Objectives This study aimed to explore the lagged and cumulative effects of risk factors on disability in older adults using distributed lag non-linear models(DLNMs).Methods We utilized data from the China Health and ...Objectives This study aimed to explore the lagged and cumulative effects of risk factors on disability in older adults using distributed lag non-linear models(DLNMs).Methods We utilized data from the China Health and Retirement Longitudinal Study(CHARLS).After feature selection via Elastic Net Regularization,we applied DLNMs to evaluate the lagged effects of risk factors.Disability was defined as the presence of any difficulties in basic activities of daily living(BADL).The cumulative relative risk(CRR)was calculated by summing the lag-specific risk estimates,representing the cumulative disability risk over the specified lag period.Effect modifications and sensitivity analyses were also performed.Results This study included a total of 2,318 participants.Early-phase lag factors,such as the difficulty in stooping(CRR=3.58;95%CI:2.31-5.55;P<0.001)and walking(CRR=2.77;95%CI:1.39-5.55;P<0.001),exerted the strongest effects immediately upon occurrence.Mid-phase lag factors,such as arthritis(CRR=1.51;95%CI:1.10-2.06;P=0.001),showed a resurgence in disability risk within 2-3 years.Late-phase lag factors,including depressive symptoms(CRR=2.38;95%CI:1.30-4.35;P<0.001)and elevated systolic blood pressure(CRR=1.64;95%CI:1.06-2.79;P=0.02),exhibited significant long-term cumulative risks.Conversely,grip strength(CRR=0.80;95%CI:0.54-0.95;P=0.02)and social participation(CRR=0.89;95%CI:0.73-0.99;P=0.04)were significant protective factors.Conclusions The findings underscore the importance of tailored interventions that account for various lag characteristics of different factors to effectively mitigate disability risk.Future studies should explore the underlying biological and sociological mechanisms of these lagged effects,identify intervention strategies that target risk factors with different lagged patterns,and evaluate their effectiveness.展开更多
There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given...There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.展开更多
This paper focuses on China's primary provinces along its Belt and Road Initiative,measures and analyses the provincial green total factor productivity (GTFP) development by GML index based on SBM directional dist...This paper focuses on China's primary provinces along its Belt and Road Initiative,measures and analyses the provincial green total factor productivity (GTFP) development by GML index based on SBM directional distance function,discusses the temporal evolution characteristics of spatial convergence of the provincial GTFP under multiple spatial weight matrices,and estimates the net effect of China's Belt and Road Initiative on the development gap of provincial GTFP by regression discontinuity.The research shows that the provincial GTFP is generally good while the internal gap is relatively large.There is spatial absolute βconvergence and condition βconvergence in provincial GTFP,and the convergence speed has been signifcantly accelerated since the construction of China's Belt and Road Initiative.The current low economy level and infrastructure allocation efficiency of primary provinces restrict the GTFP development,while government expenditure has promoted the GTFP development,trade between provinces and countries along China's Belt and Road Initiative is negative to GTFP.China's Belt and Road Initiative has significantly narrowed the gap of provincial GTFP development with the net effect of-0.016.展开更多
In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Comb...In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.展开更多
A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial differ...A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial difference. The second stage is to identify the convergence club of DCP. The last stage is to examine the initial factors that may affect the formation of the convergence club. Construction industry data from 30 provinces in China's Mainland from 2005 to 2016 were adopted to conduct an empirical study. The empirical results showed that (1) the arithmetic mean value of China’s provincial DCP showed an upward trend and the standard deviation showed an expanding trend.(2) There are five convergence clubs, but 13 provinces failed to converge to any club.(3) The higher the degree of construction industry marketization in 2005, the greater the probability that the provinces belong to a club with higher DCP. To improve the DCP, the effective diffusion of low-carbon construction technologies and the market-oriented reform of state-owned construction companies should be promoted. The three-stage method can also be applied to study different industries in different countries or regions.展开更多
First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setti...First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.展开更多
The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix sp...The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.展开更多
A Particle Swarm Optimizer （PSO） exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and r...A Particle Swarm Optimizer （PSO） exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and restrictive conditions, which can affect the performance of the algorithm. In this paper, the sufficient conditions for the asymptotic stability of an acceleration factor and inertia weight are deduced, the value of the inertia weight w is enhanced to （ 1, 1）. Furthermore a new adaptive PSO algorithm - Acceleration Factor Harmonious PSO （AFHPSO） is proposed, and is proved to be a global search algorithm. AFHPSO is used for the parameter design of a fuzzy controller for a linear motor driving servo system. The performance of the nonlinear model for the servo system demonstrates the effectiveness of the optimized fuzzy controller and AFHPSO.展开更多
On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent me...On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.展开更多
Based on the practice of oil and gas exploration and the analysis of shallow lithologic reservoirs,combined with the allocation relationship and enrichment law of oil and gas accumulation factors,main controlling fact...Based on the practice of oil and gas exploration and the analysis of shallow lithologic reservoirs,combined with the allocation relationship and enrichment law of oil and gas accumulation factors,main controlling factors and models of hydrocarbon accumulation of large lithologic reservoirs in shallow strata around the Bozhong sag are summarized,and favorable exploration areas are proposed.The coupling of the four factors of“ridge-fault-sand-zone”is crucial for the hydrocarbon enrichment in the shallow lithologic reservoirs.The convergence intensity of deep convergence ridges is the basis for shallow oil and gas enrichment,the activity intensity of large fault cutting ridges and the thickness of cap rocks control the vertical migration ability of oil and gas,the coupling degree of large sand bodies and fault cutting ridges control large-scale oil and gas filling,the fault sealing ability of structural stress concentration zones affects the enrichment degree of lithologic oil and gas reservoirs.Three enrichment models including uplift convergence type,steep slope sand convergence type and depression uplift convergence type are established through the case study of lithologic reservoirs in shallow strata around the Bozhong sag.展开更多
In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the con...In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.展开更多
In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimate...In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker–Planck operator.展开更多
In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued frac...In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.展开更多
In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accurac...In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.展开更多
A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main ob...A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.展开更多
基金supported by ScientificResearch Fund of National Health Commission of the People’s Republic of China-Major Science and Technology Program for Medicine and Health in Zhejiang Province(WKJ-ZJ-2406).
文摘Objectives This study aimed to explore the lagged and cumulative effects of risk factors on disability in older adults using distributed lag non-linear models(DLNMs).Methods We utilized data from the China Health and Retirement Longitudinal Study(CHARLS).After feature selection via Elastic Net Regularization,we applied DLNMs to evaluate the lagged effects of risk factors.Disability was defined as the presence of any difficulties in basic activities of daily living(BADL).The cumulative relative risk(CRR)was calculated by summing the lag-specific risk estimates,representing the cumulative disability risk over the specified lag period.Effect modifications and sensitivity analyses were also performed.Results This study included a total of 2,318 participants.Early-phase lag factors,such as the difficulty in stooping(CRR=3.58;95%CI:2.31-5.55;P<0.001)and walking(CRR=2.77;95%CI:1.39-5.55;P<0.001),exerted the strongest effects immediately upon occurrence.Mid-phase lag factors,such as arthritis(CRR=1.51;95%CI:1.10-2.06;P=0.001),showed a resurgence in disability risk within 2-3 years.Late-phase lag factors,including depressive symptoms(CRR=2.38;95%CI:1.30-4.35;P<0.001)and elevated systolic blood pressure(CRR=1.64;95%CI:1.06-2.79;P=0.02),exhibited significant long-term cumulative risks.Conversely,grip strength(CRR=0.80;95%CI:0.54-0.95;P=0.02)and social participation(CRR=0.89;95%CI:0.73-0.99;P=0.04)were significant protective factors.Conclusions The findings underscore the importance of tailored interventions that account for various lag characteristics of different factors to effectively mitigate disability risk.Future studies should explore the underlying biological and sociological mechanisms of these lagged effects,identify intervention strategies that target risk factors with different lagged patterns,and evaluate their effectiveness.
基金Supported by the National Natural Science Foundation of china
文摘There are many accelerating convergence factors (ACFs) for limit periodic continued fraction K(an/1)(an→a≠0). In this paper, some characteristics and comparative theorems are ob tained on ACFs. Two results are given for most frequently used ACFs.
文摘This paper focuses on China's primary provinces along its Belt and Road Initiative,measures and analyses the provincial green total factor productivity (GTFP) development by GML index based on SBM directional distance function,discusses the temporal evolution characteristics of spatial convergence of the provincial GTFP under multiple spatial weight matrices,and estimates the net effect of China's Belt and Road Initiative on the development gap of provincial GTFP by regression discontinuity.The research shows that the provincial GTFP is generally good while the internal gap is relatively large.There is spatial absolute βconvergence and condition βconvergence in provincial GTFP,and the convergence speed has been signifcantly accelerated since the construction of China's Belt and Road Initiative.The current low economy level and infrastructure allocation efficiency of primary provinces restrict the GTFP development,while government expenditure has promoted the GTFP development,trade between provinces and countries along China's Belt and Road Initiative is negative to GTFP.China's Belt and Road Initiative has significantly narrowed the gap of provincial GTFP development with the net effect of-0.016.
文摘In this paper, a new class of three term memory gradient method with non-monotone line search technique for unconstrained optimization is presented. Global convergence properties of the new methods are discussed. Combining the quasi-Newton method with the new method, the former is modified to have global convergence property. Numerical results show that the new algorithm is efficient.
文摘A three-stage method is proposed to study the convergence clubs for the dynamic total factor carbon productivity (DCP) and the initial conditions. The first stage is to measure the DCP that reflects the initial difference. The second stage is to identify the convergence club of DCP. The last stage is to examine the initial factors that may affect the formation of the convergence club. Construction industry data from 30 provinces in China's Mainland from 2005 to 2016 were adopted to conduct an empirical study. The empirical results showed that (1) the arithmetic mean value of China’s provincial DCP showed an upward trend and the standard deviation showed an expanding trend.(2) There are five convergence clubs, but 13 provinces failed to converge to any club.(3) The higher the degree of construction industry marketization in 2005, the greater the probability that the provinces belong to a club with higher DCP. To improve the DCP, the effective diffusion of low-carbon construction technologies and the market-oriented reform of state-owned construction companies should be promoted. The three-stage method can also be applied to study different industries in different countries or regions.
文摘First a general model for a three-step projection method is introduced, and second it has been applied to the approximation solvability of a system of nonlinear variational inequality problems in a Hilbert space setting. Let H be a real Hilbert space and K be a nonempty closed convex subset of H. For arbitrarily chosen initial points x0, y0, z0 ∈ K, compute sequences xn, yn, zn such thatT ： K→ H is a nonlinear mapping onto K. At last three-step models are applied to some variational inequality problems.
基金The National Natural Science Foundations of China (12202219)the Natural Science Foundations of Ningxia (2024AAC02009, 2023AAC05001)the Ningxia Youth Top Talents Training Project。
文摘The fast solution of linear equations has always been one of the hot spots in scientific computing.A kind of the diagonal matrix splitting iteration methods are provided,which is different from the classical matrix splitting methods.Taking the decomposition of the diagonal elements for coefficient matrix as the key point,some new preconditioners are constructed.Taking the tri-diagonal coefficient matrix as an example,the convergence domains and optimal relaxation factor of the new method are analyzed theoretically.The presented new iteration methods are applied to solve linear algebraic equations,even 2D and 3D diffusion problems with the fully implicit discretization.The results of numerical experiments are matched with the theoretical analysis,and show that the iteration numbers are reduced greatly.The superiorities of presented iteration methods exceed some classical iteration methods dramatically.
基金The work was supported by the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutes of MOE, PRC
文摘A Particle Swarm Optimizer （PSO） exhibits good performance for optimization problems, although it cannot guarantee convergence to a global, or even local minimum. However, there are some adjustable parameters, and restrictive conditions, which can affect the performance of the algorithm. In this paper, the sufficient conditions for the asymptotic stability of an acceleration factor and inertia weight are deduced, the value of the inertia weight w is enhanced to （ 1, 1）. Furthermore a new adaptive PSO algorithm - Acceleration Factor Harmonious PSO （AFHPSO） is proposed, and is proved to be a global search algorithm. AFHPSO is used for the parameter design of a fuzzy controller for a linear motor driving servo system. The performance of the nonlinear model for the servo system demonstrates the effectiveness of the optimized fuzzy controller and AFHPSO.
基金Project(2013CB036004) supported by the National Basic Research Program of ChinaProjects(51178468,51378510) supported by the National Natural Science Foundation of ChinaProject(CX2013B077) supported by Hunan Provincial Innovation Foundation for Postgraduate,China
文摘On the basis of upper bound theorem, non-associated flow rule and non-linear failure criterion were considered together.The modified shear strength parameters of materials were obtained with the help of the tangent method. Employing the virtual power principle and strength reduction technique, the effects of dilatancy of materials, non-linear failure criterion, pore water pressure,surface loads and buried depth, on the stability of shallow tunnel were studied. In order to validate the effectiveness of the proposed approach, the solutions in the present work agree well with the existing results when the non-associated flow rule is reduced to the associated flow rule and the non-linear failure criterion is degenerated to the linear failure criterion. Compared with dilatancy of materials, the non-linear failure criterion exerts greater impact on the stability of shallow tunnels. The safety factor of shallow tunnels decreases and the failure surface expands outward when the dilatancy coefficient decreases. While the increase of nonlinear coefficient, the pore water pressure coefficient, the surface load and the buried depth results in the small safety factor. Therefore, the dilatancy as well as non-linear failure criterion should be taken into account in the design of shallow tunnel supporting structure. The supporting structure must be reinforced promptly to prevent potential mud from gushing or collapse accident in the areas with abundant pore water, large surface load or buried depth.
基金Supported by the China National Science and Technology Major Project(2011ZX05023-006-002,2016ZX05024-003).
文摘Based on the practice of oil and gas exploration and the analysis of shallow lithologic reservoirs,combined with the allocation relationship and enrichment law of oil and gas accumulation factors,main controlling factors and models of hydrocarbon accumulation of large lithologic reservoirs in shallow strata around the Bozhong sag are summarized,and favorable exploration areas are proposed.The coupling of the four factors of“ridge-fault-sand-zone”is crucial for the hydrocarbon enrichment in the shallow lithologic reservoirs.The convergence intensity of deep convergence ridges is the basis for shallow oil and gas enrichment,the activity intensity of large fault cutting ridges and the thickness of cap rocks control the vertical migration ability of oil and gas,the coupling degree of large sand bodies and fault cutting ridges control large-scale oil and gas filling,the fault sealing ability of structural stress concentration zones affects the enrichment degree of lithologic oil and gas reservoirs.Three enrichment models including uplift convergence type,steep slope sand convergence type and depression uplift convergence type are established through the case study of lithologic reservoirs in shallow strata around the Bozhong sag.
文摘In this research article,we interrogate two new modifications in inverse Weierstrass iterative method for estimating all roots of non-linear equation simultaneously.These modifications enables us to accelerate the convergence order of inverse Weierstrass method from 2 to 3.Convergence analysis proves that the orders of convergence of the two newly constructed inverse methods are 3.Using computer algebra system Mathematica,we find the lower bound of the convergence order and verify it theoretically.Dynamical planes of the inverse simultaneous methods and classical iterative methods are generated using MATLAB(R2011b),to present the global convergence properties of inverse simultaneous iterative methods as compared to classical methods.Some non-linear models are taken from Physics,Chemistry and engineering to demonstrate the performance and efficiency of the newly constructed methods.Computational CPU time,and residual graphs of the methods are provided to present the dominance behavior of our newly constructed methods as compared to existing inverse and classical simultaneous iterative methods in the literature.
基金This paper is partially supported by the Bulgarian Mutistry of Education SciencesTechnologies Project MM-515/97+1 种基金partially supported by the National Natural Science Foundation of Chinaby Natu-ral Science Foundation of Zhejiang Province.
文摘In this paper we consider some parallel iterations for splitting quadratic factors of polynomials and their convergence.
基金partially supported by Fundamental Research Funds for the Central Universities,NSFC(11871335)by the SJTU’s SMC Projection
文摘In this article, we establish the exponential time decay of smooth solutions around a global Maxwellian to the non-linear Vlasov–Poisson–Fokker–Planck equations in the whole space by uniform-in-time energy estimates. The non-linear coupling of macroscopic part and Fokker–Planck operator in the model brings new difficulties for the energy estimates, which is resolved by adding tailored weighted-in-v energy estimates suitable for the Fokker–Planck operator.
基金Supported by the National Natural Science Foundation of China(Grant No.11571071)the Natural Science Key Foundation of Education Department of Anhui Province(Grant No.KJ2013A183)+1 种基金the Project of Leading Talent Introduction and Cultivation in Colleges and Universities of Education Department of Anhui Province(Grant No.gxfxZD2016270)the Incubation Project of the National Scientific Research Foundation of Bengbu University(Grant No.2018GJPY04)
文摘In this paper, we propose a new single-step iterative method for solving non-linear equations in a variable. This iterative method is derived by using the approximation formula of truncated Thiele's continued fraction. Analysis of convergence shows that the order of convergence of the introduced iterative method for a simple root is four. To illustrate the efficiency and performance of the proposed method we give some numerical examples.
文摘In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.
文摘A mathematical model for the fluidized bed biofilm reactor (FBBR) is discussed. An approximate analytical solution of concentration of phenol is obtained using modified Adomian decomposition method (MADM). The main objective is to propose an analytical method of solution, which do not require small parameters and avoid linearization and physically unrealistic assumptions. Theoretical results obtained can be used to predict the biofilm density of a single bioparticle. Satisfactory agreement is obtained in the comparison of approximate analytical solution and numerical simulation.
