is 5\Gamma. The main theorem of the paper states that the corresponding operator U is ergodic in the sense that only the constant functions are fixed by U.Comment: 34 page

The weight-inclusive vs. weight-normative approach to health: Evaluating the evidence for prioritizing well-being over weight

Using an ethical lens, this review evaluates two methods of working within patient care and public health: the weight-normative approach (emphasis on weight and weight loss when defining health and well-being) and the weight-inclusive approach (emphasis on viewing health and well-being as multifaceted while directing efforts toward improving health access and reducing weight stigma). Data reveal that the weight-normative approach is not effective for most people because of high rates of weight regain and cycling from weight loss interventions, which are linked to adverse health and well-being. Its predominant focus on weight may also foster stigma in health care and society, and data show that weight stigma is also linked to adverse health and well-being. In contrast, data support a weight-inclusive approach, which is included in models such as Health at Every Size for improving physical (e.g., blood pressure), behavioral (e.g., binge eating), and psychological (e.g., depression) indices, as well as acceptability of public health messages. Therefore, the weight-inclusive approach upholds nonmaleficience and beneficience, whereas the weight-normative approach does not. We offer a theoretical framework that organizes the research included in this review and discuss how it can guide research efforts and help health professionals intervene with their patients and community

Franck-Condon Factors and Radiative Lifetime of the A^{2}\Pi_{1/2} - X^{2}\Sigma^{+} Transition of Ytterbium Monoflouride, YbF

The fluorescence spectrum resulting from laser excitation of the A^{2}\Pi_{1/2} - X^{2}\Sigma^{+} (0,0) band of ytterbium monofluoride, YbF, has been recorded and analyzed to determine the Franck-Condon factors. The measured values are compared with those predicted from Rydberg-Klein-Rees (RKR) potential energy curves. From the fluorescence decay curve the radiative lifetime of the A^{2}\Pi_{1/2} state is measured to be 28\pm2 ns, and the corresponding transition dipole moment is 4.39\pm0.16 D. The implications for laser cooling YbF are discussed.Comment: 5 pages, 5 figure

Reactions of C+ + Cl-, Br-, and I--A comparison of theory and experiment.

Rate constants for the reactions of C+ + Cl-, Br-, and I- were measured at 300 K using the variable electron and neutral density electron attachment mass spectrometry technique in a flowing afterglow Langmuir probe apparatus. Upper bounds of &lt;10-8 cm3 s-1 were found for the reaction of C+ with Br- and I-, and a rate constant of 4.2 ± 1.1 × 10-9 cm3 s-1 was measured for the reaction with Cl-. The C+ + Cl- mutual neutralization reaction was studied theoretically from first principles, and a rate constant of 3.9 × 10-10 cm3 s-1, an order of magnitude smaller than experiment, was obtained with spin-orbit interactions included using a semiempirical model. The discrepancy between the measured and calculated rate constants could be explained by the fact that in the experiment, the total loss of C+ ions was measured, while the theoretical treatment did not include the associative ionization channel. The charge transfer was found to take place at small internuclear distances, and the spin-orbit interaction was found to have a minor effect on the rate constant

Two wheeled lunar dumptruck

The design of a two wheel bulk material transport vehicle is described in detail. The design consists of a modified cylindrical bowl, two independently controlled direct drive motors, and two deformable wheels. The bowl has a carrying capacity of 2.8 m (100 ft) and is constructed of aluminum. The low speed, high HP motors are directly connected to the wheels, thus yielding only two moving parts. The wheels, specifically designed for lunar applications, utilize the chevron tread pattern for optimum traction. The vehicle is maneuvered by varying the relative angular velocities of the wheels. The bulk material being transported is unloaded by utilizing the motors to oscillate the bowl back and forth to a height at which dumping is achieved. The analytical models were tested using a scaled prototype of the lunar transport vehicle. The experimental data correlated well with theoretical predictions. Thus, the design established provides a feasible alternative for the handling of bulk material on the moon

Tectonically controlled subglacial lakes on the flanks of the Gamburtsev Subglacial Mountains, East Antarctica

The morphology of surface lakes strongly influences their ecology and limnology (Wetzel, 2001). This morphology is a result of both the geologic processes that produce topographic basins and the regional climatic and local hydrologic processes that control water depth and sediment infilling (Carroll and Bohacs, 1999). Although basin forming processes range from glacial scour to meteorite impacts (Cohen, 2003), the deepest, oldest surface lakes are tectonically controlled (Meybeck, 1995) and contain diverse exotic ecosystems (Rossiterm and Kawanabe, 2000). Subglacial lakes are also thought to be ancient systems that may contain exotic biota (Bulat et al., 2004; Karl et al., 1999; Priscu et al., 1999). Here we present evidence for the scale and configuration of 2 large subglacial lakes in East Antarctica that together with Lake Vostok define a province of major lakes on the flanks of the Gamburtsev Subglacial Mountains. Spatially-defined in the new Moderate Resolution Imaging Spectroradiometer (MODIS) imagery of Antarctica (T. Scambos et al., A MODIS-based mosaic of Antarctica: MOA, submitted to Remote Sensing of Environment, 2005, hereinafter referred to as Scambos et al., submitted manuscript, 2005), these lakes are aligned parallel to Lake Vostok. Other data shows that they are distinguished by distinct gravity lows, flat ice surface slopes and have estimated water depths of at least 900 m. Surface elevation data indicates that large deep subglacial lakes have a profound influence on the regional ice sheet topography and probably ice sheet flow. These deep subglacial lakes with elongate, rectilinear morphology are tectonically controlled features. Unlike the shallow lakes in West Antarctica and beneath Dome Concordia, these deep subglacial lakes remained stable environments through many glacial cycles since their origin 10-35 Ma enabling the development of novel ecosystems