On subset sums of pseudo–recursive sequences

Let a0 = a 2 N, fMig1i =1 be an infinite set of integers and fb1; b2; : : : ; bkg be a finite set of integers. We say that faig1 i=0 is a pseudo-recursive sequence if an+1 = Mn+1an + bjn+1 (bjn+1 2 fb1; b2; : : : bkg) holds. In the first part of the paper, we investigate the subset sum of a generalized version of A := fan = b2nc : n = 0; 1; 2; : : : g, which is a special pseudorecursive sequence. In the second part, we use A for an encryption algorith

Relative photometry of HAT-P-1b occultations

We present HST STIS observations of two occultations of the transiting exoplanet HAT-P-1b. By measuring the planet to star flux ratio near opposition, we constrain the geometric albedo of the planet, which is strongly linked to its atmospheric temperature gradient. An advantage of HAT-P-1 as a target is its binary companion ADS 16402 A, which provides an excellent photometric reference, simplifying the usual steps in removing instrumental artifacts from HST time-series photometry. We find that without this reference star, we would need to detrend the lightcurve with the time of the exposures as well as the first three powers of HST orbital phase, and this would introduce a strong bias in the results for the albedo. However, with this reference star, we only need to detrend the data with the time of the exposures to achieve the same per-point scatter, therefore we can avoid most of the bias associated with detrending. Our final result is a 2 sigma upper limit of 0.64 for the geometric albedo of HAT-P-1b between 577 and 947 nm.Comment: 8 pages, 2 figures, 3 table

Safety and Efficacy of Weekly 30,000 IU Vitamin D Supplementation as a Slower Loading Dose Administration Compared to a Daily Maintenance Schedule in Deficient Patients: a Randomized, Controlled Clinical Trial

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Photocatalytic hollow TiO2 and ZnO nanospheres prepared by atomic layer deposition

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Periastron Precession Measurements in Transiting Extrasolar Planetary Systems at the Level of General Relativity

Transiting exoplanetary systems are surpassingly important among the planetary systems since they provide the widest spectrum of information for both the planet and the host star. If a transiting planet is on an eccentric orbit, the duration of transits T_D is sensitive to the orientation of the orbital ellipse relative to the line of sight. The precession of the orbit results in a systematic variation in both the duration of individual transit events and the observed period between successive transits, P_obs. The periastron of the ellipse slowly precesses due to general relativity and possibly the presence of other planets in the system. This secular precession can be detected through the long-term change in P_obs (transit timing variations, TTV) or in T_D (transit duration variations, TDV). We estimate the corresponding precession measurement precision for repeated future observations of the known eccentric transiting exoplanetary systems (XO-3b, HD 147506b, GJ 436b and HD 17156b) using existing or planned space-borne instruments. The TDV measurement improves the precession detection sensitivity by orders of magnitude over the TTV measurement. We find that TDV measurements over a ~4 year period can typically detect the precession rate to a precision well exceeding the level predicted by general relativity.Comment: Accepted for publication in MNRAS, 8+epsilon pages, 2 figure

Decoration of Vertically Aligned Carbon Nanotubes with Semiconductor Nanoparticles Using Atomic Layer Deposition

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