The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces...The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces the recovery of titanaugite while having no evident impact on ilmenite flotation.Subsequent bench-scale flotation tests further confirm a remarkable improvement in separation efficiency upon the introduction of AP.Contact angle and adsorption tests reveal a stronger affinity of AP towards the titanaugite surface in comparison to ilmenite.Zeta potential measurements and X-ray photoelectron spectroscopy(XPS)analyses exhibit favorable adsorption characteristics of AP on titanaugite,resulting from a synergy of electrostatic attraction and chemical interaction.In contrast,electrostatic repulsion hinders any significant interaction between AP and the ilmenite surface.These findings highlight the potential of AP as a highly efficient depressant for ilmenite flotation,paving the way for reduced reliance on sulfuric acid in the industry.展开更多
The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is establishe...The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.展开更多
Almost all the coal is produced from open cut mines in Indonesia. As a consequence of open cut mine application, a great deal of coal is left out in the highwalls of the mined-out pits. Highwall mining systems can be ...Almost all the coal is produced from open cut mines in Indonesia. As a consequence of open cut mine application, a great deal of coal is left out in the highwalls of the mined-out pits. Highwall mining systems can be used to recover this coal. The use of highwall mining systems has increasingly come into play in the US and Australia. However, it is not common in Indonesia. Moreover, Indonesia coal measure is categorized as weak geological condition. Some problems are likely to arise during the application of the highwall mining system for example instability of openings and highwalls due to the roof and pillar failures. Therefore, study of highwall mining system application in Indonesia is needed in order to increase the recovery rate of coal mining in Indonesia. This paper described the characteristics of the highwa!l mining system and discussed the appropriate highwall mining system application in weak geological condition, Indonesia. From the results of a series of laboratory tests and numerical analyses, it can be concluded that the stability of pillars and mine openings in auger mining systems is much higher than that in CHM and an auger mining system is suitable for such as very weak/poor strata conditions. Moreover, the application of backfilling system is very effective for improvement of the stability of pillar and openings.展开更多
The purpose of this research is to study the effect of longwall mining on the stability of main roadway in the underground coal mine. The PT GDM （Gerbang Daya Mandiri） underground coal mine in Indonesia, where the r...The purpose of this research is to study the effect of longwall mining on the stability of main roadway in the underground coal mine. The PT GDM （Gerbang Daya Mandiri） underground coal mine in Indonesia, where the rocks are weak, was selected as a representative study site. To accomplish the objective of the research, the finite difference code software FLAC3D was used as a tool for the numerical simulations. The longwall mining of several panel and barrier pillar widths at various depths was simulated and discussed. Based on the simulation results, it indicates that the effect of coal panel extraction on the main roadway stability depends on the width of panel and barrier pillar. The greatest effect occurs when the large panel width and the small barrier pillar width are applied, whereas the smallest effect happens when the narrow panel width and the large barrier pillar width are adopted. In this paper, therefore, to maintain the stability of the main roadway with the aim of maximizing the coal recovery, the appropriate size of panel and barrier pillar width is proposed for each mining depth for this underground coal mine.展开更多
The conflict between the dynamics postulate（unitary evolution） and the measurement postulate（wavepacket collapse） of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys.Re...The conflict between the dynamics postulate（unitary evolution） and the measurement postulate（wavepacket collapse） of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys.Rev. A 76（2007） 052110], and has further been extended to a more general scenario [Phys. Rev. A 87（2013） 052111].In this paper, we reconsider Zurek＇s new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.展开更多
A considerable amount of tunnelling has been going on in India for various projects such as hydroelectric power, irrigation, roads and railways. Most of these projects are located in Himalayas, far away from the urban...A considerable amount of tunnelling has been going on in India for various projects such as hydroelectric power, irrigation, roads and railways. Most of these projects are located in Himalayas, far away from the urban areas. Tunnelling through weak and jointed rock masses such as the one in the Himalayas is a challenging task for the planners, designers, engineers and geologists because of high overburden, thickly vegetated surface, weak, poor and fragile rocks and highly varying geology with the presence of numerous small and big shear zones, faults, etc. Due to these reasons, various tunnelling problems have been faced in the past and are still being encountered. Failures and the problems may be regarded as challenges and opportunities for generating new knowledge base and thereby increasing self-reliance in tunnelling. The experiences of Himalayan tunnelling through weak and fragile rocks covering varying and mixed geology, understanding on tunnelling in squeezing ground conditions and applicability of TBM in Himalayas are presented. It has also been highlighted that the probe holes planning, drilling and monitoring shall be followed seriously to reduce the geological surprises.展开更多
As is the basic principle in interactive evolutionary computation(IEC)that the optima evolved by the algorithm should be the individuals that the user is most satisfied with.A rational user will keep consistent domina...As is the basic principle in interactive evolutionary computation(IEC)that the optima evolved by the algorithm should be the individuals that the user is most satisfied with.A rational user will keep consistent dominated relationship between the assigned fitness and his/her preference for the individuals.Even for rational users,it is unavoidable that the fitness he/she assigned contains noise.The result that the fitness noise caused by a rational user will not damage the basic principle in IEC is concluded.In order to prove the conclusion,two theorems separately named as strong condition and weak condition are put forward.The experiments and their results validate the theorems.As the successive issue,the relationship between the two conditions,the relationship between weak condition and fitness scaling,the true fitness in IEC,the definition of noise in IEC and so on are discussed.The results establish necessary foundation for future research.展开更多
In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|&...In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.展开更多
This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak s...This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable y, and a stochastic-Lipschitz condition in the state variable z. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [25] and Liu et al. [15]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities.展开更多
In this paper, the authors consider the behaviors of a class of parametricMarcinkiewicz integrals μ_Ω~ρ, μ_（Ω,）^（＊,）~ρ_λ and μ_Ω~ρ,S on BMO（Rn） and Campanato spaces with com-plex parameter ρ and the ...In this paper, the authors consider the behaviors of a class of parametricMarcinkiewicz integrals μ_Ω~ρ, μ_（Ω,）^（＊,）~ρ_λ and μ_Ω~ρ,S on BMO（Rn） and Campanato spaces with com-plex parameter ρ and the kernel Ω in Llog~＋ L（S^（n-1））. Here μ_（Ω,）^（＊,）~ρ_λand μ_Ω~ρ,S are parametricMarcinkiewicz functions corresponding to the Littlewood-Paley g_λ~＊-function and the Lusin areafunction S, respectively. Under certain weak regularity condition on Ω, the authors prove thatif f belongs to BMO（Rn） or to a certain Campanato space, then [μ_（Ω,）^（＊,）~ρ_λ（f）]~2, [μ_Ω~ρ,_S（f）]~2 and[μ_Ω~ρ（f）]~2 are either infinite everywhere or finite almost everywhere, and in the latter case, somekind of boundedness are also established.展开更多
This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approx...This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.展开更多
By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well ...By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well as the superlinear nonlinearities.展开更多
In this paper, we consider certain mappings. M, sufficiently close to an integrable one, which is weakly reversible with respect to the mappings G sufficiently close to an involution of type (m.n). where m, n∈Z_+ are...In this paper, we consider certain mappings. M, sufficiently close to an integrable one, which is weakly reversible with respect to the mappings G sufficiently close to an involution of type (m.n). where m, n∈Z_+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for proving the existence of a Cantor family of m-tori invariant under the reversible mappings M and the reversing mapping G.展开更多
In this paper, by using weak dissipative type conditions and weak noncompact conditions, we give the existence of weak solutions of differential equations in weak complete Banach spaces.
The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned...The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned above, is equivalent to the one introduced and studied by HytSnen （2010） in his remarkable framework, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.展开更多
The recently proposed numerical algorithm,deep BSDE method,has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations(FBSDEs)and parabolic partial differential equa...The recently proposed numerical algorithm,deep BSDE method,has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations(FBSDEs)and parabolic partial differential equations(PDEs).This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs.In particular,a posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks.Numerical results are presented to demonstrate the accuracy of the analyzed algorithm in solving high-dimensional coupled FBSDEs.展开更多
A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boun...A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.展开更多
This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,...This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings.展开更多
基金supported by the National Key Research and Development Program of China(No.2019YFC1803501)the National Natural Science Foundation of China(No.52074357)+2 种基金the Natural Science Foundation of Hunan Province,China(No.2022JJ30713)the Vanadium Titanium Union Foundationthe Project of Technology Innovation Center for Comprehensive Utilization of Strategic Mineral Resources,Ministry of Natural Resources,China。
文摘The potential of 2-amino-1-propanol(AP)as a novel depressant in selectively floating ilmenite from titanaugite under weakly acidic conditions was investigated.Micro-flotation results show that AP significantly reduces the recovery of titanaugite while having no evident impact on ilmenite flotation.Subsequent bench-scale flotation tests further confirm a remarkable improvement in separation efficiency upon the introduction of AP.Contact angle and adsorption tests reveal a stronger affinity of AP towards the titanaugite surface in comparison to ilmenite.Zeta potential measurements and X-ray photoelectron spectroscopy(XPS)analyses exhibit favorable adsorption characteristics of AP on titanaugite,resulting from a synergy of electrostatic attraction and chemical interaction.In contrast,electrostatic repulsion hinders any significant interaction between AP and the ilmenite surface.These findings highlight the potential of AP as a highly efficient depressant for ilmenite flotation,paving the way for reduced reliance on sulfuric acid in the industry.
文摘The iteration maps of Euler family for finding zeros of an operatorf in Banach spaces is defined as the partial sum of Taylor expansion of the local inversef z -1 off atz. The unified convergence theorem is established for the iterations of Euler family under the assumption that $\alpha \leqslant 3 - 2\sqrt 2 $ , while the strong condition thatf is analytic in Smale’s criterion α is replaced by the weak condition thatf is of finite order derivative.
文摘Almost all the coal is produced from open cut mines in Indonesia. As a consequence of open cut mine application, a great deal of coal is left out in the highwalls of the mined-out pits. Highwall mining systems can be used to recover this coal. The use of highwall mining systems has increasingly come into play in the US and Australia. However, it is not common in Indonesia. Moreover, Indonesia coal measure is categorized as weak geological condition. Some problems are likely to arise during the application of the highwall mining system for example instability of openings and highwalls due to the roof and pillar failures. Therefore, study of highwall mining system application in Indonesia is needed in order to increase the recovery rate of coal mining in Indonesia. This paper described the characteristics of the highwa!l mining system and discussed the appropriate highwall mining system application in weak geological condition, Indonesia. From the results of a series of laboratory tests and numerical analyses, it can be concluded that the stability of pillars and mine openings in auger mining systems is much higher than that in CHM and an auger mining system is suitable for such as very weak/poor strata conditions. Moreover, the application of backfilling system is very effective for improvement of the stability of pillar and openings.
文摘The purpose of this research is to study the effect of longwall mining on the stability of main roadway in the underground coal mine. The PT GDM （Gerbang Daya Mandiri） underground coal mine in Indonesia, where the rocks are weak, was selected as a representative study site. To accomplish the objective of the research, the finite difference code software FLAC3D was used as a tool for the numerical simulations. The longwall mining of several panel and barrier pillar widths at various depths was simulated and discussed. Based on the simulation results, it indicates that the effect of coal panel extraction on the main roadway stability depends on the width of panel and barrier pillar. The greatest effect occurs when the large panel width and the small barrier pillar width are applied, whereas the smallest effect happens when the narrow panel width and the large barrier pillar width are adopted. In this paper, therefore, to maintain the stability of the main roadway with the aim of maximizing the coal recovery, the appropriate size of panel and barrier pillar width is proposed for each mining depth for this underground coal mine.
基金Supported by National Natural Science Foundation of China under Grant Nos.11461045,11326099,11361042,11265010 Natural Science Foundation of Jiangxi Province of China under Grant Nos.20142BAB211016,20132BAB201001,20132BAB212009
文摘The conflict between the dynamics postulate（unitary evolution） and the measurement postulate（wavepacket collapse） of quantum mechanics has been reconciled by Zurek from an information transfer perspective [Phys.Rev. A 76（2007） 052110], and has further been extended to a more general scenario [Phys. Rev. A 87（2013） 052111].In this paper, we reconsider Zurek＇s new derivation by using weak repeatability postulate or covariant condition instead of repeatability postulate.
文摘A considerable amount of tunnelling has been going on in India for various projects such as hydroelectric power, irrigation, roads and railways. Most of these projects are located in Himalayas, far away from the urban areas. Tunnelling through weak and jointed rock masses such as the one in the Himalayas is a challenging task for the planners, designers, engineers and geologists because of high overburden, thickly vegetated surface, weak, poor and fragile rocks and highly varying geology with the presence of numerous small and big shear zones, faults, etc. Due to these reasons, various tunnelling problems have been faced in the past and are still being encountered. Failures and the problems may be regarded as challenges and opportunities for generating new knowledge base and thereby increasing self-reliance in tunnelling. The experiences of Himalayan tunnelling through weak and fragile rocks covering varying and mixed geology, understanding on tunnelling in squeezing ground conditions and applicability of TBM in Himalayas are presented. It has also been highlighted that the probe holes planning, drilling and monitoring shall be followed seriously to reduce the geological surprises.
文摘As is the basic principle in interactive evolutionary computation(IEC)that the optima evolved by the algorithm should be the individuals that the user is most satisfied with.A rational user will keep consistent dominated relationship between the assigned fitness and his/her preference for the individuals.Even for rational users,it is unavoidable that the fitness he/she assigned contains noise.The result that the fitness noise caused by a rational user will not damage the basic principle in IEC is concluded.In order to prove the conclusion,two theorems separately named as strong condition and weak condition are put forward.The experiments and their results validate the theorems.As the successive issue,the relationship between the two conditions,the relationship between weak condition and fitness scaling,the true fitness in IEC,the definition of noise in IEC and so on are discussed.The results establish necessary foundation for future research.
基金Supported by the Youth FoundationNatural Science Foundation, People's Republic of China.
文摘In this paper, we get the existence of a weak solution of the following inhomogeneous quasilinear elliptic equation with critical growth conditions: where N≥2, f（x,u）～|u|<sup>m-1</sup>e<sup>b|u|<sup>γ</sup></sup>at +∞, with γ=N/N-1, m≥1, b】0.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2017XKZD11)the National Natural Science Foundation of China(Grant No.12171471).
文摘This paper establishes an existence and uniqueness result for the adapted solution of a general time interval multidimensional backward stochastic differential equation (BSDE), where the generator g satisfies a weak stochastic-monotonicity condition and a general growth condition in the state variable y, and a stochastic-Lipschitz condition in the state variable z. This unifies and strengthens some known works. In order to prove this result, we develop some ideas and techniques employed in Xiao and Fan [25] and Liu et al. [15]. In particular, we put forward and prove a stochastic Gronwall-type inequality and a stochastic Bihari-type inequality, which generalize the classical ones and may be useful in other applications. The martingale representation theorem, Itô’s formula, and the BMO martingale tool are used to prove these two inequalities.
基金Project 10671062 supported by NSF of ChinaProject 20094306110004 supported by RFDP of high education of China
文摘In this paper, the authors consider the behaviors of a class of parametricMarcinkiewicz integrals μ_Ω~ρ, μ_（Ω,）^（＊,）~ρ_λ and μ_Ω~ρ,S on BMO（Rn） and Campanato spaces with com-plex parameter ρ and the kernel Ω in Llog~＋ L（S^（n-1））. Here μ_（Ω,）^（＊,）~ρ_λand μ_Ω~ρ,S are parametricMarcinkiewicz functions corresponding to the Littlewood-Paley g_λ~＊-function and the Lusin areafunction S, respectively. Under certain weak regularity condition on Ω, the authors prove thatif f belongs to BMO（Rn） or to a certain Campanato space, then [μ_（Ω,）^（＊,）~ρ_λ（f）]~2, [μ_Ω~ρ,_S（f）]~2 and[μ_Ω~ρ（f）]~2 are either infinite everywhere or finite almost everywhere, and in the latter case, somekind of boundedness are also established.
基金supported by National Natural Science Foundation of China (Grant No. 11571279)Education Department of Jiangxi Province (Grant No. GJJ151036)Youth Innovation Group of Applied Mathematics in Yichun University (Grant No. 2012TD006)
文摘This paper treats the system of motion for an incompressible non-Newtonian fluids of the stress tensor described by p-potential function subject to slip boundary conditions in R_+~3. Making use of the Oseentype approximation to this model and the L~∞-truncation method, one can establish the existence theorem of weak solutions for p-potential flow with p ∈(8/5, 2] provided that large initial are regular enough.
文摘By weakening or dropping the superquadraticity condition （SQC）, the existence of positive solutions for a class of elliptic equations is established. In particular, we deal with the asymptotieal linearities as well as the superlinear nonlinearities.
文摘In this paper, we consider certain mappings. M, sufficiently close to an integrable one, which is weakly reversible with respect to the mappings G sufficiently close to an involution of type (m.n). where m, n∈Z_+ are arbitrary. Under some weak non-degeneracy condition, we construct a uniform KAM iteration for proving the existence of a Cantor family of m-tori invariant under the reversible mappings M and the reversing mapping G.
基金Project is supportedby the Natural Science Foundation of Shangdong Province.
文摘In this paper, by using weak dissipative type conditions and weak noncompact conditions, we give the existence of weak solutions of differential equations in weak complete Banach spaces.
基金supported by National Natural Science Foundation of China(Grant No.61203249)
文摘The purpose of this paper is to extend the Littlewood-Paley theory to a geometrically doubling metric space with a non-doubling measure satisfying a weak growth condition. Moreover, we prove that our setting mentioned above, is equivalent to the one introduced and studied by HytSnen （2010） in his remarkable framework, i.e., the geometrically doubling metric space with a non-doubling measure satisfying a so-called upper doubling condition. As an application, we obtain the T1 theorem in this more general setting. Moreover, the Gaussian measure is also discussed.
文摘The recently proposed numerical algorithm,deep BSDE method,has shown remarkable performance in solving high-dimensional forward-backward stochastic differential equations(FBSDEs)and parabolic partial differential equations(PDEs).This article lays a theoretical foundation for the deep BSDE method in the general case of coupled FBSDEs.In particular,a posteriori error estimation of the solution is provided and it is proved that the error converges to zero given the universal approximation capability of neural networks.Numerical results are presented to demonstrate the accuracy of the analyzed algorithm in solving high-dimensional coupled FBSDEs.
基金supported by the National Science Foundation under Award No.0948304 and by the Southern California Earthquake Center.SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008(SCEC contribution number 1806).The work by the last author was carried out within the Swedish e-science Research Centre(SeRC)and supported by the Swedish Research Council(VR).
文摘A new weak boundary procedure for hyperbolic problems is presented.We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique.The new boundary procedure is applied near boundaries in an extended domain where data is known.We show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries.The new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary conditions.Numerical results that corroborate the analysis are presented.
文摘This paper shows that if a Gateaux differentiable functional f has a finite lower bound(although it need not attain it),then,for everyε>0,there exists some point zεsuch that‖f′(zε)‖ε1+h(‖zε‖),where h:[0,∞)→[0,∞)is a continuous function such that∫∞011+h(r)dr=∞.Applications are given to extremum problem and some surjective mappings.
