A note on the Landau constants

In this paper we establish new asymptotic expansions for the nth Landau constant G_n. An open problem is indicated as well.     

New asymptotic expansion for the Gamma function

Using a series transformation, the Stirling-De Moivre asymptotic series approximation to the Gamma function is converted into a new one with better convergence properties. The new formula is being compared with those of Stirling, Laplace, and Ramanujan for real arguments greater than 0.5 and turns out to be, for equal number of “correction” terms, numerically superior to all of them. As a side benefit, a closed-form approximation has turned up during the analysis which is about as good as 3rd order Stirling’s (maximum relative error smaller than 1e − 10 for real arguments greater or equal to 24).     

Ablation and analysis of small cell populations and single cells by consecutive laser pulses

Laser ablation of single cells through a sharpened optical fiber is used for the detection of metabolites by laser ablation electrospray ionization (LAESI) mass spectrometry (MS). Ablation of the same Allium cepa epidermal cell by consecutive pulses indicates the rupture of the cell wall by the second shot. Intracellular sucrose heterogeneity is detected by subsequent laser pulses pointing to rupturing the vacuolar membrane by the third exposure. Ion production by bursts of laser pulses shows that the drying of ruptured A. cepa cells occurs in ∼50 s at low pulse rates (10 pulses/s bursts) and significantly faster at high pulse rates (100 pulses/s bursts). These results point to the competing role of cytoplasm ejection and evaporative drying in diminishing the LAESI-MS signal in ∼50 s or 100 laser pulses, whichever occurs first.     

Asymptotic expansion for log <Emphasis Type="Italic">n</Emphasis>! in terms of the reciprocal of a triangular number

Ramanujan suggested an expansion for the nth partial sum of the harmonic series which employs the reciprocal of the nth triangular number. This has been proved in 2006 by Villarino, who speculated that there might also exist a similar expansion for the logarithm of the factorial. This study shows that such an asymptotic expansion indeed exists and provides formulas for its generic coefficient and for the bounds on its errors.     

On the Casimir energy for a massive quantum scalar field and the cosmological constant

We present a rigorous, regularization-independent local quantum field theoretic treatment of the Casimir effect for a quantum scalar field of mass μ≠0 which yields closed form expressions for the energy density and pressure. As an application we show that there exist special states of the quantum field in which the expectation value of the renormalized energy–momentum tensor is, for any fixed time, independent of the space coordinate and of the perfect fluid form g_μ,νρ with ρ>0, thus providing a concrete quantum field theoretic model of the cosmological constant. This ρ represents the energy density associated to a state consisting of the vacuum and a certain number of excitations of zero momentum, i.e., the constituents correspond to lowest energy and pressure p0.     

Rotation-vibration analysis of the Coriolis-coupled ν5g, ν6g, ν8g and ν9 bands of H2CCO

Medium resolution infrared grating spectra of gaseous ketene, H₂CCO were recorded between 1000 and 400 cm^?1, both at instrument temperature (40°C) and with cooling (?40°C). Interferometric Fourier spectra were also measured at ?70°C with resolution 0.22 cm^?1 between 450 and 330 cm^?1. The K structure of the fundamentals ν₅, ν₆, ν₈, and ν₉ was assigned. These fundamentals are coupled by a-axis Coriolis interactions. These couplings were analysed on the symmetric top basis for setting up the perturbation matrix and by utilizing the K-dependent Coriolis shifts of levels. A preliminary analysis of the Coriolis intensity anomalies was also undertaken.Band center values from combination differences are $\text{ν}{}_5{}^0\text{= 587.30 (27)}$ and $\text{ν}{}_6{}^0\text{= 528.36 (39)}\text{cm}{}^{\mathrm{?1}}$. Synthetic spectra indicate the band origins of ν₈ and ν₉ to be close to 977.8 and 439.0 cm^?1, respectively. Estimates of Coriolis coupling constants obtained from synthetic spectra are $\text{ζ}{}_{58}{}^{\mathrm{a}}\text{= + 0.33 (5)}$, $\text{ζ}{}_{68}{}^{\mathrm{a}}\text{= + 0.714 (20)}$, $\text{ζ}{}_{59}{}^{\mathrm{a}}\text{= ? 0.774 (20)}$, and $\text{ζ}{}_{69}{}^{\mathrm{a}}\text{= ? 0.30 (2)}$. Approximate ratios of unperturbed vibrational transition moments obtained from spectral simulations are $\text{M}{}_8{}^0\text{:±iM}{}_5{}^0\text{:±iM}{}_6{}^0\text{:M}{}_9{}^0\text{≈ +2:?9:+10:+0.5}$.     

Monte Carlo simulation of carbon fragmentation at high energies

The dominating decay channels of fragmenting carbon nuclei in high-energy proton-carbon collisions were studied by means of a Monte Carlo simulation. We study the influence of the Coulomb interaction on the energy spectra and two-fragment (energy and angular) correlations between the various fragments in the context of a statistical model. We show that the Coulomb interaction between the fragments strongly affects their energy and angular correlation functions. Qualitative predictions for the exclusive analysis of the various final states are given. Comparison with experiments of this type should soon be possible.     

Collisional spreading of small amplitude nuclear vibrations

We present a microscopic treatment of the spreading widths of giant resonances — a collisional RPA (with complex frequencies,z=iω+γ) which turns out to have a very simple analytical form. Its essential ingredients are:a) The usual mean field contribution, which reproduces the frequencies of the collisionless RPA andb) non-unitary (collision) contributions which arise from the inclusion of quantum correlation effects in the weak coupling approximation. This collisional RPA equation can be easily put to quantitative use in realistic nuclear structure problems.     

A new validated high-performance liquid chromatographic method for the determination of EGIS-9933 in rat plasma

Summary A new highly sensitive high-performance liquid chromatographic (HPLC) procedure for determination of EGIS-9933 (a newly developed anxiolytic compound) in rat plasma is described. A gradient, elution method with UV detection at 270 nm has been developed using a mobile phase of a mixture of A: methanol:acetonitrile 1:9 and B:0.5% triethilamine in water, the pH of B was adjusted to 3 with phosphoric acid. Solid phase extraction (SPE) was used for the sample preparation. The calibration was linear in the 10–10000 ng mL⁻¹ concentration range. The limit of quantification was 10 ng mL⁻¹. The bioanalytical method was validated according to internationally accepted criteria for biological samples. Presented at: Balaton Symposium on High-Performance Separation Methods, Siófok, Hungary, September 3–5, 1997.