Variational principle for the Wheeler-Feynman electrodynamics

We adapt the formally-defined Fokker action into a variational principle for the electromagnetic two-body problem. We introduce properly defined boundary conditions to construct a Poincare-invariant-action-functional of a finite orbital segment into the reals. The boundary conditions for the variational principle are an endpoint along each trajectory plus the respective segment of trajectory for the other particle inside the lightcone of each endpoint. We show that the conditions for an extremum of our functional are the mixed-type-neutral-equations with implicit state-dependent-delay of the electromagnetic-two-body problem. We put the functional on a natural Banach space and show that the functional is Frechet-differentiable. We develop a method to calculate the second variation for C2 orbital perturbations in general and in particular about circular orbits of large enough radii. We prove that our functional has a local minimum at circular orbits of large enough radii, at variance with the limiting Kepler action that has a minimum at circular orbits of arbitrary radii. Our results suggest a bifurcation at some radius below which the circular orbits become saddle-point extrema. We give a precise definition for the distributional-like integrals of the Fokker action and discuss a generalization to a Sobolev space of trajectories where the equations of motion are satisfied almost everywhere. Last, we discuss the existence of solutions for the state-dependent delay equations with slightly perturbated arcs of circle as the boundary conditions and the possibility of nontrivial solenoidal orbits

On integers for which the sum of divisors is the square of the squarefree core

We study integers n > 1 satisfying the relation σ(n) = γ(n) ² , where σ(n) and γ(n) are the sum of divisors and the product of distinct primes dividing n, respectively. We show that the only solution n with at most four distinct prime factors is n = 1782. We show that there is no solution which is fourth power free. We also show that the number of solutions up to x > 1 is at most x ⅟⁴⁺ᵉ for any ε > 0 and all x > xε. Further, call n primitive if no proper unitary divisor d of n satisfies σ(d) | γ(d) ² . We show that the number of primitive solutions to the equation up to x is less than xᵉ for x > xₑ

Covariant EBK quantization of the electromagnetic two-body problem

We discuss a method to transform the covariant Fokker action into an implicit two-degree-of-freedom Hamiltonian for the electromagnetic two-body problem with arbitrary masses. This dynamical system appeared 100 years ago and it was popularized in the 1940's by the still incomplete Wheeler and Feynman program to quantize it as a means to overcome the divergencies of perturbative QED. Our finite-dimensional implicit Hamiltonian is closed and involves no series expansions. The Hamiltonian formalism is then used to motivate an EBK quantization based on the classical trajectories with a non-perturbative formula that predicts energies free of infinities.Comment: 21 page

A Few Considerations on Structural and Logical Composition in Specification Theories

Over the last 20 years a large number of automata-based specification theories have been proposed for modeling of discrete,real-time and probabilistic systems. We have observed a lot of shared algebraic structure between these formalisms. In this short abstract, we collect results of our work in progress on describing and systematizing the algebraic assumptions in specification theories.Comment: In Proceedings FIT 2010, arXiv:1101.426

Chandra astrometry sets a tight upper limit to the proper motion of SGR 1900+14

The soft gamma-ray repeater (SGR) SGR 1900+14 lies a few arcminutes outside the edge of the shell supernova remnant (SNR) G42.8+0.6. A physical association between the two systems has been proposed - for this and other SGR-SNR pairs - based on the expectation of high space velocities for SGRs in the framework of the magnetar model. The large angular separation between the SGR and the SNR center, coupled with the young age of the system, suggest a test of the association with a proper motion measurement. We used a set of three Chandra/ACIS observations of the field spanning 5 years to perform accurate relative astrometry in order to measure the possible angular displacement of the SGR as a function of time. Our investigation sets a 3-sigma upper limit of 70 mas/yr to the overall proper motion of the SGR. Such a value argues against an association of SGR 1900+14 with G42.8+0.6 and adds further support to the mounting evidence for an origin of the SGR within a nearby, compact cluster of massive stars.Comment: Accepted for publication in The Astrophysical Journal. 4 pages in emulate-apj styl

A critical analysis of Popper's experiment

An experiment which could decide against the Copenhagen interpretation of quantum mechanics has been proposed by K. Popper and, subsequently, it has been criticized by M.J. Collett and R. Loudon. Here we show that both the above mentioned arguments are not correct because they are based on a misuse of basic quantum rules.Comment: 12 pages, 3 figures, RevTex; to be published on PR

Supergiant Fast X-ray Transients uncovered by the EXTraS project: flares reveal the development of magnetospheric instability in accreting neutron stars

The low luminosity, X-ray flaring activity, of the sub-class of high mass X-ray binaries called Supergiant Fast X-ray Transients, has been investigated using XMM-Newton public observations, taking advantage of the products made publicly available by the EXTraS project. One of the goals of EXTraS was to extract from the XMM-Newton public archive information on the aperiodic variability of all sources observed in the soft X-ray range with EPIC (0.2-12 keV). Adopting a Bayesian block decomposition of the X-ray light curves of a sample of SFXTs, we picked out 144 X-ray flares, covering a large range of soft X-ray luminosities (1e32-1e36 erg/s). We measured temporal quantities, like the rise time to and the decay time from the peak of the flares, their duration and the time interval between adjacent flares. We also estimated the peak luminosity, average accretion rate and energy release in the flares. The observed soft X-ray properties of low-luminosity flaring activity from SFXTs is in qualitative agreement with what is expected by the application of the Rayleigh-Taylor instability model in accreting plasma near the neutron star magnetosphere. In the case of rapidly rotating neutron stars, sporadic accretion from temporary discs cannot be excluded.Comment: Accepted for publication in MNRAS (accepted 2019 May 1; received 2019 April 30; in original form 2019 February 25). 22 pages, 16 figures, 3 tables

A web-based survey of the motivations and challenges faced by emerging researchers in the chiropractic profession

OBJECTIVE: To investigate the motivations, challenges and perceptions of the educational environment of emerging researchers in chiropractic. METHODS: A descriptive web-based survey of higher-degree chiropractic research students was performed between October and November 2013. The survey consisted of open and closed questions and the Dundee Ready Education Environment Measure. RESULTS: Twenty-two students currently enrolled in a higher-degree research program participated. Students were most commonly enrolled in a doctor of philosophy program at a part-time rate. Motivations of research were desire to improve the clinical care aspects of chiropractic for the public and belief that chiropractic research is lacking. The greatest challenges were the negative attitudes towards chiropractic, finding enough time to do everything required, and feelings of isolation. The higher-degree research educational environment was perceived to be more positive than negative, with the stimulating nature of research a positive feature. A negative feature of the educational environment was poor undergraduate preparation for higher-degree research. CONCLUSION: This study is the first study to describe higher-degree chiropractic research students. Primary motivations included building research, while challenges included not only negative attitudes toward the chiropractic profession but also negative attitudes toward researchers from within the profession. The higher-degree research educational environment was perceived to be positive. By acknowledging the issues that surround emerging researchers in chiropractic, the profession is better placed to foster academics and build research capacity

Perceived time and temporal structure: neural entrainment to isochronous stimulation increases duration estimates

Distortions of perceived duration can give crucial insights into the mechanisms that underlie the processing and representation of stimulus timing. One factor that affects duration estimates is the temporal structure of stimuli that fill an interval. For example, regular filling (isochronous interval) leads to an overestimation of perceived duration as compared to irregular filling (anisochronous interval). In the present article, we use electroencephalography (EEG) to investigate the neural basis of this subjective lengthening of perceived duration with isochrony. In a two-interval forced choice task, participants judged which of two intervals lasts longer – one always being isochronous, the other one anisochronous. Response proportions confirm the subjective overestimation of isochronous intervals. At the neural level, isochronous sequences are associated with enhanced pairwise phase consistency (PPC) at the stimulation frequency, reflecting the brain's entrainment to the regular stimulation. The PPC over the entrainment channels is further enhanced for isochronous intervals that are reported to be longer, and the magnitude of this PCC effect correlates with the amount of perceptual bias. Neural entrainment has been proposed as a mechanism of attentional selection, enabling increased neural responsiveness toward stimuli that arrive at an expected point in time. The present results support the proposed relationship between neural response magnitudes and temporal estimates: An increase in neural responsiveness leads to a more pronounced representation of the individual stimuli filling the interval and in turn to a subjective increase in duration

The distance to the Vela pulsar gauged with HST parallax oservations

The distance to the Vela pulsar (PSR B0833-45) has been traditionally assumed to be 500 pc. Although affected by a significant uncertainty, this value stuck to both the pulsar and the SNR. In an effort to obtain a model free distance measurement, we have applied high resolution astrometry to the pulsar V~23.6 optical counterpart. Using a set of five HST/WFPC2 observations, we have obtained the first optical measurement of the annual parallax of the Vela pulsar. The parallax turns out to be 3.4 +/- 0.7 mas, implying a distance of 294(-50;+76) pc, i.e. a value significantly lower than previously believed. This affects the estimate of the pulsar absolute luminosity and of its emission efficiency at various wavelengths and confirms the exceptionally high value of the N_e towards the Vela pulsar. Finally, the complete parallax data base allows for a better measurement of the Vela pulsar proper motion (mu_alpha(cos(delta))=-37.2 +/- 1.2 mas/yr; mu_delta=28.2 +/- 1.3 mas/yr after correcting for the peculiar motion of the Sun) which, at the parallax distance, implies a transverse velocity of ~65 km/s. Moreover, the proper motion position angle appears specially well aligned with the axis of symmetry of the X-ray nebula as seen by Chandra. Such an alignment allows to assess the space velocity of the Vela pulsar to be ~81 km/s.Comment: LaTeX, 21 pages, 5 figures. Accepted for publication in Ap