On $ n $-tuplewise IP-sensitivity and thick sensitivity

<p style='text-indent:20px;'>Let <inline-formula><tex-math id="M2">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> be a topological dynamical system and <inline-formula><tex-math id="M3">\begin{document}$ n\geq 2 $\end{document}</tex-math></inline-formula>. We say that <inline-formula><tex-math id="M4">\begin{document}$ (X,T) $\end{document}</tex-math></inline-formula> is <inline-formula><tex-math id="M5">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive (resp. <inline-formula><tex-math id="M6">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive) if there exists a constant <inline-formula><tex-math id="M7">\begin{document}$ \delta&gt;0 $\end{document}</tex-math></inline-formula> with the property that for each non-empty open subset <inline-formula><tex-math id="M8">\begin{document}$ U $\end{document}</tex-math></inline-formula> of <inline-formula><tex-math id="M9">\begin{document}$ X $\end{document}</tex-math></inline-formula>, there exist <inline-formula><tex-math id="M10">\begin{document}$ x_1,x_2,\dotsc,x_n\in U $\end{document}</tex-math></inline-formula> such that</p><p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \Bigl\{k\in \mathbb{N}\colon \min\limits_{1\le i&lt;j\le n}d(T^k x_i,T^k x_j)&gt;\delta\Bigr\} $\end{document} </tex-math></disp-formula></p><p style='text-indent:20px;'>is an IP-set (resp. a thick set).</p><p style='text-indent:20px;'>We obtain several sufficient and necessary conditions of a dynamical system to be <inline-formula><tex-math id="M11">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive or <inline-formula><tex-math id="M12">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive and show that any non-trivial weakly mixing system is <inline-formula><tex-math id="M13">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise IP-sensitive for all <inline-formula><tex-math id="M14">\begin{document}$ n\geq 2 $\end{document}</tex-math></inline-formula>, while it is <inline-formula><tex-math id="M15">\begin{document}$ n $\end{document}</tex-math></inline-formula>-tuplewise thickly sensitive if and only if it has at least <inline-formula><tex-math id="M16">\begin{document}$ n $\end{document}</tex-math></inline-formula> minimal points. We characterize two kinds of sensitivity by considering some kind of factor maps. We introduce the opposite side of pairwise IP-sensitivity and pairwise thick sensitivity, named (almost) pairwise IP<inline-formula><tex-math id="M17">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuity and (almost) pairwise syndetic equicontinuity, and obtain dichotomies results for them. In particular, we show that a minimal system is distal if and only if it is pairwise IP<inline-formula><tex-math id="M18">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuous. We show that every minimal system admits a maximal almost pairwise IP<inline-formula><tex-math id="M19">\begin{document}$ ^* $\end{document}</tex-math></inline-formula>-equicontinuous factor and admits a maximal pairwise syndetic equicontinuous factor, and characterize them by the factor maps to their maximal distal factors.</p>

GIS-Based Landslide Disaster Risk Areas and Ground Movements Mapping to Support Disaster Mitigation Activities (Case Study: Tasikmalaya Regency)

Tasikmalaya Regency is an area that is prone to landslides and ground movements. The availability of comprehensive and accurate information in controlling land use for regional development in areas prone to landslides and ground movements is very important for casualty prevention and other losses such as physical, social and economic. This information must be disseminated to the public as an early warning system to support disaster mitigation efforts. Identification of the characteristics of landslide and ground movement prone areas requires the mapping of risk areas to mitigate disasters. This can be done using Geographic Information System (GIS). This mapping activity was carried out using the method of collecting digital data from five vulnerability controlling factors of landslides and ground movements, namely rainfall, rock type, soil type, land cover and slope. The analysis is continued by weighting the factors that influence landslides and ground motion and then overlaying the five controlling factor maps (with their respective weight values) to produce a landslides and ground movement vulnerability level map which is then inputted into WebGIS. This map can then be used by local governments and the public as an information medium to support disaster mitigation activities.

Loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli

Foreman and Weiss [Measure preserving diffeomorphisms of the torus are unclassifiable. Preprint, 2020, arXiv:1705.04414] obtained an anti-classification result for smooth ergodic diffeomorphisms, up to measure isomorphism, by using a functor $\mathcal {F}$ (see [Foreman and Weiss, From odometers to circular systems: a global structure theorem. J. Mod. Dyn.15 (2019), 345–423]) mapping odometer-based systems, $\mathcal {OB}$ , to circular systems, $\mathcal {CB}$ . This functor transfers the classification problem from $\mathcal {OB}$ to $\mathcal {CB}$ , and it preserves weakly mixing extensions, compact extensions, factor maps, the rank-one property, and certain types of isomorphisms. Thus it is natural to ask whether $\mathcal {F}$ preserves other dynamical properties. We show that $\mathcal {F}$ does not preserve the loosely Bernoulli property by providing positive and zero-entropy examples of loosely Bernoulli odometer-based systems whose corresponding circular systems are not loosely Bernoulli. We also construct a loosely Bernoulli circular system whose corresponding odometer-based system has zero entropy and is not loosely Bernoulli.

Identifying critical source areas of nonpoint source pollution in a watershed with SWAT–ECM and AHP methods

Identification of critical source areas (CSAs) is pivotal for the management of nonpoint source (NPS) pollution of watersheds. Most studies focus on source (S) factors and ignore the driving (D) factors of such pollution. The Soil and Water Assessment Tool (SWAT) model and the export coefficient method (ECM) were incorporated to quantify the S factors of ammonia nitrogen (NH4–N) and total phosphorus (TP) as NPS pollution. Specifically, S factors coupled with D factors, including precipitation, slope, soil and land use, were regarded as multi–factors. Moreover, the analytical hierarchy process (AHP) method was adopted to determine the respective weights of multi–factors after overlaying the factor maps to identify the CSAs. These CSAs accounted for 23.86% of the total area, and generated 54.94% of NH4–N and 42.59% of the TP loads. In contrast with single and multi–factors, we found that using multi–factors having differing weights was more accurate for identifying CSAs. Our study results indicate this approach is reasonable for CSAs' identification in watersheds, and it can provide insights into different pollution sources and migration, thus providing a sounder basis for future decision–making.

Risk Areas Zoning Using a New 3D Seismic Refraction Technique in the Gas Pipeline Right-of Way of a Gas and Condensed Field in the Peruvian Jungle

The use of the new three-dimensional refraction technique was applied around the right-of-way (DDV) of the hydrocarbon gathering pipeline system (U-200), approximately 14.4 km long and 1.5 km wide. This technique included: a) processing of field seismic gathers data in conjunction with LIDAR-DTM topographic information, with which a 3D model of P-wave velocities was constructed; b) calibration of the P-velocity model with field data; and c) interpretation of the final P-velocity model. The application of the new technique allowed the three-dimensional study of the subsurface around the U-200 by including the geological characterization of the velocities and the elaboration of several predictive geological maps (lithology, structural, topography, etc.). Correlations of these maps allowed the building of risk factor maps, in which areas with higher or lower geodynamic risk can be directly identified. These areas represented the zones where the pipeline/flowline was most prone to collapse.

Einführung eines heterogenen Kontaktmodells rauer Oberflächen in EHD-Simulationen zur Simulation von faserverstärkten Polymeren in Radialgleitlagern

The EHL-simulation methods for homogenous materials have to be enhanced to model heterogeneous fiber-reinforced plastics. Because of micro and macro scale material properties, several parameters have to be considered in contact models, e.g. thermal dependency of material properties, material heterogeneity and material non-linearity or viscoelasticity. This paper shows the impact of the stiffness on the micro and macro scale in a fiber-reinforced plastic-steel contact on EHL-simulation results. Especially in the area of micromechanics, the correct combination of the material model and the topography shows a significant influence on the calculated contact stiffness and hence the flow factor maps. Depending on the fiber orientation and film thickness, the contact stiffness variates by a factor of nearly 7.

Landslide Susceptibility Assessment based on Information Value Model in Amzaz Watershed in Northern Morocco

This paper aims to identify potential areas of landslides in the Amzaz watershed in northern Morocco with its precarious environmental balance using the Information Value (IV) Model. Van Westen (1994) defines bivariate methods as a modified form of the quantitative map combination with the exception that weightings are assigned based upon the statistical relationship between past landslides and various factor maps, individual factor maps (independent variable). A set of factor maps were overlaid with a landslide map (dependent variable) to create cross-tabulations for each one and class. The landslide inventory is used to result in the susceptibility maps for better mitigation of the risks and losses related to this phenomenon. The results demonstrated that the percentage of rotational landslides varies between 8.79 and 30.08%, and between 9.79 and 23.36% for translational slides susceptibility in the Amzaz watershed.

Regional Analyses of Rainfall-Induced Landslide Initiation in Upper Gudbrandsdalen (South-Eastern Norway) Using TRIGRS Model

In Norway, shallow landslides are generally triggered by intense rainfall and/or snowmelt events. However, the interaction of hydrometeorological processes (e.g., precipitation and snowmelt) acting at different time scales, and the local variations of the terrain conditions (e.g., thickness of the surficial cover) are complex and often unknown. With the aim of better defining the triggering conditions of shallow landslides at a regional scale we used the physically based model TRIGRS (Transient Rainfall Infiltration and Grid-based Regional Slope stability) in an area located in upper Gudbrandsdalen valley in South-Eastern Norway. We performed numerical simulations to reconstruct two scenarios that triggered many landslides in the study area on 10 June 2011 and 22 May 2013. A large part of the work was dedicated to the parameterization of the numerical model. The initial soil-hydraulic conditions and the spatial variation of the surficial cover thickness have been evaluated applying different methods. To fully evaluate the accuracy of the model, ROC (Receiver Operating Characteristic) curves have been obtained comparing the safety factor maps with the source areas in the two periods of analysis. The results of the numerical simulations show the high susceptibility of the study area to the occurrence of shallow landslides and emphasize the importance of a proper model calibration for improving the reliability.

Capacitive versus Overlap Decoupling of Adjacent Radio Frequency Phased Array Coil Elements: An Imaging Robustness Comparison When Sample Load Varies for 3 Tesla MRI

Phased array (PA) receive coils are built such that coil elements approximate independent antenna behavior. One method of achieving this goal is to use an available decoupling method to decouple adjacent coil elements. The purpose of this work was to compare the relative performance of two decoupling methods as a function of variation in sample load. Two PA receive coils with 5 channels (5-ch) each, equal outer dimensions, and formed on 12 cm diameter cylindrical phantoms of conductivities 0.3, 0.6, and 0.9 S/m were evaluated for relative signal-to-noise ratio (SNR) and parallel imaging performance. They were only tuned and matched to the 0.6 S/m phantom. Simulated and measured axial, sagittal, and coronal 5-ch PA coil SNR ratios were compared by dividing the overlap by the capacitive decoupled coil SNR results. Issues related to the selection of capacitor values for the two decoupling methods were evaluated by taking the ratio of the match and tune capacitors for large and small 2 channel (2-ch) PA coils. The SNR ratios showed that the SNR of the two decoupling methods were very similar. The inverse geometry-factor maps showed similar but better overall parallel imaging performance for the capacitive decoupled method. The quotients for the 2-ch PA coils’ maximum and minimum capacitor value ratios are 3.28 and 1.38 for the large and 3.28 and 2.22 for the small PA. The results of this paper demonstrate that as the sample load varies, the capacitive and overlap decoupling methods are very similar in relative SNR and this similarity continues for parallel imaging performance. Although, for the 5-ch coils studied, the capacitive decoupling method has a slight SNR and parallel imaging advantage and it was noted that the capacitive decoupled coil is more likely to encounter unbuildable PA coil configurations.

On generalized compensation functions for factor maps between shift spaces on countable alphabets

We show the existence of generalized compensation functions for a particular type of one-block factor maps [Formula: see text] between countable subshifts [Formula: see text] and [Formula: see text]. For factor maps between compact spaces, continuous compensation functions were studied by Walters in relation to the theory of relative pressure. Applying the thermodynamic formalism for sequences on countable subshifts, we generalize some existing results on factor maps between compact spaces to non-compact spaces. For related questions, we also study the existence of a preimage measure on [Formula: see text] of an invariant measure on [Formula: see text], and their relations.