Analogue Of Space Research Articles

Microimaging VIS‐IR spectroscopy of ancient volcanic rocks as Mars analogues

AbstractThe SPectral Imager (SPIM) facility is a laboratory VIS‐IR spectrometer developed to support spaceborne observations of rocky bodies of the solar system. Currently, this laboratory setup is used to support the Dawn NASA mission and to support the 2018 ExoMars mission in the spectral investigation of Martian subsurface. Specifically, for this mission, a selection of relevant Mars analogue materials has been characterized and stored in the International Space Analogue Rockstore (ISAR), hosted in Orléans, France. In this investigation, two volcanic rock samples from the ISAR collection were analyzed. These two samples were chosen because of their similarity in mineralogical composition and age with Martian basalts and volcanic sands. Moreover, volcanic sands are particularly interesting because they can contain fossils of primitive life forms. The analysis of data collected by SPIM resulted in good agreement with the mineralogical phases detected in these two samples by mineralogical and petrographical techniques, demonstrating the effectiveness of the high spatial and spectral resolution of SPIM for identifying and for mapping different mineralogical species on cut rock and mineral samples.

OPERATOR-VALUED FUNCTION SPACE INTEGRALS VIA CONDITIONAL INTEGRALS ON AN ANALOGUE WIENER SPACE II

In the present paper, using a simple formula for the conditional expectations given a generalized conditioning function over an analogue of vector-valued Wiener space, we prove that the analytic operator-valued Feynman integrals of certain classes of functions over the space can be expressed by the conditional analytic Feynman integrals of the functions. We then provide the conditional analytic Feynman integrals of several functions which are the kernels of the analytic operator-valued Feynman integrals.

A note on badly approximabe sets in projective space

Recently, Ghosh \& Haynes \cite{HG} proved a Khintchine-type result for the problem of Diophantine approximation in certain projective spaces. In this note we complement their result by observing that a Jarn\'{\i}k-type result also holds for `badly approximable' points in real projective space. In particular, we prove that the natural analogue in projective space of the classical set of badly approximable numbers has full Hausdorff dimension when intersected with certain compact subsets of real projective space. Furthermore, we also establish an analogue of Khintchine's theorem for convergence relating to `intrinsic' approximation of points in these compact sets.

The rational homology of spaces of long links

We provide a complete understanding of the rational homology of the space of long links of m strands in the euclidean space of dimension d > 3. First, we construct explicitly a cosimplicial chain complex whose totalization is quasi-isomorphic to the singular chain complex of the space of long links. Next we show (using the fact that the Bousfield-Kan spectral sequence associated to this cosimplcial chain complex collapses at the page 2) that the homology Bousfield-Kan spectral sequence associated to the Munson-Volic cosimplicial model for the space of long links collapses at the page 2 rationally, and this solves a conjecture of Munson-Volic. Our method enables us also to determine the rational homology of the high dimensional analogues of spaces of long links. The last result of this paper states that the radius of convergence of the Poincar\'e series for the space of long links (modulo immersions) tends to zero as m goes to the infinity.

Lessons from a Space Analog on Adaptation for Long-Duration Exploration Missions.

Exploration missions to asteroids and Mars will bring new challenges associated with communication delays and more autonomy for crews. Mission safety and success will rely on how well the entire system, from technology to the human elements, is adaptable and resilient to disruptive, novel, or potentially catastrophic events. The recent NASA Extreme Environment Missions Operations (NEEMO) 20 mission highlighted this need and produced valuable "lessons learned" that will inform future research on team adaptation and resilience. A team of NASA, industry, and academic members used an iterative process to design a tripod shaped structure, called the CORAL Tower, for two astronauts to assemble underwater with minimal tools. The team also developed assembly procedures, administered training to the crew, and provided support during the mission. During the design, training, and assembly of the Tower, the team learned first-hand how adaptation in extreme environments depends on incremental testing, thorough procedures and contingency plans that predict possible failure scenarios, and effective team adaptation and resiliency for the crew and support personnel. Findings from NEEMO 20 provide direction on the design and testing process for future space systems and crews to maximize adaptation. This experience also underscored the need for more research on team adaptation, particularly how input and process factors affect adaption outcomes, the team adaptation iterative process, and new ways to measure the adaptation process.

Effects of isolation and confinement on humans-implications for manned space explorations.

Human psychology and physiology are significantly altered by isolation and confinement. In light of planned exploration class interplanetary missions, the related adverse effects on the human body need to be explored and defined as they have a large impact on a mission's success. Terrestrial space analogs offer an excellent controlled environment to study some of these stressors during a space mission in isolation without the complex environment of the International Space Station. Participants subjected to these space analog conditions can encounter typical symptoms ranging from neurocognitive changes, fatigue, misaligned circadian rhythm, sleep disorders, altered stress hormone levels, and immune modulatory changes. This review focuses on both the psychological and the physiological responses observed in participants of long-duration spaceflight analog studies, such as Mars500 or Antarctic winter-over. They provide important insight into similarities and differences encountered in each simulated setting. The identification of adverse effects from confinement allows not only the crew to better prepare for but also to design feasible countermeasures that will help support space travelers during exploration class missions in the future.

Integral Transforms on a Function Space with Change of Scales Using Multivariate Normal Distributions

Using simple formulas for generalized conditional Wiener integrals on a function space which is an analogue of Wiener space, we evaluate two generalized analytic conditional Wiener integrals of a generalized cylinder function which is useful in Feynman integration theories and quantum mechanics. We then establish various integral transforms over continuous paths with change of scales for the generalized analytic conditional Wiener integrals. In these evaluation formulas and integral transforms we use multivariate normal distributions so that the orthonormalization process of projection vectors which are needed to establish the conditional Wiener integrals can be removed in the existing change of scale transforms. Consequently the transforms in the present paper can be expressed in terms of the generalized cylinder function itself.

Model oblique derivative problem for the heat equation in the Zygmund space H 1

The third boundary value problem and the oblique derivative problem for the heat equation are considered in model formulations. A difference compatibility condition is introduced for the initial and boundary functions. Under suitable assumptions made about the problem data, the solutions are shown to belong to the parabolic Zygmund space H1, which is the analogue of the parabolic Holder space for an integer smoothness exponent.

Tropical Linear Spaces and Tropical Convexity

In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the converse is true: Each tropical variety that is also tropically convex is supported on the complex of a valuated matroid. We also prove a tropical local-to-global principle: Any closed, connected, locally tropically convex set is tropically convex.

Mini-Workshop: Coideal Subalgebras of Quantum Groups

Coideal subalgebras of quantized enveloping algebras appear naturally if one considers quantum group analogs of Lie subalgebras. Examples appear in the theory of quantum integrable systems with boundary and in harmonic analysis on quantum group analogs of Riemannian symmetric spaces. Recently, much progress has been made to develop a deeper representation theoretic understanding of these examples. On the other hand, coideal subalgebras play a fundamental role in the theory of Nichols algebras. The workshop aimed to discuss these theories in view of the recent developments.

THE ARCSINE LAW IN THE ANALOGUE OF WIENER SPACE

In this note, we prove the theorems in analogue of Wiener space corresponding to the second and the third arcsine laws in the concrete Wiener space [1, 2] and we show that our results are exactly same to the concrete Wiener case when the initial condition gives the Dirac measure at the origin.

Formula omitted]-Finite distributions on p-adic groups

For a real reductive group G, the center z(U(g)) of the universal enveloping algebra of the Lie algebra g of G acts on the space of distributions on G. This action proved to be very useful (see e.g. [17,18,32,8]).Over non-Archimedean local fields, one can replace the action of z(U(g)) by the action of the Bernstein center z of G, i.e. the center of the category of smooth representations. However, this action is not well studied. In this paper we provide some tools to work with this action and prove the following results.•The wavefront set of any z-finite distribution ξ on G over any point g∈G lies inside the nilpotent cone of Tg⁎G≅g.•Let H1,H2⊂G be symmetric subgroups. Consider the space J of H1×H2-invariant distributions on G. We prove that the z-finite distributions in J form a dense subspace. In fact we prove this result in wider generality, where the groups Hi are spherical subgroups of certain type and the invariance condition is replaced by equivariance.Further we apply those results to density and regularity of relative characters.The first result can be viewed as a version of Howe's expansion of characters.The second result can be viewed as a spherical space analog of a classical theorem on density of characters of finite length representations. It can also be viewed as a spectral version of Bernstein's localization principle.In the Archimedean case, the first result is well-known and the second remains open.

Presenting the frame of the unit circle

We present the frame L(T) of the unit circle by generators and relations in two alternative ways. The first is the localic counterpart of the Alexandroff compactification of the real line while the other can be understood as a localic analogue of the quotient space R/Z. With an eye towards a prospective point-free description of Pontryagin duality, we then show how the usual group operations of the frame of reals can be lifted to the new frame L(T), endowing it with a canonical localic group structure.

Tropical geometry of moduli spaces of weighted stable curves

Hassett's moduli spaces of weighted stable curves form an important class of alternate modular compactifications of the moduli space of smooth curves with marked points. In this article we define a tropical analogue of these moduli spaces and show that the naive set-theoretic tropicalization map can be identified with a natural deformation retraction onto the non-Archimedean skeleton. This result generalizes work of Abramovich, Caporaso, and Payne treating the Deligne-Knudsen-Mumford compactification of the moduli space of smooth curves with marked points. We also study tropical analogues of the tautological maps, investigate the dependence of the tropical moduli spaces on the weight data, and consider the example of Losev-Manin spaces.

CONVERGENCE THEOREMS FOR A PAIR OF ASYMPTOTICALLY AND MULTIVALUED NONEXPANSIVE MAPPING IN CAT(0) SPACES

In this paper, we prove <TEX>${\Delta}$</TEX>-convergence theorems for Ishikawa iteration of asymptotically and multivalued nonexpansive mapping in CAT(0) spaces. This results we obtain are analogs of Banach spaces results of Sokhuma [13].

Hyperpolygons and Hitchin Systems

We study the hyperk\"ahler analogues of moduli spaces of semistable n-gons in complex projective space. We prove that the hyperk\"ahler Kirwan map is surjective and produce a formula that recursively calculates the Betti numbers of these spaces for all ranks. Building on a natural analogy between hyperpolygons and parabolic Higgs bundles, we identify hyperpolygon spaces with certain degenerate Hitchin systems, and use this to establish their complete integrability, for ranks up to and including 3.

Operator space and operator system analogs of Kirchberg's nuclear embedding theorem

The Gurarij operator space NG introduced by Oikhberg is the unique separable 1-exact operator space that is approximately injective in the category of 1-exact operator spaces and completely isometric linear maps. We prove that a separable operator space X is nuclear if and only if there exist a linear complete isometry φ:X→NG and a completely contractive projection from NG onto the range of φ. This can be seen as the operator space analog of Kirchberg's nuclear embedding theorem. With similar methods we also establish the natural operator system analog of Kirchberg's nuclear embedding theorem involving the Gurarij operator system GS.

MODULI SPACES OF (G, h)-CONSTELLATIONS

Given an infinite reductive group G acting on an affine scheme X over C and a Hilbert function h: Irr G \to N_0, we construct the moduli space M_{\theta}(X) of \theta-stable (G,h)-constellations on X, which is a generalization of the invariant Hilbert scheme after Alexeev and Brion and an analogue of the moduli space of \theta-stable G-constellations for finite groups introduced by Craw and Ishii. Our construction of a morphism M_{\theta}(X) \to X//G makes this moduli space a candidate for a resolution of singularities of the quotient X//G.

Sounds and Other Denizens of Time

On the basis of the No-Space world thought experiment put forward by Strawson in his Individuals , we attempt to clarify in what sense there may be individual entities that exist only in time and to what extent such entities may qualify as belonging to an objective reality. For Strawson it is sounds which are the individuals of the No-Space world, and on Strawson’s view sounds can belong to objective reality provided that they can be related to an auditory analogue of space. We argue that such an analogue of space can be specified in terms of a system of “master-sounds” that function as analogues of spatial bodies. We then extend our treatment of Strawson’s thought experiment to include parts of the social world that, just like sounds, may be taken to exist only in time. We conclude by proposing a characterization of poems, games of (blind) chess, obligations, debts, and certain other social entities as “No-Space artifacts” since they, too, can exist not only in our spatial world but also in the No-Space world sketched by Strawson.

Testing the ability of the ExoMars 2018 payload to document geological context and potential habitability on Mars

The future ExoMars rover mission (ESA/Roscosmos), to be launched in 2018, will investigate the habitability of the Martian surface and near subsurface, and search for traces of past life in the form of textural biosignatures and organic molecules. In support of this mission, a selection of relevant Mars analogue materials has been characterised and stored in the International Space Analogue Rockstore (ISAR), hosted in Orléans, France. Two ISAR samples were analysed by prototypes of the ExoMars rover instruments used for petrographic study. The objective was to determine whether a full interpretation of the rocks could be achieved on the basis of the data obtained by the ExoMars visible-IR imager and spectrometer (MicrOmega), the close-up imager (CLUPI), the drill infrared spectrometer (Ma_Miss) and the Raman spectrometer (RLS), first separately then in their entirety. In order to not influence the initial instrumental interpretation, the samples were sent to the different teams without any additional information. This first step was called the “Blind Test” phase. The data obtained by the instruments were then complemented with photography of the relevant outcrops (as would be available during the ExoMars mission) before being presented to two geologists tasked with the interpretation. The context data and photography of the outcrops and of the samples were sufficient for the geologists to identify the rocks. This initial identification was crucial for the subsequent, iterative interpretation of the spectroscopic data. The data from the different spectrometers was, thus, cross-calibrated against the photographic interpretations and against each other. In this way, important mineralogical details, such as evidence of aqueous alteration of the rocks, provided relevant information concerning potential habitable conditions. The final conclusion from this test is that, when processed together, the ExoMars payload instruments produce complementary data allowing reliable interpretation of the geological context and potential for habitable environments. This background information is fundamental for the analysis and interpretation of organics in the processed Martian rocks.