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Infrared observations provide the dust composition in the protoplanetary discs surface layers, but cannot probe the dust **chemistry** in the mid-plane, where planet formation occurs. Meteorites show ... to be considered if we are to understand the global **chemistry** in discs. 1D radial condensation sequences can only simulate one disc layer at a time and cannot describe the global **chemistry** or the

In this paper we use observations of molecular tracers in metal-rich and α-enhanced galaxies to study the effect of abundance changes on molecular **chemistry**. We selected a sample of metal-rich spiral ... neighbourhood
(Shields & Ferland 1994; Maeda et al. 2002)
. In the next decade,
as the power of millimetre wavelength facilities continues to grow
we will be able to investigate in greater detail the **chemistry**

when self-gravity is important. In this case, spiral waves and shocks cause temperature and density variations that affect the **chemistry**. We have adopted a dynamical model of a solar-mass star surrounded ... -gravitating disc, similar to those that may be found around Class 0 and early Class I protostars, in a study of disc **chemistry**. We find that for each of a number of species, e.g. H2O, adsorption and desorption

rays.
Historically, the cosmic ray ionization rate in Galactic diffuse and
molecular clouds has normally been determined by treating it as a free
parameter and matching the predicted **chemistry** to that ... observed
(e.g. Black & Dalgarno 1977; Hartquist, Doyle & Dalgarno 1978a;
Hartquist, Black & Dalgarno 1978b). Here, it is necessary to
reverse that procedure and to compute the variation of the **chemistry**
as

in order to characterize
the CTI effects. Monte Carlo (e.g. Prod’homme et al. 2011) and
**analytical** models have also been developed which go some way to
reproducing Gaia radiation test data. However ...
present our conclusions.
2 B AC K G R O U N D T O T H E M O D E L
The objective is to derive an **analytical** CDM that takes into
account recent illumination and charge injection history5 and is based
upon

Galactic bulge planetary nebulae show evidence of mixed **chemistry** with emission from both silicate dust and polycyclic aromatic hydrocarbons (PAHs). This mixed **chemistry** is unlikely to be related to ... Telescope (HST ) images and Ultraviolet and Visual Echelle Spectrograph (UVES) spectra show that the mixed **chemistry** is not related to the presence of emission-line stars, as it is in the Galactic disc

High-order **analytical** solutions around the triangular libration points in the circular restricted three-body problem (CRTBP) are constructed in this paper. It is known that the linearized equations ... all be parametrized. To check the validity of series expansions, numerically integrated orbits with the same initial states as **analytical** orbits are computed, and the practical convergence of **analytical**

We present yields from stars of mass in the range M⊙ ≤ M ≤ 8 M⊙ of metallicities Z = 3 × 10−4 and 8 × 10−3, thus encompassing the **chemistry** of low- and high-Z globular clusters. The yields are based ... third dredge-up, thus ejecting into their surroundings gas enriched in carbon and nitrogen. Conversely, hot bottom burning is mainly responsible for the modification of the surface **chemistry** of more

)
. Here we present
**analytical** expressions for inferring the magnetic field vector from
the observed Stokes profiles induced by the Zeeman effect in the
weak-field approximation.
The weak-field ... approximation is broadly applied for the inference
of solar and stellar magnetic fields from the observation of the
Stokes profiles. It is an **analytical** solution to the radiative transfer
equation whose main

of the shock front, typically travelling at a few
hundred km s1 through a molecular cloud. Raga & Williams (2000)
investigated, using a simple **chemistry**, the effect of a moving field
on the expected ... morphology of the emission but the full
consequences on the **chemistry** of allowing the radiation source to move
have not been explored.
In this scenario, the HHO (the source of the radiation driving the

gas (T= 100–1000 K) by gas-phase photochemistry in the absence of grain surface **chemistry**. We derive **analytical** solutions, taking into account the major neutral–neutral reactions for gases at T > 100 K ... because of the difference in activation energy between deuteration enrichment and the back reactions. The **analytical** solutions were confirmed by the time-dependent chemical results in a 10−3 M disc around a

An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct **analytical**

. The scaling laws that exist between coronal parameters arise from the dimensions of the terms in the energy balance equation. Here, **analytical** approximations to numerical solutions for Emdt(Te) are ... ). It is shown that, for the energy balance and geometry adopted, the **analytical** values of the emission measure and electron pressure at To and Tc depend on only three parameters: the stellar surface

We examine several different simplified approaches for modelling the **chemistry** of CO in 3D numerical simulations of turbulent molecular clouds. We compare the different models both by looking at the ... -scale **chemistry** is modelled.
molecular processes - ISM; clouds - ISM; molecules - galaxies; ISM
1 I N T R O D U C T I O N
Carbon monoxide (CO) is a key constituent of the gas making
up the giant

to discuss some recent results of Braithwaite on MBEq formation by relaxation from an initial non-equilibrium state. We next present two families of exact **analytical** axisymmetric MBEqs with ... results established in
Appendices A and B, we derive in particular integral relations involving
various energies. Thus, we present explicit **analytical** solutions for
both MBEqs and MTEqs, the one based on a

In this paper, we derive the **analytical** solution of a satellite orbit disturbed by atmospheric drag. The disturbance force vector is first transformed and rotated to the orbital frame so that it can ... with respect to M , (ω, i) and t, respectively, to obtain the **analytical** solutions of satellite orbits disturbed by atmospheric drag. Some interesting conclusions are obtained theoretically. The

In this paper, we present a framework which provides an **analytical** (i.e. infinitely differentiable) transformation between spatial coordinates and orbital elements for the solution of the ... use
instead of M. Since is an integral of the motion, = M = n.
Therefore for circular orbits 0 and equations (4) and (5) should
be replaced by
To obtain an **analytical** solution to the problem, i.e

**analytical** formulae, derived by Hikage et al., which can be used to constrain the coupling parameter fNL without the need for non-Gaussian simulations. We find −770 < fNL < 500 at 95 per cent CL, significantly ... temperature fluctuation f T /T
normalized by its standard deviation f 2 1/2. Following the
formalism by Matsubara (2003) and Hikage et al. (2006), we can
write the **analytical** formula for the kth MF of weakly

–Zel’dovich (SZ) studies, though many of the results also apply to isotropic dispersion-supported stellar dynamical systems. Here we present **analytical** formulae for galaxy clusters described by a gravitational ... different biases owing to spherical averaging, which leads to an offset in the spherically averaged YSZ-YX relation. A potentially useful application of the **analytical** formulae presented is to assess the

independent techniques based on angular cross-correlations and the properties of the photometric redshift probability distributions. Our covariance matrix is determined using an **analytical** approach, verified ... .
(2012) as this estimate can be used to directly populate numerical
simulations to create an unweighted mock galaxy catalogue, and it is
also used in the creation of the **analytical** covariance (Section 5.3