Entire curves avoiding given sets in C^n

Let $F\subset\Bbb C^n$ be a proper closed subset of $\Bbb C^n$ and $A\subset\Bbb C^n\setminus F$ at most countable ($n\geq 2$). We give conditions of $F$ and $A$, under which there exists a holomorphic immersion (or a proper holomorphic embedding) $\phi:\Bbb C\to\Bbb C^n$ with $A\subset\phi(\Bbb C)\subset\Bbb C^n\setminus F$.Comment: 10 page

Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in 158^{158}Er at ultrahigh spin

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in $^{158}$Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes -- as done in previous cranking calculations -- two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation $\gamma$. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal axis cranking approach. Several TSD configurations have been predicted, including a highly deformed band expected to cross lesser elongated TSD bands at the highest spins. Its transitional quadrupole moment $Q_t \approx 10.5$\,eb is close to the measured value of $\sim$11\,eb; hence, it is a candidate for the structure observed in experiment.Comment: 5 pages, 5 figure

Jacobi Identity for Vertex Algebras in Higher Dimensions

Vertex algebras in higher dimensions provide an algebraic framework for investigating axiomatic quantum field theory with global conformal invariance. We develop further the theory of such vertex algebras by introducing formal calculus techniques and investigating the notion of polylocal fields. We derive a Jacobi identity which together with the vacuum axiom can be taken as an equivalent definition of vertex algebra.Comment: 35 pages, references adde

Probabilistic Model of Onset Detection Explains Paradoxes in Human Time Perception

A very basic computational model is proposed to explain two puzzling findings in the time perception literature. First, spontaneous motor actions are preceded by up to 1–2 s of preparatory activity (Kornhuber and Deecke, 1965). Yet, subjects are only consciously aware of about a quarter of a second of motor preparation (Libet et al., 1983). Why are they not aware of the early part of preparation? Second, psychophysical findings (Spence et al., 2001) support the principle of attention prior entry (Titchener, 1908), which states that attended stimuli are perceived faster than unattended stimuli. However, electrophysiological studies reported no or little corresponding temporal difference between the neural signals for attended and unattended stimuli (McDonald et al., 2005; Vibell et al., 2007). We suggest that the key to understanding these puzzling findings is to think of onset detection in probabilistic terms. The two apparently paradoxical phenomena are naturally predicted by our signal detection theoretic model

Proper holomorphic mappings between symmetrized ellipsoids

We characterize the existence of proper holomorphic mappings in the special class of bounded $(1,2,...,n)$-balanced domains in $\mathbb{C}^n$, called the symmetrized ellipsoids. Using this result we conclude that there are no non-trivial proper holomorphic self-mappings in the class of symmetrized ellipsoids. We also describe the automorphism groupof these domains.Comment: 10 pages, some modification

Departure from the constant-period ephemeris for the transiting exoplanet WASP-12 b

Most hot Jupiters are expected to spiral in towards their host stars due to transfering of the angular momentum of the orbital motion to the stellar spin. Their orbits can also precess due to planet-star interactions. Calculations show that both effects could be detected for the very-hot exoplanet WASP-12 b using the method of precise transit timing over a timespan of the order of 10 yr. We acquired new precise light curves for 29 transits of WASP-12 b, spannning 4 observing seasons from November 2012 to February 2016. New mid-transit times, together with literature ones, were used to refine the transit ephemeris and analyse the timing residuals. We find that the transit times of WASP-12 b do not follow a linear ephemeris with a 5 sigma confidence level. They may be approximated with a quadratic ephemeris that gives a rate of change in the orbital period of -2.56 +/- 0.40 x 10^{-2} s/yr. The tidal quality parameter of the host star was found to be equal to 2.5 x 10^5 that is comparable to theoretical predictions for Sun-like stars. We also consider a model, in which the observed timing residuals are interpreted as a result of the apsidal precession. We find, however, that this model is statistically less probable than the orbital decay.Comment: Accepted for publication in A&A Letter

Dimensional Reduction of Dirac Operator

We construct an explicit example of dimensional reduction of the free massless Dirac operator with an internal SU(3) symmetry, defined on a twelve-dimensional manifold that is the total space of a principal SU(3)-bundle over a four-dimensional (nonflat) pseudo-Riemannian manifold. Upon dimensional reduction the free twelve-dimensional Dirac equation is transformed into a rather nontrivial four-dimensional one: a pair of massive Lorentz spinor SU(3)-octets interacting with an SU(3)-gauge field with a source term depending on the curvature tensor of the gauge field. The SU(3) group is complicated enough to illustrate features of the general case. It should not be confused with the color SU}(3) of quantum chromodynamics where the fundamental spinors, the quark fields, are SU(3) triplets rather than octets.Comment: 11 pages, LATEX