Classes of Analytic Functions Defined by a Differential Operator Related to Conic Domains

Let A be the class of functions f(z) = z + ∑ k = 2∞ a k z k analytic in an open unit disc ∆. We use a generalized linear operator closely related to the multiplier transformation to study certain subclasses of A mapping ∆ onto conic domains. Using the principle of the differential subordination and the techniques of convolution, we investigate several properties of these classes, including some inclusion relations and convolution and coefficient bounds. In particular, we get many known and new results as special cases.Нехай A — клас функцій f(z) = z + ∑∞k = 2akzk, аналітичних у відкритому одиничному крузі Δ. До вивчення деяких підкласів A, що відображають Δ на конічні області, застосовано узагальнений лінійний оператор, тісно пов'язаний з перетворенням множення. За допомогою принципу диференціального підпорядкування та техніки згорток вивчено деякі властивості цих класів, що включають деякі співвідношення включення та згорток, а також оцінки для коефіцієнтів. Наприклад, низку відомих та нових результатів отримано як частинні випадки

Assessment of detectability of neutral interstellar deuterium by IBEX observations

The abundance of deuterium in the interstellar gas in front of the Sun gives insight into the processes of filtration of neutral interstellar species through the heliospheric interface and potentially into the chemical evolution of the Galactic gas. We investigate the possibility of detection of neutral interstellar deuterium at 1 AU from the Sun by direct sampling by the Interstellar Boundary Explorer (IBEX). We simulate the flux of neutral interstellar D at IBEX for the actual measurement conditions. We assess the number of interstellar D atom counts expected during the first three years of IBEX operation. We also simulate observations expected during an epoch of high solar activity. In addition, we calculate the expected counts of D atoms from the thin terrestrial water layer, sputtered from the IBEX-Lo conversion surface by neutral interstellar He atoms. Most D counts registered by IBEX-Lo are expected to originate from the water layer, exceeding the interstellar signal by 2 orders of magnitude. However, the sputtering should stop once the Earth leaves the portion of orbit traversed by interstellar He atoms. We identify seasons during the year when mostly the genuine interstellar D atoms are expected in the signal. During the first 3 years of IBEX operations about 2 detectable interstellar D atoms are expected. This number is comparable with the expected number of sputtered D atoms registered during the same time intervals. The most favorable conditions for the detection occur during low solar activity, in an interval including March and April each year. The detection chances could be improved by extending the instrument duty cycle, e.g., by making observations in the special deuterium mode of IBEX-Lo.Comment: Accepted for Astronomy & Astrophysic

Exploring the Possibility of O And Ne Contamination in Ulysses Observations of Interstellar Helium

We explore the possibility that interstellar O and Ne may be contributing to the particle signal from the GAS instrument on Ulysses, which is generally assumed to be entirely He. Motivating this study is the recognition that an interstellar temperature higher than any previously estimated from Ulysses data could potentially resolve a discrepancy between Ulysses He measurements and those from the Interstellar Boundary Explorer (IBEX). Contamination by O and Ne could lead to Ulysses temperature measurements that are too low. We estimate the degree of O and Ne contamination necessary to increase the inferred Ulysses temperature to 8500 K, which would be consistent with both the Ulysses and IBEX data given the same interstellar flow speed. We find that producing the desired effect requires a heavy element contamination level of ~9% of the total Ulysses/GAS signal. However, this degree of heavy element contribution is about an order of magnitude higher than expected based on our best estimates of detection efficiencies, ISM abundances, and heliospheric survival probabilities, making it unlikely that heavy element contamination is significantly affecting temperatures derived from Ulysses data

On some first-order differential subordination

AbstractLet A denote the class of functions f that are analytic in the unit disc D and normalized by f(0)=f′(0)−1=0. In this paper, we investigate the class of functions such that Re{f′(z)+zf″(z)-β}>α in D. We determine conditions for α and β under which the function f is univalent, close-to-convex, and convex. To obtain this, we first estimate ∣Arg{f′(z)}∣ which improves the earlier results

The downwind hemisphere of the heliosphere: Eight years of IBEX-Lo observations

We present a comprehensive study of energetic neutral atoms (ENAs) of 10 eV to 2.5 keV from the downwind hemisphere of the heliosphere. These ENAs are believed to originate mostly from pickup protons and solar wind protons in the inner heliosheath. This study includes all low-energy observations made with the Interstellar Boundary Explorer over the first 8 years. Since the protons around 0.1 keV dominate the plasma pressure in the inner heliosheath in downwind direction, these ENA observations offer the unique opportunity to constrain the plasma properties and dimensions of the heliosheath where no in-situ observations are available. We first derive energy spectra of ENA intensities averaged over time for 49 macropixels covering the entire downwind hemisphere. The results confirm previous studies regarding integral intensities and the roll-over around 0.1 keV energy. With the expanded dataset we now find that ENA intensities at 0.2 and 0.1 keV seem to anti-correlate with solar activity. We then derive the product of total plasma pressure and emission thickness of protons in the heliosheath to estimate lower limits on the thickness of the inner heliosheath. The temporally averaged ENA intensities support a rather spherical shape of the termination shock and a heliosheath thickness between 150 and 210 au for most regions of the downwind hemisphere. Around the nominal downwind direction of 76{\deg} ecliptic longitude, the heliosheath is at least 280 au thick. There, the neutral hydrogen density seems to be depleted compared to upwind directions by roughly a factor of 2.Comment: Preprint of article in The Astrophysical Journa

Synthesis and Properties of High Tilted Antiferroelectric Esters with Partially Fluorinated Alkoxyalkoxy Terminal Chains

Novel chiral esters with partially fluorinated alkoxyalkoxy terminal chains are described. Their phase transition temperatures, enthalpies, and electrooptical properties are reported. A helical pitch in pure compounds and their mixtures based on selective reflection of light is also characterized

Warm Breeze from the starboard bow: a new population of neutral helium in the heliosphere

We investigate the signals from neutral He atoms observed from Earth orbit in 2010 by IBEX. The full He signal observed during the 2010 observation season can be explained as a superposition of pristine neutral interstellar He gas and an additional population of neutral He that we call the Warm Breeze. The Warm Breeze is approximately two-fold slower and 2.5 times warmer than the primary interstellar He population, and its density in front of the heliosphere is ~7% that of the neutral interstellar helium. The inflow direction of the Warm Breeze differs by ~19deg from the inflow direction of interstellar gas. The Warm Breeze seems a long-term feature of the heliospheric environment. It has not been detected earlier because it is strongly ionized inside the heliosphere, which brings it below the threshold of detection via pickup ion and heliospheric backscatter glow observations, as well as by the direct sampling of GAS/Ulysses. Possible sources for the Warm Breeze include (1) the secondary population of interstellar helium, created via charge exchange and perhaps elastic scattering of neutral interstellar He atoms on interstellar He+ ions in the outer heliosheath, or (2) a gust of interstellar He originating from a hypothetic wave train in the Local Interstellar Cloud. A secondary population is expected from models, but the characteristics of the Warm Breeze do not fully conform to modeling results. If, nevertheless, this is the explanation, IBEX-Lo observations of the Warm Breeze provide key insights into the physical state of plasma in the outer heliosheath. If the second hypothesis is true, the source is likely to be located within a few thousand of AU from the Sun, which is the propagation range of possible gusts of interstellar neutral helium with the Warm Breeze characteristics against dissipation via elastic scattering in the Local Cloud.Comment: submitted to ApJ