Improvement of Cemented Gangue Backfill Material with Barium Hydroxide in Acid Mine Water

As a kind of green concrete,the mechanical properties and durability of cemented gangue backfill material(CGBM)will be affected if they are in acid mine water with sulfate ions in the long term.To improve the performance of CGBM in acid mine water with sulfate ions,CGBM specimens with different doses of barium hydroxide were immersed in sulfuric acid solutions of different concentrations for 270 days.The changes of mass,ultrasonic pulse velocity(UPV)and compressive strength of the specimens at different ages were analyzed.Scanning electron microscopy(SEM)and X-ray diffraction(XRD)were used to analyze the microstructure and composition of the specimens.The results show that incorporation of barium hydroxide into CGBM specimen can promote the formation of barium sulfate precipitation and inhibit the generation of corrosion products such as ettringite.Meanwhile,barium sulfate precipitation blocks the pore channel invaded by sulfuric acid solution,delaying the progress of corrosion reaction and making the interior of CGBM specimen more complete.And the specimen with 2.0 kg/m^(3)barium hydroxide was more effective in improving performance.This study provides a basis for the ratio design of CGBM in acid mine water with sulfate ions.

Creep properties and resistivity-ultrasonic-AE responses of cemented gangue backfill column under high-stress area

To investigate the creep and instability properties of a cemented gangue backfill column under a highstress area,the uniaxial compression creep tests were conducted by single-step and multi-step loading of prismatic samples made of cemented gangue backfill material(CGBM)under the high stressstrength ratio.The creep damage was monitored using an electrical resistivity device,ultrasonic testing device,and acoustic emission(AE)instrument.The results showed that the CGBM sample has a creep hardening property.The creep failure strength(CFS)is slightly larger than the uniaxial compressive strength(UCS),ranging in ratio from 108.9%to 116.5%.The instantaneous strain,creep strain,and creep rate increase with increasing stress-strength ratio in the single-step loading creep tests.The instantaneous strain and creep strain decrease first and then increase during the multi-step loading creep process.The axial creep strain of the CGBM column can be expressed by the viscoelastic-plastic creep model.Creep instability is caused by the accumulation of strain energy under multi-step loading and the continuous lateral expansion at the unconstrained middle position during the creep process.The creep stability of a CGBM column in a high-stress area can be monitored based on the variation of electrical resistivity,ultrasonic pulse velocity(UPV),and AE signals.

New existence of multi-spike solutions for the fractional Schrodinger equations

We consider the following fractional Schr¨odinger equation:(-Δ)^(s)u+V(y)u=u^(p);u>0 in R^(N);(0.1)where s ∈(0,1),1<p<N+2s/N-2s,and V(y)is a positive potential function and satisfies some expansion condition at infinity.Under the Lyapunov-Schmidt reduction framework,we construct two kinds of multi-spike solutions for(0.1).The first k-spike solution uk is concentrated at the vertices of the regular k-polygon in the(y1;y2)-plane with k and the radius large enough.Then we show that uk is non-degenerate in our special symmetric workspace,and glue it with an n-spike solution,whose centers lie in another circle in the(y3;y4)-plane,to construct infinitely many multi-spike solutions of new type.The nonlocal property of(-Δ)^(s)is in sharp contrast to the classical Schr¨odinger equations.A striking difference is that although the nonlinear exponent in(0.1)is Sobolev-subcritical,the algebraic(not exponential)decay at infinity of the ground states makes the estimates more subtle and difficult to control.Moreover,due to the non-locality of the fractional operator,we cannot establish the local Pohozaev identities for the solution u directly,but we address its corresponding harmonic extension at the same time.Finally,to construct new solutions we need pointwise estimates of new approximate solutions.To this end,we introduce a special weighted norm,and give the proof in quite a different way.

带深井位势双调和方程的解

本文研究下述双调和方程极小能量解的存在性:?~2u+[λV (x)-δ]u=|u|_(p-2)u, x∈R^N,(0.1)其中N≥5,λ> 0. p是次临界或临界的Sobolev指标,即2 <p≤2**,这里2**=2N/N-4为临界的Sobolev指标, V (x)是非负连续的深井位势,其零集V^(-1)(0):={x∈R^N:V (x)=0}的内部int V^(-1)(0)是R^N中非空的有界光滑区域.令μ0为定义在int V^(-1)(0)中齐次边界条件下?~2的第一特征值.对任意的0 <δ<μ0,本文证明:当λ> 0充分大时,(0.1)存在一个在V^(-1)(0)附近的极小能量解.

SOLUTIONS FOR SINGULAR p-LAPLACIAN EQUATION IN R^n

In this paper, the authors study the existence and non-existence of positive solutions for singular p-Laplacian equation --Δpu=f（x）u^-α ＋ λg（x）u^β in RN, where N ≥3, 1 〈 p 〈 N, λ〉 0, 0 〈 α〈 1,max（p, 2） 〈 β＋ 1 〈 p＊ = Np/N-p We prove that there exists a critical value A such that the problem has at least two solutions if 0 〈 λ 〈 A; at least one solution if λ= A; and no solutions if λ〉A.

Asymptotical behavior of ground state solutions for critical quasilinear Schrodinger equation

This paper is concerned with the existence and asymptotical behavior of positive ground state solutions for a class of critical quasilinear Schrodinger equation.By using a change of variables and variational argument,we prove the existence of positive ground state solution and discuss their asymptotical behavior。