The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflectio...The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflection points of H-D models.The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset.The six models were the Wykoff(WYK),Schumacher(SCH),Curtis(CUR),HossfeldⅣ(HOS),von Bertalanffy-Richards(VBR),and Gompertz(GPZ)models.The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution.The distributions of the estimated inflection points were similar between the two-parameter models WYK,SCH,and CUR,but were different between the threeparameter models HOS,VBR,and GPZ.GPZ produced some of the largest inflection points.HOS and VBR produced concave H-D curves without inflection points for 12.7%and 39.7%of the tree species.Evergreen species or decreasing shade tolerance resulted in larger inflection points.The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape.Furthermore,HOS could produce concave H-D curves for portions of the landscape.Based on the studied behaviors,the choice between two-parameter models may not matter.We recommend comparing seve ral three-parameter model forms for consistency in estimated inflection points before deciding on one.Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one.Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.展开更多
A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects ...A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points展开更多
A spectrophotometric technique is developed to simultaneously quantify nitrate and nitrite in plasma treated water.The measurement is based on examining the inflection points(wavelengths)in the derivative absorbance o...A spectrophotometric technique is developed to simultaneously quantify nitrate and nitrite in plasma treated water.The measurement is based on examining the inflection points(wavelengths)in the derivative absorbance of the nitrate or nitrite solution.At the inflection points of the pure nitrate solution,the derivative absorbance is zero and independent of the nitrate’s concentration,and thus the nitrite’s concentration in a mixed nitrate and nitrite solution can be obtained by using the Beer’s law at these points.The nitrate’s concentration can also be achieved from the inflection points of nitrite in the same manner.The relation between the tested substance’s(nitrate or nitrite)concentration and the second-or the third-order absorbances is obtained at these inflection points.Test measurements for mixed aqueous solutions of nitrate and nitrite with or without hydrogen peroxide confirm the reliability of this technique.We applied this technique to quantify the nitrate and nitrite generated in air plasma treated aqueous solutions.The results indicate that both nitrate and nitrite concentrations increase with the plasma treatment time,and the nitrite species is found to be generated prior to the nitrate species in the air plasma treated aqueous solution.Moreover,the production rate of total nitrogen species is independent of the solutions’p H value.These results are relevant to diverse applications of plasma activated solutions in materials processing,biotechnology,medicine and other fields.展开更多
文摘The inflection point is an important feature of sigmoidal height-diameter(H-D)models.It is often cited as one of the properties favoring sigmoidal model forms.However,there are very few studies analyzing the inflection points of H-D models.The goals of this study were to theoretically and empirically examine the behaviors of inflection points of six common H-D models with a regional dataset.The six models were the Wykoff(WYK),Schumacher(SCH),Curtis(CUR),HossfeldⅣ(HOS),von Bertalanffy-Richards(VBR),and Gompertz(GPZ)models.The models were first fitted in their base forms with tree species as random effects and were then expanded to include functional traits and spatial distribution.The distributions of the estimated inflection points were similar between the two-parameter models WYK,SCH,and CUR,but were different between the threeparameter models HOS,VBR,and GPZ.GPZ produced some of the largest inflection points.HOS and VBR produced concave H-D curves without inflection points for 12.7%and 39.7%of the tree species.Evergreen species or decreasing shade tolerance resulted in larger inflection points.The trends in the estimated inflection points of HOS and VBR were entirely opposite across the landscape.Furthermore,HOS could produce concave H-D curves for portions of the landscape.Based on the studied behaviors,the choice between two-parameter models may not matter.We recommend comparing seve ral three-parameter model forms for consistency in estimated inflection points before deciding on one.Believing sigmoidal models to have inflection points does not necessarily mean that they will produce fitted curves with one.Our study highlights the need to integrate analysis of inflection points into modeling H-D relationships.
文摘A rational parametric planar cubic H spline curve is defined by a set of control vertices in a plane and percentage factors of line segments between every two control vertices. Movement of any control vertex affects three curve segments. This paper is the succession and development of reference of Tang Yuehong. We analyze the geometric features like cusps and inflection points in the curve and calculate the cusps and inflection points, then give a necessary and sufficient condition to the inflection points in the curve when it is non degenerative, and finally show that the curves have no cusps in the interval (0,1). In many applications, it is desirable to analyze the parametric curves for undesirable features like cusps and inflection points
基金National Natural Science Foundation of China(No.52077185)the Basic Research Program of Science and Technology of Shenzhen,China(No.JCYJ20190809162617137)for partial financial support。
文摘A spectrophotometric technique is developed to simultaneously quantify nitrate and nitrite in plasma treated water.The measurement is based on examining the inflection points(wavelengths)in the derivative absorbance of the nitrate or nitrite solution.At the inflection points of the pure nitrate solution,the derivative absorbance is zero and independent of the nitrate’s concentration,and thus the nitrite’s concentration in a mixed nitrate and nitrite solution can be obtained by using the Beer’s law at these points.The nitrate’s concentration can also be achieved from the inflection points of nitrite in the same manner.The relation between the tested substance’s(nitrate or nitrite)concentration and the second-or the third-order absorbances is obtained at these inflection points.Test measurements for mixed aqueous solutions of nitrate and nitrite with or without hydrogen peroxide confirm the reliability of this technique.We applied this technique to quantify the nitrate and nitrite generated in air plasma treated aqueous solutions.The results indicate that both nitrate and nitrite concentrations increase with the plasma treatment time,and the nitrite species is found to be generated prior to the nitrate species in the air plasma treated aqueous solution.Moreover,the production rate of total nitrogen species is independent of the solutions’p H value.These results are relevant to diverse applications of plasma activated solutions in materials processing,biotechnology,medicine and other fields.
