New Results Subclasses of Analytic Functions Define by Opooladifferential Operator

In this paper, using Opooladifferential operator, we introduce new subclasses of univalent functions andprovide δ -Neigbhourhoods properties, Inclusion relations for the subclasses of univalent functions.

Functional diversity dominates positive species mixture effects on ecosystem multifunctionality in subtropical plantations

Mixed-species plantations generally exhibit higher ecosystem multifunctionality than monospecific plantations.However,it is unclear how tree species functional composition influences species mixture effects on ecosystem multifunctionality.We selected 171 monospecific and mixed-species plantations from nine regions across subtropical China,and quantified 13 key ecosystem functional properties to investigate how species mixture effects on ecosystem multifunctionality are modulated by functional diversity and identity.We found that ecosystem multifunctionality was significantly higher(p<0.05)in mixed tree plantations than in monospecific plantations except the mixed-conifer species plantations.Across all regions,ecosystem multifunctionality was significantly higher(p<0.05)in mixed conifer-broadleaf plantations than in monospecific plantations of the corresponding species,but not different between mixed and monospecific coniferous plantations.The magnitude of species mixture effects on ecosystem multifunctionality varied greatly with tree species compositions.Taking Cunninghamia lanceolata Lamb.as an example,the effects varied from a range of 2.0%–9.6%when mixed with a conifer species to 36%–87%when mixed with a broadleaf species.The functional diversity was the dominate driver shaping ecosystem multifunctionality,while functional identity,as expressed by community-weighted mean of specific leaf area,also had a positive effect on ecosystem multifunctionality through the increased below-ground nitrogen and phosphorus stocks regulated by specific leaf area of the mixing tree species.Our study highlights the important role of functional diversity in shaping ecosystem multifunctionality across region-wide environmental conditions.Mixed conifer-broadleaf tree plantations with distinct functional traits benefit the enhancement of ecosystem multifunctionality,and the magnitude of species mixture effects is modulated by the functional identity of tree species composition;those relationships deserve a special consideration in multifunctional management context of subtropical plantations.

Effects of biodiversity,stand factors and functional identity on biomass and productivity during the restoration of subtropical forests in Central China

Biodiversity is found to have a significant promotion effect on ecosystem functions in manipulation experiments on grassland communities.However,its relative role compared with stand factors or functional identity is still controversial in natural forests.Here,we examined their relative effects on biomass and productivity during forest restoration.We investigated stand biomass and productivity for 24 plots(600 m2)across restoration stages in the subtropical forests of Mt.Shennongjia,Central China.We measured five key functional traits and calculated functional diversity(functional richness,evenness and dispersion)and community-weighted mean of traits.We used general linear models,variation partitioning methods to test the relative importance of stand factors(density,stand age,maximum height,etc.),functional identity,species and functional diversity on biomass and productivity.Our results illustrated that stand biomass and productivity increased significantly as forest restoration,and that community species richness increased,while functional dispersion decreased significantly.Variation partitioning analyses showed that diversity had no significant pure effects on biomass and productivity.However,diversity may affect biomass and productivity through the joint effect with stand factors and functional identity.Overall,we found that stand factors had the strongest effect on biomass and productivity,while functional identity significantly affects productivity but not biomass,suggesting that modulating stand structure and species identity are effective ways to enhance forest carbon storage and sequestrations potential in forest management.

K_(3)C_(60)表面量子自旋诱导的YSR多重态和量子相变

Magnetic impurities in superconductors are of increasing interest due to emergent Yu-Shiba-Rusinov(YSR)states and Majorana zero modes for fault-tolerant quantum computation.However,a direct relationship between the YSR multiple states and magnetic anisotropy splitting of quantum impurity spins remains poorly characterized.By using scanning tunneling microscopy,we systematically resolve individual transition-metal(Fe,Cr,and Ni)impurities induced YSR multiplets as well as their Zeeman effects in the K_(3)C_(60)superconductor.The YSR multiplets show identical d orbital-like wave functions that are symmetry-mismatched to the threefold K_(3)C_(60)(111)host surface,breaking point-group symmetries of the spatial distribution of YSR bound states in real space.Remarkably,we identify an unprecedented fermion-parity-preserving quantum phase transition between ground states with opposite signs of the uniaxial magnetic anisotropy that can be manipulated by an external magnetic field.These findings can be readily understood in terms of anisotropy splitting of quantum impurity spins,and thus elucidate the intricate interplay between the magnetic anisotropy and YSR multiplets.

Partition Identities Arising from Theta Function Identities

The authors show that certain theta function identities of Schroeter and Ramanujan imply elegant partition identities.

Certain Additive Maps on （m ＋ n ＋ 1）-Power Closed Lie Ideals

Let R be a prime ring and m, n be fixed non-negative integers such that m＋n ≠ 0. Suppose L is an （m＋m＋1）-power closed Lie ideal, and this means ure＋n＋1 ∈ L for all u ∈ L. If charR = 0 or a prime p 〉 2（m ＋ n）, we characterize the additive maps d： L → R satisfying d（um＋n＋1） = （m -＋n ＋ 1）umd（u）un （resp., d（um＋n＋l） = umd（u）un） for all u ∈ L.

A note on generalized Lie derivations of prime rings

Let R be a prime ring of characteristic not 2, A be an additive subgroup of R, and F, T, D, K： A →R be additive maps such that F（[x, y]） = F（x）y - yg（x） - T（y）x ＋ xD（y） for all x, y ∈ A. Our aim is to deal with this functional identity when A is R itself or a noncentral Lie ideal of R. Eventually, we are able to describe the forms of the mappings F, T, D, and K in case A = R with deg（R） 〉 3 and also in the case A is a noncentral Lie ideal and deg（R） 〉 9. These enable us in return to characterize the forms of both generalized Lie derivations, D-Lie derivations and Lie centralizers of R under some mild assumptions. Finally, we give a generalization of Lie homomorphisms on Lie ideals.

On the Gosper’s q-constant Ⅱ_q

Gosper introduced the functions sinq z and cosq z as q-analogues for the trigonometric functions sin z and cos z respectively. He stated a variety of identities involving these two q-trigonometric functions along with certain constants denoted by Πqn （n ∈ N）. Gosper noticed that all his formulas on these constants have more than two of the Πqn. So, it is natural to raise the question of establishing identities involving only two of the Πqn. In this paper, our main goal is to give examples of such formulas in only two Πqn.

OSCILLATION OF A CLASS OF HILLE EQUATION

This paper studies a class of Hille equation. A formula for solutions of a class of Hille equation is given. Under some suitable conditions the oscillation and nonoscillation of a class of Hille equation are established. Our results generalize the known Hille＇s ones.