On the basis of a general model of fuel cells, the entropy production rates of a fuel cell system under different conditions are derived by using theories of electrochemistry and thermodynamics. In order to analyze th...On the basis of a general model of fuel cells, the entropy production rates of a fuel cell system under different conditions are derived by using theories of electrochemistry and thermodynamics. In order to analyze the influence of the irreversible losses existing in an actual fuel cell, the equivalent circuit of the fuel cell is introduced, so that the irreversible factor of the fuel cell may be determined directly as a function of the internal, leak and load resistances. Moreover, the maximum power output and efficiency of the fuel cell are calculated, the optimal operation of the fuel cell is discussed, and the matching condition of the load resistance is determined.展开更多
The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point...The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.展开更多
The entropy production rate was determined for avascular tumor growth. The proposed formula relates the fractal dimension of the tumor contour with the quotient between mitosis and apoptosis rate, which can be used to...The entropy production rate was determined for avascular tumor growth. The proposed formula relates the fractal dimension of the tumor contour with the quotient between mitosis and apoptosis rate, which can be used to characterize the degree of proliferation of tumor cells. The entropy production rate was determined for fourteen tumor cell lines as a physical function of cancer robustness. The entropy production rate is a hallmark that allows us the possibility of prognosis of tumor proliferation and invasion capacities, key fac-tors to improve cancer therapy.展开更多
The high strength low-alloy steels are welded by underwater wet welding with stainless steel electrodes. The microstructural and electrochemical corrosion study of base metal(BM), weld zone(WZ) and heat affected zone(...The high strength low-alloy steels are welded by underwater wet welding with stainless steel electrodes. The microstructural and electrochemical corrosion study of base metal(BM), weld zone(WZ) and heat affected zone(HAZ) are carried out to understand the influence of the corrosion product layer generated on the high strength low-alloy steels welded by underwater wet welding with stainless steel electrodes, methods used including, potentiodynamic polarization, electrochemical impedance spectroscopy(EIS) and scanning electron microscope(SEM). The results indicate that the WZ acts as a cathode and there is no corrosion product on it throughout the immersion period in seawater. The HAZ and BM acts as anodes. The corrosion rates of the HAZ and BM change with the immersion time increasing. In the initial immersion period, the HAZ has the highest corrosion rate because it has a coarse tempered martensite structure and the BM exhibites a microstructure with very fine grains of ferrite and pearlite. After a period of immersion, the BM has the highest corrosion rate. The reason is that the corrosion product layer on the HAZ is dense and has a better protective property while that on the BM is loose and can not inhibit the diffusion of oxygen.展开更多
According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli (E. coil) infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lys...According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli (E. coil) infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.展开更多
Copepod fecal pellets are ubiquitous throughout the oceans. Their production and export can represent a highly efficient pathway of carbon export. However, the role these fecal pellets play in carbon export in the Cha...Copepod fecal pellets are ubiquitous throughout the oceans. Their production and export can represent a highly efficient pathway of carbon export. However, the role these fecal pellets play in carbon export in the Changjiang(Yangtze) River estuary is not well known. Two cruises were carried out in the Changjiang estuary in the spring and summer of 2013, during which time carbon biomass, production, and export of copepod fecal pellets were studied. Spring and summer fecal pellet carbon biomass ranged 0.30–1.01 mg C/m^3(mean=0.56±0.20 mg C/m^3) and 0.31–1.18 mg C/m^3(mean=0.64±0.24 mg C/m^3), respectively, significantly lower than phytoplankton. At most stations, fecal pellet carbon biomass was higher in surface or subsurface layers than deeper layers. Production rates ranged 0.65–1.49 pellets/(ind.?h)(mean=1.02±0.27 pellets/(ind.?h)) in spring and 0.62–1.34 pellets/(ind.?h)(mean=0.98±0.22 pellets/(ind.?h)) in summer, within the range reported in previous studies. Higher production rates of fecal pellets occurred at stations with higher chlorophyll a concentrations, and production rates of copepods of size 500–1 000 μm greater than copepods >1 000 μm during both cruises. The potential export flux of fecal pellets was slightly higher in summer(mean=68.95±14.37 mg C/(m^2 ?d)) than spring(mean=52.08±11.33 mg C/(m^2 ?d)) owing to higher summer copepod abundances. To our knowledge, this study is the first of its kind in the Changjiang estuary, and it confirms the significant role of copepod fecal pellets in local carbon export.展开更多
Thermal manikin plays important roles in simulating thethermal state of human bodies to facilitate the evaluationof thermal comfort properties of various clothing assem-blies.Based on the heat balance principle and an...Thermal manikin plays important roles in simulating thethermal state of human bodies to facilitate the evaluationof thermal comfort properties of various clothing assem-blies.Based on the heat balance principle and analysis ofrelated factors,the heat production rate of manikin isrecommended as an efficient evaluation index.Whereas,its inside heat production which occurs as a result of theexistence of temperature difference between its insidepart and outside surface,should not be ignored.Through a series of theoretical analysis and calculations,a compensative equation is deduced in this paper.展开更多
The apparent degradation rate constant of fluticasone propionate(FLT) in 0.1 M NaOH:methanol=1:1 at 37 °C was previously reported to be 0.169 ± 0.003 h^(-1), and four degradation products(products 1–4) were...The apparent degradation rate constant of fluticasone propionate(FLT) in 0.1 M NaOH:methanol=1:1 at 37 °C was previously reported to be 0.169 ± 0.003 h^(-1), and four degradation products(products 1–4) were observed in the solution. The aims of the present study were to assess the degradation rates of FLT in other alkaline solutions and clarify the chemical structures of the four degradation products in order to obtain basic data for designing an enema for inflammatory bowel disease. The apparent degradation rate constants in 0.05 M NaOH and 0.1 M NaOH:CH_3CN=1:1 were 0.472 ± 0.013 h^(-1) and 0.154 ± 0.000 h^(-1)(n=3), respectively. The chemical structures of products 1–4 in 0.1 M NaOH:methanol=1:1 were revealed by nuclear magnetic resonance(NMR)and mass spectrometry data. The chemical structure of products 2 was that the 17-position of the thioester moiety of FLT was substituted by a carboxylic acid. The degradation product in 0.1 M NaOH:CH_3CN=1:1 was found to be product 2 based on ~1H NMR data. The degradation product in 0.05 M NaOH was considered to be product 2 based on the retention time of HPLC. These results are useful for detecting the degradation products of FLT by enzymes of the intestinal bacterial flora in the large intestine after dosing FLT as an enema.展开更多
A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision ...A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region(T 〈 100 K). Meanwhile, three product angular distributions P(θr), P(φr), and P(θr, φr) are presented, which reflect the positive effect on the rotational angular momentum j' polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections(PDDCSs), PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.展开更多
A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second,...A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.展开更多
Based upon broad-band CCD observation data of comet Hale-Bopp obtained by a 60cm telescope at Xinglong Station of Beijing Astronomical Observatory during March-August, 1996, the photometric results of comet Hale-Bopp ...Based upon broad-band CCD observation data of comet Hale-Bopp obtained by a 60cm telescope at Xinglong Station of Beijing Astronomical Observatory during March-August, 1996, the photometric results of comet Hale-Bopp are reported. Using the photometric results, the dust production rate, radius and mass of nucleus of comet Hale-Bopp are estimated as follows: dM/dt~1.5×10 5 kgs -1, R n~35.5km, and M n~5.65×10 16kg.展开更多
In this paper a time dependent inventory model is developed on the basis of constant production rate and market demands which are exponentially decreasing. It advances in quest of total average optimum cost considerin...In this paper a time dependent inventory model is developed on the basis of constant production rate and market demands which are exponentially decreasing. It advances in quest of total average optimum cost considering those products which have finite shelf-life. The model also considers the small amount of decay. Without having any sort of backlogs, production starts. Reaching at the desired level of inventories, it stops production. After that due to demands along with the deterioration of the items it initiates its depletion and after certain periods the inventory gets zero. The decay of the products is level dependent. The objective of this paper is to find out the optimum inventory cost and optimum time cycle. The model has also been justified with proving the convex property and by giving a numerical example.展开更多
A desorption simulation experiment with the condition of simulated strata was designed. The experiment, under different depressurizing rates and the same fluid saturation, was conducted on the sample from 3# coal of D...A desorption simulation experiment with the condition of simulated strata was designed. The experiment, under different depressurizing rates and the same fluid saturation, was conducted on the sample from 3# coal of Daning coal mine in Jincheng, Shanxi Province. The gas production rate and pressure change at both ends of the sample were studied systematically, and the mechanisms of some phenomena in the experiment were discussed. The experimental results show that, whether at fast or slow depressurizing rate, the methane adsorbed to high-rank coal can effectively desorb and the desorption efficiency can reach above 90%. There is an obvious inflection point on the gas yield curve during the desorption process and it appears after the pressure on the lump of coal reduces below the desorption pressure. The desorption of methane from high-rank coal is mainly driven by differential pressure, and high pressure difference is conducive to fast desorption. In the scenario of fast depressurization, the desorption inflection appears earlier and the gas production rate in the stage of rapid desorption is higher. It is experimentally concluded that the originally recognized strategy of long-term slow CBM production is doubtful and the economic benefit of CBM exploitation from high-rank coal can be effectively improved by rapid drainage and pressure reduction. The field experiment results in pilot blocks of Fanzhuang and Zhengzhuang show that by increasing the drainage depressurization rate, the peak production of gas well would increase greatly, the time of gas well to reach the economic production shortened, the average time for a gas well to reach expected production reduced by half, and the peak gas production is higher.展开更多
The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constan...The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.展开更多
A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined...A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.展开更多
文摘On the basis of a general model of fuel cells, the entropy production rates of a fuel cell system under different conditions are derived by using theories of electrochemistry and thermodynamics. In order to analyze the influence of the irreversible losses existing in an actual fuel cell, the equivalent circuit of the fuel cell is introduced, so that the irreversible factor of the fuel cell may be determined directly as a function of the internal, leak and load resistances. Moreover, the maximum power output and efficiency of the fuel cell are calculated, the optimal operation of the fuel cell is discussed, and the matching condition of the load resistance is determined.
基金This work is supported by NSFC (10271008 and 10531070)
文摘The entropy production rate of stationary minimal diffusion processes with smooth coefficients is calculated. As a byproduct, the continuity of paths of the minimal diffusion processes is discussed, and that the point at infinity is absorbing is proved.
文摘The entropy production rate was determined for avascular tumor growth. The proposed formula relates the fractal dimension of the tumor contour with the quotient between mitosis and apoptosis rate, which can be used to characterize the degree of proliferation of tumor cells. The entropy production rate was determined for fourteen tumor cell lines as a physical function of cancer robustness. The entropy production rate is a hallmark that allows us the possibility of prognosis of tumor proliferation and invasion capacities, key fac-tors to improve cancer therapy.
基金the financial support by the National Natural Science Foundation of China(Nos.5120 9129 and 21203034)
文摘The high strength low-alloy steels are welded by underwater wet welding with stainless steel electrodes. The microstructural and electrochemical corrosion study of base metal(BM), weld zone(WZ) and heat affected zone(HAZ) are carried out to understand the influence of the corrosion product layer generated on the high strength low-alloy steels welded by underwater wet welding with stainless steel electrodes, methods used including, potentiodynamic polarization, electrochemical impedance spectroscopy(EIS) and scanning electron microscope(SEM). The results indicate that the WZ acts as a cathode and there is no corrosion product on it throughout the immersion period in seawater. The HAZ and BM acts as anodes. The corrosion rates of the HAZ and BM change with the immersion time increasing. In the initial immersion period, the HAZ has the highest corrosion rate because it has a coarse tempered martensite structure and the BM exhibites a microstructure with very fine grains of ferrite and pearlite. After a period of immersion, the BM has the highest corrosion rate. The reason is that the corrosion product layer on the HAZ is dense and has a better protective property while that on the BM is loose and can not inhibit the diffusion of oxygen.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11047180,90403010,and 200408020102Scientific Research Startup Foundation of University of Electronic Science and Technology of China
文摘According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli (E. coil) infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.
基金Supported by the Innovation Plan of Science and Technology for Ao Shan(No.2016ASKJ02)the National Basic Research Program of China(973 Program)(No.2014CB441504)+1 种基金the “Strategic Priority Research Program-Western Pacific Ocean System” of Chinese Academy of Sciences(No.XDA11030204)the National Natural Science Foundation of China(No.31700425)
文摘Copepod fecal pellets are ubiquitous throughout the oceans. Their production and export can represent a highly efficient pathway of carbon export. However, the role these fecal pellets play in carbon export in the Changjiang(Yangtze) River estuary is not well known. Two cruises were carried out in the Changjiang estuary in the spring and summer of 2013, during which time carbon biomass, production, and export of copepod fecal pellets were studied. Spring and summer fecal pellet carbon biomass ranged 0.30–1.01 mg C/m^3(mean=0.56±0.20 mg C/m^3) and 0.31–1.18 mg C/m^3(mean=0.64±0.24 mg C/m^3), respectively, significantly lower than phytoplankton. At most stations, fecal pellet carbon biomass was higher in surface or subsurface layers than deeper layers. Production rates ranged 0.65–1.49 pellets/(ind.?h)(mean=1.02±0.27 pellets/(ind.?h)) in spring and 0.62–1.34 pellets/(ind.?h)(mean=0.98±0.22 pellets/(ind.?h)) in summer, within the range reported in previous studies. Higher production rates of fecal pellets occurred at stations with higher chlorophyll a concentrations, and production rates of copepods of size 500–1 000 μm greater than copepods >1 000 μm during both cruises. The potential export flux of fecal pellets was slightly higher in summer(mean=68.95±14.37 mg C/(m^2 ?d)) than spring(mean=52.08±11.33 mg C/(m^2 ?d)) owing to higher summer copepod abundances. To our knowledge, this study is the first of its kind in the Changjiang estuary, and it confirms the significant role of copepod fecal pellets in local carbon export.
文摘Thermal manikin plays important roles in simulating thethermal state of human bodies to facilitate the evaluationof thermal comfort properties of various clothing assem-blies.Based on the heat balance principle and analysis ofrelated factors,the heat production rate of manikin isrecommended as an efficient evaluation index.Whereas,its inside heat production which occurs as a result of theexistence of temperature difference between its insidepart and outside surface,should not be ignored.Through a series of theoretical analysis and calculations,a compensative equation is deduced in this paper.
文摘The apparent degradation rate constant of fluticasone propionate(FLT) in 0.1 M NaOH:methanol=1:1 at 37 °C was previously reported to be 0.169 ± 0.003 h^(-1), and four degradation products(products 1–4) were observed in the solution. The aims of the present study were to assess the degradation rates of FLT in other alkaline solutions and clarify the chemical structures of the four degradation products in order to obtain basic data for designing an enema for inflammatory bowel disease. The apparent degradation rate constants in 0.05 M NaOH and 0.1 M NaOH:CH_3CN=1:1 were 0.472 ± 0.013 h^(-1) and 0.154 ± 0.000 h^(-1)(n=3), respectively. The chemical structures of products 1–4 in 0.1 M NaOH:methanol=1:1 were revealed by nuclear magnetic resonance(NMR)and mass spectrometry data. The chemical structure of products 2 was that the 17-position of the thioester moiety of FLT was substituted by a carboxylic acid. The degradation product in 0.1 M NaOH:CH_3CN=1:1 was found to be product 2 based on ~1H NMR data. The degradation product in 0.05 M NaOH was considered to be product 2 based on the retention time of HPLC. These results are useful for detecting the degradation products of FLT by enzymes of the intestinal bacterial flora in the large intestine after dosing FLT as an enema.
基金supported by the Jilin University,China(Grant No.419080106440)the Chinese National Fusion Project for the International Thermonuclear Experimental Reactor(ITER)(Grant No.2010GB104003)the National Natural Science Foundation of China(Grant No.10974069)
文摘A quasi-classical trajectory(QCT) calculation is used to investigate the vector and scalar properties of the D + Br O → DBr + O reaction based on an ab initio potential energy surface(X1A state) with collision energy ranging from 0.1 kcal/mol to 6 kcal/mol. The reaction probability, the cross section, and the rate constant are studied. The probability and the cross section show decreasing behaviors as the collision energy increases. The distribution of the rate constant indicates that the reaction favorably occurs in a relatively low-temperature region(T 〈 100 K). Meanwhile, three product angular distributions P(θr), P(φr), and P(θr, φr) are presented, which reflect the positive effect on the rotational angular momentum j' polarization of the DBr product molecule. In addition, two of the polarization-dependent generalized differential cross sections(PDDCSs), PDDCS00 and PDDCS20, are computed as well. Our results demonstrate that both vector and scalar properties have strong energy dependence.
文摘A new linear integration was developed. First, effective strain rate for slab forging with bulge was expressed in terms of two-dimensional strain rate vector, and its inner-product was integrated term by term. Second, a summation process of term by term integrated results and a formula of the bulging were introduced, and an analytical solution of stress effective factor was obtained. It is proved that the expression of power by the above linear integration is the same as that of traditional immediate integration. Also, the solution was simplified by series expansion and compared by slab forging test with the others. It turns out that the calculated result of total forging pressure is basically in agreement with measured value in the actual press test.
文摘Based upon broad-band CCD observation data of comet Hale-Bopp obtained by a 60cm telescope at Xinglong Station of Beijing Astronomical Observatory during March-August, 1996, the photometric results of comet Hale-Bopp are reported. Using the photometric results, the dust production rate, radius and mass of nucleus of comet Hale-Bopp are estimated as follows: dM/dt~1.5×10 5 kgs -1, R n~35.5km, and M n~5.65×10 16kg.
文摘In this paper a time dependent inventory model is developed on the basis of constant production rate and market demands which are exponentially decreasing. It advances in quest of total average optimum cost considering those products which have finite shelf-life. The model also considers the small amount of decay. Without having any sort of backlogs, production starts. Reaching at the desired level of inventories, it stops production. After that due to demands along with the deterioration of the items it initiates its depletion and after certain periods the inventory gets zero. The decay of the products is level dependent. The objective of this paper is to find out the optimum inventory cost and optimum time cycle. The model has also been justified with proving the convex property and by giving a numerical example.
基金Supported by the China National Science and Technology Major Project(2017ZX05064)
文摘A desorption simulation experiment with the condition of simulated strata was designed. The experiment, under different depressurizing rates and the same fluid saturation, was conducted on the sample from 3# coal of Daning coal mine in Jincheng, Shanxi Province. The gas production rate and pressure change at both ends of the sample were studied systematically, and the mechanisms of some phenomena in the experiment were discussed. The experimental results show that, whether at fast or slow depressurizing rate, the methane adsorbed to high-rank coal can effectively desorb and the desorption efficiency can reach above 90%. There is an obvious inflection point on the gas yield curve during the desorption process and it appears after the pressure on the lump of coal reduces below the desorption pressure. The desorption of methane from high-rank coal is mainly driven by differential pressure, and high pressure difference is conducive to fast desorption. In the scenario of fast depressurization, the desorption inflection appears earlier and the gas production rate in the stage of rapid desorption is higher. It is experimentally concluded that the originally recognized strategy of long-term slow CBM production is doubtful and the economic benefit of CBM exploitation from high-rank coal can be effectively improved by rapid drainage and pressure reduction. The field experiment results in pilot blocks of Fanzhuang and Zhengzhuang show that by increasing the drainage depressurization rate, the peak production of gas well would increase greatly, the time of gas well to reach the economic production shortened, the average time for a gas well to reach expected production reduced by half, and the peak gas production is higher.
文摘The proposed model considers the products with finite shelf-life which causes a small amount of decay. The market demand is assumed to be level dependent and in a linear form. The model has also considered the constant production rate which stops attaining a desired level of inventories and that is the highest level of inventories. Production starts with a buffer stock and without any sort of backlogs. Due to the market demand and product’s decay, the inventory reduces to the level of buffer stock where again the production cycle starts. With a numerical search procedure the proof of the proposed model has been shown. The objective of the model is to obtain the total average optimum inventory cost and optimum ordering cycle.
基金Project(50474015) supported by the National Natural Science Foundation of China
文摘A new linear integration for plastic power was proposed.The effective strain rate for disk forging with bulge was expressed in terms of two-dimensional strain rate vector,and then its direction cosines were determined by the ratio of coordinate increments.Furthermore,inner-product of the vector for plastic power was term integrated by term and summed.Thereafter,through a formula for determination of bulge an analytical solution of stress effective factor was obtained.Finally,through compression tests,the calculated results of above formula were compared with those of Avitzur’s approximate solution and total indicator readings of the testing machine.It is indicated that the calculated compression forces are basically in agreement with the measured ones if the pass reduction is less than 13.35%.However,when the reduction gets up to 25.34% and 33.12%,the corresponding errors between the calculated and measured results also get up to 6% and 13.5%,respectively.