Expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta and Gamma functions

Starting from equations obeyed by functions involving the first or the second derivatives of the biconfluent Heun function, we construct two expansions of the solutions of the biconfluent Heun equation in terms of incomplete Beta functions. The first series applies single Beta functions as expansion functions, while the second one involves a combination of two Beta functions. The coefficients of expansions obey four- and five-term recurrence relations, respectively. It is shown that the proposed technique is potent to produce series solutions in terms of other special functions. Two examples of such expansions in terms of the incomplete Gamma functions are presente

Adiabatic tracking for photo- and magneto-association of Bose-Einstein condensates with Kerr nonlinearities

We develop the method of adiabatic tracking for photo- and magneto-association of Bose-Einstein atomic condensates with models that include Kerr type nonlinearities. We show that the inclusion of these terms can produce qualitatively important modifications in the adiabatic dynamics, like the appearance of bifurcations, in which the trajectory that is being tracked loses its stability. As a consequence the adiabatic theorem does not apply and the adiabatic transfer can be strongly degraded. This degradation can be compensated by using fields that are strong enough compared with the values of the Kerr terms. The main result is that, despite these potentially detrimental features, there is always a choice of the detuning that leads to an efficient adiabatic tracking, even for relatively weak fields

New powerful outburst of the unusual young star V1318 Cyg S (LkH{\alpha} 225)

Young double star V1318 Cyg, which is associated with a small isolated star-forming region around HAeBe star BD+40o4124, has very unusual photometric and spectral behavior. We present results of photometric and spectroscopic observations in the optical range. We carried out BVRI CCD photometric observations of V1318 Cyg from 2015 Sept. to 2017 July. For the same period we acquired medium- and low-resolution spectra. Observations were performed with the 2.6 m telescope. We analyze the historical light curve for V1318 Cyg and demonstrate that the southern component, V1318 Cyg S, after being rather bright in the 1970s (V$\approx$14 mag) started to lower its brightness and in 1990 became practically invisible in the optical. After its reappearance in the second half of the 1990s the star started to become very slowly brighter. Between 2006 and 2010 V1318 Cyg S started brightening more quickly, and in 2015 had become brighter by more than five magnitudes in visible light. Since this time V1318 Cyg S has remained at this maximum. Its spectrum shows little variability and consists of a mixture of emission and absorption lines, which has allowed for estimates of its spectral type as early Ae, with obvious evidence of matter outflow. We derive its current A(V)$\approx$ 7.2 and L = 750 L(sun) thus confirming that V1318 Cyg S should belong to the Herbig Ae stars, making it, along with BD+40o4124 and V1686 Cyg, the third luminous young star in the group. It is very probable that we observe V1318 Cyg S near the pole and that the inclination of its dense and slow ($\approx$ 100 km/s) outflow is low. The unusual variability and other features of V1318 Cyg S make it difficult to classify this star among known types of eruptive young stars. It could be an extreme, higher-mass example of an EXor, or an object of intermediate class between EXors and FUors, like V1647 Ori.Comment: 9 pages, 7 figure

The sensitivity of refractive index sensors based on defected 1D photonic crystals: an analytical approach

In this paper, an analytical formula for the sensitivity of optical sensors based on one-dimensional photonic crystals (PCs) with a defect was derived for the first time. Based on this formula, a comparative analysis of the sensitivity of defected PCs with and without mirror symmetry was carried out. In addition, the exact values of sensitivity in the limit of an infinite PC with a quarter-wave unit cell were obtained. It was shown that the sensitivity of a defective PC with an infinitely thick defect layer is equal to that of a perfectly reflecting Fabry-Perot resonator and does not depend on the specific structure of the PC. The results of this work provide a significant simplification of the analysis and optimization of optical sensors based on defective PCs, as well as a better understanding of the numerous numerical results obtained previously.Comment: 13 pages, 3 figure

The Effect of Patent Foramen Ovale Closure on Visual Aura Without Headache or Typical Aura With Migraine Headache

ObjectivesThe aim of this study was to assess the prevalence of right-to-left (R to L) shunt in patients with visual aura and evaluate the effect of shunt closure on resolution of aura.BackgroundRight-to-left shunting is associated with migraine headache (MH) with aura. Some patients present with visual aura without headaches. It is unclear whether visual aura without headache is a form of migraine or a transient neurologic dysfunction.MethodsOf patients referred to the University of California, Los Angeles for suspected patent foramen ovale (PFO), 225 had visual aura with or without MH. Patients were assessed for a shunt and evaluated for MH and/or visual aura. They were divided into 3 groups: 1) visual aura associated with MH; 2) visual aura unrelated in time to MH; and 3) visual aura without MH. The frequency of R to L shunt was compared with a control group of 200 patients. Eighty patients underwent PFO closure. Residual shunts, MH, and visual aura were reassessed after 3 and 12 months.ResultsThe prevalence of R to L shunt in Groups A, B, and C was 96%, 72%, and 67%, respectively, versus 18% in the control group (p < 0.0001). The frequency of shunting was similar in Group B versus Group C, but much higher in all 3 groups compared with control subjects. Twelve months after PFO closure, symptoms of aura were resolved in 52%, 75%, and 80% of patients in Groups A, B, and C, respectively (p = NS).ConclusionsThe similar distribution of R to L shunting in all 3 patient groups and the correlation between PFO closure and improvement of aura suggests a similar pathophysiology between the presence of PFO and the visual aura phenomenon, whether or not headache is present in the symptom complex