The clinical study of solute removal index (SRI) was performed in 20 stable maintenance hemodialysis patients in order to find a proper hemodialydsis dosage and improve the life quality of the patients.Plasma BUN leve...The clinical study of solute removal index (SRI) was performed in 20 stable maintenance hemodialysis patients in order to find a proper hemodialydsis dosage and improve the life quality of the patients.Plasma BUN levels were tested pre-hemodialysis and 0, 1 hr post-hemodialysis. Urea generation rate (G)、protein catabolic rate(PCR)、solute removal amount(R)、SRI were calculated by double pools urea kinetic model . The result showed that urea rebound rate was 18.5±3.35 % 1 hr after hemodialysis,R was 13.82±5.48 g, G was 4.85±1.39 g, PCR was 0.94±0.29 g/kg.d, SRI was 71.33±6.8% respectively, which indicated that SRI was a better index to quantitate the adequacy of hemodialysis.展开更多
A monotonicity formula for stable solutions to a class of weighted semilinear elliptic equations with ＂negative exponent＂ is established. It is well known that such a monotonieity formula plays an essential role in ...A monotonicity formula for stable solutions to a class of weighted semilinear elliptic equations with ＂negative exponent＂ is established. It is well known that such a monotonieity formula plays an essential role in the study of finite Morse index solutions of equations with ＂positive exponent＂. Unlike the positive exponent case, we will see that both the monotonicity formula and the sub-harmonicity play crucial roles in classifying positive finite Morse index solutions to the equations with negative exponent and obtaining sharp results for their asymptotic behaviors.展开更多
We prove Liouville type theorems for stable and finite Morse index H_(loc)^(1)∩L_(loc)^(∞)solutions of the nonlinear Schrodinger equation -Δu+λ|x|^(a)u=|x|b|^(u)|^(p-1)u in R^(N),where N≥2,λ>0,a,b>-2 and p...We prove Liouville type theorems for stable and finite Morse index H_(loc)^(1)∩L_(loc)^(∞)solutions of the nonlinear Schrodinger equation -Δu+λ|x|^(a)u=|x|b|^(u)|^(p-1)u in R^(N),where N≥2,λ>0,a,b>-2 and p>1,Our analysis reveals that all stable solutions of the equation must be zero for all p>1,Furthermore,finite Morse index solutions must be zero if N≥3 an p≥(N+2+2b)/(N-2).The main tools we use are integral estimates,a Pohozaev type identity and a monotonicity formula.展开更多
In this paper,we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part.Firstly,we study the qualitative properties,such as the symmetry,r...In this paper,we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part.Firstly,we study the qualitative properties,such as the symmetry,regularity and asymptotic behavior of the positive solutions.Secondly,we classify the non-positive solutions by proving some Liouville type theorems for the finite Morse index solutions and stable solutions to the nonlocal elliptic equations with double weights.展开更多
文摘The clinical study of solute removal index (SRI) was performed in 20 stable maintenance hemodialysis patients in order to find a proper hemodialydsis dosage and improve the life quality of the patients.Plasma BUN levels were tested pre-hemodialysis and 0, 1 hr post-hemodialysis. Urea generation rate (G)、protein catabolic rate(PCR)、solute removal amount(R)、SRI were calculated by double pools urea kinetic model . The result showed that urea rebound rate was 18.5±3.35 % 1 hr after hemodialysis,R was 13.82±5.48 g, G was 4.85±1.39 g, PCR was 0.94±0.29 g/kg.d, SRI was 71.33±6.8% respectively, which indicated that SRI was a better index to quantitate the adequacy of hemodialysis.
基金supported by National Natural Science Foundation of China(Grant Nos.11171092 and 11271133)Innovation Scientists and Technicians Troop Construction Projects of Henan Province(Grant No.114200510011)
文摘A monotonicity formula for stable solutions to a class of weighted semilinear elliptic equations with ＂negative exponent＂ is established. It is well known that such a monotonieity formula plays an essential role in the study of finite Morse index solutions of equations with ＂positive exponent＂. Unlike the positive exponent case, we will see that both the monotonicity formula and the sub-harmonicity play crucial roles in classifying positive finite Morse index solutions to the equations with negative exponent and obtaining sharp results for their asymptotic behaviors.
基金Supported by University of Economics and Law,VNU-HCM。
文摘We prove Liouville type theorems for stable and finite Morse index H_(loc)^(1)∩L_(loc)^(∞)solutions of the nonlinear Schrodinger equation -Δu+λ|x|^(a)u=|x|b|^(u)|^(p-1)u in R^(N),where N≥2,λ>0,a,b>-2 and p>1,Our analysis reveals that all stable solutions of the equation must be zero for all p>1,Furthermore,finite Morse index solutions must be zero if N≥3 an p≥(N+2+2b)/(N-2).The main tools we use are integral estimates,a Pohozaev type identity and a monotonicity formula.
基金supported by National Natural Science Foundation of China(Grant Nos.11971436 and 12011530199)Natural Science Foundation of Zhejiang(Grant No.LD19A010001)。
文摘In this paper,we study the qualitative properties and classification of the solutions to the elliptic equations with Stein-Weiss type convolution part.Firstly,we study the qualitative properties,such as the symmetry,regularity and asymptotic behavior of the positive solutions.Secondly,we classify the non-positive solutions by proving some Liouville type theorems for the finite Morse index solutions and stable solutions to the nonlocal elliptic equations with double weights.
