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The result is established for a Jordan measurable region with rectifiable boundary. The integrand F for the new plane integral to be used is a function of axis-parallel rectangles, finitely additive on non-overlapping ones, hence unambiguously defined and additive on "figures" (i.e. finite unions of axis-parallel rectangles). Define its integral over Jordan measurable S as the limit of its value on the figures, which contain a subfigure of S and are contained in a figure containing S, as the former/complements of the latter expand directedly to fill out S/the complement of S. The integral over every Jordan measurable region exists when additive F is "absolutely continuous" in the sense of converging to zero as the area enclosed by its argument does, or with F the circumferential line integral $\oint P dx + Q dy$ for $P$, $Q$ continuous at the rectifiable boundary of S and integrable along axis - parallel line segments. Thus the equality of this area integral with the line integral around the boundary, to be proved, follows for the various integrals of divergence presented in: Pfeffer, W.F. The Riemann Approach to Integration, Cambridge Univ. Press, New York, 1993., Comment: 5 pages, no figures green.tex is an AMS-TeX file. To process, run the command > amstex green.tex

The Mars Exploration Rover Spirit ended its mission in Gusev crater on sol 2210 after it had become stuck in a deposit of fined-grained and sulfate rich soil with dust covered solar panels unfavorably pointed toward the sun. Final analysis of remaining data from Spirit's Moessbauer spectrometer (Fe redox and mineralogy) for sols 1529 through 2071 is now complete. We focus here on chemical (APXS) and MB data for targets having high-SiO2 or high-SO3 and process link the targets through mixing and geochemical modelling to an acid-sulfate system centered at Home Plate, which is considered to be a hydrovolcanic complex.

The Mars Exploration Rover Opportunity encountered sedimentary outcrop rocks at its landing site. Spherules with diameters in the millimeter range were found to weather from the outcrop rocks. With Opportunity s miniaturised M ssbauer spectrometer MIMOS II, hematite was detected in spherules and in the outcrop matrix [1,2]. Figure 1 shows the target Berry Bowl, where brushed outcrop and an accumulation of spherules could be investigated on sols 46 and 48 of Opportunity s mission. Hematite undergoes a transition from a weakly ferromagnetic above to an antiferromagnetic state below the Morin temperature (T(sub M) approx.265 K for chemically pure, crystalline hematite). The magnetic hyperfine splitting (B(sub hf)) shows a general decrease with increasing temperature and a drop of approx.0.8 T at T(sub M). The quadrupole splitting ((Delta)EQ) changes its sign at T(sub M), with negative values above and positive values below the transition. Crystallinity and particle size influence the magnitude and temperature dependence of the magnetic splitting and the quadrupole splitting [3].

Mossbauer spectrometers [1] on the two Mars Exploration Rovers (MERs) have been making measurements of surface rocks and soils since January 2004, recording spectra in 10-K-wide temperature bins ranging from 180 K to 290 K. Initial analyses focused on modeling individual spectra directly as acquired or, to increase statistical quality, as sums of single-rock or soil spectra over temperature or as sums over similar rock or soil type [2, 3]. Recently, we have begun to apply simultaneous fitting procedures [4] to Mars Mossbauer data [5-7]. During simultaneous fitting (simfitting), many spectra are modeled similarly and fit together to a single convergence criterion. A satisfactory simfit with parameter values consistent among all spectra is more likely than many single-spectrum fits of the same data because fitting parameters are shared among multiple spectra in the simfit. Consequently, the number of variable parameters, as well as the correlations among them, is greatly reduced. Here we focus on applications of simfitting to interpret the hematite signature in Moessbauer spectra acquired at Meridiani Planum, results of which were reported in [7]. The Spectra. We simfit two sets of spectra with large hematite content [7]: 1) 60 rock outcrop spectra from Eagle Crater; and 2) 46 spectra of spherule-rich lag deposits (Table 1). Spectra of 10 different targets acquired at several distinct temperatures are included in each simfit set. In the table, each Sol (martian day) represents a different target, NS is the number of spectra for a given sol, and NT is the number of spectra for a given temperature. The spectra are indexed to facilitate definition of parameter relations and constraints. An example spectrum is shown in Figure 1, together with a typical fitting model. Results. We have shown that simultaneous fitting is effective in analyzing a large set of related MER Mossbauer spectra. By using appropriate constraints, we derive target-specific quantities and the temperature dependence of certain parameters. By examining different fitting models, we demonstrate an improved fit for martian hematite modeled with two sextets rather than as a single sextet, and show that outcrop and spherule hematite are distinct. For outcrop, the weaker sextet indicates a Morin transition typical of well-crystallized and chemically pure hematite, while most of the outcrop hematite remains in a weakly ferromagnetic state at all temperatures. For spherule spectra, both sextets are consistent with weakly ferromagnetic hematite with no Morin transition. For both hematites, there is evidence for a range of particle sizes.

The Mars Exploration Rover Opportunity has encountered four iron meteorites at its landing site in Meridiani Planum. The first one, informally named "Heat Shield Rock", measuring approx.30 by 15 cm, was encountered in January 2005 [1, 2] and officially recognized as the first iron meteorite on the martian surface with the name "Meridiani Planum" after the location of its find [3]. We will refer to it as "Heat Shield Rock" to avoid confusion with the site. Between July and October 2009, separated approx.10 km from Heat Shield Rock, three other iron meteorite fragments were encountered, informally named "Block Island" (approx.60 cm across), "Shelter Island" (approx.50 by 20 cm), and "Mackinac Island" (approx.30 cm across). Heat Shield Rock and Block Island, the two specimens investigated in detail, are shown in Figure 1. Here, we focus on the meteorites chemistry and mineralogy. An overview in the mission context is given in [4]; other abstracts discuss their morphology [5], photometric properties [6], and their provenance [7].

While rolling over the Meridiani Planum sedimentary terrane, the rover Opportunity has occasionally discovered large, > 10 cm erratics. Most of these have proven to be meteorites [1], but one - Bounce Rock - is a martian basaltic rock similar in composition to the meteorite EETA79001 lithology B [2]. Presently, Opportunity is intensively investigating an --30 cm tall rock named Marquette Island that may be a distinct type of martian mafic lithology. We report the results of its continuing investigation using the Microscopic Imager (MI); Mossbauer Spectrometer (MB) and Alpha Particle X-ray Spectrometer (APXS). A companion abstract discusses the results of Panoramic Camera (Pancam) imaging of the rock [3].

The Mars Exploration Rover (MER) Opportunity has been studying Meridiani Planum for five years. On sol 1634 of its mission, Opportunity left Victoria crater after investigating it for approximately 682 sols [1] and is now on a journey towards Endeavour, a 24 km diameter crater about 12 km southeast of Victoria. A priority along the way is the investigation of cobbles, which in the jargon of the MER science team denotes any loose rock fragment larger than a couple of centimeters. Cobbles investigated thus far are of diverse origin [2] and provide the only means to investigate material other than the ubiquitous sulfate-rich outcrop, basaltic sand or hematiterich spherules dubbed blueberries. Some of these cobbles are meteorites [3]. Meteorites on Mars are not just a curiosity that make Mars a more Earth-like planet. Metallic iron in meteorites, for example, may be used as a more sensitive tracer for volatile surface interactions compared to igneous minerals [4]. Between sols 1713 and 1749, including the period of Mars solar conjunction, Opportunity investigated a cobble informally named Santorini. Its chemical and mineralogical composition is very similar to Barberton and Santa Catarina, two cobbles that were identified as meteorites and which are probably related to each other [3]. Santorini was investigated with the rover s Panoramic Camera (Pancam), Microscopic Imager (MI), Alpha-Particle X-ray Spectrometer (APXS) and Moessbauer (MB) spectrometer. The miniature Thermal Emission Spectrometer (mini-TES) was not operational at the time. The Rock Abrasion Tool (RAT) could not be used to brush off potential dust coatings because of unfavorable geometry.

The two Miniaturized Moessbauer Spectrometers (MIMOS II) on board the two Mars Exploration Rovers Spirit and Opportunity have now been collecting important scientific data for more than four years. The spectrometers provide information about Fe-bearing mineral phases and determine Fe oxidation states. The total amount of targets analized exceeds 600, the total integration time exceeds 260 days for both rovers. Since landing, more than five half-lives of the Co-57 MB sources have past (intensity at the time of landing approx. 150 mCi). Current integration times are about 50 hours in order to achieve reasonable statistics as opposed to 8 hours at the beginning of the mission. In total, 13 different mineral phases were detected: Olivine, pyroxene, hematite, magnetite and nanophase ferric oxide were detected at both landing sites. At Gusev, ilmenite, goethite, a ferric sulfate phase and a yet unassigned phase (in the rock Fuzzy Smith) were detected. At Meridiani, jarosite, metallic iron in meteoritic samples (kamacite), troilite, and an unassigned ferric phase were detected. Jarosite and goethite are of special interest, as these minerals are indicators for water activity. In this abstract, an overview of Moessbauer results will be given, with a focus on data obtained since the last martian winter. The MER mission has proven that Moessbauer spectroscopy is a valuable tool for the in situ exploration of extraterrestrial bodies and for the study of Febearing samples. The experience gained through the MER mission makes MIMOS II a obvious choice for future missions to Mars and other targets. Currently, MIMOS II is on the scientific payload of two approved future missions: Phobos Grunt (Russian Space Agency; 2009) and ExoMars (European Space Agency; 2013).

The miniaturized Moessbauer (MB) spectrometers MIMOS II [1] on board of the two Mars Exploration Rovers Spirit and Opportunity have obtained more than 600 spectra of more than 300 different rock and soil targets [2-7]. Both instruments have simultaneously collected 6.4 keV X-ray and 14.4 keV .-ray spectra in backscattering geometry [1]. With Spirit's MB spectrometer, 6.4 keV and 14.4 keV spectra have been obtained for all targets through sol 461. After this date, only 14.4 keV spectra were collected. With Opportunity's spectrometer, 6.4 keV and 14.4 keV spectra have been collected for all targets to date. The Fe-mineralogy of rock and soil targets at both landing sites reported to date has been exclusively extracted from 14.4 keV spectra [2-5]. The comparison of 6.4 keV and 14.4 keV spectra provides depth selective information about a sample, but interpretation is not always straightforward [8].

The Mars Exploration Rover Spirit landed in Gusev crater on Jan. 4, 2004. Spirit has traversed the Gusev crater plains, ascended to the top of Husband Hill, and entered into the Inner Basin of the Columbia Hills. The Athena science payload onboard Spirit has recorded numerous measurements on the chemistry and mineralogy of materials encountered during nearly 2 Mars years of operation within the crater. Rocks and soils have been grouped into classes based upon their unique differences in mineralogy and chemistry [1-3]. Some of the most significant chemical discoveries include the composition of Adirondack class flood basalts [4-6]; high sulfur in Clovis and Peace Class rocks [7,2]; high P and Ti in Wishstone Class rocks [7,2]; composition of alkalic basalts [2,6]; very high S in Paso Robles class soils [7,2], and the possible occurrence of a smectite-like chemical composition in Independence class rocks [8]. Water has played a significant role in the alteration of rocks and soils in the Columbia Hills. The occurrence of goethite and ferric sulfate alone suggests that liquid water was involved in their formation [3]. The pervasively altered materials in Husband Hill outcrops and rocks may have formed by the aqueous alteration of basaltic rocks, volcaniclastic materials, and/or impact ejecta by solutions that were rich in acid-volatile elements [2]. The objective of this paper is to provide an update on the health of the Alpha Particle X-ray Spectrometer (APXS) and to expand the geochemical dataset from sol 470 to sol 1368. Specific objectives are to (1) update the rock and soil classifications, (2) characterize elemental relationships among the major rock and soil classes, and (3) evaluate the involvement of water in the formation or alteration of the materials in these classes.

The Moessbauer spectrometer on Spirit measured the oxidation state of Fe, identified Fe-bearing phases, and measured relative abundances of Fe among those phases for surface materials on the plains and in the Columbia Hills of Gusev crater. Eight Fe-bearing phases were identified: olivine, pyroxene, ilmenite, magnetite, nanophase ferric oxide (npOx), hematite, goethite, and a Fe(3+)-sulfate. Adirondack basaltic rocks on the plains are nearly unaltered (Fe(3+)/Fe(sub T)<0.2) with Fe from olivine, pyroxene (Ol>Px), and minor npOx and magnetite. Columbia Hills basaltic rocks are nearly unaltered (Peace and Backstay), moderately altered (WoolyPatch, Wishstone, and Keystone), and pervasively altered (e.g., Clovis, Uchben, Watchtower, Keel, and Paros with Fe(3+)/Fe(sub T) approx.0.6-0.9). Fe from pyroxene is greater than Fe from olivine (Ol sometimes absent), and Fe(2+) from Ol+Px is 40-49% and 9-24% for moderately and pervasively altered materials, respectively. Ilmenite (Fe from Ilm approx.3-6%) is present in Backstay, Wishstone, Keystone, and related rocks along with magnetite (Fe from Mt approx. 10-15%). Remaining Fe is present as npOx, hematite, and goethite in variable proportions. Clovis has the highest goethite content (Fe from Gt=40%). Goethite (alpha-FeOOH) is mineralogical evidence for aqueous processes because it has structural hydroxide and is formed under aqueous conditions. Relatively unaltered basaltic soils (Fe(3+)/Fe(sub T) approx. 0.3) occur throughout Gusev crater (approx. 60-80% Fe from Ol+Px, approx. 10-30% from npOx, and approx. 10% from Mt). PasoRobles soil in the Columbia Hills has a unique occurrence of high concentrations of Fe(3+)-sulfate (approx. 65% of Fe). Magnetite is identified as a strongly magnetic phase in Martian soil and dust.

The miniaturized Mossbauer (MB) spectrometer MIMOS II [1] is part of the Athena payload of NASA s twin Mars Exploration Rovers "Spirit" (MER-A) and "Opportunity" (MER-B). It determines the Fe-bearing mineralogy of Martian soils and rocks at the Rovers respective landing sites, Gusev crater and Meridiani Planum. Both spectrometers performed successfully during first year of operation. Total integration time is about 49 days for MERA (79 samples) and 34 days for MER-B (85 samples). For curiosity it might be interesting to mention that the total odometry of the oscillating part of the MB drive exceeds 35 km for both rovers.