Some General Inequalities for Choquet Integral

With the development of fuzzy measure theory, the integral inequalities based on Sugeno integral are extensively investigated. We concern on the inequalities of Choquuet integral. The main purpose of this paper is to prove the H?lder inequality for any arbitrary fuzzy measure-based Choquet integral whenever any two of these integrated functions f, g and h are comonotone, and there are three weights. Then we prove Minkowski inequality and Lyapunov inequality for Choquet integral. Moreover, when any two of these integrated functions f1, f2, …, fn are comonotone, we also obtain the Hölder inequality, Minkowski inequality and Lyapunov inequality hold for Choquet integral.

Resource prediction and assessment based on 3D/4D big data modeling and deep integration in key ore districts of North China

The North China district has been subjected to significant research with regard to the ore-forming dynamics,processes,and quantitative forecasting of gold deposits;it accounts for the highest number of gold reserves and annual products in China.Based on the top-level design of geoscience theory and the method adopted by the National Key R&D Project(deep process and metallogenic mechanism of North China Craton(NCC)metallogenic system),this paper systematically collects and constructs the geoscience data(district,camp,and deposit scales)in four key gold districts of North China(Jiaojia-Sanshandao,Southern Zhaoping,Wulong,and Qingchengzi).The settings associated with the geological dynamics of gold deposits were quantitatively and synthetically analyzed,namely:NCC destruction,metallogenic events,genetic models,and exploration models.Three-dimensional(3D)and four-dimensional(4D)geological modeling was performed using the big data on the districts,while the district-scale 3D exploration criteria were integrated to construct a quantitative exploration model.Among them,FLAC3D modelling and the Geo Cube software(version 3.0)were used to implement the numerical simulation of the 3D geological models and the constraints of the fluid saturation parameters of the Jiaojia fault to reconstruct the 4D fault structure models of the Jiaojia fault(with a depth of 5000 m).Using Geo Cube3.0,multiple integration modules(general weights of evidence(Wof E),Boost Wof E,Fuzzy Wof E,Logistic Regression,Information Entropy,and Random Forest)and exploration criteria were integrated,while the C-V fractal classification of A,B and C targets in four districts was carried out.The research results are summarized in the following four areas:(1)Four gold districts in the study area have more than three targets(the depth is 3000 m),and the class A,B and C targets exhibit a good spatial correlation with gold bodies that are controlled by mining engineering at depths greater than 1000 m.(2)The Boost Wof E method was used to identify the target optimization in 3D spaces(at depths of 3000–5000 m)of the Jiaojia-Sanshandao,Southern Zhaoping,and Wulong districts.(3)The general Wof E method is based on the Bayesian theory in 3D space and provides robust integration and target optimization that are suitable for the Jiaojia-Sanshandao and Southern Zhaoping districts in the Jiaodong area;it can also be applied to the Wulong district in the Liaodong area using a quantitative genetic model and an exploration model.Random forest is a multi-objective integration and target optimization method for 3D spaces,and it is suitable for the complex exploration model in the Qingchengzi district of the Liaodong area.The genetic model and exploration criteria associated with the exploration model of the Qingchengzi district were constrained by the common characteristics of the gold fault structure,magmatic rock emplacement in North China,and the strata fold and interlayer detachment structure.(4)Based on the gold reserves and the 3D block unit model of the Sanshandao gold deposit in the Jiaojia-Sanshandao district,the gold contents of the 3D block units in class A and B targets of the ore concentration were estimated to be 65.5%and 25.1%,respectively.The total Au resources of the optimized targets below a depth of 3000 m were 3908 t(including 1700 t reserves),and the total Au resources of the targets at depths from 3000 to 5000 m were 936 t.The study shows that the deep gold deposits in the four gold districts of North China exhibit a strong"transport-deposition"spatial correlation with potential targets.These"transport-deposition"spatial models represent the tectonic-magmatic-hydrothermal activities of the metallogenic system associated with the NCC destruction events and indicate the Au enrichment zones.

Inhibition of osteosarcoma growth and metastasis using a polysaccharide derivative of Amy-g-PLLD for the delivery of AEG-1 siRNA

Osteosarcoma is the most common primary malignant neoplasm of the bone in children and adolescents and has a high risk of relapse and metastasis. Of the various methods to treat osteosarcoma, the use of genetic approaches to inhibit the rapid growth of osteosarcoma while limiting tumor metastasis has presented a challenge in its implementation. Here, we successfully synthesized a polysaccharide derivative （Amy-g-PLLD） for delivery of astrocyte elevated gene-1 （AEG-1） small-interfering RNA （siRNA） （siAEG-1）, and used it for the first time to suppress osteosarcoma tumors in vitro and in vivo. Amy-g-PLLD/ siAEG-1 complexes were delivered into 143B human osteosarcoma cells with low resultant cytotoxicity. Osteosarcoma tumor proliferation and invasion were inhibited in vitro. Intratumoral injection of Amy-g-PLLD/siAEG-1 complexes markedly inhibited tumor growth and lung metastasis in 143B tumor-bearing mice. This biocompatible and effective approach employing a natural material- siRNA complex should pave the way for more genetic research in treating osteosarcoma.