In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility...In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.展开更多
The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory sy...The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called "perfectibility" parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.展开更多
Concrete filled steel tube structures have gained booming development in recent decades, especially in China. Simplified methods have been proposed in design codes, such as the Eurocode 4 (EC4) and the China engineeri...Concrete filled steel tube structures have gained booming development in recent decades, especially in China. Simplified methods have been proposed in design codes, such as the Eurocode 4 (EC4) and the China engineering and construction specification (CECS). In EC4, the confinement effect is reasonably related to slenderness and load eccentricity. The CECS method is much straight forward in that the slenderness ratio and load eccentricity are treated as independent reduction factors. To make use of the advantages of both the CECS and the EC4 methods, the CECS method is modified to consider the confinement effect associated with slenderness and load eccentricity. It is shown that the proposed method can predict well the ultimate load capacity of circular section concrete filled steel tube columns.展开更多
Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical proper...Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasi- bility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column com- posed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.展开更多
The Sargent dividing wall column can implement four products separation sequences in one column based on Fully Thermally Coupled Distillation Column. The initial design parameters are required for the design optimizat...The Sargent dividing wall column can implement four products separation sequences in one column based on Fully Thermally Coupled Distillation Column. The initial design parameters are required for the design optimization or dynamic control of the Sargent dividing wall column, and in order to make the rigorous simulation of the Sargent dividing wall column more conducive to convergence, a ten column model for complex Sargent column is established in this paper,and the shortcut design method of this model is proposed. The internal minimum vapor and liquid flow are obtained by the Underwood equations and the mass balance method and the V-min method. The separation for a 4-component shortcut mixture of pentane, hexane, heptane and octane was considered, while the initial values of design parameters and the ratio of vapor-liquid distribution of each column were calculated by using the shortcut design method of a ten column model. And by comparing the shortcut calculations with rigorous simulation results, the practicality and reliability of shortcut calculations were verified. The reason for energy saving was analyzed based on back-mixing. A virtual heat exchanger is proposed to make the Sargent dividing wall column more energy efficient.展开更多
The column bioleaching of copper flotation tailings was comparatively investigated using layered heap construction method(LM),agglomerate heap construction method(AM),and pellets-sintering heap construction method(PM)...The column bioleaching of copper flotation tailings was comparatively investigated using layered heap construction method(LM),agglomerate heap construction method(AM),and pellets-sintering heap construction method(PM).The bacterial communities of free,attached,weakly-attached,and strongly-attached microbes in the later bioleaching stage were investigated.In AM group,the addition of lump sulphide ore resulted in the low leachate pH,high ferric iron concentration,and rapid microbial adsorption,which obtained the maximum copper extraction(60.1%)compared with LM(54.6%)and PM(43.9%)groups.The relative abundance of dominant genera and microbial communities of different microbiota underwent changes in three heap construction methods.The alpha-diversity indexes of attached,weakly-attached,and strongly-attached microbes were different,while no significant change was observed in free bacteria.The variation of whole bacterial community was significantly associated with solution pH,total iron,and ferric iron concentrations.Pearson correlation analysis and partial least square path model both indicated that attached bacteria made larger contribution to the copper extraction of tailings.展开更多
Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the bu...Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.展开更多
The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The ...The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.展开更多
MnO 2 was prepared by column method from normal spinel LiMn 2O 4 with purity of 99.38%.The influence of LiMn 2O 4 grain size and acidity of leaching solution on the lithium leaching process was studied.The result...MnO 2 was prepared by column method from normal spinel LiMn 2O 4 with purity of 99.38%.The influence of LiMn 2O 4 grain size and acidity of leaching solution on the lithium leaching process was studied.The results show that the appropriate range of LiMn 2O 4 grain size was 60-160 meshes and the concentration of leaching solution HCl was 0.1 mol·L -1.The adsorption capacity Q of λ-MnO 2 for lithium increased with the increase of pH and changed markedly at pH 6.0-10.0.It was 3.80mmol/g at pH 12.0.The distribution coefficients K d of Li + and Na + were 3.406×10 4 and 2.300 respectively,and the separation coefficient α Li Na was 1.481×10 4 at pH 6.5.As a result,λ-MnO 2 is a high performance ion-sieve material for lithium ion.展开更多
In this study, the concept of a new seawater desalination method and equipment using liquid columns of seawater and desalinated fresh water, decompression boiling and evaporation, condensation, and recovery of condens...In this study, the concept of a new seawater desalination method and equipment using liquid columns of seawater and desalinated fresh water, decompression boiling and evaporation, condensation, and recovery of condensation latent heat are proposed. The equipment consists of seawater and freshwater columns approximately 10 m high with top spaces. The pressure of the top space, the evaporation and condensation area, of the seawater column, for example, is reduced approximately 30 mmHg (abs.) using the seawater column, after which it is heated from the general seawater temperature of 25°C to 30°C to boil and evaporate the seawater. The vapor is cooled by the seawater at approximately 25°C in a heat exchanger, and then, it is condensed and sent to the fresh water column. At this time, the condensation latent heat is recovered to preheat the newly flowing seawater. The evaporation or condensation rate, namely, the production rate of freshwater, by the new desalination equipment is also estimated by the results of the existing quadruplex effect vacuum evaporator used in the salt production industry. This new desalination method and its associated equipment also can be used to purify polluted water and waste water.展开更多
The complex tunnelling constructive environment in urban area in similar green field situations is faced through analytical evaluations in order to control the design calculation process and subsequently manage the in...The complex tunnelling constructive environment in urban area in similar green field situations is faced through analytical evaluations in order to control the design calculation process and subsequently manage the interventions techniques with the aim of totally reducing the typical settlements trough above the tunnel either during the construction stage or during the serviceability stage. Recently, the author has proposed an operative and mathematical method by an opportune choice of tensioned anchors to control the tunnel lining settlements. In order to completely eliminate the remainder typical soft soil trough which is normal to the line of the tunnel, it is here proposed to use and properly calculate the interventions of stone columns by the SAVE (silent, advanced, vibration-erasing) Compozer method, in combination with the anchorages.展开更多
Nicotine and cotinine in hair are good biomarkers for assessing long-term exposure to smoking. However, analytical devices such as GC/MS are associated with high cost and are not widely used. HPLC/UV is used widely in...Nicotine and cotinine in hair are good biomarkers for assessing long-term exposure to smoking. However, analytical devices such as GC/MS are associated with high cost and are not widely used. HPLC/UV is used widely in laboratories, but is unsuitable for measurement of minor constituents, except when using the column-switching method. Thus, we aimed to establish a simple, inexpensive and sensitive method based on HPLC/UV with column switching for measuring nicotine and cotinine in hair. First, we compared the presence and absence of a column selection unit. We then measured amounts of nicotine and cotinine in hair samples collected from the general population, and compared both the corresponding levels and the detection limits with those in previous studies. Finally, initial and running costs of HPLC/UV were compared with other analytical methods. As one of the results, the areas of nicotine and cotinine measured by HPLC/UV with column-switching method were 12.9 and 16.9 times greater, respectively, than those without the column-switching method. The amount of nicotine and cotinine in hair was significantly correlated to number of cigarettes smoked per day (r = 0.228, p = 0.040). In addition, the HPLC/UV method showed similar sensitivity and detection limit (nicotine, 0.10 ng/mg;cotinine, 0.08 ng/mg) as reported in previous studies. The cost of the HPLC/UV method is lower than that of other analytical methods. We were able to establish a low-cost method with good sensitivity for measuring nicotine and cotinine in hair. The HPLC/UV with a column-switching method will be useful as a first step in screening surveys in order to better understand the effects of smoking exposure.展开更多
In this paper, we prove the local and Supcrlinear convergence theorem of the column-updating method for n>2. This is an oped problem for the convergene theory of the column-updating method given by Martinez in the ...In this paper, we prove the local and Supcrlinear convergence theorem of the column-updating method for n>2. This is an oped problem for the convergene theory of the column-updating method given by Martinez in the Intcrnational Conference of the NATO-ASI (Italy, 1994).展开更多
基金This work was supported by the National Natural Science Foundation of China(Grant no.U22A20603)Sichuan Science and Technology Program-China(Grant No.2023ZYD0149)CAS"Light of West China"Program-China(Grant No.Fangwei Yu).In addition,a special acknowledgement should be expressed to a famous Chinese television drama:My Chief and My Regiment that accompanied me(Dr.Fangwei Yu)through the loneliness time of completing this study.
文摘In order to understand the dynamics of granular flow on an erodible base soil,in this paper,a series of material point method-based granular column collapse tests were conducted to investigate numerically the mobility and dynamic erosion process of granular flow subjected to the complex settings,i.e.,the aspect ratio,granular mass,friction and dilatancy resistance,gravity and presence of water.A set of power scaling laws were proposed to describe the final deposit characteristics of granular flow by the relations of the normalized run-out distance and the normalized final height of granular flow against the aspect ratio,being greatly affected by the complex geological settings,e.g.,granular mass,the friction and dilatancy resistance of granular soil,and presence of water in granular flow.An index of the coefficient of friction of granular soil was defined as a ratio of the target coefficient of friction over the initial coefficient of friction to quantify the scaling extent of friction change(i.e.,friction strengthening or weakening).There is a characteristic aspect ratio of granular column corresponding to the maximum mobility of granular flow with the minimum index of the apparent coefficient of friction.The index of the repose coefficient of friction of granular flow decreased gradually with the increase in aspect ratio because higher potential energy of granular column at a larger aspect ratio causes a larger kinetic energy of granular soil to weaken the friction of granular soil as a kind of velocity-related friction weakening.An increase in granular mass reduces gradually the indexes of the apparent and repose coefficients of friction of granular soil to enhance the mobility of granular flow.The mobility of granular flow increases gradually with the decrease in friction angle or increase in dilatancy angle of granular soil.However,the increase of gravity accelerates granular flow but showing the same final deposit profile without any dependence on gravity.The mobility of granular flow increases gradually by lowering the indexes of the apparent and repose coefficients of friction of granular flow while changing the surroundings,in turn,the dry soil,submerged soil and saturated soil,implying a gradually increased excessive mobility of granular flow with the friction weakening of granular soil.Presence of water in granular flow may be a potential catalyzer to yield a long run-out granular flow,as revealed in comparison of water-absent and water-present granular flows.In addition,the dynamic erosion and entrainment of based soil induced by granular flow subjected to the complex geological settings,i.e.,the aspect ratio,granular mass,gravity,friction and dilatancy resistance,and presence of water,were comprehensively investigated as well.
文摘The aim of this study is to calculate the critical load of variable inertia columns. The example studied in this paper can be used as a paradigm for other non-uniform columns. The wavelength of equivalent vibratory system is used to calculate the critical load of the trigonometrically varied inertia column. In doing so, the equilibrium equation of the column is theoretically studied using the perturbation method. Accuracy of the calculated results is evaluated by comparing the solution with numerical results. Effect of improving the initial guess on the solution accuracy is investigated. Effects of varying parameters of the trigonometrically varied inertia and the uniformly tapered columns on their stability behavior are studied. Finally, using the so-called "perfectibility" parameter, two design goals, i.e., being lightweight and being strong, are studied for the discussed columns.
文摘Concrete filled steel tube structures have gained booming development in recent decades, especially in China. Simplified methods have been proposed in design codes, such as the Eurocode 4 (EC4) and the China engineering and construction specification (CECS). In EC4, the confinement effect is reasonably related to slenderness and load eccentricity. The CECS method is much straight forward in that the slenderness ratio and load eccentricity are treated as independent reduction factors. To make use of the advantages of both the CECS and the EC4 methods, the CECS method is modified to consider the confinement effect associated with slenderness and load eccentricity. It is shown that the proposed method can predict well the ultimate load capacity of circular section concrete filled steel tube columns.
基金Foundation of Key Laboratory of Coast Civil Structure Safety (Tianjin University),Ministry of EducationChinese Program for New Century Excellent Talents in University+1 种基金Seed Foundation of Tianjin UniversitySeed Foundation of Xinjiang University
文摘Based on the characteristics of an L-shaped column composed of concrete-filled square steel tubes, the axial compression experiment and nonlinear finite element analysis were carried out to study the mechanical property of the L-shaped column. The load-displacement curve for the L-shaped column, the deflection and load-strain curves for the mono columns were obtained by the axial compression experiment. The results show that the L-shaped column exhibits a flexural-torsional buckling failure mode. The numerical simulation by the finite element analysis shows that the bearing capacity and failure mode are in accordance with those of the axial compression experiment and the feasi- bility of the finite element analysis is proved. For the calculation of the bearing capacity of the L-shaped column com- posed of concrete-filled square steel tubes, an analytical method is proposed based on the theory of the elastic stability and spatial truss model. The results of the analytical method are in good agreement with those of the axial compression experiment and the finite element analysis.
基金supported by the High-level Talents Program of Hebei Province (A 2017002032)
文摘The Sargent dividing wall column can implement four products separation sequences in one column based on Fully Thermally Coupled Distillation Column. The initial design parameters are required for the design optimization or dynamic control of the Sargent dividing wall column, and in order to make the rigorous simulation of the Sargent dividing wall column more conducive to convergence, a ten column model for complex Sargent column is established in this paper,and the shortcut design method of this model is proposed. The internal minimum vapor and liquid flow are obtained by the Underwood equations and the mass balance method and the V-min method. The separation for a 4-component shortcut mixture of pentane, hexane, heptane and octane was considered, while the initial values of design parameters and the ratio of vapor-liquid distribution of each column were calculated by using the shortcut design method of a ten column model. And by comparing the shortcut calculations with rigorous simulation results, the practicality and reliability of shortcut calculations were verified. The reason for energy saving was analyzed based on back-mixing. A virtual heat exchanger is proposed to make the Sargent dividing wall column more energy efficient.
基金financial supports from the National Key R&D Program of China(No.2018YFC1801804)the Shandong Provincial Natural Science Foundation,China(Nos.ZR2020QD120 and ZR2018LD001)Project of Introducing and Cultivating Young Talent in the Universities of Shandong Province,China(No.QC2019YY144)。
文摘The column bioleaching of copper flotation tailings was comparatively investigated using layered heap construction method(LM),agglomerate heap construction method(AM),and pellets-sintering heap construction method(PM).The bacterial communities of free,attached,weakly-attached,and strongly-attached microbes in the later bioleaching stage were investigated.In AM group,the addition of lump sulphide ore resulted in the low leachate pH,high ferric iron concentration,and rapid microbial adsorption,which obtained the maximum copper extraction(60.1%)compared with LM(54.6%)and PM(43.9%)groups.The relative abundance of dominant genera and microbial communities of different microbiota underwent changes in three heap construction methods.The alpha-diversity indexes of attached,weakly-attached,and strongly-attached microbes were different,while no significant change was observed in free bacteria.The variation of whole bacterial community was significantly associated with solution pH,total iron,and ferric iron concentrations.Pearson correlation analysis and partial least square path model both indicated that attached bacteria made larger contribution to the copper extraction of tailings.
文摘Elastic critical buckling load of a column depends on various parameters,such as boundary conditions,material,and crosssection geometry.The main purpose of this work is to present a new method for investigating the buckling load of tapered columns subjected to axial force.The proposed method is based on modified buckling mode shape of tapered structure and perturbation theory.The mode shape of the damaged structure can be expressed as a linear combination of mode shapes of the intact structure.Variations in length in piecewise form can be positive or negative.The method can be used for single-span and continuous columns.Comparison of results with those of finite element and Timoshenko methods shows the high accuracy and efficiency of the proposed method for detecting buckling load.
文摘The dynamical stability of a homogeneous, simple supported column, subjected to a periodic axial force, is investigated. The viscoelastic material is assumed to obey the Leaderman nonlinear constitutive relation. The equation of motion was derived as a nonlinear integro-partial-differential equation, and was simplified into a nonlinear integro-differential equation by the Galerkin method. The averaging method was employed to carry out the stability analysis. Numerical results are presented to compare with the analytical ones. Numerical results also indicate that chaotic motion appears.
基金theNationalNaturalScienceFoundationofChi na (No .5 9972 0 2 7)theNaturalScienceFoundationofHubeiProvince (No .2 0 0 2AB0 74) )
文摘MnO 2 was prepared by column method from normal spinel LiMn 2O 4 with purity of 99.38%.The influence of LiMn 2O 4 grain size and acidity of leaching solution on the lithium leaching process was studied.The results show that the appropriate range of LiMn 2O 4 grain size was 60-160 meshes and the concentration of leaching solution HCl was 0.1 mol·L -1.The adsorption capacity Q of λ-MnO 2 for lithium increased with the increase of pH and changed markedly at pH 6.0-10.0.It was 3.80mmol/g at pH 12.0.The distribution coefficients K d of Li + and Na + were 3.406×10 4 and 2.300 respectively,and the separation coefficient α Li Na was 1.481×10 4 at pH 6.5.As a result,λ-MnO 2 is a high performance ion-sieve material for lithium ion.
文摘In this study, the concept of a new seawater desalination method and equipment using liquid columns of seawater and desalinated fresh water, decompression boiling and evaporation, condensation, and recovery of condensation latent heat are proposed. The equipment consists of seawater and freshwater columns approximately 10 m high with top spaces. The pressure of the top space, the evaporation and condensation area, of the seawater column, for example, is reduced approximately 30 mmHg (abs.) using the seawater column, after which it is heated from the general seawater temperature of 25°C to 30°C to boil and evaporate the seawater. The vapor is cooled by the seawater at approximately 25°C in a heat exchanger, and then, it is condensed and sent to the fresh water column. At this time, the condensation latent heat is recovered to preheat the newly flowing seawater. The evaporation or condensation rate, namely, the production rate of freshwater, by the new desalination equipment is also estimated by the results of the existing quadruplex effect vacuum evaporator used in the salt production industry. This new desalination method and its associated equipment also can be used to purify polluted water and waste water.
文摘The complex tunnelling constructive environment in urban area in similar green field situations is faced through analytical evaluations in order to control the design calculation process and subsequently manage the interventions techniques with the aim of totally reducing the typical settlements trough above the tunnel either during the construction stage or during the serviceability stage. Recently, the author has proposed an operative and mathematical method by an opportune choice of tensioned anchors to control the tunnel lining settlements. In order to completely eliminate the remainder typical soft soil trough which is normal to the line of the tunnel, it is here proposed to use and properly calculate the interventions of stone columns by the SAVE (silent, advanced, vibration-erasing) Compozer method, in combination with the anchorages.
文摘Nicotine and cotinine in hair are good biomarkers for assessing long-term exposure to smoking. However, analytical devices such as GC/MS are associated with high cost and are not widely used. HPLC/UV is used widely in laboratories, but is unsuitable for measurement of minor constituents, except when using the column-switching method. Thus, we aimed to establish a simple, inexpensive and sensitive method based on HPLC/UV with column switching for measuring nicotine and cotinine in hair. First, we compared the presence and absence of a column selection unit. We then measured amounts of nicotine and cotinine in hair samples collected from the general population, and compared both the corresponding levels and the detection limits with those in previous studies. Finally, initial and running costs of HPLC/UV were compared with other analytical methods. As one of the results, the areas of nicotine and cotinine measured by HPLC/UV with column-switching method were 12.9 and 16.9 times greater, respectively, than those without the column-switching method. The amount of nicotine and cotinine in hair was significantly correlated to number of cigarettes smoked per day (r = 0.228, p = 0.040). In addition, the HPLC/UV method showed similar sensitivity and detection limit (nicotine, 0.10 ng/mg;cotinine, 0.08 ng/mg) as reported in previous studies. The cost of the HPLC/UV method is lower than that of other analytical methods. We were able to establish a low-cost method with good sensitivity for measuring nicotine and cotinine in hair. The HPLC/UV with a column-switching method will be useful as a first step in screening surveys in order to better understand the effects of smoking exposure.
文摘In this paper, we prove the local and Supcrlinear convergence theorem of the column-updating method for n>2. This is an oped problem for the convergene theory of the column-updating method given by Martinez in the Intcrnational Conference of the NATO-ASI (Italy, 1994).