Search

A connected graph G of diameter diam (G) ≥ ℓ is ℓ -distance-balanced if | W xy | = | W yx | for every x , y ∈ V (G) with d G (x , y) = ℓ , where W xy is the set of vertices of G that are closer to x than to y. We prove that the generalized Petersen graph GP(n, k) is diam (G P (n , k)) -distance-balanced provided that n is large enough relative to k. This partially solves a conjecture posed by Miklavič and Šparl (Discrete Appl Math 244:143–154, 2018). We also determine diam (G P (n , k)) when n is large enough relative to k. [ABSTRACT FROM AUTHOR]

In this paper, we consider the main eigenvalues of connected chain graphs. We provide some properties of the eigenvectors corresponding to the main eigenvalues, upper and lower bounds on the number of main eigenvalues in connected chain graphs as well as examples that show that these bounds are attainable. As a consequence, we show that, for any positive integer k there exists a chain graph with k main eigenvalues. We also prove that there is no connected controllable chain graph. Our results make a bridge between the spectral properties of tridiagonal matrices and of chain graphs. [ABSTRACT FROM AUTHOR]

Let G be a graph. The Steiner distance of W ⊆ V (G) is the minimum size of a connected subgraph of G containing W. Such a subgraph is necessarily a tree called a Steiner W-tree. The set A ⊆ V (G) is a k-Steiner general position set if V (T B) ∩ A = B holds for every set B ⊆ A of cardinality k, and for every Steiner B-tree T B . The k-Steiner general position number sgp k (G) of G is the cardinality of a largest k-Steiner general position set in G. Steiner cliques are introduced and used to bound sgp k (G) from below. The k-Steiner general position number is determined for trees, cycles and joins of graphs. Lower bounds are presented for split graphs, infinite grids and lexicographic products. The lower bound for the latter product leads to an exact formula for the general position number of an arbitrary lexicographic product. [ABSTRACT FROM AUTHOR]

Let T be a tree on n vertices and algebraic connectivity α (T). The trees on n ≥ 45 vertices and α (T) ≥ 5 - 21 2 have already been completely characterized. In case of α (T) ≥ 2 - 3 , it was proved that this set of trees can be partitioned in six classes, C i , 1 ≤ i ≤ 6 , ordered by algebraic connectivity, in the sense that α (T i) > α (T j) whenever T i ∈ C i , T j ∈ C j , and 1 ≤ i < j ≤ 6. In this work, we extend both results by studying four classes of trees, C i , 7 ≤ i ≤ 10. We prove that, for n ≥ 45 , 2 1 - cos π 7 ≤ α (T) < 5 - 21 2 if and only if T ∈ C 9 ∪ C 10 . Moreover, the set of trees with 2 1 - cos π 7 ≤ α (T) < 2 - 3 can be partitioned in the classes C i , 7 ≤ i ≤ 10 , also ordered by algebraic connectivity. [ABSTRACT FROM AUTHOR]

The transmission of a vertex v in a graph is the sum of the distances from v to all other vertices of the graph. In a transmission irregular graph, the transmissions of all vertices are pairwise distinct. It is known that almost all graphs are not transmission irregular. Some infinite family of transmission irregular trees was constructed by Alizadeh and Klavžar [Appl.Math. Comput. 328, 113-118 (2018)] and the following problemwas formulated: Is there an infinite family of 2-connected graphs with the property? In this article, we construct an infinite family of 2-connected transmission irregular graphs. [ABSTRACT FROM AUTHOR]

The MAVEN Solar Wind Electron Analyzer (SWEA) is a symmetric hemispheric electrostatic analyzer with deflectors that is designed to measure the energy and angular distributions of 3-4600-eV electrons in the Mars environment. This energy range is important for impact ionization of planetary atmospheric species, and encompasses the solar wind core and halo populations, shock-energized electrons, auroral electrons, and ionospheric primary photoelectrons. The instrument is mounted at the end of a 1.5-meter boom to provide a clear field of view that spans nearly 80 % of the sky with ∼20° resolution. With an energy resolution of 17 % ( $\Delta E/E$), SWEA readily distinguishes electrons of solar wind and ionospheric origin. Combined with a 2-second measurement cadence and on-board real-time pitch angle mapping, SWEA determines magnetic topology with high (∼8-km) spatial resolution, so that local measurements of the plasma and magnetic field can be placed into global context. [ABSTRACT FROM AUTHOR]

The MAVEN SupraThermal And Thermal Ion Compostion (STATIC) instrument is designed to measure the ion composition and distribution function of the cold Martian ionosphere, the heated suprathermal tail of this plasma in the upper ionosphere, and the pickup ions accelerated by solar wind electric fields. STATIC operates over an energy range of 0.1 eV up to 30 keV, with a base time resolution of 4 seconds. The instrument consists of a toroidal 'top hat' electrostatic analyzer with a $360^{\circ} \times 90^{\circ}$ field-of-view, combined with a time-of-flight (TOF) velocity analyzer with $22.5^{\circ}$ resolution in the detection plane. The TOF combines a $-15~\mbox{kV}$ acceleration voltage with ultra-thin carbon foils to resolve $\mathrm{H}^{+}$, $\mathrm{He}^{++}$, $\mathrm{He}^{+}$, $\mathrm{O}^{+}$, $\mathrm{O}_{2}^{+}$, and $\mathrm{CO}_{2}^{+}$ ions. Secondary electrons from carbon foils are detected by microchannel plate detectors and binned into a variety of data products with varying energy, mass, angle, and time resolution. To prevent detector saturation when measuring cold ram ions at periapsis ( $\sim10^{1 1}~\mbox{eV/cm}^{2}\,\mbox{s}\,\mbox{sr}\,\mbox{eV}$), while maintaining adequate sensitivity to resolve tenuous pickup ions at apoapsis ( $\sim10^{3}~\mbox{eV/cm}^{2}\,\mbox{s}\,\mbox{sr}\,\mbox{eV}$), the sensor includes both mechanical and electrostatic attenuators that increase the dynamic range by a factor of $10^{3}$. This paper describes the instrument hardware, including several innovative improvements over previous TOF sensors, the ground calibrations of the sensor, the data products generated by the experiment, and some early measurements during cruise phase to Mars. [ABSTRACT FROM AUTHOR]

The Solar Wind Ion Analyzer (SWIA) on the MAVEN mission will measure the solar wind ion flows around Mars, both in the upstream solar wind and in the magneto-sheath and tail regions inside the bow shock. The solar wind flux provides one of the key energy inputs that can drive atmospheric escape from the Martian system, as well as in part controlling the structure of the magnetosphere through which non-thermal ion escape must take place. SWIA measurements contribute to the top level MAVEN goals of characterizing the upper atmosphere and the processes that operate there, and parameterizing the escape of atmospheric gases to extrapolate the total loss to space throughout Mars' history. To accomplish these goals, SWIA utilizes a toroidal energy analyzer with electrostatic deflectors to provide a broad 360×90 field of view on a 3-axis spacecraft, with a mechanical attenuator to enable a very high dynamic range. SWIA provides high cadence measurements of ion velocity distributions with high energy resolution (14.5 %) and angular resolution (3.75×4.5 in the sunward direction, 22.5×22.5 elsewhere), and a broad energy range of 5 eV to 25 keV. Onboard computation of bulk moments and energy spectra enable measurements of the basic properties of the solar wind at 0.25 Hz. [ABSTRACT FROM AUTHOR]

Palestine has a wide range of agro-ecological concerns and hosts a large variety of plants. Grapes are part of the cultural heritage and provide an indispensable food ingredient. Local cultivars have been traditionally identified on the basis of morphological traits, geographical origin, or names of the vineyard owner; therefore, the occurrence of homonymy, synonymy, and misnaming significantly prevents their valorization. DNA profiling by 22 common SSR markers was used to characterize 43 putative cultivars grown mainly for local table grape consumption at the southern highland regions of West-Bank, to further evaluate genetic diversity and relationships of the population. Consistent matching of SSR markers with grapevines cultivated in neighboring countries or maintained in European germplasm collections was found for 8 of the 21 different non-redundant genotypes discovered, suggesting possible synonyms as well as the occurrence of breeding selections formerly developed in the USA. Genetic relationships inferred from SSR markers clearly assigned Palestinian cultivars to the Proles orientalis subpr. Antasiatica ancestral population, and they even remarked the connection between local resources and cultivars generated from international table grape breeding. This study supports the value of collection and conservation of vines endemic to a region of immense historical importance for viticulture. [ABSTRACT FROM AUTHOR]

Monitoring of solar wind parameters is a key problem of the Space Weather program. The paper presents a description of a novel fast solar wind monitor (Bright Monitor of the Solar Wind, BMSW) and the first results of its measurements of plasma moments with a time resolution ranging from seconds to 31 ms. The method of the fast monitoring is based on simultaneous measurements of the total ion flux and ion integral energy spectrum by six nearly identical Faraday cups (FCs). Three of them are dedicated to determination of the ion flow direction, whereas other three equipped with control grids supplied by a retarding potential are used for a determination of the density, temperature, and speed of the plasma flow. The paper introduces not only the measuring methods, the FCs design, and modes of operation, but brings the examples of time series of measurements and their comparison with the observations of other spacecraft as well as the first results of an analysis of frequency spectra of solar wind fluctuations within the ion kinetic scale, examples of rapid measurements at the ramp of an interplanetary shock and investigations of fast variations of alpha particle content. [ABSTRACT FROM AUTHOR]

The rheological behavior of Dibenzylidene D-Sorbitol (DBS) gels formed in ethylene glycol, glycerol, mineral oil, ethanol, and chlorobenzene was studied using oscillatory squeezing flow viscometry. The storage ( G) and loss ( G) moduli were measured as a function of gellant concentration (0.5-2 w/ w) and type of solvent. As expected greater values of gel strength ( G) were observed for gels containing higher concentrations of DBS. In addition, both storage and loss moduli of 2% systems were mostly frequency independent over the studied range, whereas 0.5% gels did exhibit some degree of dependence. We also found that the solvent plays an important role in the properties of the gels. Among the parameters that affect the viscoelastic properties of DBS gels, the solvent polarity and its ability to form hydrogen bonding may have significant effects on the gel rheology. [ABSTRACT FROM AUTHOR]

We present observations from the first passage through the lunar plasma wake by one of two spacecraft comprising ARTEMIS (Acceleration, Reconnection, Turbulence, and Electrodynamics of the Moon's Interaction with the Sun), a new lunar mission that re-tasks two of five probes from the THEMIS magnetospheric mission. On Feb 13, 2010, ARTEMIS probe P1 passed through the wake at ∼3.5 lunar radii downstream from the Moon, in a region between those explored by Wind and the Lunar Prospector, Kaguya, Chandrayaan, and Chang'E missions. ARTEMIS observed interpenetrating proton, alpha particle, and electron populations refilling the wake along magnetic field lines from both flanks. The characteristics of these distributions match expectations from self-similar models of plasma expansion into vacuum, with an asymmetric character likely driven by a combination of a tilted interplanetary magnetic field and an anisotropic incident solar wind electron population. On this flyby, ARTEMIS provided unprecedented measurements of the interpenetrating beams of both electrons and ions naturally produced by the filtration and acceleration effects of electric fields set up during the refilling process. ARTEMIS also measured electrostatic oscillations closely correlated with counter-streaming electron beams in the wake, as previously hypothesized but never before directly measured. These observations demonstrate the capability of the comprehensively instrumented ARTEMIS spacecraft and the potential for new lunar science from this unique two spacecraft constellation. [ABSTRACT FROM AUTHOR]

The THEMIS plasma instrument is designed to measure the ion and electron distribution functions over the energy range from a few eV up to 30 keV for electrons and 25 keV for ions. The instrument consists of a pair of “top hat” electrostatic analyzers with common 180°×6° fields-of-view that sweep out 4 π steradians each 3 s spin period. Particles are detected by microchannel plate detectors and binned into six distributions whose energy, angle, and time resolution depend upon instrument mode. On-board moments are calculated, and processing includes corrections for spacecraft potential. This paper focuses on the ground and in-flight calibrations of the 10 sensors on five spacecraft. Cross-calibrations were facilitated by having all the plasma measurements available with the same resolution and format, along with spacecraft potential and magnetic field measurements in the same data set. Lessons learned from this effort should be useful for future multi-satellite missions. [ABSTRACT FROM AUTHOR]