In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, ...In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and originating a class of new strategy to transform ordinary control into general integral control. By using Lyapunov method along with LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the highlight point of this integral control strategy is that the integrator output could tend to infinity but the integral control action is finite. Therefore, a simple and ingenious method to design general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole domain of interest can all be achieved by a set of the same control gains, even under the case that the payload is changed abruptly.展开更多
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
In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In...In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler＇s constant γ.展开更多
This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex bod...This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.展开更多
Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invaria...Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invariant valuations on concave functions and log-concave functions are completely classified, respectively.展开更多
文摘In this paper, a class of fire-new general integral control, named general concave integral control, is proposed. It is derived by normalizing the bounded integral control action and concave function gain integrator, introducing the partial derivative of Lyapunov function into the integrator and originating a class of new strategy to transform ordinary control into general integral control. By using Lyapunov method along with LaSalle’s invariance principle, the theorem to ensure regionally as well as semi-globally asymptotic stability is established only by some bounded information. Moreover, the highlight point of this integral control strategy is that the integrator output could tend to infinity but the integral control action is finite. Therefore, a simple and ingenious method to design general integral control is founded. Simulation results showed that under the normal and perturbed cases, the optimum response in the whole domain of interest can all be achieved by a set of the same control gains, even under the case that the payload is changed abruptly.
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.
基金Supported by the National Natural Science Foundation of China(11171307)
文摘In this paper, the authors show some monotonicity and concavity of the classical psi function, by which several known results are improved and some new asymptotically sharp estimates are obtained for this function. In addition, applying the new results to the psi function, the authors improve the well-known lower and upper bounds for the approximate evaluation of Euler＇s constant γ.
基金Supported by the Natural Science Foundation of China（10771086） Supported by the Natural Science Foundation of Fujian Province（S0650021）
文摘This paper shows some properties of symmetry function induced by a convex body in a normal linear space. Some relationships between symmetry function induced by a convex body and Minkowski functional of the convex body are presented.
基金Supported by Foundation of China Scholarship Council(201808430267)the Education Department of Hunan Province(16C0635)the Natural Science Foundation of Hunan Province(2017JJ3085)
文摘Recently, the theory of valuations on function spaces has been rapidly growing. It is more general than the classical theory of valuations on convex bodies. In this paper, all continuous, SL(n) and translation invariant valuations on concave functions and log-concave functions are completely classified, respectively.
