DISCUSSION ON″THE BOUNDEDNESS AND ASYMPTOTIC BEHAVIOR OR SOLUTION DIFFERENTIAL SYSTEM OF SECOND-ORDER WITH VARIABLE COEFFICIENT" (App1ied Mathematics and Mechanics,Vo1.3,No.4,1982)

After reading the article "The Boundedness and Asymptotic Behavior of Solution of Differential System of Second-Order with Variable Coefficient" in "Applied Mathematics and Mechanics", Vol. 3, No. 4, 1982, we would like to put forward a few points to discuss with the author and the readers. Our opinions are presented as follows:

OSCILLATION AND ASYMPTOTIC BEHAVIOR OF SOME SECOND-ORDER RETARDED DIFFERENTIAL EQUATIONS

In this paper, we consider the following second order retarded differential equations x″(t)+cx′(t)=qx(t-σ)-lx(t-δ) (1) x″(t)+p(t)x(t-τ)=0 (2) We give some sufficient conditions for the oscillation of all solutions of Eq. (1) in the case where q, ι, σ, δ are positive numbers and c is a real number. And also, we study the asymptotic behavior of the nonoscillatory solutions. If necessary, we give some examples to illustrate our results. At last, we study Eq. (2) with some conditions on p(t).

Asymptotic Behavior of Solutions of Retarded Differential Equations

A sufficient condition is obtained for every solution of the nonlinear retarded differential equationx'(t) +f(t,x(t-τ)) =0to tend to zero as t→∞ , which extends and improves the corresponding results obtained by Ladas, Sficas and Gopalsamy.

Controlling effects of differential swelling index on evolution of coal permeability

Coal permeability measurements are normally conducted under the assumption that gas pressure in the matrix is equalized with that in fracture and that gas sorption-induced swelling/shrinking strain is uniformly distributed within the coal.However,the validity of this assumption has long been questioned and differential strain between the fracture strain and the bulk strain has long been considered as the primary reason for the inconsistency between experimental data and poroelasticity solutions.Although efforts have been made to incorporate the impact into coal permeability models,the fundamental nature of those efforts to split the matrix strain between fracture and coal bulk remains questionable.In this study,a new concept of differential swelling index(DSI)was derived to theoretically define the relation among sorption-induced strains of the coal bulk,fracture,and coal matrix at the equilibrium state.DSI was a function of the equilibrium pressure and its magnitudes were regulated by the Langmuir constants of both the matrix and the coal bulk.Furthermore,a spectrum of DSI-based coal permeability models was developed to explicitly consider the effect of differential strains.These models were verified with the experimental data under the conditions of uniaxial strain,constant confining pressure,and constant effective stress.

Asymmetric competition for seeds between two sympatric food hoarding rodents:implications for coexistence

Asymmetric competition occurs when some species have distinct advantages over their competitors and is common in animals with overlapping habitats and diet.However,the mechanism allowing coexistence between asymmetric competitors is not fully clear.Chinese white-bellied rats(Niviventer confucianus,CWR)and Korean field mice(Apodemus peninsulae,KFM)are common asymmetric competitors in shrublands and forests west of Beijing city.They share similar diet(e.g.plant seeds)and activity(nocturnal),but differ in body size(CWR are bigger than KFM),food hoarding habit(CWR:mainly larder hoarding;KFM:both larder and scatter hoarding),and ability to protect cached food(CWR are more aggressive than KFM).Here,we tested seed competition in 15 CWR-KFM pairs over a 10-day period under semi-natural enclosure conditions to uncover the differences in food hoarding,cache pilferage,and food protection between the 2 rodents,and discuss the implication for coexistence.Prior to pilferage,CWR harvested and ate more seeds than KFM.CWR tended to larder hoard seeds,whereas KFM preferred to scatter hoard seeds.Following pilferage,CWR increased consumption,decreased intensity of hoarding,and pilfered more caches from KFM than they lost,while KFM increased consumption more than they hoarded,and they preferred to hoard seeds in low and medium competition areas.Accordingly,both of the 2 rodent species increased their total energy consumption and hoarding following pilferage.Both rodent species tended to harvest seeds from the source,rather than pilfer caches from each other to compensate for cache loss via pilferage.Compared to CWR,KFM consumed fewer seeds when considering seed number,but hoarded more seeds when considering the seeds’relative energy(energy of hoarded seeds/rodent body mass2/3)at the end of the trials.These results suggest that asymmetric competition for food exists between CWR and KFM,but differentiation in hoarding behavior could help the subordinate species(i.e.KFM)hoard more energy than the dominant species(i.e.CWR),and may contribute to their coexistence in the field.

Carbon-doping-induced negative differential resistance in armchair phosphorene nanoribbons

By using a combined method of density functional theory and non-equilibrium Green＇s function formalism,we investigate the electronic transport properties of carbon-doped armchair phosphorene nanoribbons（APNRs）.The results show that C atom doping can strongly affect the electronic transport properties of the APNR and change it from semiconductor to metal.Meanwhile,obvious negative differential resistance（NDR） behaviors are obtained by tuning the doping position and concentration.In particular,with reducing doping concentration,NDR peak position can enter into m V bias range.These results provide a theoretical support to design the related nanodevice by tuning the doping position and concentration in the APNRs.