7,040 research outputs found
Exploring the Origins of Earth's Nitrogen: Astronomical Observations of Nitrogen-bearing Organics in Protostellar Environments
It is not known whether the original carriers of Earth's nitrogen were
molecular ices or refractory dust. To investigate this question, we have used
data and results of Herschel observations towards two protostellar sources: the
high-mass hot core of Orion KL, and the low-mass protostar IRAS 16293-2422.
Towards Orion KL, our analysis of the molecular inventory of Crockett et al.
(2014) indicates that HCN is the organic molecule that contains by far the most
nitrogen, carrying of nitrogen-in-organics. Following this
evidence, we explore HCN towards IRAS 16293-2422, which we consider a solar
analog. Towards IRAS 16293-2422, we have reduced and analyzed Herschel spectra
of HCN, and fit these observations against "jump" abundance models of IRAS
16293-2422's protostellar envelope. We find an inner-envelope HCN abundance
and an outer-envelope HCN
abundance . We also find the
sublimation temperature of HCN to be ~K; this
measured enables us to predict an HCN binding energy
~K. Based on a comparison of the HCN/H2O ratio
in these protostars to N/H2O ratios in comets, we find that HCN (and, by
extension, other organics) in these protostars is incapable of providing the
total bulk N/H2O in comets. We suggest that refractory dust, not molecular
ices, was the bulk provider of nitrogen to comets. However, interstellar dust
is not known to have 15N enrichment, while high 15N enrichment is seen in both
nitrogen-bearing ices and in cometary nitrogen. This may indicate that these
15N-enriched ices were an important contributor to the nitrogen in
planetesimals and likely to the Earth.Comment: Accepted to ApJ; 21 pages, 4 figure
Integral equation solution for truncated slab structures by using a fringe current formulation
On C*-algebras generated by pairs of q-commuting isometries
We consider the C*-algebras O_2^q and A_2^q generated, respectively, by
isometries s_1, s_2 satisfying the relation s_1^* s_2 = q s_2 s_1^* with |q| <
1 (the deformed Cuntz relation), and by isometries s_1, s_2 satisfying the
relation s_2 s_1 = q s_1 s_2 with |q| = 1. We show that O_2^q is isomorphic to
the Cuntz-Toeplitz C*-algebra O_2^0 for any |q| < 1. We further prove that
A_2^{q_1} is isomorphic to A_2^{q_2} if and only if either q_1 = q_2 or q_1 =
complex conjugate of q_2. In the second part of our paper, we discuss the
complexity of the representation theory of A_2^q. We show that A_2^q is *-wild
for any q in the circle |q| = 1, and hence that A_2^q is not nuclear for any q
in the circle.Comment: 18 pages, LaTeX2e "article" document class; submitted. V2 clarifies
the relationships between the various deformation systems treate
On the expected diameter, width, and complexity of a stochastic convex-hull
We investigate several computational problems related to the stochastic
convex hull (SCH). Given a stochastic dataset consisting of points in
each of which has an existence probability, a SCH refers to the
convex hull of a realization of the dataset, i.e., a random sample including
each point with its existence probability. We are interested in computing
certain expected statistics of a SCH, including diameter, width, and
combinatorial complexity. For diameter, we establish the first deterministic
1.633-approximation algorithm with a time complexity polynomial in both and
. For width, two approximation algorithms are provided: a deterministic
-approximation running in time, and a fully
polynomial-time randomized approximation scheme (FPRAS). For combinatorial
complexity, we propose an exact -time algorithm. Our solutions exploit
many geometric insights in Euclidean space, some of which might be of
independent interest
Fringe integral equation method for a truncated grounded dielectric slab
The problem of scattering by a semi-infinite grounded dielectric slab illuminated by an arbitrary incident TM z polarized electric field is studied by solving a new set of "fringe" integral equations (F-IEs), whose functional unknowns are physically associated to the wave diffraction processes occuring at the truncation. The F-IEs are obtained by subtracting from the surface/surface integral equations pertinent to the truncated slab, an auxiliary set of equations obtained for the canonical problem of an infinite grounded slab illuminated by the same source. The F-IEs are solved by the method of moments by using a set of subdomain basis functions close to the truncation and semi-infinite domain basis functions far from it. These latter functions are properly shaped to reproduce the asymptotic behaviour of the diffracted waves, which is obtained by physical inspection. The present solution is applied to the case of an electric line source located at the air-dielectric interface of the slab. Numerical results are compared with those calculated by a physical optics approach and by an alternative solution, in which the integral equation is constructed from the field continuity through an aperture orthogonal to the slab. The applications of the solution to an array of line currents are also presented and discussed
Approximate Minimum Diameter
We study the minimum diameter problem for a set of inexact points. By
inexact, we mean that the precise location of the points is not known. Instead,
the location of each point is restricted to a contineus region (\impre model)
or a finite set of points (\indec model). Given a set of inexact points in
one of \impre or \indec models, we wish to provide a lower-bound on the
diameter of the real points.
In the first part of the paper, we focus on \indec model. We present an
time
approximation algorithm of factor for finding minimum diameter
of a set of points in dimensions. This improves the previously proposed
algorithms for this problem substantially.
Next, we consider the problem in \impre model. In -dimensional space, we
propose a polynomial time -approximation algorithm. In addition, for
, we define the notion of -separability and use our algorithm for
\indec model to obtain -approximation algorithm for a set of
-separable regions in time
- …