Radiation Mechanism of the Soft Gamma-ray Pulsar PSR B1509-58

The outer gap model is used here to explain the spectrum and the energy dependent light curves of the X-ray and soft gamma-ray radiations of the spin-down powered pulsar PSR B1509-58.In the outer gap model, most pairs inside the gap are created around the null charge surface and the gap's electric field separates the two charges to move in opposite directions. Consequently, the region from the null charge surface to the light cylinder is dominated by the outflow of particles and that from the null charge surface to the star is dominated by the inflow of particles. The inflow and outflow of particles move along the magnetic field lines and emit curvature photons, and the incoming curvature photons are converted to pairs by the strong magnetic field of the star. These pairs emit synchrotron photons. We suggest that the X-rays and soft gamma-rays of PSR B1509-58 result from the synchrotron radiation of these pairs, and the viewing angle of PSR B1509-58 only receives the inflow radiation. The magnetic pair creation requires a large pitch angle, which makes the pulse profile of the synchrotron radiation distinct from that of the curvature radiation. We carefully trace the pulse profiles of the synchrotron radiation with different pitch angles. We find that the differences between the light curves of different energy bands are due to the different pitch angles of the secondary pairs, and the second peak appearing at E>10MeV comes from the region near the star, where the stronger magnetic field allows the pair creation to happen with a smaller pitch angle.Comment: 5 pages, 8 figures, 2012 Fermi Symposium proceedings - eConf C12102

Quantum-like modeling of the order effect in decision making: POVM viewpoint on the Wang-Busemeyer QQ-equality

In recent years, quantum mechanics has been actively used in areas outside of physics, such as psychology, sociology, theory of decision-making, game theory, and others. In particular, quantum mechanics is used to explain the paradoxes arising in cognitive psychology and decision making. Wang and Busemeyer invented a quantum model and approach as well as non-parametric equality (so-called QQ-equality), explaining the questions order effect. The primary objective of this note is to test the possibility to expand the Wang-Busemeyer model by considering questions which are mathematically represented by positive operator valued measures. We found that, for such observables, the QQ-equality can be violated. But, we also showed that, in principle, it is possible to reduce expanded model to the original Wang-Busemeyer model by expanding the context of the questions

Replies to Wang, Speaks, and Pautz

Replies for a symposium on Propositions

On the qq-log-convexity conjecture of Sun

In his study of Ramanujan-Sato type series for $1/\pi$, Sun introduced a sequence of polynomials $S_n(q)$ as given by $$S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k,$$ and he conjectured that the polynomials $S_n(q)$ are $q$-log-convex. By imitating a result of Liu and Wang on generating new $q$-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the $q$-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture