Sublinear Higson corona and Lipschitz extensions

The purpose of the paper is to characterize the dimension of sublinear Higson corona $\nu_L(X)$ of $X$ in terms of Lipschitz extensions of functions: Theorem: Suppose $(X,d)$ is a proper metric space. The dimension of the sublinear Higson corona $\nu_L(X)$ of $X$ is the smallest integer $m\ge 0$ with the following property: Any norm-preserving asymptotically Lipschitz function $f'\colon A\to \R^{m+1}$, $A\subset X$, extends to a norm-preserving asymptotically Lipschitz function $g'\colon X\to \R^{m+1}$. One should compare it to the result of Dranishnikov \cite{Dr1} who characterized the dimension of the Higson corona $\nu(X)$ of $X$ is the smallest integer $n\ge 0$ such that $\R^{n+1}$ is an absolute extensor of $X$ in the asymptotic category \AAA (that means any proper asymptotically Lipschitz function $f\colon A\to \R^{n+1}$, $A$ closed in $X$, extends to a proper asymptotically Lipschitz function $f'\colon X\to \R^{n+1}$). \par In \cite{Dr1} Dranishnikov introduced the category \tilde \AAA whose objects are pointed proper metric spaces $X$ and morphisms are asymptotically Lipschitz functions $f\colon X\to Y$ such that there are constants $b,c > 0$ satisfying $|f(x)|\ge c\cdot |x|-b$ for all $x\in X$. We show $\dim(\nu_L(X))\leq n$ if and only if $\R^{n+1}$ is an absolute extensor of $X$ in the category \tilde\AAA. \par As an application we reprove the following result of Dranishnikov and Smith \cite{DRS}: Theorem: Suppose $(X,d)$ is a proper metric space of finite asymptotic Assouad-Nagata dimension \asdim_{AN}(X). If $X$ is cocompact and connected, then \asdim_{AN}(X) equals the dimension of the sublinear Higson corona $\nu_L(X)$ of $X$.Comment: 13 page

Venus Interior Structure Mission (VISM): Establishing a Seismic Network on Venus

Magellan radar data show the surface of Venus to contain a wide range of geologic features (large volcanoes, extensive rift valleys, etc.). Although networks of interconnecting zones of deformation are identified, a system of spreading ridges and subduction zones like those that dominate the tectonic style of the Earth do not appear to be present. In addition, the absence of a mantle low-viscosity zone suggests a strong link between mantle dynamics and the surface. As a natural follow-on to the Magellan mission, establishing a network of seismometers on Venus will provide detailed quantitative information on the large scale interior structure of the planet. When analyzed in conjunction with image, gravity, and topography information, these data will aid in constraining mechanisms that drive surface deformation

Compact maps and quasi-finite complexes

The simplest condition characterizing quasi-finite CW complexes $K$ is the implication $X\tau_h K\implies \beta(X)\tau K$ for all paracompact spaces $X$. Here are the main results of the paper: Theorem: If $\{K_s\}_{s\in S}$ is a family of pointed quasi-finite complexes, then their wedge $\bigvee\limits_{s\in S}K_s$ is quasi-finite. Theorem: If $K_1$ and $K_2$ are quasi-finite countable complexes, then their join $K_1\ast K_2$ is quasi-finite. Theorem: For every quasi-finite CW complex $K$ there is a family $\{K_s\}_{s\in S}$ of countable CW complexes such that $\bigvee\limits_{s\in S} K_s$ is quasi-finite and is equivalent, over the class of paracompact spaces, to $K$. Theorem: Two quasi-finite CW complexes $K$ and $L$ are equivalent over the class of paracompact spaces if and only if they are equivalent over the class of compact metric spaces. Quasi-finite CW complexes lead naturally to the concept of $X\tau {\mathcal F}$, where ${\mathcal F}$ is a family of maps between CW complexes. We generalize some well-known results of extension theory using that concept.Comment: 20 page

Deep space 2: The Mars Microprobe Mission

The Mars Microprobe Mission will be the second of the New Millennium Program's technology development missions to planetary bodies. The mission consists of two penetrators that weigh 2.4 kg each and are being carried as a piggyback payload on the Mars Polar Lander cruise ring. The spacecraft arrive at Mars on December 3, 1999. The two identical penetrators will impact the surface at similar to 190 m/s and penetrate up to 0.6 m. They will land within 1 to 10 km of each other and similar to 50 km from the Polar Lander on the south polar layered terrain. The primary objective of the mission is to demonstrate technologies that will enable future science missions and, in particular, network science missions. A secondary goal is to acquire science data. A subsurface evolved water experiment and a thermal conductivity experiment will estimate the water content and thermal properties of the regolith. The atmospheric density, pressure, and temperature will be derived using descent deceleration data. Impact accelerometer data will be used to determine the depth of penetration, the hardness of the regolith, and the presence or absence of 1.0 cm scale layers

Volcanic and Tectonic Constraints on the Evolution of Venus

Surface geologic features form a detailed record of Venus’ evolution. Venus displays a profusion of volcanic and tectonics features, including both familiar and exotic forms. One challenge to assessing the role of these features in Venus’ evolution is that there are too few impact craters to permit age dates for specific features or regions. Similarly, without surface water, erosion is limited and cannot be used to evaluate age. These same observations indicate Venus has, on average, a very young surface (150–1000 Ma), with the most recent surface deformation and volcanism largely preserved on the surface except where covered by limited impact ejecta. In contrast, most geologic activity on Mars, the Moon, and Mercury occurred in the 1st billion years. Earth’s geologic processes are almost all a result of plate tectonics. Venus’ lacks such a network of connected, large scale plates, leaving the nature of Venus’ dominant geodynamic process up for debate. In this review article, we describe Venus’ key volcanic and tectonic features, models for their origin, and possible links to evolution. We also present current knowledge of the composition and thickness of the crust, lithospheric thickness, and heat flow given their critical role in shaping surface geology and interior evolution. Given Venus’ hot lithosphere, abundant activity and potential analogues of continents, roll-back subduction, and microplates, it may provide insights into early Earth, prior to the onset of true plate tectonics. We explore similarities and differences between Venus and the Proterozoic or Archean Earth. Finally, we describe the future measurements needed to advance our understanding of volcanism, tectonism, and the evolution of Venus

SEIS: Insight's Seismic Experiment for Internal Structure of Mars.

By the end of 2018, 42 years after the landing of the two Viking seismometers on Mars, InSight will deploy onto Mars' surface the SEIS (Seismic Experiment for Internal Structure) instrument; a six-axes seismometer equipped with both a long-period three-axes Very Broad Band (VBB) instrument and a three-axes short-period (SP) instrument. These six sensors will cover a broad range of the seismic bandwidth, from 0.01 Hz to 50 Hz, with possible extension to longer periods. Data will be transmitted in the form of three continuous VBB components at 2 sample per second (sps), an estimation of the short period energy content from the SP at 1 sps and a continuous compound VBB/SP vertical axis at 10 sps. The continuous streams will be augmented by requested event data with sample rates from 20 to 100 sps. SEIS will improve upon the existing resolution of Viking's Mars seismic monitoring by a factor of ∼ 2500 at 1 Hz and ∼ 200 000 at 0.1 Hz. An additional major improvement is that, contrary to Viking, the seismometers will be deployed via a robotic arm directly onto Mars' surface and will be protected against temperature and wind by highly efficient thermal and wind shielding. Based on existing knowledge of Mars, it is reasonable to infer a moment magnitude detection threshold of M w ∼ 3 at 40 ∘ epicentral distance and a potential to detect several tens of quakes and about five impacts per year. In this paper, we first describe the science goals of the experiment and the rationale used to define its requirements. We then provide a detailed description of the hardware, from the sensors to the deployment system and associated performance, including transfer functions of the seismic sensors and temperature sensors. We conclude by describing the experiment ground segment, including data processing services, outreach and education networks and provide a description of the format to be used for future data distribution.Electronic supplementary materialThe online version of this article (10.1007/s11214-018-0574-6) contains supplementary material, which is available to authorized users

First Atmospheric Results from InSight APSS

NASA’s Mars InSight Spacecraft landed on Nov 26, 2018 (Ls=295°) in Elysium Planitia (~4.5°N, 136°E). InSight’s main scientific purpose is to investigate the interior structure and heat flux from Mars, but it is also equipped with instrumentation that can serve as a very capable meteorological station. To remove unwanted environmental noise from the seis- mic signals, InSight carries a very precise pressure sensor (PS) and the first magnetometer (IFG) to the surface of Mars. Additionally, to aid in removing the atmospheric pressure-induced seismic noise, and to identify periods when wind-induced seismic noise may reduce sensitivity, InSight also carries a pair of Wind and Air temperature sensors (TWINS). These three sensors comprise the Auxiliary Payload Sensor Suite (APSS) [1]. Complementing this are a radiometer in the HP3 suite to measure surface radiance, the seismic measurements of SEIS which can record interesting atmospheric phenomena, and the InSight cameras to image clouds and dust devils and estimate atmospheric opacity from dust or clouds. The Lander also carried accelerometers that can be used to reconstruct the at- mospheric structure during descent. We will discuss results drawn from atmospheric measurements on board InSight from the first months of operation, high- lighting the new perspectives permitted by the novel high-frequency, and continuous nature of the InSight data acquisition. Details on pre-landing scientific perspectives for atmospheric science with InSight are found in [2]

Near Surface Properties of Martian Regolith Derived From InSight HP3-RAD Temperature Observations During Phobos Transits

The Mars moon Phobos passed in front of the Sun from the perspective of the InSight lander on several occasions. The Mars surface temperatures measured by the lander became slightly colder during these transits due to the lower amount of sunlight the surface received at this time. The transits only last 20–35 s and therefore only the very top layer, about 0.3–0.8 mm, of the ground has time to cool significantly. The top layer cools and heats up faster than we expected based on the temperature changes of the day-night cycle, which affects about 4 cm of the ground. Based on this observation we conclude that the material in the top mm of the ground is different from that below. A possible explanation would be an increase of density with depth, a larger fraction of smaller particles such as dust at the top, or a layer where particles are slightly cemented together beginning at 0.2–4 mm below the surface.Additional co-authors: Axel Hagermann, Matthew Siegler, and W Bruce Banerd