Flame spectroscopy of TiO: Radiative lifetimes and oscillator strengths of the α (C3Δ-X3Δ) system

Lifetimes of the C³Δ state of TiO have been measured for vibrational levels v′ = 0 to 2 from the decay of photoluminescence excited in a chemiluminescent flame by a short-pulsed (5 nsec) tunable dye laser. Radiative lifetimes of τ_v′=0 = 37 ± 9 nsec, τ_v′=1 = 29 ± 7 nsec, τ_v′=2 = 28 ± 7 nsec were obtained and were used to estimate oscillator strengths which were found to be in good agreement with earlier values based on intensity measurements.     

Riesz transforms on a solvable Lie group of polynomial growth

We study Riesz transforms associated with a sublaplacian H on a solvable Lie group G, where G has polynomial volume growth. It is known that the standard second order Riesz transforms corresponding to H are generally unbounded in L^p(G). In this paper, we establish boundedness in L^p for modified second order Riesz transforms, which are defined using derivatives on a nilpotent group G_N associated with G. Our method utilizes a new algebraic approach which associates a distinguished choice of Cartan subalgebra with the sublaplacian H. We also obtain estimates for higher derivatives of the heat kernel of H, and give a new proof (without the use of homogenization theory) of the boundedness of first order Riesz transforms. Our results can be generalized to an arbitrary (possibly non-solvable) Lie group of polynomial growth.     

Electronic states of the CeO molecule: Absorption,emission, and laser spectroscopy

The electronic spectrum of the CeO molecule is characterized by the existence of many 0-0 bands resulting from transitions between various Ω components of excited states and the 16 lower Ω states which arise from the lowest configuration… (4f)(6s). Classical studies of rotational structure of absorption and emission spectra have been extended, and argon-ion and tunable dye (coumarin 460, rhodamine 6G, rhodamine 101) lasers have been used to excite known transitions in bands which had previously been rotationally analyzed. The resulting fluorescence spectra have been used to establish the relative energies of the lower states. By tuning the lasers to excite analyzed transitions from different known electronic states it has been possible to determine the energies of 16 low-lying states, to assign quantum numbers to 14 with certainty, and to suggest assignments for the other 2. The resulting energy level diagram of lower states is discussed and shown to correlate well with the 4f6s configuration of the Ce²⁺ ion. From the energies of the low-lying states, those of the higher excited states are calculated and in some cases new values of vibrational and rotational constants are derived.     

Examination of two new low-lying electronic states of SiS observed in chemiluminescent flame spectra

Diatomic silicon sulfide molecules have been produced in the chemiluminescent reaction of silicon atoms with OCS. Spectra of the resulting flame consist mainly of two new band systems in the region 350–400 and 385–600 nm. These systems have been assigned as b ³Π_r-X ¹Σ⁺ and a ³Σ⁺-X ¹Σ⁺ on the basis of band structure, spin-orbit splitting, molecular constants, and comparison with chemiluminescent spectra of isovalent molecules. Vibrational assignments were made with the help of the isotope effect and vibrational constants were obtained. Rotational structure was observed in some a-X bands and a partial analysis yielded an approximate rotational constant, B 0.247 ± 0.007 cm⁻¹, for the a ³Σ⁺ state. Franck-Condon factors, calculated for the a-X system, are shown to fit the general trend of the intensity distribution. Irregularities in spin-orbit splitting and in relative intensities of the spin-orbit components of the b ³Π-X ¹Σ⁺ system were observed and an attempt is made to explain them in terms of interactions with neighboring states. Addition of active nitrogen to the flame was shown to greatly increase the intensity of the b-X system relative to the a-X system. Constants (in cm⁻¹) obtained for the new state are: a³σ⁺: T_e=24 582.1 ± 1.3, ω_e=503.8±1.0, ω_ex_e=1.86±0.21b³σ⁺: T_e=27 314.5 ± 2.2, ω_e=619.4±2.0, ω_ex_e=5.75±0.52b³σ⁺: T_e=27 407.9 ± 1.1, ω_e=524.3±1.2, ω_ex_e=3.97±0.28     

Coal Handleability — A good or a bad coal?

The avalanching behaviour of two coal types was determined, one of good and the other of poor handleability characteristics. This revealed significant differences in the nature of flow of the coals. Analysis of the strange attractors of the weight series of avalanches enabled quanitification of this difference, and the establishment of practical, relative criteria for the measurement of coal handleability. These criteria will now enable a structured study of the variables that affect handleability, for example proportion of fines and moisture content, and industrial consumers of coal to specify minimum acceptable limits for its transport characteristics.     

Testing set proportionality and the Ádám isomorphism of circulant graphs

Given two k element subsets , we give a quasi-linear algorithm to either find such that S=λT or prove that no such λ exists.This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature.     

Comments on ultra-high-energy photons and D-foam models

We revisit the constraints that the non-observation of ultra-high-energy photons due to the GZK cutoff can impose on models of Lorentz violation in photon propagation, following recent work by Maccione, Liberati and Sigl (2010) [arXiv:1003.5468] that carries further an earlier analysis by the present authors [J. Ellis et al., Phys. Rev. D 63 (2001) 12402, hep-th/0012216]. We argue that the GZK cutoff constraint is naturally evaded in the D-brane model of space–time foam presented recently by the present authors [J. Ellis et al., Phys. Lett. B 665 (2008) 412, arXiv:0804.3566], in which Lorentz-violating effects on photon propagation are independent of possible effects during interactions. We also note a novel absorption mechanism that could provide a GZK-like cutoff for photons in low-scale string models.     

A high resolution visible spectrum of iridium monophosphide

Laser induced fluorescence spectra of iridium monophosphide, IrP, have been obtained at low and high resolution in the blue region of the visible spectrum. Two electronic transitions were observed with origins near 459.6 and 471.9 nm. Three vibronic bands in each of these transitions have been observed at high resolution allowing for full characterization of the states. A J-independent doubling of the rotational lines has been ascribed to nuclear electric quadrupole coupling in the ground state. Multireference configuration interaction (MRCI) calculations have been performed in order to confirm the nature of the ground state and aid in the assignment of the excited states. The two observed transitions have been assigned as the [21.7]¹Σ⁺-X¹Σ⁺ and the [21.2] ³Σ⁺-X¹Σ⁺ electronic systems based on comparison with the theoretical calculations. The v + 2 level of each of these electronic transitions was found to be heavily perturbed and a successful deperturbation analysis was performed allowing for a complete global fit of the data.     

Gaiotto’s Lagrangian Subvarieties via Derived Symplectic Geometry

Let Bun_G be the moduli space of G-bundles on a smooth complex projective curve. Motivated by a study of boundary conditions in mirror symmetry, Gaiotto (2016) associated to any symplectic representation of G a Lagrangian subvariety of T^?Bun_G. We give a simple interpretation of (a generalization of) Gaiotto’s construction in terms of derived symplectic geometry. This allows to consider a more general setting where symplectic G-representations are replaced by arbitrary symplectic manifolds equipped with a Hamiltonian G-action and with an action of the multiplicative group that rescales the symplectic form with positive weight.     

Second-Order Optimality and Beyond: Characterization and Evaluation Complexity in Convexly Constrained Nonlinear Optimization

High-order optimality conditions for convexly constrained nonlinear optimization problems are analysed. A corresponding (expensive) measure of criticality for arbitrary order is proposed and extended to define high-order \(\epsilon \)-approximate critical points. This new measure is then used within a conceptual trust-region algorithm to show that if derivatives of the objective function up to order \(q \ge 1\) can be evaluated and are Lipschitz continuous, then this algorithm applied to the convexly constrained problem needs at most \(O(\epsilon ^{-(q+1)})\) evaluations of f and its derivatives to compute an \(\epsilon \)-approximate qth-order critical point. This provides the first evaluation complexity result for critical points of arbitrary order in nonlinear optimization. An example is discussed, showing that the obtained evaluation complexity bounds are essentially sharp.