Bounds for the logarithm of the Euler gamma function and its derivatives

We consider differences between $\log \Gamma(x)$ and truncations of certain classical asymptotic expansions in inverse powers of $x-\lambda$ whose coefficients are expressed in terms of Bernoulli polynomials $B_n(\lambda)$, and we obtain conditions under which these differences are strictly completely monotonic. In the symmetric cases $\lambda=0$ and $\lambda=1/2$, we recover results of Sonin, N\"orlund and Alzer. Also we show how to derive these asymptotic expansions using the functional equation of the logarithmic derivative of the Euler gamma function, the representation of $1/x$ as a difference $F(x+1)-F(x)$, and a backward induction.Comment: 15 page

Degradation of Fe-Mg silicates in hot CO2 atmospheres: Applications to Venus

Experiments demonstrated that oxidation of ferromagnesian silicates and magnetite occurs when these minerals are heated at 800 C in 1 atmosphere of CO2, under which conditions hematite is thermodynamically stable. The 30 ppm oxygen impurity in CO2 presumably facilitates the oxidation of some of the ferrous iron initially present in the crystal structures of the minerals. Mossbauer spectral measurements reveal, however, that only CO2 degraded olivine and pigeonite is hematite formed as a magnetically ordered phase at ambient temperatures. In orthopyroxene, some of the ferric iron produced by oxidation is present as nanophase hematite which, because it remains superparamagnetic until 4.2 K, must exist as particles less than or equal to 4 nm in diameter. In the calcic pyroxenes much of the oxidized ferrous iron may still remain as structural Fe3(+) in the host silicates. Some ferric iron may also be present as unit cell sized Fe2O3 inclusions in the pyroxenes, or be segregated along cleavage planes, or be coating mineral grains. In these states of aggregation, the Fe2O3 is unidentifiable by x ray diffraction and in low temperature Mossbauer spectra. Applications of this research to the surface of Venus are discussed

Mixed-valence iron minerals on Venus: Fe(2+)-Fe(3+) oxides and oxy-silicates formed by surface-atmosphere interactions

Inferences from these investigations are that Fe(3+)-bearing minerals such as hematite magnesioferrite, acmite, and epidote are thermodynamically unstable, and that magnetite is the predominant mixed-valence iron oxide mineral on venus. Recently, the Fe(2+)-Fe(3+) silicate mineral laihunite was proposed to be a reaction product of olivine with the venusian atmosphere. This possibility is discussed further here. We suggest that other mixed-valence Fe(2+)-Fe(3+)-Oz-OH(-) silicates could also result from surface-atmosphere interactions on Venus. Topics discussed include the following: (1) conversion of hematite to magnetite; (2) stability of laihunite; (3) the possible existence of oxy-amphiboles and oxy-micas on Venus; and (4) other mixed-valence Fe(2+)-Fe(3+) silicates likely to exist on Venus

Interpreting for the Deaf in a Psychiatric Setting

Non

Analysis of Genetic Changes in Single-Variety Ryegrass Swards

Ryegrass varieties are synthetics, with a wide within-variety genetic variance for most traits. Ryegrass swards are likely to experience genetic changes with seasons and years because of plant death, asymmetric vegetative reproduction or plant recruitment through reproduction or seed immigration. These changes may be related to or induce changes in agronomic traits, such as biomass production or dry matter composition. The present research was undertaken to measure genetic changes in swards obtained from sowings of a single variety of ryegrass. These changes were evaluated using both neutral molecular markers and morphological traits. The present paper deals with the molecular markers

On the Existence of Linearly Oscillating Galaxies

We consider two classes of steady states of the three-dimensional, gravitational Vlasov-Poisson system: the spherically symmetric Antonov-stable steady states (including the polytropes and the King model) and their plane symmetric analogues. We completely describe the essential spectrum of the self-adjoint operator governing the linearized dynamics in the neighborhood of these steady states. We also show that for the steady states under consideration, there exists a gap in the spectrum. We then use a version of the Birman-Schwinger principle first used by Mathur to derive a general criterion for the existence of an eigenvalue inside the first gap of the essential spectrum, which corresponds to linear oscillations about the steady state. It follows in particular that no linear Landau damping can occur in the neighborhood of steady states satisfying our criterion. Verification of this criterion requires a good understanding of the so-called period function associated with each steady state. In the plane symmetric case we verify the criterion rigorously, while in the spherically symmetric case we do so under a natural monotonicity assumption for the associated period function. Our results explain the pulsating behavior triggered by perturbing such steady states, which has been observed numerically

Anti-phospholipid-antibodies in patients with relapsing polychondritis

Relapsing polychondritis (RP) is an extremly rare multisystemic disease thought to be of autoimmune origin. In order to assess if RP is associated with anti-phospholipid antibodies (aPL), clinical data and sera of 21 patients with RP were collected in a multicentre study. Concentration of anti-cardiolipin antibodies (aCL) (IgG-, IgM-and IgA-isotypes), anti-phosphatidylserine-antibodies (aPS) (IgG-and IgM-isotypes) and anti-β-2-glycoprotein I-antibodies (aβ2 GPI) were measured by ELISA. In eight patients aCL were found to be elevated. One patient had elevated aPS. No patient had elevated aβ2 GPI. No patient had clinical signs and symptoms of a aPL syndrome. Interestingly, the two RP patients with the highest aPL had concomitant systemic lupus erythematosus (SLE). Therefore the presence of elevated aPL in RP is probably more closely related to an associated SLE than to RP itself. There is no convincing evidence that aPL are associated with RP

Overlap of electron core states for very high compressions

At normal density and for modest compressions, the electronic structure of a metal can be accurately described by treating the conduction electrons and their interactions with the usual methods of band theory. The core electrons remain essentially the same as for an isolated free atom and do not participate in the bonding forces responsible for creating a condensed phase. As the density increases, the core electrons begin to ''see'' one another as the overlap of the tails of wave functions can no longer be neglected. The electronic structure of the core electrons is responsible for an effective repulsive interaction that eventually becomes free-electron-like at very high compressions. The electronic structure of the interacting core electrons may be treated in a simple manner using the Atomic Surface Method (ASM). The ASM is a first-principles treatment of the electronic structure involving a rigorous integration of the Schroedinger equation within the atomic-sphere approximation. Solid phase wave functions are constructed from isolated atom wave functions and the band width W/sub l/ and the center of gravity of the band C/sub l/ are obtained from simple formulas. The ASM can also utilize analytic forms of the atomic wave functions and thus provide direct functional dependence of various aspects of the electronic structure. Of particular use in understanding the behavior of the core electrons, the ASM provides the analytic density dependence of the band widths and positions. 8 refs., 2 figs., 1 tab