The enamines, iminium ions, and oxazolidinones are thought to be the key intermediates in the proline-catalyzed reactions of aldehydes or ketones, but there is an extensive contro- versy about their roles. Here, the c...The enamines, iminium ions, and oxazolidinones are thought to be the key intermediates in the proline-catalyzed reactions of aldehydes or ketones, but there is an extensive contro- versy about their roles. Here, the corresponding transition states connecting any two of the three kinds of species are located at the wB97XD/6-311++G** level of theory. The calcula- tions demonstrate that the oxazolidinones are the predominant species in both the gas phase and solvents; there exists tautomeric equilibrium among these species and the equilibriums are controlled by the employed solvents and temperature in the reaction. These results demonstrate that the concentration and role of the mentioned species are controlled by the employed solvent and temperature. A new reaction pathway is presented herein for the trans- formation between iminium ions and oxazolidinones through iminium ion-water complex and oxazolidinone-water complex. The calculations demonstrate that the rate-limiting step in proline-catalyzed Mannich reaction between acetaldehyde/keteones and N-Boc imines is the formation of the C-C bond rather than the intermediates tautomerization. These calculations rationalize the available experimental observations and can be valuable in optimizing the experimental conditions of asymmetric organic-catalyzed reactions of aldehydes or ketones.展开更多
Hepatocellular carcinoma(HCC) is one of the leading causes of cancer-related deaths worldwide. Although recent advances in therapeutic approaches for treating HCC have improved the prognoses of patients with HCC, this...Hepatocellular carcinoma(HCC) is one of the leading causes of cancer-related deaths worldwide. Although recent advances in therapeutic approaches for treating HCC have improved the prognoses of patients with HCC, this cancer is still associated with a poor survival rate mainly due to late diagnosis. Therefore, a diagnosis must be made sufficiently early to perform curative and effective treatments. There is a need for a deeper understanding of the molecular mechanisms underlying the initiation and progression of HCC because these mechanisms are critical for making early diagnoses and developing novel therapeutic strategies. Over the past decade, much progress has been made in elucidating the molecular mechanisms underlying hepatocarcinogenesis. In particular, recent advances in next-generation sequencing technologies have revealed numerous genetic alterations, including recurrently mutated genes and dysregulated signaling pathways in HCC. A better understanding of the genetic alterations in HCC could contribute to identifying potential driver mutations and discovering novel therapeutic targets in the future. In this article, we summarize the current advances in research on the genetic alterations, including genomic instability, single-nucleotide polymorphisms, somatic mutations and deregulated signaling pathways, implicated in the initiation and progression of HCC. We also attempt to elucidate some of the genetic mechanisms that contribute to making early diagnoses of and developing molecularly targeted therapies for HCC.展开更多
A newalgorithm, called Magnitude Cut, to recover a signal from its phase in the transform domain, is proposed.First, the recovery problem is converted to an equivalent convex optimization problem, and then it is solve...A newalgorithm, called Magnitude Cut, to recover a signal from its phase in the transform domain, is proposed.First, the recovery problem is converted to an equivalent convex optimization problem, and then it is solved by the block coordinate descent( BCD) algorithm and the interior point algorithm. Finally, the one-dimensional and twodimensional signal reconstructions are implemented and the reconstruction results under the Fourier transform with a Gaussian random mask( FTGM), the Cauchy wavelets transform( CWT), the Fourier transform with a binary random mask( FTBM) and the Gaussian random transform( GRT) are also comparatively analyzed. The analysis results reveal that the M agnitude Cut method can reconstruct the original signal with the phase information of different transforms; and it needs less phase information to recover the signal from the phase of the FTGM or GRT than that of FTBM or CWT under the same reconstruction error.展开更多
Seasonal variation in proximate, amino acid and fatty acid composition of the body wall of sea cucumber Apostichopus japonicus was evaluated. The proximate composition, except for ash content, changed significantly am...Seasonal variation in proximate, amino acid and fatty acid composition of the body wall of sea cucumber Apostichopus japonicus was evaluated. The proximate composition, except for ash content, changed significantly among seasons (P〈0.05). Alanine, glycine, glutamic acid and asparagic acid were the most abundant amino acids. Total amino acid and essential amino acid contents both varied clearly with seasons (P〈0.05). 16:0 and 16:1n7 were the primary saturated fatty acid (SFA) and monounsaturated fatty acid (MUFA) respectively for all months. EPA (20:5n-3), AA (20:4n-6) and DHA (22:6n-3) were the major polyunsaturated fatty acids (PUFA). The proportions of SFA and PUFA yielded significant seasonal variations (P〈0.001), but MUFA did not changed significantly. The results indicated that the biochemical compositions of the body wall in A. japonieus were significantly influenced by seasons and that the body wall tissue is an excellent source of protein, MUFA and n-3 PUFA for humans.展开更多
The seasonal generation and evolution of eddies in the region of the North Pacific Subtropical Countercurrent remain poorly understood due to the scarcity of available data.We used TOPEX/POSEIDON altimetry data from 1...The seasonal generation and evolution of eddies in the region of the North Pacific Subtropical Countercurrent remain poorly understood due to the scarcity of available data.We used TOPEX/POSEIDON altimetry data from 1992 to 2007 to study the eddy field in this zone.We found that velocity shear between this region and the neighboring North Equatorial Current contributes greatly to the eddy generation.Furthermore,the eddy kinetic energy level(EKE) shows an annual cycle,maximum in April/May and minimum in December/January.Analyses of the temporal and spatial distributions of the eddy field revealed clearly that the velocity shear closely related to baroclinic instability processes.The eddy field seems to be more zonal than meridional,and the energy containing length scale shows a surprising lag of 2-3 months in comparison with the 1-D and 2-D EKE level.A similar phenomenon is observed in individual eddies in this zone.The results show that in this eddy field band,the velocity shear may drive the EKE level change so that the eddy field takes another 2-3 months to grow and interact to reach a relatively stable state.This explains the seasonal evolution of identifiable eddies.展开更多
Gray scale grades for color change of dyed fabrics are assessed via image processing technology.Digital images of groups of specimens are obtained,cropped,and saved as JPEG format.Relationships between gray scale grad...Gray scale grades for color change of dyed fabrics are assessed via image processing technology.Digital images of groups of specimens are obtained,cropped,and saved as JPEG format.Relationships between gray scale grades for color change and the corresponding color differences calculated via image processing technology are investigated,compared with those obtained from high accurate computer color matching system.Results show that the new method is acceptable with an accuracy of 92.0% when the grading errors are of not more than one grade.展开更多
Aimed at improving knowledge regarding the diurnal cycle of warm-season rainfall in northwestern China,this study investigated the diurnal variations of warm-season precipitation with different durations in Xinjiang,C...Aimed at improving knowledge regarding the diurnal cycle of warm-season rainfall in northwestern China,this study investigated the diurnal variations of warm-season precipitation with different durations in Xinjiang,China,using an hourly gauge–satellite merged precipitation product during 2008 to 2019.Results show noticeable diurnal variations with distinctive regional features.The primary peak is in the early evening.Rainfall events with duration less than 3 h occur more often across the whole of Xinjiang and contribute more than half of the precipitation amount over its northern and southern peripheries,while rainfall events with duration more than 7 h over the Tianshan Mountains are responsible for the primary peak in the diurnal variations of warm-season precipitation.展开更多
A laboratory salt-water dynamics experiment using unsaturated soils in packed silt loam and clay soil columns withdifferent soil texture profiles and groundwater levels under crops were conducted to study the changes ...A laboratory salt-water dynamics experiment using unsaturated soils in packed silt loam and clay soil columns withdifferent soil texture profiles and groundwater levels under crops were conducted to study the changes of salt-waterdynamics induced by water uptake of crops and to propose the theoretical basis for the regulation and control of salt-water dynamics as well as to predict salinity levels. The HYDRUS 1D model was applied to simulate the one-dimensionalmovement of water and salt transport in the soil columns. The results showed that the salts mainly accumulated in theplow layer in the soil columns under crops. Soil water and salt both moved towards the plow layer due to soil waterabsorption by the crop root system. The salt contents in the column with lower groundwater were mostly greater thanthose with high groundwater. The water contents in the soil columns increased from top to the bottom due to plant rootwater uptake. The changes in groundwater level had little influence on water content of the root zone in the soil columnswith crop planting. Comparison between the simulated and the determined values showed that model simulation resultswere ideal, so it is practicable to do numerical simulation of soil salt and water transport by the HYDRUS 1D model.Furthermore, if the actual movement of salt and water in fields is to be described in detail, much work needs to be done.The most important thing is to refine the parameters and select precise boundary conditions.展开更多
Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical...Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.展开更多
This paper focuses on the dynamic control of distillation column with side reactors(SRC) for methyl acetate production. To obtain the optimum integrated structure and steady state simulation, the systematic design app...This paper focuses on the dynamic control of distillation column with side reactors(SRC) for methyl acetate production. To obtain the optimum integrated structure and steady state simulation, the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate production. In addition to the basic control loops, multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed. Then, based on process simulation software Aspen Plus, dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.展开更多
Finite element(FEM)analysis was used to systematically evaluate the inhomogeneity of deformation in cylindrical samples with various sample-anvil friction coefficients,m.It was found that the level of friction strongl...Finite element(FEM)analysis was used to systematically evaluate the inhomogeneity of deformation in cylindrical samples with various sample-anvil friction coefficients,m.It was found that the level of friction strongly influences the deformation homogeneity,which increases significantly with the friction coefficient although the overall geometry of the samples almost remains the same when m >0.4.The position,at which the effective strain along the maximum radial direction in a compressed sample is equal to the equivalent strain of the sample,does not vary greatly with respect to both equivalent strain of the sample and m.Hardness measurements of compressed cylindrical 5056B Al alloy samples revealed a change of effective strain distribution similar to that revealed by FEM analysis.There exists a quantitative relationship between the hardness and the effective strain if no recrystallization or recovery occurs during the compression process.展开更多
In this paper,we consider the solvability of generalized variational inequalities involving multi-valued relaxed monotone operators in the framework of Hilbert spaces.Our results mainly improve the corresponding resul...In this paper,we consider the solvability of generalized variational inequalities involving multi-valued relaxed monotone operators in the framework of Hilbert spaces.Our results mainly improve the corresponding results announced by Verma[R U Verma,Generalized variational inequalities involving multivalued relaxed monotone operators,Appl Math Lett,1997,10:107-109]and many others.展开更多
In this paper,A strong convergence theorem for a finite family of nonexpansive mappings and relaxed cocoercive mappings based on an iterative method in the framework of Hilbert spaces is established.
A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In t...A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.展开更多
文摘The enamines, iminium ions, and oxazolidinones are thought to be the key intermediates in the proline-catalyzed reactions of aldehydes or ketones, but there is an extensive contro- versy about their roles. Here, the corresponding transition states connecting any two of the three kinds of species are located at the wB97XD/6-311++G** level of theory. The calcula- tions demonstrate that the oxazolidinones are the predominant species in both the gas phase and solvents; there exists tautomeric equilibrium among these species and the equilibriums are controlled by the employed solvents and temperature in the reaction. These results demonstrate that the concentration and role of the mentioned species are controlled by the employed solvent and temperature. A new reaction pathway is presented herein for the trans- formation between iminium ions and oxazolidinones through iminium ion-water complex and oxazolidinone-water complex. The calculations demonstrate that the rate-limiting step in proline-catalyzed Mannich reaction between acetaldehyde/keteones and N-Boc imines is the formation of the C-C bond rather than the intermediates tautomerization. These calculations rationalize the available experimental observations and can be valuable in optimizing the experimental conditions of asymmetric organic-catalyzed reactions of aldehydes or ketones.
文摘Hepatocellular carcinoma(HCC) is one of the leading causes of cancer-related deaths worldwide. Although recent advances in therapeutic approaches for treating HCC have improved the prognoses of patients with HCC, this cancer is still associated with a poor survival rate mainly due to late diagnosis. Therefore, a diagnosis must be made sufficiently early to perform curative and effective treatments. There is a need for a deeper understanding of the molecular mechanisms underlying the initiation and progression of HCC because these mechanisms are critical for making early diagnoses and developing novel therapeutic strategies. Over the past decade, much progress has been made in elucidating the molecular mechanisms underlying hepatocarcinogenesis. In particular, recent advances in next-generation sequencing technologies have revealed numerous genetic alterations, including recurrently mutated genes and dysregulated signaling pathways in HCC. A better understanding of the genetic alterations in HCC could contribute to identifying potential driver mutations and discovering novel therapeutic targets in the future. In this article, we summarize the current advances in research on the genetic alterations, including genomic instability, single-nucleotide polymorphisms, somatic mutations and deregulated signaling pathways, implicated in the initiation and progression of HCC. We also attempt to elucidate some of the genetic mechanisms that contribute to making early diagnoses of and developing molecularly targeted therapies for HCC.
基金The National Natural Science Foundation of China(No.6120134461271312+7 种基金11301074)the Specialized Research Fund for the Doctoral Program of Higher Education(No.2011009211002320120092120036)the Program for Special Talents in Six Fields of Jiangsu Province(No.DZXX-031)the Natural Science Foundation of Jiangsu Province(No.BK2012329BK2012743)the United Creative Foundation of Jiangsu Province(No.BY2014127-11)the"333"Project(No.BRA2015288)
文摘A newalgorithm, called Magnitude Cut, to recover a signal from its phase in the transform domain, is proposed.First, the recovery problem is converted to an equivalent convex optimization problem, and then it is solved by the block coordinate descent( BCD) algorithm and the interior point algorithm. Finally, the one-dimensional and twodimensional signal reconstructions are implemented and the reconstruction results under the Fourier transform with a Gaussian random mask( FTGM), the Cauchy wavelets transform( CWT), the Fourier transform with a binary random mask( FTBM) and the Gaussian random transform( GRT) are also comparatively analyzed. The analysis results reveal that the M agnitude Cut method can reconstruct the original signal with the phase information of different transforms; and it needs less phase information to recover the signal from the phase of the FTGM or GRT than that of FTBM or CWT under the same reconstruction error.
基金Supported by the National Natural Science Foundation of China(No. 40906071)National Key Technology R & D Program (No.2006BAD09A02)+1 种基金the National High Technology Research and Development Program of China (863 Program) (Nos.2006AA100304 and 2006AA10A411)the Central Public-Interest Scientific Institution Basal Research Fund (No. 2009-ts-07)
文摘Seasonal variation in proximate, amino acid and fatty acid composition of the body wall of sea cucumber Apostichopus japonicus was evaluated. The proximate composition, except for ash content, changed significantly among seasons (P〈0.05). Alanine, glycine, glutamic acid and asparagic acid were the most abundant amino acids. Total amino acid and essential amino acid contents both varied clearly with seasons (P〈0.05). 16:0 and 16:1n7 were the primary saturated fatty acid (SFA) and monounsaturated fatty acid (MUFA) respectively for all months. EPA (20:5n-3), AA (20:4n-6) and DHA (22:6n-3) were the major polyunsaturated fatty acids (PUFA). The proportions of SFA and PUFA yielded significant seasonal variations (P〈0.001), but MUFA did not changed significantly. The results indicated that the biochemical compositions of the body wall in A. japonieus were significantly influenced by seasons and that the body wall tissue is an excellent source of protein, MUFA and n-3 PUFA for humans.
基金Supported by the Key Program of the Knowledge Innovation Program of the Chinese Academy of Sciences (No.KZCX1-YW-12-04)the National Basic Research Program (973 Program) (No.2006CB403601)
文摘The seasonal generation and evolution of eddies in the region of the North Pacific Subtropical Countercurrent remain poorly understood due to the scarcity of available data.We used TOPEX/POSEIDON altimetry data from 1992 to 2007 to study the eddy field in this zone.We found that velocity shear between this region and the neighboring North Equatorial Current contributes greatly to the eddy generation.Furthermore,the eddy kinetic energy level(EKE) shows an annual cycle,maximum in April/May and minimum in December/January.Analyses of the temporal and spatial distributions of the eddy field revealed clearly that the velocity shear closely related to baroclinic instability processes.The eddy field seems to be more zonal than meridional,and the energy containing length scale shows a surprising lag of 2-3 months in comparison with the 1-D and 2-D EKE level.A similar phenomenon is observed in individual eddies in this zone.The results show that in this eddy field band,the velocity shear may drive the EKE level change so that the eddy field takes another 2-3 months to grow and interact to reach a relatively stable state.This explains the seasonal evolution of identifiable eddies.
基金Scientific Research Fund of Yancheng Institute of Technology,China(No. XKY2009029)
文摘Gray scale grades for color change of dyed fabrics are assessed via image processing technology.Digital images of groups of specimens are obtained,cropped,and saved as JPEG format.Relationships between gray scale grades for color change and the corresponding color differences calculated via image processing technology are investigated,compared with those obtained from high accurate computer color matching system.Results show that the new method is acceptable with an accuracy of 92.0% when the grading errors are of not more than one grade.
基金supported by the National Key Research and Development Project of China[Grant Nos.2018YFC1507104 and 2018YFC1507603]the National Natural Science Foundation of China[Grants Nos.91937301,41875074,and 41675060]the National Key Scientific and Technological Infrastructure Project“Earth Lab”。
文摘Aimed at improving knowledge regarding the diurnal cycle of warm-season rainfall in northwestern China,this study investigated the diurnal variations of warm-season precipitation with different durations in Xinjiang,China,using an hourly gauge–satellite merged precipitation product during 2008 to 2019.Results show noticeable diurnal variations with distinctive regional features.The primary peak is in the early evening.Rainfall events with duration less than 3 h occur more often across the whole of Xinjiang and contribute more than half of the precipitation amount over its northern and southern peripheries,while rainfall events with duration more than 7 h over the Tianshan Mountains are responsible for the primary peak in the diurnal variations of warm-season precipitation.
基金the National Key Basic Research Support Foundation (NKBRSF) of China (No. G1999011803),the National Natural Science Foundation of China (Nos. 40371058 and 40471018), the Jiangsu Provincial Society Deve-lopment Program of China (No. BS2003005), and the Institute of Geography and Limnology, Chinese Academy of Sciences(No. S250020).
文摘A laboratory salt-water dynamics experiment using unsaturated soils in packed silt loam and clay soil columns withdifferent soil texture profiles and groundwater levels under crops were conducted to study the changes of salt-waterdynamics induced by water uptake of crops and to propose the theoretical basis for the regulation and control of salt-water dynamics as well as to predict salinity levels. The HYDRUS 1D model was applied to simulate the one-dimensionalmovement of water and salt transport in the soil columns. The results showed that the salts mainly accumulated in theplow layer in the soil columns under crops. Soil water and salt both moved towards the plow layer due to soil waterabsorption by the crop root system. The salt contents in the column with lower groundwater were mostly greater thanthose with high groundwater. The water contents in the soil columns increased from top to the bottom due to plant rootwater uptake. The changes in groundwater level had little influence on water content of the root zone in the soil columnswith crop planting. Comparison between the simulated and the determined values showed that model simulation resultswere ideal, so it is practicable to do numerical simulation of soil salt and water transport by the HYDRUS 1D model.Furthermore, if the actual movement of salt and water in fields is to be described in detail, much work needs to be done.The most important thing is to refine the parameters and select precise boundary conditions.
基金Project(SKLGP2011K013)supported by the State Key Laboratory of Geohazard Prevention and Geoenvironment Protection,ChinaProject(20110073120012)supported by the Research Fund for the Doctoral Program of Higher Education of China+1 种基金Project(11PJ1405700)supported by the the Shanghai Pujiang Talent Plan,ChinaProject(41002091)supported by the National Natural Science Foundation of China
文摘Experimental evidence has indicated that clay exhibits strain-softening response under undrained compression following anisotropic consolidation.The purpose of this work was to propose a modeling method under critical state theory of soil mechanics.Based on experimental data on different types of clay,a simple double-surface model was developed considering explicitly the location of critical state by incorporating the density state into constitutive equations.The model was then used to simulate undrained triaxial compression tests performed on isotropically and anisotropically consolidated samples with different stress ratios.The predictions were compared with experimental results.All simulations demonstrate that the proposed approach is capable of describing the drained and undrained compression behaviors following isotropic and anisotropic consolidations.
基金Supported by the National Natural Science Foundation of China(61673205,61503181,21727818)National Key R&D Program of China(2017YFB0307304)+1 种基金the Natural Science Foundation of Jiangsu Province(BK20141461,BK20140953)the State Key Laboratory of Materials-Oriented Chemical Engineering Open Subject(kl16-07)
文摘This paper focuses on the dynamic control of distillation column with side reactors(SRC) for methyl acetate production. To obtain the optimum integrated structure and steady state simulation, the systematic design approach based on the concept of independent reaction amount is applied to the process of SRC for methyl acetate production. In addition to the basic control loops, multi-variable model predictive control modular with methyl acetate concentration and temperature of sensitive plate is designed. Then, based on process simulation software Aspen Plus, dynamic simulation of SRC for methyl acetate production is used to verify the effectiveness of the control scheme.
基金Project(2016JJ1016) supported by the Science Fund for Distinguished Young Scholars of Hunan Province,ChinaProject(201301G0105337290) supported by the Program of Innovation and Entrepreneur Team Introduced by Guangdong Province,China
文摘Finite element(FEM)analysis was used to systematically evaluate the inhomogeneity of deformation in cylindrical samples with various sample-anvil friction coefficients,m.It was found that the level of friction strongly influences the deformation homogeneity,which increases significantly with the friction coefficient although the overall geometry of the samples almost remains the same when m >0.4.The position,at which the effective strain along the maximum radial direction in a compressed sample is equal to the equivalent strain of the sample,does not vary greatly with respect to both equivalent strain of the sample and m.Hardness measurements of compressed cylindrical 5056B Al alloy samples revealed a change of effective strain distribution similar to that revealed by FEM analysis.There exists a quantitative relationship between the hardness and the effective strain if no recrystallization or recovery occurs during the compression process.
基金Supported by the Natural Science Foundation of Hebei Province(A2010001943) Supported by the Science Grant of Beijing Jiaotong University(2011YJS075)
文摘In this paper,we consider the solvability of generalized variational inequalities involving multi-valued relaxed monotone operators in the framework of Hilbert spaces.Our results mainly improve the corresponding results announced by Verma[R U Verma,Generalized variational inequalities involving multivalued relaxed monotone operators,Appl Math Lett,1997,10:107-109]and many others.
文摘In this paper,A strong convergence theorem for a finite family of nonexpansive mappings and relaxed cocoercive mappings based on an iterative method in the framework of Hilbert spaces is established.
文摘A mechanical model for strain softening pillar is proposed considering the characteristics of progressive shear failure and strain localization. The pillar undergoes elastic, strain softening and slabbing stages. In the elastic stage, vertical compressive stress and deformation at upper end of pillar are uniform, while in the strain softening stage there appears nonuniform due to occurrence of shear bands, leading to the decrease of load-carrying capacity. In addition, the size of failure zone increases in the strain softening stage and reaches its maximum value when slabbing begins. In the latter two stages, the size of elastic core always decreases. In the slabbing stage, the size of failure zone remains a constant and the pillar becomes thinner. Total deformation of the pillar is derived by linearly elastic Hookes law and gradient-dependent plasticity where thickness of localization band is determined according to the characteristic length. Post-peak stiffness is proposed according to analytical solution of averaged compressive stress-average deformation curve. Instability criterion of the pillar and roof strata system is proposed analytically (using) instability condition given by Salamon. It is found that the constitutive parameters of material of pillar, the geometrical size of pillar and the number of shear bands influence the stability of the system; stress gradient controls the starting time of slabbing, however it has no influence on the post-peak stiffness of the pillar.