33,178 research outputs found
The continuous postage stamp problem
For a real set consider the semigroup , additively generated by
; that is, the set of all real numbers representable as a (finite) sum of
elements of . If is open and non-empty, then is
easily seen to contain all sufficiently large real numbers, and we let . Thus, is the smallest number
with the property that any is representable as indicated above.
We show that if the measure of is large, then is small; more
precisely, writing for brevity \alpha := \mes A we have
G(A) \le
(1-\alpha) \lfloor 1/\alpha \rfloor
\quad &\text{if $0 < \alpha \le 0.1$},
(1-\alpha+\alpha\{1/\alpha\})\lfloor 1/\alpha\rfloor
\quad &\text{if $0.1 \le \alpha \le 0.5$},
2(1-\alpha)
\quad &\text{if $0.5 \le \alpha \le 1$}.
Indeed, the first and the last of these three estimates are the best
possible, attained for and
, respectively; the second is close to
the best possible and can be improved by at most.
The problem studied is a continuous analogue of the linear Diophantine
problem of Frobenius (in its extremal settings due to Erdos and Graham), also
known as the "postage stamp problem" or the "coin exchange problem"
Cost-allocation principles for pipeline capacity and usage
This paper applies principles f rom game theory to the problem o f allocating the cost o f a shared facility, such as a pipeline. The theory o f cooperative games s t r ongl y suggest s t hat no method e x i s t s for allocating costs that wi l l achieve all major policy goals. We apply results from the theory o f cooperative games a n d principles o f cost allocation to assess some c o mmo n l y adopted rules for allocating costs and def i ni ng u n i t charges. Mos t notably, the postage-stamp toll is f o u n d to fail a mi ni mal set o f commonly applied principles.cost allocation; pipeline
GREAT3 results I: systematic errors in shear estimation and the impact of real galaxy morphology
We present first results from the third GRavitational lEnsing Accuracy
Testing (GREAT3) challenge, the third in a sequence of challenges for testing
methods of inferring weak gravitational lensing shear distortions from
simulated galaxy images. GREAT3 was divided into experiments to test three
specific questions, and included simulated space- and ground-based data with
constant or cosmologically-varying shear fields. The simplest (control)
experiment included parametric galaxies with a realistic distribution of
signal-to-noise, size, and ellipticity, and a complex point spread function
(PSF). The other experiments tested the additional impact of realistic galaxy
morphology, multiple exposure imaging, and the uncertainty about a
spatially-varying PSF; the last two questions will be explored in Paper II. The
24 participating teams competed to estimate lensing shears to within systematic
error tolerances for upcoming Stage-IV dark energy surveys, making 1525
submissions overall. GREAT3 saw considerable variety and innovation in the
types of methods applied. Several teams now meet or exceed the targets in many
of the tests conducted (to within the statistical errors). We conclude that the
presence of realistic galaxy morphology in simulations changes shear
calibration biases by per cent for a wide range of methods. Other
effects such as truncation biases due to finite galaxy postage stamps, and the
impact of galaxy type as measured by the S\'{e}rsic index, are quantified for
the first time. Our results generalize previous studies regarding sensitivities
to galaxy size and signal-to-noise, and to PSF properties such as seeing and
defocus. Almost all methods' results support the simple model in which additive
shear biases depend linearly on PSF ellipticity.Comment: 32 pages + 15 pages of technical appendices; 28 figures; submitted to
MNRAS; latest version has minor updates in presentation of 4 figures, no
changes in content or conclusion
Persediaan kerjaya pelajar tahun akhir diploma akauntansi Politeknik dalam melahirkan K-Workes : satu tinjauan
This research was conducted to identify Polytechnic's Diploma in Accountancy
final year students' career preparation before enter the working environment to be
k-workers. The sample in this study consisted of 48 final year students of Diploma in
Accountancy Politeknik Sultan Haji Ahmad Shah (POLISAS), Kuantan. Questionnaire
has been chosen as an instrument to get the data. The data was analyzed by using the
Statistical Package For Social Sciences (SPSS) package to derive the percentages and
mean. The results revealed the Diploma of Accountancy final year students are quite
prepared to enter the working environment. Although the students performed very well
for their career preparation, there are still dissatisfaction in other two aspects i.e. they
lack of information career opportunity and communication in English. Therefore, the
career guideline have been proposed to give an exposure for the students to be k-workers
in their career in the future
The dependence of intrinsic alignment of galaxies on wavelength using KiDS and GAMA
The outer regions of galaxies are more susceptible to the tidal interactions
that lead to intrinsic alignments of galaxies. The resulting alignment signal
may therefore depend on the passband if the colours of galaxies vary spatially.
To quantify this, we measured the shapes of galaxies with spectroscopic
redshifts from the GAMA survey using deep gri imaging data from the KiloDegree
Survey. The performance of the moment-based shape measurement algorithm DEIMOS
was assessed using dedicated image simulations, which showed that the
ellipticities could be determined with an accuracy better than 1% in all bands.
Additional tests for potential systematic errors did not reveal any issues. We
measure a significant difference of the alignment signal between the g,r and
i-band observations. This difference exceeds the amplitude of the linear
alignment model on scales below 2 Mpc/h. Separating the sample into
central/satellite and red/blue galaxies, we find that that the difference is
dominated by red satellite galaxies.Comment: 16 pages, 13 figures, accepted, to appear in A&
The Liberalisation of the Energy Sector in the European Union
The energy sector covers the coal, oil, gas and electricity sector. The European coal and oil sector have already been liberalised in the past. The current debate concerns mainly the electricity and the gas sector. In this paper we will concentrate on the electricity sector for three reasons. First, the sector is more important in terms of value added, secondly it is considered to be more complex and, finally, the opening of the electricity market precedes that of the gas market. Obviously, this does not mean that the gas sector should not be studied as there are many challenges left. In section II, we discuss the institutional background for the liberalisation. Section III then analyses the British experience. This is of interest because the UK has liberalised its market about 10 years ago and this experience has been the subject of extensive economic research. In the sections IV to VII, we focus on the four main problems in the liberalisation of the European electricity market: the stranded costs issue, the cross-subsidies issue, the pricing of transmission and the regulation of the environment. Finally, section VIII concludes.
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