The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct...The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.展开更多
An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, ...An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.展开更多
The equation of Patwardhan and Kumar for water activities of mixed electrolyte solutions is extended to aqueous solutions containing non-electrolytes. This equation and the linear isopiestic relation are used to predi...The equation of Patwardhan and Kumar for water activities of mixed electrolyte solutions is extended to aqueous solutions containing non-electrolytes. This equation and the linear isopiestic relation are used to predict water activities of 56 ternary aqueous solutions in terms of the data of their binary subsystems. Both equation of Patwardhan and Kumar and the linear isopiestic relation can provide good predictions for water activities of the present 40 electrolyte solutions, and the linear isopiestic relation generally yields better predictions. The predictions of the extended equation of Patwardhan and Kumar and the linear isopiestic relation are in general quite reasonable for the present 8 ternary solutions of electrolytes and non-electrolytes, and the results of the linear isopiestic relation are usually better. The predictions of these two methods generally agree well with the experimental data for the 8 non-electrolyte mixtures being studied, and the linear isopiestic relation is better.展开更多
In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of mu...In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.展开更多
Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is pr...Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is presented .展开更多
As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule...To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied[bij1/2= 1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters ofpure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.展开更多
This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensiona...This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.展开更多
The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coef...The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.展开更多
The successful utilization of an eco-friendly and biocompatible parylene-C substrate for high-performance solution-processed double-walled carbon nanotube(CNT)electrode-based perovskite solar cells(PSCs)was demonstrat...The successful utilization of an eco-friendly and biocompatible parylene-C substrate for high-performance solution-processed double-walled carbon nanotube(CNT)electrode-based perovskite solar cells(PSCs)was demonstrated.Through the use of a novel inversion transfer technique,vertical separation of the binders from the CNTs was induced,rendering a stronger p-doping effect and thereby a higher conductivity of the CNTs.The resulting foldable devices exhibited a power conversion efficiency of 18.11%,which is the highest reported among CNT transparent electrode-based PSCs to date,and withstood more than 10,000 folding cycles at a radius of 0.5 mm,demonstrating unprecedented mechanical stability.Furthermore,solar modules were fabricated using entirely laser scribing processes to assess the potential of the solution-processable nanocarbon electrode.Notably,this is the only one to be processed entirely by the laser scribing process and to be biocompatible as well as eco-friendly among the previously reported nonindium tin oxide-based perovskite solar modules.展开更多
In this paper, a model is presented to correlate and predict the swelling behavior of hydrogels in aqueous solutions of electrolytes. The model is a combination of VERS-model, 'phantom network' theory and '...In this paper, a model is presented to correlate and predict the swelling behavior of hydrogels in aqueous solutions of electrolytes. The model is a combination of VERS-model, 'phantom network' theory and 'free-volume' contribution. The VERS-model is used to calculate Gibbs excess energy; 'phantom network' theory to describe the elastic properties of polymer network, and 'free-volume' contribution to account for additional difference in the size of the species. To test the model, a series of N-isopropylacrylamide based hydrogels are synthesized by free radical polymerization in oxygen-free, deionized water at 25℃ under nitrogen atmosphere. Then, the degree of swelling of all investigated gels as well as the partition of the solute between the gel phase and the surrounding coexisting liquid phase are measured in aqueous solution of sodium chloride. The model test demonstrates that the swelling behavior correlated and predicted by the model agrees with the experimental data within the experimental uncertainty. The phase transition appeared in the experiment, and the influences of the total mass fraction of polymerizable materials ζgel as well as the mole fraction of the crosslinking agent yCR on the swelling behavior of IPAAm-gels can also be predicted correctly. All these show the potential of such model for correlation and prediction of the swelling behavior of hydrogels in aqueous solutions of electrolytes.展开更多
Synthetic porphyrins have, in the last years, gained increasing interest in analytical chemistry as unique reagents for the detection of metal ions. The porphyrin is a high sensitive chromogenic reagent. Porphyrins an...Synthetic porphyrins have, in the last years, gained increasing interest in analytical chemistry as unique reagents for the detection of metal ions. The porphyrin is a high sensitive chromogenic reagent. Porphyrins and their metal complexes generally exhibit characteristic sharp and intensive absorption bands in visible region. The region from 400 to 500 nm, which is called the Soret band, shows the most intensive absorption, and molar absorptivities about 105 are often found. Soret band (400-500 nm) shows the most intensive absorption of these compounds, molar absorptivities often being about 105. The Soret band is widely used for spectro- photometric detection of metalloporphyrins. From the perspective of analytical chemistry, the porphyrin ligand has turned out to be very versatile, and almost all metals have been combined with porphyrin. From this point of view several porphyrins become useful as the spectrophotometric reagents for the determination of metal ions.展开更多
In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by Leray-Schauder fixed point theorem and Galerkin method under appr...In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by Leray-Schauder fixed point theorem and Galerkin method under appropriate conditions.展开更多
In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform ...In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.展开更多
Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation...Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.展开更多
This paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u, Ω is a bounded domain in Rn (n > 3), 1 < p < n, p = -pn/n-p is the critical ex...This paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u, Ω is a bounded domain in Rn (n > 3), 1 < p < n, p = -pn/n-p is the critical exponent for the Sobolev imbedding, λ > 0 and f(x, u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(x,u) = |u|q-2u, where 1 < q < p, are generalized.展开更多
Background and objective Atypical 'cardiac' chest pain (ACCP) is not usually caused by myocardial ischaemia. Current noninvasive investigations for these symptoms are not yet as accurate as invasive coronary a...Background and objective Atypical 'cardiac' chest pain (ACCP) is not usually caused by myocardial ischaemia. Current noninvasive investigations for these symptoms are not yet as accurate as invasive coronary angiography. The latest 64-row multi-detector computed tomography (MDCT) technology is non-invasive, has high specificity and negative predictive values for the detection of significant coronary disease. Our aim was to investigate if this modality can provide more information in the assessment of outpatients with ACCP in addition to established cardiovascular risk scores. Methods Seventy consecutive patients presenting to the outpatient clinic with ACCP underwent 64-row MDCT scan of the coronary arteries. They were categorized into low, medium or high risk groups based upon the Framingham and PROCAM scores. We defined a clinically abnormal MDCT scan as coronary stenosis =50% or calcium score ＞400 Agatston. Results Fifty-three (75.7%) patients did not have clinically abnormal scans. Framingham score classified 43 patients as low-risk while PROCAM classified 59 patients as low-risk. MDCT scans were abnormal for 18.6% and 22.0% of the respective low-risk group of patients. For patients with medium-to-high risk, 33.3% and 36.4% of Framingham and PROCAM patient groups respectively had abnormal MDCT scans. Conclusion MDCT adds valuable information in the assessment of patients with ACCP by identifying a significant proportion of patients categorized as low-risk to have underlying significant coronary stenosis and coronary calcification by established cardiovascular risk scores.展开更多
文摘The author considers the Feigenbaum's functional equation fp(λx) = λf(x) for each p > 2. The existence of nonsingle-valley continuous solutions to this equation is discussed and a feasible method to construct such solutions is given.
文摘An existence theorem of positive solution is established for a nonlinear third-order three-point boundary value problem. Here, we concentrated on the case that the nonlinear term is neither superlinear nor sublinear, and is not asymptotic at zero and infinity.
基金the National Natural Science Foundation of China (No. 20276037, No. 20006010).
文摘The equation of Patwardhan and Kumar for water activities of mixed electrolyte solutions is extended to aqueous solutions containing non-electrolytes. This equation and the linear isopiestic relation are used to predict water activities of 56 ternary aqueous solutions in terms of the data of their binary subsystems. Both equation of Patwardhan and Kumar and the linear isopiestic relation can provide good predictions for water activities of the present 40 electrolyte solutions, and the linear isopiestic relation generally yields better predictions. The predictions of the extended equation of Patwardhan and Kumar and the linear isopiestic relation are in general quite reasonable for the present 8 ternary solutions of electrolytes and non-electrolytes, and the results of the linear isopiestic relation are usually better. The predictions of these two methods generally agree well with the experimental data for the 8 non-electrolyte mixtures being studied, and the linear isopiestic relation is better.
基金The NSF (01BXL002) of Xuzhou Normal University and the NSF (03KJB110137) of Jingsu Education Committee.
文摘In this paper, we first obtain some new results about the existence of multiple positive solutions for singular impulsive boundary value problems, and then to illustrate our main results we studied the existence of multiple positive solutions for an infinite system of scalar equations.
基金the National Natural Science Foundation of China( 19971054,40175014)
文摘Based on stratification theory, the existence theorems of formal solutions of partial differential equation (PDE) are given . And the relationship between formal solutions and protective limit of Ehresmann chain is presented .
文摘As an important aspect of applications, it is discussed how to find periodic solutions for ordinary differential equations. By using the homotopy method, a global method for finding those solutions is proposed.
文摘To extend the PSRK (predictive Soave-Redlich-Kwong equation of state) model to vapor-liquid equilibria of polymer solutions, a new EOS-gE mixing rule is applied in which the term ∑ xi ln(b/bi) in the PSRK mixing rule for the parameter a, and the combinatorial part in the original universal functional activity coefficient (UNIFAC) model are cancelled. To take into account the free volume contribution to the excess Gibbs energy in polymer solution, a quadratic mixing rule for the cross co-volume bij with an exponent equals to 1/2 is applied[bij1/2= 1/2(bi1/2+bj1/2)]. The literature reported Soave-Redlich-Kwong equation of state (SRK EOS) parameters ofpure polymer are employed. The PSRK model with the modified mixing rule is used to predict the vapor-liquid equilibrium (VLE) of 37 solvent-polymer systems over a large range of temperature and pressure with satisfactory results.
文摘This survey is concerned with the new developments on existence and uniqueness of solutions of some basic models in atmospheric dynamics, such as two-and three-dimensional quasi-geostrophic models and three-dimensional balanced model. The main aim of this paper is to introduce some results about the global and local (with respect to time) existence of solutions given by the authors in recent years, but others' important contributions and the literature on this subject are also quoted. We discuss briefly the relationships among the existence and uniqueness, physical instability and computational instability. In the appendixes, some key mathematical techniques in obtaining our results are presented, which are of vital importance to other problems in geophysical fluid dynamics as well.
基金the Natural Science Foundation of Zhejiang Province of China (100039)
文摘The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.
基金supported by the National Research Foundation of Korea funded by the Ministry of Science and ICT (MSIT),Korea (NRF-2021R1C1C1009200 and 2023R1A2C3007358)supported by the Defense Challengeable Future Technology Program of the Agency for Defense Development,Republic of Koreasupported by Technology Innovation Program of the Korea Evaluation Institute of Industrial Technology (KEIT) (20016588)funded by Ministry of Trade,Industry and Energy (MOTIE).
文摘The successful utilization of an eco-friendly and biocompatible parylene-C substrate for high-performance solution-processed double-walled carbon nanotube(CNT)electrode-based perovskite solar cells(PSCs)was demonstrated.Through the use of a novel inversion transfer technique,vertical separation of the binders from the CNTs was induced,rendering a stronger p-doping effect and thereby a higher conductivity of the CNTs.The resulting foldable devices exhibited a power conversion efficiency of 18.11%,which is the highest reported among CNT transparent electrode-based PSCs to date,and withstood more than 10,000 folding cycles at a radius of 0.5 mm,demonstrating unprecedented mechanical stability.Furthermore,solar modules were fabricated using entirely laser scribing processes to assess the potential of the solution-processable nanocarbon electrode.Notably,this is the only one to be processed entirely by the laser scribing process and to be biocompatible as well as eco-friendly among the previously reported nonindium tin oxide-based perovskite solar modules.
基金Supported by the Scientific Research Foundation for the Returned Overseas Chineses Sehiors of State Education Ministry, Science Technology Ministry of Fujian (No. 2001Z046).
文摘In this paper, a model is presented to correlate and predict the swelling behavior of hydrogels in aqueous solutions of electrolytes. The model is a combination of VERS-model, 'phantom network' theory and 'free-volume' contribution. The VERS-model is used to calculate Gibbs excess energy; 'phantom network' theory to describe the elastic properties of polymer network, and 'free-volume' contribution to account for additional difference in the size of the species. To test the model, a series of N-isopropylacrylamide based hydrogels are synthesized by free radical polymerization in oxygen-free, deionized water at 25℃ under nitrogen atmosphere. Then, the degree of swelling of all investigated gels as well as the partition of the solute between the gel phase and the surrounding coexisting liquid phase are measured in aqueous solution of sodium chloride. The model test demonstrates that the swelling behavior correlated and predicted by the model agrees with the experimental data within the experimental uncertainty. The phase transition appeared in the experiment, and the influences of the total mass fraction of polymerizable materials ζgel as well as the mole fraction of the crosslinking agent yCR on the swelling behavior of IPAAm-gels can also be predicted correctly. All these show the potential of such model for correlation and prediction of the swelling behavior of hydrogels in aqueous solutions of electrolytes.
文摘Synthetic porphyrins have, in the last years, gained increasing interest in analytical chemistry as unique reagents for the detection of metal ions. The porphyrin is a high sensitive chromogenic reagent. Porphyrins and their metal complexes generally exhibit characteristic sharp and intensive absorption bands in visible region. The region from 400 to 500 nm, which is called the Soret band, shows the most intensive absorption, and molar absorptivities about 105 are often found. Soret band (400-500 nm) shows the most intensive absorption of these compounds, molar absorptivities often being about 105. The Soret band is widely used for spectro- photometric detection of metalloporphyrins. From the perspective of analytical chemistry, the porphyrin ligand has turned out to be very versatile, and almost all metals have been combined with porphyrin. From this point of view several porphyrins become useful as the spectrophotometric reagents for the determination of metal ions.
文摘In this paper, the existence of the periodic solutions for a forced Burgers equation coupled to a non-homogeneous Ginzburg-Landau equation is proved by Leray-Schauder fixed point theorem and Galerkin method under appropriate conditions.
文摘In this paper we present a general existence result of periodic solutions for functional differential inclusions with nonconvex right hand sides, by using the asymptotic fixed point theory. In our result, the uniform boundedness and ultimate boundedness are only assumed to the solutions with bounded initial functions. On the other hand, the dissipativity is sought on a suitable bounded convex subset of the state space of solutions. This becomes difficult for the systems with infinite delay since in this case the subset is probably not forward invariant for the orbits of solutions. These are also considerable even for the usual functional differential equations with infinite delay. As an application, we answer an open problem on the existence of an equilibrium state for multivalued permanent systems.
基金The Project Supported by NSFC (19801014,10171065,19971026)
文摘Consider the linear neutral FDEd/dt[x(t) + Ax(t - r)] = R [dL(s)]x(t + s) + f(t)where x and / are ra-dimensional vectors; A is an n x n constant matrix and L(s) is an n x n matrix function with bounded total variation. Some necessary and sufficient conditions are given which guarantee the existence and uniqueness of periodic solutions to the above equation.
基金Supported by NSFC(10171032) NSF of Guangdong Proviance (011606)
文摘This paper is concerned with the following nonlinear Dirichlet problem:where △pu = div(| ▽u|p- 2 ▽u) is the p-Laplacian of u, Ω is a bounded domain in Rn (n > 3), 1 < p < n, p = -pn/n-p is the critical exponent for the Sobolev imbedding, λ > 0 and f(x, u) satisfies some conditions. It reaches the conclusion that this problem has infinitely many solutions. Some results as p = 2 or f(x,u) = |u|q-2u, where 1 < q < p, are generalized.
文摘Background and objective Atypical 'cardiac' chest pain (ACCP) is not usually caused by myocardial ischaemia. Current noninvasive investigations for these symptoms are not yet as accurate as invasive coronary angiography. The latest 64-row multi-detector computed tomography (MDCT) technology is non-invasive, has high specificity and negative predictive values for the detection of significant coronary disease. Our aim was to investigate if this modality can provide more information in the assessment of outpatients with ACCP in addition to established cardiovascular risk scores. Methods Seventy consecutive patients presenting to the outpatient clinic with ACCP underwent 64-row MDCT scan of the coronary arteries. They were categorized into low, medium or high risk groups based upon the Framingham and PROCAM scores. We defined a clinically abnormal MDCT scan as coronary stenosis =50% or calcium score ＞400 Agatston. Results Fifty-three (75.7%) patients did not have clinically abnormal scans. Framingham score classified 43 patients as low-risk while PROCAM classified 59 patients as low-risk. MDCT scans were abnormal for 18.6% and 22.0% of the respective low-risk group of patients. For patients with medium-to-high risk, 33.3% and 36.4% of Framingham and PROCAM patient groups respectively had abnormal MDCT scans. Conclusion MDCT adds valuable information in the assessment of patients with ACCP by identifying a significant proportion of patients categorized as low-risk to have underlying significant coronary stenosis and coronary calcification by established cardiovascular risk scores.
