In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured ...In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.展开更多
In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Ba...In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.展开更多
In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde...In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.展开更多
Della Vecchia et al. （see [2]） introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwi...Della Vecchia et al. （see [2]） introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bemsetin operators.展开更多
We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators o...We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .展开更多
The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a...The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.展开更多
A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly wi...A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.展开更多
Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the...Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.展开更多
Fuel consumption in the COREX-3000 process run in Baosteel is currently higher than the design index. Therefore, mass and heat balance equations for the COREX process were established using the basic principles in- cl...Fuel consumption in the COREX-3000 process run in Baosteel is currently higher than the design index. Therefore, mass and heat balance equations for the COREX process were established using the basic principles in- cluded in the Rist operating diagram for blast furnace （BF） as a reference. Thermodynamic calculations were then used to modify the Rist operating diagram so that it was suitable for the COREX process. The modified Rist operating dia- gram was then applied for the evaluation of metallization rate （MR） and fuel structure to reduce the energy consump- tion in the COREX process. The modified Rist operating diagram for the shaft furnace （SF） provided a nearly ideal value for the restriction point W when the metallization rate was increased, while the point P on the operating line for the melter gasifier （MG） moved upward due to reduction in the heat required in hearth. The feasibility of reduc- ing the energy consumption during the COREX process by changing the fuel structure was also demonstrated.展开更多
The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce t...The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.展开更多
Effective management of water resources,especially groundwater,is crucial and requires a precise understanding of aquifer characteristics,imposed stresses,and the groundwater balance.Simulation-optimization models pla...Effective management of water resources,especially groundwater,is crucial and requires a precise understanding of aquifer characteristics,imposed stresses,and the groundwater balance.Simulation-optimization models plays a vital role in guiding planners toword sustainable long-term aquifer exploita-tion.This study simulated monthly water table variations in the Kashan Plain over a ten-year period from 2008 to 2019 across 125 stress periods using the GMS model.The model was calibrated for both steady-state and transient conditions for the 2008–2016 period and validated for the 2016–2019 period.Results indicated a 4.4 m decline in groundwater levels over the 10-year study period.Given the plain's location in a arid climatic zone with limited effective precipitation for aquifer recharge,the study focused on ground-water extraction management.A modified two-point hedging policy was employed as a solution to mitigate critical groundwater depletion,reducing the annual drawdown rate from 0.44 m to 0.31 m and conserving 255 million cubic meters(mcm)of water annually.Although this approach slightly decreased reliability(i.e.the number of months meeting full water demands),it effectively minimized the risk of severe droughts and irreparable damages.This policy offers managers a dynamical and intelligent tool for regulating groundwater extraction,balancing aquifer sustainability with agricultural and urban water requirements.展开更多
The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some gr...The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.展开更多
BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in g...BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in general physical activity.As a better ventilatory strategy,extracorporeal membrane oxygenation(ECMO) provides gas exchange via an extracorporeal circuit,and is increasingly being used to improve respiratory and circulatory function.After the modified Fontan operation,circulation is different from that of patients who are not subjected to the procedure.This paper describe a successful case using ECMO in curing influenza A infection in a young man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The special cardiac structure and circulatory characteristics are explored in this case.CASE SUMMARY We report a successful case using ECMO in curing influenza A infection in a 23-year-old man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The man was admitted to the intensive care unit with severe acute respiratory distress syndrome as a result of influenza A infection.He was initially treated by veno-venous(VV) ECMO,which was switched to veno-venous-arterial ECMO(VVA ECMO) 5 d later.As circulation and respiratory function gradually improved,the VVA ECMO equipment was removed on May 1,2018.The patient was successfully withdrawn from artificial ventilation on May 28,2018 and then discharged from hospital on May 30,2018.CONCLUSION After the modified Fontan operation,circulation is different compared with that of patients who are not subjected to the procedure.There are certainly many differences between them when they receive the treatment of ECMO.Due to the special cardiac structure and circulatory characteristics,an individualized liquid management strategy is necessary and it might be better for them to choose an active circulation support earlier.展开更多
The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta functio...The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.展开更多
This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed....This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed.In the perioperative period,the combined gallbladder was excised;the duration of the operation was 5 h and volume of blood loss was approximately 500 ml.Postoperatively,the liver function temporarily returned and after a liver protection treatment,it returned to normal within 2 weeks.The liver had normal arterial blood supply,and the postoperative course was uneventful.It is safe and feasible to resect the whole pancreatic body and tail tumor combined with celiac stem resection.It can improve the resection rate of tumor and relieve pain.展开更多
Objective To study microsurgical effectiveness Foerster-Dandy’s endoscope-assisted operation for treatment of spasmodic torticollis. Methods 183 cases of spasmodic torticollis patients were treated by microsurgical m...Objective To study microsurgical effectiveness Foerster-Dandy’s endoscope-assisted operation for treatment of spasmodic torticollis. Methods 183 cases of spasmodic torticollis patients were treated by microsurgical modified Foerster-Dandy’s operation from July 2001 to June 2009,which was randomly展开更多
A new feeding mode for a simulated moving bed(SMB) is proposed.The outlet stream from zone II is collected at regular intervals.The concentration of the solution is increased by dissolving raw materials and then fed t...A new feeding mode for a simulated moving bed(SMB) is proposed.The outlet stream from zone II is collected at regular intervals.The concentration of the solution is increased by dissolving raw materials and then fed to zone III as the feed stream during the next collection interval.In this feeding mode,the concentration of the stream fed to zone III is identical to that of original feed,while in a conventional SMB,the feed is diluted by mix-ing with the outlet stream of zone II before feeding to zone III.The new feeding mode increases the inlet concentra-tion of zone III.A modeling investigation shows that higher inlet concentration of zone III increases the height of concentration band in SMB,improving the separation performance significantly.In comparison with the traditonal feeding mode,the new feeding mode increases the productivity by 23.52%and decreases the solvent consumption by 22.56%,so as to increase the raffinate and extract concentrations by 53.17%and 20.38%,respectively.The col-lection interval for the outlet stream from zone II has no effect on the separation performance after reaching the steady state,so that the collection interval can be increased to make the operation more convenient.展开更多
The dark Korteweg-de Vries （KdV） systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar...The dark Korteweg-de Vries （KdV） systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar classification for dark modified KdV （MKdV） systems is obtained by requiring the existence of higher order differential polynomial symmetries. Different to the nine classes of the dark KdV case, there exist twelve independent classes of the dark MKdV equations. Fhrthermore, for the every class of dark MKdV system, there is a free parameter. Only for a fixed parameter, the dark MKdV can be related to dark KdV via suitable Miura transformation. The reeursion operators of two classes of dark MKdV systems are also given.展开更多
基金supported by the NSF of Ningxia(2022AAC03234)the NSF of China(11761004),the Construction Project of First-Class Disciplines in Ningxia Higher Education(NXYLXK2017B09)the Postgraduate Innovation Project of North Minzu University(YCX23074).
文摘In this article, we consider a backward problem in time of the diffusion equation with local and nonlocal operators. This inverse problem is ill-posed because the solution does not depend continuously on the measured data. Inspired by the classical Landweber iterative method and Fourier truncation technique, we develops a modified Landweber iterative regularization method to restore the continuous dependence of solution on the measurement data. Under the a-priori and a-posteriori choice rules for the regularized parameter, the convergence estimates for the regularization method are derived. Some results of numerical simulation are provided to verify the stability and feasibility of our method in dealing with the considered problem.
基金Research supported by Council of ScientificIndustrial Research, India under award no.9/143(163)/91-EMR-1.
文摘In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.
基金Supported both by the Teaching and Research Award Fund for Outstanding Young Teachers inHigher Educational Institutions of MOEChinaand by the Dawn Program Fund in Shanghai
文摘In order to find roots of maximal monotone operators, this paper introduces and studies the modified approximate proximal point algorithm with an error sequence {e k} such that || ek || \leqslant hk || xk - [(x)\tilde]k ||\left\| { e^k } \right\| \leqslant \eta _k \left\| { x^k - \tilde x^k } \right\| with ?k = 0￥ ( hk - 1 ) < + ￥\sum\limits_{k = 0}^\infty {\left( {\eta _k - 1} \right)} and infk \geqslant 0 hk = m\geqslant 1\mathop {\inf }\limits_{k \geqslant 0} \eta _k = \mu \geqslant 1 . Here, the restrictions on {η k} are very different from the ones on {η k}, given by He et al (Science in China Ser. A, 2002, 32 (11): 1026–1032.) that supk \geqslant 0 hk = v < 1\mathop {\sup }\limits_{k \geqslant 0} \eta _k = v . Moreover, the characteristic conditions of the convergence of the modified approximate proximal point algorithm are presented by virtue of the new technique very different from the ones given by He et al.
文摘Della Vecchia et al. （see [2]） introduced a kind of modified Bernstein operators which can be used to approximate functions with singularities at endpoints on [0,1]. In the present paper, we obtain a kind of pointwise Stechkin-type inequalities for weighted approximation by the modified Bemsetin operators.
文摘We study the multiplication operator M by z2 and the q-Bessel operator Δq,αon a Hilbert spaces Fq,α of entire functions on the disk D( o, ) , 0qq,α into itself. Next, we study a generalized translation operators on Fq,α .
文摘The modified Bernstein-Durrmeyer operators discussed in this paper are given by M_nf≡M_n(f,x)=(n+2)P_(n,k)∫_0~1p_n+1.k(t)f(t)dt, where We will show,for 0<α<1 and 1≤p≤∞ M,f-f_p=O(n^-a)ω_Φ~2(f,t)_p=O(t^(2a)), |M_n f-f(x)|≤M(x(1-x)/n+1/_n2)~a/2ω(f,t)=O(t^a), where otherwise.
文摘A modified wide-angle beam propagation based on the Douglas operators is presented.The truncation error in the modified wide-angle beam propagation is reduced to o (Δ x ) 4 in the transverse direction nearly without any increase of the computation time,whereas the error in the ordinary wide-angle beam propagation method is typically o (Δ x ) 2.With trivial programming changes,the accuracy is higher,especially in wide-angle propagation.
基金Supported by the Universities Key Laboratory of System Modeling and Data Mining in Guizhou Province(Grant No.2023013)the National Natural Science Foundation of China(Grant No.12161013)the Science and Technology Program of Guizhou Province(Grant No.ZK[2023]025)。
文摘Semenov-Tian-Shansky has given the solution of the modified classical Yang-Baxter equation, which was called the modified r-matrix. Relevant studies have been extensive in recent times. In this paper, we introduce the concept and representations of modified RotaBaxter Hom-Lie algebras. We develop a cohomology of modified Rota-Baxter Hom-Lie algebras with coefficients in a suitable representation. As applications, we study formal deformations and abelian extensions of modified Rota-Baxter Hom-Lie algebras in terms of second cohomology groups.
基金Item Sponsored by National Natural Science Foundation of China(50934007,50874129)National High-tech Research and Development Program of China(2009AA06Z105)+1 种基金Special Research Foundation of Young Teachers of University of Science and Technology Liaoning of China(2014QN30)Foundation of Liaoning Educational Committee of China(L2015264)
文摘Fuel consumption in the COREX-3000 process run in Baosteel is currently higher than the design index. Therefore, mass and heat balance equations for the COREX process were established using the basic principles in- cluded in the Rist operating diagram for blast furnace （BF） as a reference. Thermodynamic calculations were then used to modify the Rist operating diagram so that it was suitable for the COREX process. The modified Rist operating dia- gram was then applied for the evaluation of metallization rate （MR） and fuel structure to reduce the energy consump- tion in the COREX process. The modified Rist operating diagram for the shaft furnace （SF） provided a nearly ideal value for the restriction point W when the metallization rate was increased, while the point P on the operating line for the melter gasifier （MG） moved upward due to reduction in the heat required in hearth. The feasibility of reduc- ing the energy consumption during the COREX process by changing the fuel structure was also demonstrated.
基金National Natural Science Foundation of China(12161013)Research Projects of Guizhou University of Commerce in 2024。
文摘The modifiedλ-differential Lie-Yamaguti algebras are considered,in which a modifiedλ-differential Lie-Yamaguti algebra consisting of a Lie-Yamaguti algebra and a modifiedλ-differential operator.First we introduce the representation of modifiedλ-differential Lie-Yamaguti algebras.Furthermore,we establish the cohomology of a modifiedλ-differential Lie-Yamaguti algebra with coefficients in a representation.Finally,we investigate the one-parameter formal deformations and Abelian extensions of modifiedλ-differential Lie-Yamaguti algebras using the second cohomology group.
文摘Effective management of water resources,especially groundwater,is crucial and requires a precise understanding of aquifer characteristics,imposed stresses,and the groundwater balance.Simulation-optimization models plays a vital role in guiding planners toword sustainable long-term aquifer exploita-tion.This study simulated monthly water table variations in the Kashan Plain over a ten-year period from 2008 to 2019 across 125 stress periods using the GMS model.The model was calibrated for both steady-state and transient conditions for the 2008–2016 period and validated for the 2016–2019 period.Results indicated a 4.4 m decline in groundwater levels over the 10-year study period.Given the plain's location in a arid climatic zone with limited effective precipitation for aquifer recharge,the study focused on ground-water extraction management.A modified two-point hedging policy was employed as a solution to mitigate critical groundwater depletion,reducing the annual drawdown rate from 0.44 m to 0.31 m and conserving 255 million cubic meters(mcm)of water annually.Although this approach slightly decreased reliability(i.e.the number of months meeting full water demands),it effectively minimized the risk of severe droughts and irreparable damages.This policy offers managers a dynamical and intelligent tool for regulating groundwater extraction,balancing aquifer sustainability with agricultural and urban water requirements.
文摘The modified generality degree distance, is defined as: ,?which is a modification of the generality degree distance. In this paper, we give some computing formulas of the modified generality degree distance of some graph operations, such as, composition, join, etc.
基金Supported by the Capital Foundation of Medical Development,No. 2018-1-2171the Seedling Plan from the Beijing Ditan Hospital,Capital Medical University,No. DTYM201802。
文摘BACKGROUND The Fontan operation is the only treatment option to change the anatomy of the heart and help improve patients’ hemodynamics.After successful operation,patients typically recover the ability to engage in general physical activity.As a better ventilatory strategy,extracorporeal membrane oxygenation(ECMO) provides gas exchange via an extracorporeal circuit,and is increasingly being used to improve respiratory and circulatory function.After the modified Fontan operation,circulation is different from that of patients who are not subjected to the procedure.This paper describe a successful case using ECMO in curing influenza A infection in a young man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The special cardiac structure and circulatory characteristics are explored in this case.CASE SUMMARY We report a successful case using ECMO in curing influenza A infection in a 23-year-old man,who was diagnosed with Tausing-Bing syndrome and underwent Fontan operation 13 years ago.The man was admitted to the intensive care unit with severe acute respiratory distress syndrome as a result of influenza A infection.He was initially treated by veno-venous(VV) ECMO,which was switched to veno-venous-arterial ECMO(VVA ECMO) 5 d later.As circulation and respiratory function gradually improved,the VVA ECMO equipment was removed on May 1,2018.The patient was successfully withdrawn from artificial ventilation on May 28,2018 and then discharged from hospital on May 30,2018.CONCLUSION After the modified Fontan operation,circulation is different compared with that of patients who are not subjected to the procedure.There are certainly many differences between them when they receive the treatment of ECMO.Due to the special cardiac structure and circulatory characteristics,an individualized liquid management strategy is necessary and it might be better for them to choose an active circulation support earlier.
文摘The present paper aims at introducing and investigating a new class of generalized double zeta function i.e. modified double zeta function which involves the Riemann, Hurwitz, Hurwitz-Lerch, Barnes double zeta function and Bin-Saad generalized double zeta function as particular cases. The results are obtained by suitably applying Riemann-Liouville type and Tremblay fractional integral and differential operators. We derive the expansion formula for the proposed function with some of its properties via fractional operators and discuss the link with known results.
文摘This is a case of a pancreatic tumor with invasion of the celiac stem treated using the modified Appleby operation.Preoperatively,routine B-ultrasound,computed tomography,and magnetic resonance imaging were performed.In the perioperative period,the combined gallbladder was excised;the duration of the operation was 5 h and volume of blood loss was approximately 500 ml.Postoperatively,the liver function temporarily returned and after a liver protection treatment,it returned to normal within 2 weeks.The liver had normal arterial blood supply,and the postoperative course was uneventful.It is safe and feasible to resect the whole pancreatic body and tail tumor combined with celiac stem resection.It can improve the resection rate of tumor and relieve pain.
文摘Objective To study microsurgical effectiveness Foerster-Dandy’s endoscope-assisted operation for treatment of spasmodic torticollis. Methods 183 cases of spasmodic torticollis patients were treated by microsurgical modified Foerster-Dandy’s operation from July 2001 to June 2009,which was randomly
基金Supported by the Natural Science Foundation of Ningbo（2009A610153）
文摘A new feeding mode for a simulated moving bed(SMB) is proposed.The outlet stream from zone II is collected at regular intervals.The concentration of the solution is increased by dissolving raw materials and then fed to zone III as the feed stream during the next collection interval.In this feeding mode,the concentration of the stream fed to zone III is identical to that of original feed,while in a conventional SMB,the feed is diluted by mix-ing with the outlet stream of zone II before feeding to zone III.The new feeding mode increases the inlet concentra-tion of zone III.A modeling investigation shows that higher inlet concentration of zone III increases the height of concentration band in SMB,improving the separation performance significantly.In comparison with the traditonal feeding mode,the new feeding mode increases the productivity by 23.52%and decreases the solvent consumption by 22.56%,so as to increase the raffinate and extract concentrations by 53.17%and 20.38%,respectively.The col-lection interval for the outlet stream from zone II has no effect on the separation performance after reaching the steady state,so that the collection interval can be increased to make the operation more convenient.
基金Supported by the Global Change Research Program of China under Grant No.2015Cb953904National Natural Science Foundation of China under Grant Nos.11675054,11435005,11175092,and 11205092+1 种基金Shanghai Knowledge Service Platform for Trustworthy Internet of Things(No.ZF1213)K.C.Wong Magna Fund in Ningbo University
文摘The dark Korteweg-de Vries （KdV） systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar classification for dark modified KdV （MKdV） systems is obtained by requiring the existence of higher order differential polynomial symmetries. Different to the nine classes of the dark KdV case, there exist twelve independent classes of the dark MKdV equations. Fhrthermore, for the every class of dark MKdV system, there is a free parameter. Only for a fixed parameter, the dark MKdV can be related to dark KdV via suitable Miura transformation. The reeursion operators of two classes of dark MKdV systems are also given.
