Titanium-Oxygen Bond Length -Bond Valence Relationship

A bond length–bond valence correlation is a simple method of checking and evaluating molecular structures and is of great interest in chemistry, biology, geology, and material science. Recently, we used quantum-mechanical arguments to derive Pauling’s bond length-valence relationship and to define the adjustable fitting parameter b in terms of atomic-orbital exponents. Improved orbital exponents were generated for elements 1-103 using published atomic radii and single-bond covalent radii as well as a continuous function for effective principal quantum number. In this study, we use orbital exponents for titanium (Ti) and oxygen (O) to generate a bond length-valence relationship for Ti-O bonds. Recent crystallographic Ti-O bond lengths from 32 environments were collected and converted to Ti-O bond valences to check the reliability of the bond length-valence relationship where Ro was found (bond length of unit valence). This relationship is expected to apply to any Ti-O bond regardless of environment, physical state, or oxidation number

Gapless finite-TT theory of collective modes of a trapped gas

We present predictions for the frequencies of collective modes of trapped Bose-condensed $^{87}$Rb atoms at finite temperature. Our treatment includes a self-consistent treatment of the mean-field from finite-$T$ excitations and the anomolous average. This is the first gapless calculation of this type for a trapped Bose-Einstein condensed gas. The corrections quantitatively account for the downward shift in the $m=2$ excitation frequencies observed in recent experiments as the critical temperature is approached.Comment: 4 pages Latex and 2 postscript figure

Comparative Spectra of Oxygen-Rich vs. Carbon-Rich Circumstellar Shells: VY Canis Majoris and IRC+10216 at 215-285 GHz

A sensitive (1{\sigma} rms at 1 MHz resolution ~3 mK) 1 mm spectral line survey (214.5-285.5 GHz) of VY Canis Majoris (VY CMa) and IRC+10216 has been conducted to compare the chemistries of oxygen and carbon-rich circumstellar envelopes. This study was carried out using the Submillimeter Telescope (SMT) of the Arizona Radio Observatory (ARO) with a new ALMA-type receiver. This survey is the first to chemically characterize an O-rich circumstellar shell at millimeter wavelengths. In VY CMa, 128 emission features were detected arising from 18 different molecules, and in IRC+10216, 720 lines were observed, assigned to 32 different species. The 1 mm spectrum of VY CMa is dominated by SO2 and SiS; in IRC +10216, C4H and SiC2 are the most recurrent species. Ten molecules were common to both sources: CO, SiS, SiO, CS, CN, HCN, HNC, NaCl, PN, and HCO+. Sulfur plays an important role in VY CMa, but saturated/unsaturated carbon dominates the molecular content of IRC+10216, producing CH2NH, for example. Although the molecular complexity of IRC+10216 is greater, VY CMa supports a unique "inorganic" chemistry leading to the oxides PO, AlO, and AlOH. Only diatomic and triatomic compounds were observed in VY CMa, while species with 4 or more atoms are common in IRC+10216, reflecting carbon's ability to form strong multiple bonds, unlike oxygen. In VY CMa, a new water maser (v_2=2) has been found, as well as vibrationally-excited NaCl. Toward IRC+10216, vibrationally-excited CCH was detected for the first time.Comment: 21 pages, 3 figures, accepted for publication in Astrophysical Journal Letter

Quantized vortices and collective oscillations of a trapped Bose condensed gas

Using a sum rule approach we calculate the frequency shifts of the quadrupole oscillations of a harmonically trapped Bose gas due to the presence of a quantized vortex. Analytic results are obtained for positive scattering lengths and large N where the shift relative to excitations of opposite angular momentum is found to be proportional to the quantum circulation of the vortex and to decrease as N^{-2/5}. Results are also given for smaller values of N covering the transition between the ideal gas and the Thomas-Fermi limit. For negative scattering lengths we predict a macroscopic instability of the vortex. The splitting of the collective frequencies in toroidal configurations is also discussed.Comment: Rextex, 4 pages, 1 postscript figur

Internal Vortex Structure of a Trapped Spinor Bose-Einstein Condensate

The internal vortex structure of a trapped spin-1 Bose-Einstein condensate is investigated. It is shown that it has a variety of configurations depending on, in particular, the ratio of the relevant scattering lengths and the total magnetization.Comment: replacement; minor grammatical corrections but with additional figure

Bound and resonance states of the nonlinear Schroedinger equation in simple model systems

The stationary nonlinear Schroedinger equation, or Gross-Pitaevskii equation, is studied for the cases of a single delta potential and a delta-shell potential. These model systems allow analytical solutions, and thus provide useful insight into the features of stationary bound, scattering and resonance states of the nonlinear Schroedinger equation. For the single delta potential, the influence of the potential strength and the nonlinearity is studied as well as the transition from bound to scattering states. Furthermore, the properties of resonance states for a repulsive delta-shell potential are discussed.Comment: 19 pages, 10 figure

Psychopathology in Williams syndrome: the effect of individual differences across the lifespan

The present research aimed to comprehensively explore psychopathology in Williams syndrome (WS) across the lifespan and evaluate the relationship between psychopathology and age category (child or adult), gender and cognitive ability. The parents of 50 participants with WS, aged 6-50 years, were interviewed using the Schedule for Affective Disorders and Schizophrenia for School-Age Children (K-SADS-PL). The prevalence of a wide range of Axis I DSM-IV disorders was assessed. In addition to high rates of anxiety and Attention Deficit Hyperactivity Disorder (ADHD) (38% and 20% respectively), 14% of our sample met criteria for a depressive disorder and 42% of participants were not experiencing any significant psychopathological difficulties. There was some evidence for different patterns of psychopathology between children and adults with WS and between males and females. These relationships were largely in keeping with those found in the typically developing population, thus supporting the validity of applying theory and treatment approaches for psychopathology in the typically developing population to WS

The Retail FX Trader: Random Trading and the Negative Sum Game

With the internet boom of early 2000 making access to trading the Foreign Exchange (FX) market far simpler for members of the general public, the growth of 'retail' FX trading continues, with daily transaction volumes as high as $200 billion. Potential new entrants to the retail FX trading world may come from the recent UK pension deregulations, further increasing the volumes. The attraction of FX trading is that it offers high returns and whilst it has been understood that it is high-risk in nature, the rewards are seen as being commensurately high for the 'skilled and knowledgeable' trader who has an edge over other market participants. This paper analyses a number of independent sources of data and previous research, to examine the profitability of the Retail FX trader and compares the results with that of a simulated random trading models. This paper finds evidence to suggest that whilst approximately 20% of traders can expect to end up with a profitable account, around 40% might expect their account to be subject to a margin call. This paper finds a strong correlation between the overall profitability of traders and impact of the cost of the bid-ask spread, whilst finding little if any evidence that retail FX traders, when viewed as a group, are achieving results better than that from random trading

Temperature-Dependent Frequency Shifts in Collective Excitations of a Bose-Einstein Condensate

By including the contribution of the thermal cloud to the Lagrangian of the condensate of a Bose gas, we extend the time-dependent variational method at zero temperature to study temperature-dependent low collective excitation modes. A Gaussian trial wave function of the condensate and a static distribution density of the thermal cloud are used, and analytical expressions for temperature-dependent excitation frequencies obtained. Theoretical results are compared with measurements in the JILA and MIT experiments.Comment: 13 pages, RevTex, 2 EPS figure