Regional Boundary Observability with Constraints of the Gradient

The aim of this paper is to explore the concept of observability with constraints of the gradient for distributed parabolic system evolving in spatial domain Ω, and which the state gradient is to be observed only on a part of the boundary of the system evolution domain. It consists in the reconstruction of the initial state gradient which must be between two prescribed functions in a subregion Γ of Ω. Two necessary conditions are given. The first is formulated in terms of the subdifferential associated with a minimized functional, and the second uses the Lagrangian multiplier method. Nu-merical illustrations are given to show the efficiency of the second approach and lead to open questions.

Soil Geochemistry Changes Induced by a Foreign Soil Reconstruction Project in Three Gorges Reservoir Region of China

Fertile topsoil was added onto the surface of barren slope land in Three Gorges Reservoir region of China in an anthropogenic process known as the foreign soil reconstruction project. The main goal of this paper was to reveal the influence of anthropogenic activities on pedogenic processes and soil classifications. Chemical weathering indices and comparative analysis were applied to discuss changes in geochemical compositions and weathering features of purplish soils(Cambisols) before and after the project. Results showed that:(1) The foreign soil reconstruction project slightly altered the major element composition of topsoil and improved the soil structure. Although the distributions of major elements in the original topsoil, original subsoil, foreign topsoil and newly constructed topsoil were all similar to that in upper continental crust, newly constructed topsoil was the most similar soil.(2) The chemical index of alteration was more sensitive than the weathering index of Parker at indicating chemical weathering status of purplish soil. The chemical weathering status of newly constructed topsoil was higher than that of the original topsoil and lower than that of foreign topsoil.(3) Anthropogenic activities may provide a promising new thought for the anthropogenic soil classification system. The scope and subgroups of Anthrosols should be extended and strengthened. Or there may be a need to combine Anthrosols and Technosols orders to create a new soil order. The results may be used for optimizing soil mellowing engineering activities and enriching the soil classification system.

Reconstruction method of differentiated backprojection-projection onto convex sets in the interior problem and design of bone-nail model

This work focuses on the application of the reconstruction method of differentiated backprojection （DBP）-projection onto convex sets （POCS） in the interior problem.First,we present the definition of the interior problem and real truncated Hilbert transform,and then outline the implementation steps of DBP-POCS.After that,we introduce the middle-part known condition for region of interest （ROI） accurate reconstruction and the unique condition of the interior problem,and verify the uniqueness and stability of the interior problem accurate reconstruction through numerical experiments,and then compare the results for the interior problem in reconstruction images using filtered backprojection （FBP）.In addition,the authors also design the application models of ROI reconstruction and make an initial attempt to the application of DBP-POCS method in the interior problem.

Regional gradient observability for semilinear hyperbolic systems： HUM approach

The paper aims to extend the notion of regional observability of the gradient to the semilinear hyperbolic case, in order to reconstruct the gradient of the initial conditions in a subregion w of the domain evolution Ω. We start with an asymptotically linear system, the approach is based on an extension of the Hilbert uniqueness method （HUM） and Schauder＇s fixed point theorem. The analysis leads to an algorithm which is successfully numerically implemented and illustrated with examples and simulations.

Region stepwise reconstruction method based on two source–detector-separation groups for reconstructing background optical properties of two-layered slab sample

The accuracy of the background optical properties has a considerable effect on the quality of reconstructed images in near-infrared functional brain imaging based on continuous wave diffuse optical tomography（CW-DOT）. We propose a region stepwise reconstruction method in CW-DOT scheme for reconstructing the background absorption and reduced scattering coefficients of the two-layered slab sample with the known geometric information. According to the relation between the thickness of the top layer and source– detector separation, the conventional measurement data are divided into two groups and are employed to reconstruct the top and bottom background optical properties, respectively. The numerical simulation results demonstrate that the proposed method can reconstruct the background optical properties of two-layered slab sample effectively. The region-of-interest reconstruction results are better than those of the conventional simultaneous reconstruction method.

The summer standardized precipitation evapotranspiration index(SPEl)dataset for six European regions over the past millennium reconstructed by tree-ring chronologies

Accurate reconstructed series are crucial for studying the differences in regional hydroclimatic variations in Europe over the past millennium.Using hierarchical clustering analysis and stepwise regression methods,we reconstructed yearly time series of the summer standardized precipitation evapotranspiration index(SPEl)for six European regions over the past millennium.Our analysis also revealed prominent regional hydroclimatic differences in multidecadal signals over the past 500 years.For instance,in the 1500s-1570s(from the beginning of the 1500s to the end of the 1570s),drying trends were observed in northern and southeastern Europe,whereas southwestern Europe experienced a wetting trend.Moreover,drying trends were observed in northern and central Europe in the 1640s-1670s.Additionally,wetting trends were observed in western and central Europe during the 1830s-1850s,with drying trends in northern and southeastern Europe.Notably,the hydroclimatic variations in most European regions showed drying trends in the 1920s-1950s,especially in southern Europe.By utilizing large amounts of tree-ring samples and directly comparing regional hydroclimatic variations,our reconstructions provide a consistent and comprehensive dataset for further analysis.The reconstructed dataset is available at https://doi.org/10.57760/sciencedb.07215.