236,444 research outputs found
Least squares estimation of regression coefficients of singular random fields observed on a sphere
No full textWe present some results on the rate of convergence to the normal law of the least square estimates of the regression coefficient of random fields with long range dependence observed on a sphere
L-invariants for cohomological representations of PGL(2) over arbitrary number fields
No full textGehrmann L, Pati MR. L-invariants for cohomological representations of PGL(2) over arbitrary number fields. Forum of Mathematics, Sigma. 2024;12: e71.**Abstract**
Let
be a cuspidal, cohomological automorphic representation of an inner form
G
of
over a number field
F
of arbitrary signature. Further, let
be a prime of
F
such that
G
is split at
and the local component
of
at
is the Steinberg representation. Assuming that the representation is noncritical at
, we construct automorphic
-invariants for the representation
. If the number field
F
is totally real, we show that these automorphic
-invariants agree with the Fontaine–Mazur
-invariant of the associated
p
-adic Galois representation. This generalizes a recent result of Spieß respectively Rosso and the first named author from the case of parallel weight
to arbitrary cohomological weights.
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L-functions of twisted elliptic curves over function fields
No full texttextTraditionally number theorists have studied, both theoretically and
computationally, elliptic curves and their L-functions over number fields, in particular over the rational numbers. Much less work has been done over function fields, especially computationally, where the underlying geometry of the function field plays an intimate role in the arithmetic of elliptic curves.
We make use of this underlying geometry to develop a method to compute
the L-function of an elliptic curve and its twists over the function field of the projective line over a finite field. This method requires computing the number of points on an elliptic curve over a finite field, for which we present a novel algorithm. If the j-invariant of an elliptic curve over a function field is non-constant, its L-function is a polynomial, hence its analytic rank and value at
a given point can be computed exactly. We present data in this direction for a
family of quadratic twists of four fixed elliptic curves over a few function fields
of differing characteristic. First we present analytic rank data that confirms a conjecture of Goldfeld, in stark contrast to the corresponding data in the number field setting. Second, we present data on the integral moments of the value of the L-function at the symmetry point, which on the surface appears
to refute random matrix theory conjectures.Mathematic
Inflation-produced magnetic fields in RnF2 and IF2 models
No full textWe reanalyze the production of seed magnetic fields during inflation in (R/m2)nFμνFμν and IFμνFμν models, where n is a positive integer, R the Ricci scalar, m a mass parameter, and Iηα a power-law function of the conformal time η, with α a positive real number. If m is the electron mass, the produced fields are uninterestingly small for all n. Taking m as a free parameter, we find that, for n≥2, the produced magnetic fields can be sufficiently strong in order to seed the dynamo mechanism and then to explain galactic magnetism. For α 2, there is always a window in the parameters defining inflation such that the generated magnetic fields are astrophysically interesting. Moreover, if inflation is (almost) de Sitter and the produced fields almost scale invariant (α 4), their intensity can be strong enough to directly explain the presence of microgauss galactic magnetic fields. © 2008 The American Physical Society
The effect of static electric fields on Drosophila behaviour
No full textElectric fields are present in the environment and generated from natural sources, such as a thunderstorm or artificially from electrical devices and transmission lines. The electric field is defined as the space surrounding an electric charge, which exerts forces on other charged objects. In recent years, the existence of artificial electric and magnetic fields (EMF) in the environment has provoked concern regarding potential adverse effects on public health, including childhood leukaemia, brain tumours and cardiovascular diseases. Establishing experimental procedures to investigate causal relationships in a human system is fraught with difficulties. Invertebrate model systems are often used as an alternative for basic research. Drosophila melanogaster is one such system. Previous studies have shown that exposure of insects to static and alternating electric fields induces changes in their behaviour in relation to field strength. Unfortunately, the majority of these publications are not comprehensive (focused on either behaviour or harmful effects) and tend to be on invertebrates that are not established model systems.The present study focused on developing a thorough quantitative analysis of the interactions between static electric fields and Drosophila melanogaster. Firstly, this required developing novel bioassay procedures to measure detection and avoidance behaviour to static electric fields, detailed mapping of electric fields in the apparatus and investigating the potential mechanisms of detection. Secondly, to establish a suitable bioassay procedure to test whether the exposure of Drosophila to static electric field leads to harmful effects, by measuring knockdown and mortality. Most of the previously published research investigated the EMF component which included both electric and magnetic fields. Thus, it is difficult to separate and identify the individual effect of each of them as they are usually emitted together (for example, AC power lines). In this study, only the static electric field was used in order to identify its effects.The results showed that D. melanogaster, in a novel Y-tube bioassay avoided static electric fields, after applying 0.5 kV as threshold level (corresponding to a modeled electric field strength of 26-34 kV/m). As the applied voltage increased from 1kV to 3kV so did the level of avoidance. Wing movement caused by electrical field forces were associated with avoidance. This became clear when vestigial winged mutants and wild-type flies with cut wings were exposed to these fields. They exhibited avoidance behaviour only when the highest voltage potentials (2 kV and 3 kV) were applied. In addition, the field strength required to raise the intact and excised wing in females was greater than in males due to the bigger size of the female wing. It was found that the field strength required to raise the intact wings in live and dead male flies was similar, indicating that movement of the wing in response to a static electric field is uncontrolled even with live flies. It is postulated that the electric field imposes physical forces on the wings due to polarization between opposite charges, causing wing movement and ultimately inducing a change in behaviour.To assess the harmful effects of longer term exposure (up to 168 hours), a novel vertical tube design was developed. There was a significant relationship between field strengths and mortality with a (lethal time) LT50 value of 6.48 h in males and 13.02 h in females with field strengths between 89-100 kV/m. The results showed that Drosophila mortality occurred at higher field strength than those that induced avoidance behaviour.This research provides new results and experimental designs to underpin future research using Drosophila as a model system to understand the other possible effects of sublethal static electric fields, such as the induction of stress proteins. Although not the remit of this thesis, the results also provide evidence for the potential ecological effects of static electric fields on organisms in the environment
Artin L-Functions for Abelian Extensions of Imaginary Quadratic Fields
No full textLet F be an abelian extension of an imaginary quadratic field K with Galois group G. We form the Galois-equivariant L-function of the motive h(Spec F)(j) where the Tate twists j are negative integers. The leading term in the Taylor expansion at s=0 decomposes over the group algebra Q[G] into a product of Artin L-functions indexed by the characters of G. We construct a motivic element via the Eisenstein symbol and relate the L-value to periods via regulator maps. Working toward the equivariant Tamagawa number conjecture, we prove that the L-value gives a basis in etale cohomology which coincides with the basis given by the p-adic L-function according to the main conjecture of Iwasawa theory
Static electric field detection and behavioural avoidance in cockroaches
No full textElectric fields are pervasively present in the environment and occur both as a result of man-made activities and through natural occurrence. We have analysed the behaviour of cockroaches to static electric fields and determined the physiological mechanisms that underlie their behavioural responses. The behaviour of animals in response to electric fields was tested using a Y-choice chamber with an electric field generated in one arm of the chamber. Locomotory behaviour and avoidance were affected by the magnitude of the electric fields with up to 85% of individuals avoiding the charged arm when the static electric field at the entrance to the arm was above 8–10kVm–1. Electric fields were found to cause a deflection of the antennae but when the antennae were surgically ablated, the ability of cockroaches to avoid electric fields was abolished. Fixation of various joints of the antennae indicated that hair plate sensory receptors at the base of the scape were primarily responsible for the detection of electric fields, and when antennal movements about the head–scape joint were prevented cockroaches failed to avoid electric fields. To overcome the technical problem of not being able to carry out electrophysiological analysis in the presence of electric fields, we developed a procedure using magnetic fields combined with the application of iron particles to the antennae to deflect the antennae and analyse the role of thoracic interneurones in signalling this deflection. The avoidance of electric fields in the context of high voltage power lines is discussed
Tagging of Biomedical Articles on CiteULike: A Comparison of User, Author and Professional Indexing
No full textThis paper examines the context of online indexing from the viewpoint of three different groups: users, authors, and professional indexers. User tags, author keywords and descriptors were collected from academic journal articles, which were both indexed in Pubmed and tagged on CiteULike, and analysed. Descriptive statistics, informetric measures, and thesaural term comparison shows that there are important differences in the use of keywords between the three groups in addition to similarities which can be used to enhance support for search and browse. While tags and author keywords were found that matched descriptors exactly, other terms which did not match but provided important expansion to the indexing lexicon were found. These additional terms could be used to enhance support for searching and browsing in article databases as well as to provide invaluable data for entry vocabulary and emergent terminology for regular updates to indexing systems. Additionally, the study suggests that tags support organisation by association to task, projects and subject while making important connections to traditional systems which classify into subject categories
Electromagnetic fields and life
No full textA broad region of the electromagnetic spectrum long assumed to have no influence on living systems under natural conditions has been critically re-examined over the past decade. This spectral region extends from the superhigh radio frequencies, through de creasing frequencies, to and including essentially static electric and magnetic fields. The author of this monograph, A. S. Presman, has reviewed not only the extensive Russian literatur!;"l, but also all most equally comprehensively the non-Russian literature, dealing with biological influences of these fields. Treated also is literature shedding some light on possible theoretical foundations for these phenomena. A substantial, rapidly increasing number of studies in many laboratories and countries has now clearly established bio logical influences which are independent of the theoretically predictable, simple thermal effects. Indeed many of the effects are produced by field strengths very close to those within the natural environment. The author has, even more importantly, set forth a novel, imaginative general hypothesis in which it is postulated that such electromagnetic fields normally serve as conveyors of information from the environment to the organism, within the organism, and among organisms. He postulates that in the course of evolution organisms have come to employ these fields in conjunction with the well-known sensory, nervous, and endocrine systems in effecting coordination and integration
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