Supplemental Material: Late Triassic successive amalgamation between the South China and North China blocks: Insights from structural analysis and magnetic fabrics study of the Bikou Terrane and its adjacent area, northwestern Yangtze block, central China

Text: Basic principles of anisotropy of magnetic susceptibility (AMS); Figure S1: Photographs of supplementary shearing indicators of the structural kinematics; Figure S2: Complete magnetic hysteresis data set for specimen selected from 34 sites; Figure S3: Measurements of isothermal remanent magnetization of specimen selected from 34 representative sites of the Bikou Terrane; Figure S4: Thermo-magnetic experiments of specimen selected from 12 representative sites; Figure S5: Mrs/Ms versus Hcr/Hc diagram from the selected specimen of the representative sites to define the size of magnetite; Figure S6: Stereographic projection of the AMS directional fabrics and structural fabrics.

Application of Improved Stereographic Projection Method to Quantify Lithospheric Plate Motion Trajectory

The traditional method of studying plate motion still cannot be used to obtain plate motion trajectory quantitatively. In this paper, we proposed a new method to quantitative determine plate motion trajectory. Depending on the paleomagnetic data of lithosphere plate and the stereographic projection principle. We selected the Wulff net as the basic projection net, improved and transformed the traditional stereographic projection methods. Projecting the paleomagnetic data (magnetic declination, palaeolatitude and geomagnetic pole coordinate) of the lithosphere plate into the improved stereographic projection net, we can get the analysis results of lithosphere plate stereographic projection. In our study, we took the Indian plate as an example, projected the paleomagnetic data (from Cretaceous) into the stereographic projection net, got the analysis results of motion trajectory of the Indian plate from Cretaceous. This method can be applied to quantify lithospheric plate motion trajectory.

Supplemental Material: Late Triassic successive amalgamation between the South China and North China blocks: Insights from structural analysis and magnetic fabrics study of the Bikou Terrane and its adjacent area, northwestern Yangtze block, central China

Text: Basic principles of anisotropy of magnetic susceptibility (AMS); Figure S1: Photographs of supplementary shearing indicators of the structural kinematics; Figure S2: Complete magnetic hysteresis data set for specimen selected from 34 sites; Figure S3: Measurements of isothermal remanent magnetization of specimen selected from 34 representative sites of the Bikou Terrane; Figure S4: Thermo-magnetic experiments of specimen selected from 12 representative sites; Figure S5: Mrs/Ms versus Hcr/Hc diagram from the selected specimen of the representative sites to define the size of magnetite; Figure S6: Stereographic projection of the AMS directional fabrics and structural fabrics.

Classification by decomposition: a novel approach to classification of symmetric $$2\times 2$$ games

In this paper, we provide a detailed review of previous classifications of $$2\times 2$$ 2 × 2 games and suggest a mathematically simple way to classify the symmetric $$2\times 2$$ 2 × 2 games based on a decomposition of the payoff matrix into a cooperative and a zero-sum part. We argue that differences in the interaction between the parts is what makes games interesting in different ways. Our claim is supported by evolutionary computer experiments and findings in previous literature. In addition, we provide a method for using a stereographic projection to create a compact 2-d representation of the game space.

On the induced metric of a photon qubit for different points of action in Bloch sphere

Travelling with harmonical actions about the referential line, the moment the photon qubit emits form the atom as a packet, not only embedded by the envelopes of quadratic nature overlap but also by the non-quadratic overlap effect as well in concurrent. This paper followed on by the subsistence of both ways of overlapping, focuses mainly on the induced metric of photon qubit, which concluded to be in 3-sphere by the local parameterization so called as Hopf coordinates. The protruded photon qubit in the induced Riemannian metric, for different points of the Bloch sphere, are in a manner that the stereographic projection of volume enveloped in 3-sphere determines the circular geometry in 2-sphere with the cross-sectional function in perpendicular to the continuum line of travel.

Rock Slope Stability Assessment Using Kinematic Analysis of the Limestone Quarries in Al Huson-Shatana Area, Jordan

The current study presents the first results of a kinematic analysis to investigate the type of failures in six abandoned limestone quarries in the Al-Huson-Shatana area, North Jordan. A serious problem appears in abandoned quarries. When the work in the quarry finish and the companies withdraw their equipment and workers, they leave behind unstable rock masses due to the repeated explosives. This may cause hazards in properties and civilians especially when they are close enough to residential areas. Both stereographic projection and kinematic analysis were used as tools in this study, to determine the mode and orientation of the failures. Results show that toppling, planar and wedge failures are likely to occur in all stations mainly along structural discontinuities, faults and joints. This indicates the role of structures in the rock landslides, particularly those related to planar, wedge and toppling failures. In addition, rock falls were observed in most stations that have steep slope cutting.

STEREO GRAPHIC PROJECTION AND ITS APPLICATIONS

In this paper, we introduce stereographic projection and its applications. In today’s time, this is one of the most widely used stereo projections. This projection is used in polar areas and also used in small-scale maps. This is a very useful tool to solving the orientation problems in structural geology, mathematics, and also in the studying of crystal structures and helpful to deduce how those structures relate to planes with crystal.

Random Walks with Invariant Loop Probabilities: Stereographic Random Walks

Random walks with invariant loop probabilities comprise a wide family of Markov processes with site-dependent, one-step transition probabilities. The whole family, which includes the simple random walk, emerges from geometric considerations related to the stereographic projection of an underlying geometry into a line. After a general introduction, we focus our attention on the elliptic case: random walks on a circle with built-in reflexing boundaries.