2,759 research outputs found
On Elkies' method for bounding the transitivity degree of Galois groups
In 2013 Elkies described a method for bounding the transitivity degree of
Galois groups. Our goal is to give additional applications of this technique,
in particular verifying that the monodromy group of the degree-276 cover
defined over a degree-12 number field computed by Monien is isomorphic to the
sporadic Conway group Co3.Comment: 6 pages. v2: structural changes and a new exampl
Mapping High-Temperature Superconductors - A Scientometric Approach
This study has been carried out to analyze the research field of
high-temperature superconductivity and to demonstrate the potential of modern
databases and search systems for generating meta-information. The alkaline
earth (A2) rare earth (RE) cuprate high-temperature superconductors as a
typical inorganic compound family and the corresponding literature were
analyzed by scientometric methods. The time-dependent overall number of
articles and patents and of the publications related to specific compound
subsets and subject categories are given. The data reveal a significant
decrease of basic research activity in this research field. The A2 RE cuprate
species covered by the CAS compound file were analyzed with respect to the
occurrence of specific elements in order to visualize known and unknown
substances and to identify characteristic patterns. The quaternary and
quinternary cuprates were selected and the number of compound species as
function of specific combinations of A2 and RE elements is given. The Cu/O and
RE/A2 ratios of the quaternary cuprate species as function of A2 and RE atoms
are shown. In addition, the research landscape of the MgB2 related publications
was established using STN AnaVist, an analysis tool recently developed by STN
International.Comment: 22 pages, 16 figures, 1 table; discussion of the data given in
figures 1-2 changed to avoid misinterpretatio
A study of elliptic partial differential equations with jump diffusion coefficients
As a simplified model for subsurface flows elliptic equations may be
utilized. Insufficient measurements or uncertainty in those are commonly
modeled by a random coefficient, which then accounts for the uncertain
permeability of a given medium. As an extension of this methodology to flows in
heterogeneous\fractured\porous media, we incorporate jumps in the diffusion
coefficient. These discontinuities then represent transitions in the media.
More precisely, we consider a second order elliptic problem where the random
coefficient is given by the sum of a (continuous) Gaussian random field and a
(discontinuous) jump part. To estimate moments of the solution to the resulting
random partial differential equation, we use a pathwise numerical approximation
combined with multilevel Monte Carlo sampling. In order to account for the
discontinuities and improve the convergence of the pathwise approximation, the
spatial domain is decomposed with respect to the jump positions in each sample,
leading to pathdependent grids. Hence, it is not possible to create a nested
sequence of grids which is suitable for each sample path a-priori. We address
this issue by an adaptive multilevel algorithm, where the discretization on
each level is sample-dependent and fulfills given refinement conditions
Belyi map for the sporadic group J1
We compute the genus 0 Belyi map for the sporadic Janko group J1 of degree
266 and describe the applied method. This yields explicit polynomials having J1
as a Galois group over K(t), [K:Q] = 7.Comment: 5 pages, the data for the Belyi map is contained in an ancillary fil
Explicit Belyi maps over Q having almost simple primitive monodromy groups
We present all Belyi maps P^1(C) -> P^1(C) having almost simple primitive
monodromy groups (not isomorphic to A_n or S_n) containing rigid and rational
generating triples of degree between 50 and 250. This also leads to new
polynomials having almost simple Galois groups over Q(t).Comment: 11 page
Belyi map for the sporadic group J2
We present a genus 0 Belyi map for the sporadic Janko group J2 of degree 280.
As a consequence we obtain a polynomial having Aut(J2) as a Galois group over
K(t) where K is a number field of degree 10.Comment: 3 pages, the data for the Belyi map is contained in the ancillary
file
A one-parameter family of degree 36 polynomials with PSp(6,2) as Galois group over Q(t)
We present a one-parameter family of degree 36 polynomials with the
symplectic 2-transitive group PSp(6,2) as Galois group over Q(t).Comment: 4 page
On the virtual level of two-body interactions and applications to three-body systems in higher dimensions
We consider a system of three particles in dimension 4 and higher interacting
via short-range potentials, where the two-body Hamiltonians have a virtual
level at the bottom of the essential spectrum. In dimensions 2 (in case of
fermions) and 3 the corresponding three-body Hamiltonian admits an infinite
number of bound states, which is known as the Efimov effect. In this work we
prove that this is not the case in higher dimensions. We investigate how the
dimension and symmetries of the system influence this effect and prove the
finiteness of the discrete spectrum of the corresponding three-body
Hamiltonian.Comment: 24 page
Detecting the historical roots of research fields by reference publication year spectroscopy (RPYS)
We introduce the quantitative method named "reference publication year
spectroscopy" (RPYS). With this method one can determine the historical roots
of research fields and quantify their impact on current research. RPYS is based
on the analysis of the frequency with which references are cited in the
publications of a specific research field in terms of the publication years of
these cited references. The origins show up in the form of more or less
pronounced peaks mostly caused by individual publications which are cited
particularly frequently. In this study, we use research on graphene and on
solar cells to illustrate how RPYS functions, and what results it can deliver.Comment: Accepted for publication in the Journal of the American Society for
Information Science and Technolog
On the origins and the historical roots of the Higgs boson research from a bibliometric perspective
Subject of our present paper is the analysis of the origins or historical
roots of the Higgs boson research from a bibliometric perspective, using a
segmented regression analysis in a reference publication year spectroscopy
(RPYS). Our analysis is based on the references cited in the Higgs boson
publications published since 1974. The objective of our analysis consists of
identifying concrete individual publications in the Higgs boson research
context to which the scientific community frequently had referred to. As a
consequence, we are interested in seminal works which contributed to a high
extent to the discovery of the Higgs boson. Our results show that researchers
in the Higgs boson field preferably refer to more recently published papers -
particular papers published since the beginning of the sixties. For example,
our analysis reveals seven major contributions which appeared within the
sixties: Englert and Brout (1964), Higgs (1964, 2 papers), and Guralnik et al.
(1964) on the Higgs mechanism as well as Glashow (1961), Weinberg (1967), and
Salam (1968) on the unification of weak and electromagnetic interaction. Even
if the Nobel Prize award highlights the outstanding importance of the work of
Peter Higgs and Francois Englert, bibliometrics offer the additional
possibility of getting hints to other publications in this research field
(especially to historical publications), which are of vital importance from the
expert point of view
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