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