A generalized Fourier inversion theorem

In this work we define operator-valued Fourier transforms for suitable integrable elements with respect to the Plancherel weight of a (not necessarily Abelian) locally compact group. Our main result is a generalized version of the Fourier inversion Theorem for strictly-unconditionally integrable Fourier transforms. Our results generalize and improve those previously obtained by Ruy Exel in the case of Abelian groups.Comment: 15 pages; some typos correcte

Laser-Nucleus Interactions: The Quasiadiabatic Regime

The interaction between nuclei and a strong zeptosecond laser pulse with coherent MeV photons is investigated theoretically. We provide a first semi-quantitative study of the quasiadiabatic regime where the photon absorption rate is comparable to the nuclear equilibration rate. In that regime, multiple photon absorption leads to the formation of a compound nucleus in the so-far unexplored regime of excitation energies several hundred MeV above the yrast line. The temporal dynamics of the process is investigated by means of a set of master equations that account for dipole absorption, stimulated dipole emission, neutron decay and induced fission in a chain of nuclei. That set is solved numerically by means of state-of-the-art matrix exponential methods also used in nuclear fuel burnup and radioactivity transport calculations. Our quantitative estimates predict the excitation path and range of nuclei reached by neutron decay and provide relevant information for the layout of future experiments.Comment: 14 pages, 9 figures; v2 minor modifications in text, results unchange

Generalized fixed point algebras for coactions of locally compact quantum groups

We extend the construction of generalized fixed point algebras to the setting of locally compact quantum groups – in the sense of Kustermans and Vaes – following the treatment of Marc Rieffel, Ruy Exel and Ralf Meyer in the group case. We mainly follow Meyer’s approach analyzing the constructions in the realm of equivariant Hilbert modules. We generalize the notion of continuous square-integrability, which is exactly what one needs in order to define generalized fixed point algebras. As in the group case, we prove that there is a correspondence between continuously square-integrable Hilbert modules over an equivariant C*-algebra B and Hilbert modules over the reduced crossed product of B by the underlying quantum group. The generalized fixed point algebra always appears as the algebra of compact operators of the associated Hilbert module over the reduced crossed product

A floor sensor system for gait recognition

This paper describes the development of a prototype floor sensor as a gait recognition system. This could eventually find deployment as a standalone system (eg. a burglar alarm system) or as part of a multimodal biometric system. The new sensor consists of 1536 individual sensors arranged in a 3 m by 0.5 m rectangular strip with an individual sensor area of 3 cm2. The sensor floor operates at a sample rate of 22 Hz. The sensor itself uses a simple design inspired by computer keyboards and is made from low cost, off the shelf materials. Application of the sensor floor to a small database of 15 individuals was performed. Three features were extracted : stride length, stride cadence, and time on toe to time on heel ratio. Two of these measures have been used in video based gait recognition while the third is new to this analysis. These features proved sufficient to achieve an 80 % recognition rate

The prospects for mathematical logic in the twenty-first century

The four authors present their speculations about the future developments of mathematical logic in the twenty-first century. The areas of recursion theory, proof theory and logic for computer science, model theory, and set theory are discussed independently.Comment: Association for Symbolic Logi

How willing are you to accept sexual requests from slightly unattractive to exceptionally attractive imagined requestors?

This is the post print version of the article. The official published version can be accessed from the link below.In their classic study of differences in mating strategies (Clark & Hatfield, 1989), men and women demonstrated a striking difference in interest in casual sex. The current study examined the role of requestor physical attractiveness (slightly unattractive, moderately attractive and exceptionally attractive) on men's and women's willingness to accept three different requests (go out, come to apartment, go to bed) in a questionnaire study. We tested two hypotheses, using a sample of 427 men and 443 women from three countries. Hypothesis 1 states that men, relative to women, will demonstrate a greater willingness to accept the “come to apartment” and “go to bed” requests but not the “go out” request for all three levels of requestor attractiveness. This hypothesis reflects Clark and Hatfield's (1989) main findings. Hypothesis 2 states that the physical attractiveness of a potential partner will have a greater effect on women's than on men's willingness to accept all three requests, and particularly for the explicit request for casual sex. The results partially supported Hypothesis 1 and fully supported Hypothesis 2. The discussion highlights limitations of the current research and presents directions for future research

Pseudo-distances on symplectomorphism groups and applications to flux theory

Starting from a given norm on the vector space of exact 1-forms of a compact symplectic manifold, we produce pseudo-distances on its symplectomorphism group by generalizing an idea due to Banyaga. We prove that in some cases (which include Banyaga's construction), their restriction to the Hamiltonian diffeomorphism group is equivalent to the distance induced by the initial norm on exact 1-forms. We also define genuine "distances to the Hamiltonian diffeomorphism group" which we use to derive several consequences, mainly in terms of flux groups.Comment: 21 pages, no figure; v2. various typos corrected, some references added. Published in Mathematische Zeitschrif