In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contracti...In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.展开更多
Both the photosynthetic light curves and CO2 curves of Juglans regia L. and Ziziphus jujuba Mill. var. spinosa in three seasons were measured using a LI-6400 portable photosynthesis system. The maximal net photosynthe...Both the photosynthetic light curves and CO2 curves of Juglans regia L. and Ziziphus jujuba Mill. var. spinosa in three seasons were measured using a LI-6400 portable photosynthesis system. The maximal net photosynthetic rate （Amax）, apparent quantum efficiency（φ）, maximal carboxylation rate （Vcmax） and water use efficiency （WUE） of the two species were calculated based on the curves. The results showed that Amax of J. regia reached its maximum at the late-season, while the highest values of Amax of Z. jujuba occurred at the mid-season. The Amax of J. regia was more affected by relative humidity （RH） of the atmosphere, while that of Z. jujuba was more affected by the air temperature. Light saturation point （LSP） and Light compensation point （LCP） of J. regia had a higher correlation with RH of the atmosphere, those of Z. jujuba, however, had a higher correlation with air temperature. Vcmax of both J. regia and Z. jujuba had negative correlation with RH of the atmosphere. WUE of J. regia would decrease with the rise of the air temperature while that of Z. jujuba increased. Thus it could be seen that RH, temperature and soil moisture had main effect on photosynthesis and WUE of J. regia and Z. jujuba. Incorporating data on the physiological differences among tree species into forest carbon models will greatly improve our ability to predict alterations to the forest carbon budgets under various environmental scenarios such as global climate change, or with differing species composition.展开更多
The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ...The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.展开更多
The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the...The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.展开更多
文摘In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.
基金the State Key Basic Research and Development Plan of China(2002CB111504)the Project of Turning Cropland to Forest of State Forestry Administration and the Distinguished Young Scientist Fund of the NationalNatural Science Foundation of China (2002002002).
文摘Both the photosynthetic light curves and CO2 curves of Juglans regia L. and Ziziphus jujuba Mill. var. spinosa in three seasons were measured using a LI-6400 portable photosynthesis system. The maximal net photosynthetic rate （Amax）, apparent quantum efficiency（φ）, maximal carboxylation rate （Vcmax） and water use efficiency （WUE） of the two species were calculated based on the curves. The results showed that Amax of J. regia reached its maximum at the late-season, while the highest values of Amax of Z. jujuba occurred at the mid-season. The Amax of J. regia was more affected by relative humidity （RH） of the atmosphere, while that of Z. jujuba was more affected by the air temperature. Light saturation point （LSP） and Light compensation point （LCP） of J. regia had a higher correlation with RH of the atmosphere, those of Z. jujuba, however, had a higher correlation with air temperature. Vcmax of both J. regia and Z. jujuba had negative correlation with RH of the atmosphere. WUE of J. regia would decrease with the rise of the air temperature while that of Z. jujuba increased. Thus it could be seen that RH, temperature and soil moisture had main effect on photosynthesis and WUE of J. regia and Z. jujuba. Incorporating data on the physiological differences among tree species into forest carbon models will greatly improve our ability to predict alterations to the forest carbon budgets under various environmental scenarios such as global climate change, or with differing species composition.
文摘The paper presents a novel exploration of π through a re-calculation of formulas using Archimedes’ algorithm, resulting in the identification of a general family equation and three new formulas involving the golden ratio Φ, in the form of infinite nested square roots. Some related geometrical properties are shown, enhancing the link between the circle and the golden ratio. Applying the same criteria, a fourth formula is given, that brings to the known Dixon’s squaring the circle approximation, thus an easier approach to this problem is suggested, by a rectangle with both sides proportional to the golden ratio Φ.
文摘The focusofourwork is on themost recent results infixedpoint theoryrelated tocontractivemappings.Wedescribe variants of(s,q,φ,F)-contractions that expand,supplement and unify an important work widely discussed in the literature,based on existing classes of interpolative and F-contractions.In particular,a large class of contractions in terms of s,q,φand F for both linear and nonlinear contractions are defined in the framework of b-metric-like spaces.The main result in our paper is that(s,q,φ,F)-g-weak contractions have a fixed point in b-metric-like spaces if function F or the specified contraction is continuous.As an application of our results,we have shown the existence and uniqueness of solutions of some classes of nonlinear integral equations.
