Some Problems of Qualitative Researches on Ultrahyperbolic Equations

The prensent paper is a resume in the qualitative researches of the ultrahyperbolic equation,it involves a new proof of Asgeirsson's mean value theorem,extensions of mean value theorem,non-analyticity of the generalized potential solution,extensionality of solution,boundary problems and the elementary solution. Especially,we suggest to study ultrahyperbolie equation by means of the elementary solution,which is a natural way.

Deformation prediction and analysis of underground mining during stacking of dry gangue in open-pit based on response surface methodology

Deformation prediction and the analysis of underground goaf are important to the safe and efficient recovery of residual ore when shifting from open-pit mining to underground mining.To address the comprehensive problem of stability in the double mined-out area of the Tong-Lv-Shan(TLS)mine,which employed the dry stacked gangue technology,this paper applies the function fitting theory and a regression analysis method to screen the sensitive interval of four influencing factors based on single-factor experiments and the numerical simulation software FLAC3D.The influencing factors of the TLS mine consist of the column thickness(d),gob area span(D),boundary pillar thickness(h)and height of tailing gangue(H).The fitting degree between the four factors and the displacement of the gob roof(W)is reasonable because the correlation coefficient(R2)is greater than0.9701.After establishing29groups that satisfy the principles of Box-Behnken design(BBD),the dry gangue tailings process was re-simulated for the selected sensitive interval.Using a combination of an analysis of variance(ANOVA),regression equations and a significance analysis,the prediction results of the response surface methodology(RSM)show that the significant degree for the stability of the mined-out area for the factors satisfies the relationship of h>D>d>H.The importance of the four factors cannot be disregarded in a comparison of the prediction results of the engineering test stope in the TLS mine.By comparing the data of monitoring points and function prediction,the proposed method has shown promising results,and the prediction accuracy of RSM model is acceptable.The relative errors of the two test stopes are1.67%and3.85%,respectively,which yield satisfactory reliability and reference values for the mines.

Effect of copper slag recovery on hydrometallurgical cut-off grades considering environmental aspects

Determining the hydrometallurgical cut-off grades specifies the destination of low grade materials and this is subjected to more benefits in mining. Copper production rate is considered as one of the fundamental issues in hydrometallurgical cut-off grades determination. Slags are remarked as one of the main sources of copper. It is not only regarded as a waste but also identified as another resource extracting base metals. Slags are characterized by copper high grade. Thus, slag copper recovery can be led to different cut-off grades and net present value(NPV). The current research scrutinizes the effect of slag recovery by both flotation and hydrometallurgical methods on the hydrometallurgical cut-off grades. For this purpose, the optimum cut-off grade algorithms of hydrometallurgical methods are developed by considering associated environmental parameters, incomes and also the costs. Then, their optimum amounts are calculated with NPV maximization as an objective function. The results indicate that considering slag copper recovery in the hydrometallurgical cut-off grade algorithms reduces the environmental costs caused by slag dumping and leads to more NPV by 9%.