Ethnomathematics values in Temple of Heaven: An Imperial Sacrificial Altar in Beijing, China

Many studies are proving that learning mathematics with an ethnomathematical approach can improve students’ mathematical skills. Developing and using ethnomathematics concepts are important to raise history and cultural awareness of mathematics. This study aims to analyse the ethnomathematics values of the Temple of Heaven. Temple of Heaven is one of the famous heritage sites in Beijing, China, which bears many ethnomathematics concepts. The researchers applied a qualitative method in this study. The subject of this research is the Temple of Heaven building that is located in Beijing, China. Researchers identified the geometrical concept present in the exterior, interior design, and building structure of the Temple of Heaven building. This research shows the existence of mathematical concepts in the architecture of the Temple of Heaven. This research result can help teachers in making mathematical practice questions with ethnomathematics concepts.

EXOFIT field trials: experience learned from the use of ExoMars/RLS Qualification Model and representative Raman prototypes

<p><span>The ESA/Roscosmos ExoMars mission to Mars is scheduled to be launched in 2020. Seeking to prepare the ExoMars operation team to manage the engineering and scientific challenges arising from the Rosalind Franklin rover soon operating at Oxia Planum, a rover prototype equipped with representative ExoMars navigation and analytical systems was recently used in two mission simulations (ExoFit trials)</span></p><p><span>The first field test was carried out in Tabernas (Spain), a desertic area characterized by the presence of clays, partially altered sedimentary rocks and efflorescence salts. The second ExoFit trial was performed in the Atacama Desert (Chile), in a sandy flat land displaying diorite-boulders, clays patches and evaporites.</span></p><p><span>The Raman Laser Simulator (RLS) team participated in both simulations: portable spectrometers were used to determine the mineralogical composition of subsoil samples collected by the rover-drill and to investigate the possible presence of biomarkers. In-situ analysis were carried out by means of the RAD 1 system (Raman Demonstrator), which is a portable spectrometer that follows the same geometrical concept and spectral characteristics of the RLS flight model (FM).</span></p><p><span>In the case of Tabernas trial, additional analysis were performed using the RLS qualification model (EQM2) which at the moment was the most reliable tool to understand the scientific outcome that could derive from the RLS operating on Mars.</span></p><p><span>Prior to analysis, geological samples were crushed and sieved to replicate the granulometry of the powdered material produced by the ExoMars crusher. After flattening, from 8 to 10 spots were analyzed and Raman data and interpreted.</span></p><p><span>From each site, two cores were drilled and analyzed. On one side, the main mineralogical phases detected in the first Atacama core are quartz and calcium carbonate. In addition to those, the mineralogy of the second core also includes hematite and calcium sulphate.</span></p><p><span>On the other side, RAD 1 spectra gathered from Almeria core-samples confirmed the presence of quartz as main mineralogical phase. However, peaks of medium intensity at 146 and 1086 cm<sup>-1</sup> were also observed, confirming the detection of rutile and calcium carbonate respectively. The same samples were further characterized by means of the RLS-EQM2 system: beside confirming the detection of the abovementioned mineral phases, additional Raman biomarkers-related peaks were also found.</span></p><p><span>Even though deeper Raman analysis of ExoFit samples need to be performed, the preliminary results gathered in-situ suggests that Raman spectroscopy could play a kay role in the fulfillment of the ExoMars mission objectives.</span></p>

Multisource Evidence for Final State Hadrons in 3.7A GeV 16O–Nucleus Interactions

In 3.7A GeV 16O interactions with emulsion nuclei, the shower particle multiplicity characteristics are investigated. Data are presented in terms of the number of emitted particles in both forward and backward angular zones. The dependence on the target size and emission direction is presented. The target separation of events depends on Glauber's multiple scattering theory approaches. A decay mechanism seems to be a characteristic of the backward production. This production may be during the de–excitation of the excited target nucleus, regarding the nuclear limiting fragmentation hypothesis. The forward emitted particle is due to a creation system. The target size is an effective parameter as well as the projectile size in this system, considering the geometrical concept regarded in the nuclear fireball concept. The data are simulated in the framework of the modified FRITIOF model. The multisource thermal model can predict source numbers responsible for particle production.

Cassirer and the Structural Turn in Modern Geometry

The paper investigates Ernst Cassirer’s structuralist account of geometrical knowledge developed in his Substanzbegriff und Funktionsbegriff (1910). The aim here is twofold. First, to give a closer study of several developments in projective geometry that form the direct background for Cassirer’s philosophical remarks on geometrical concept formation. Specifically, the paper will survey different attempts to justify the principle of duality in projective geometry as well as Felix Klein’s generalization of the use of geometrical transformations in his Erlangen program. The second aim is to analyze the specific character of Cassirer’s geometrical structuralism formulated in 1910 as well as in subsequent writings. As will be argued, his account of modern geometry is best described as a “methodological structuralism”, that is, as a view mainly concerned with the role of structural methods in modern mathematical practice.

Modified non-Euclidean transformation on the SO(2N+2) U(N+1) Grassmannian and SO(2N + 1) random phase approximation for unified description of Bose and Fermi type collective excitations

In a slight different way from the previous one, we propose a modified non-Euclidean transformation on the [Formula: see text] Grassmannian which gives the projected [Formula: see text] Tamm–Dancoff equation. We derive a classical time-dependent (TD) [Formula: see text] Lagrangian which, through the Euler–Lagrange equation of motion for [Formula: see text] coset variables, brings another form of the previous extended-TD Hartree–Bogoliubov (HB) equation. The [Formula: see text] random phase approximation (RPA) is derived using Dyson representation for paired and unpaired operators. In the [Formula: see text] HB case, one boson and two boson excited states are realized. We, however, stress non-existence of a higher RPA vacuum. An integrable system is given by a geometrical concept of zero-curvature, i.e. integrability condition of connection on the corresponding Lie group. From the group theoretical viewpoint, we show the existence of a symplectic two-form [Formula: see text].

Comparison of Two Medieval Trusses from the Viewpoint of Geometric and Static Analysis

The subject of article is a comparison of two load bearing structures of medieval trusses in terms of their original design, based on the geometrical concept, as well as from the perspective of their current static analysis, based on modern, standardized calculation procedures. It is a roof above the sanctuary of the Roman Catholic Church in the village of Bela-Dulice from 1409d, and a roof above the sanctuary of the Church of St. Peter of Alcantara in the Franciscan monastery in Okolicne from 1499d. From a typological point of view, both the trusses have a similar rafter collar-beam construction with longitudinal stiffening frame truss and with approximately the same span. In the case of the monastery church in Okolicne, the construction of main cross truss is supplemented by the spike struts. From the geometric analysis of trusses there are obvious different geometric proportional relationships that have been applied in the original design. The aim of static analysis of the load bearing structures using current advanced computing resources is to clarify and compare the static behaviour of the both roof structures.