Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of fun...Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.展开更多
Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} c...Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.展开更多
A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asym...A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.展开更多
Usually considered a morphologically conservative group, didelphid marsupials present consider- able variation in ecology and body size, some of which were shown to relate to morphological structures. Thus, changes on...Usually considered a morphologically conservative group, didelphid marsupials present consider- able variation in ecology and body size, some of which were shown to relate to morphological structures. Thus, changes on orbit morphology are likely and could be related to that variation. We calculated orbit orientation in 873 specimens of 16 Didelphidae genera yielding estimates of orbits convergence （their position relative to midsagittal line） and verticality （their position relative to frontal plane）. We then compared similarities in these variables across taxa to ecological, morpho- logical and phylogenetic data to evaluate the influencing factors on orbit orientation in didelphids. We found an inverse relation between convergence and verticality. Didelphids orbits have low ver- ticality but are highly convergent, yet orbit orientation differs significantly between taxa, and that variation is related to morphological aspects of the cranium. Rostral variables are the only morpho- logical features correlated with orbit orientation： increasing snout length yields more convergent orbits, whereas increase on snout breadth imply in more vertical orbits. Size and encephalization quotients are uncorrelated with orbit orientation. Among ecological data, diet showed significant correlation whereas locomotion is the factor that less affects the position of orbits. Phylogeny is uncorrelated to any orbital parameters measured. Ecological factors seemingly play a more import- ant role on orbit orientation than previously expected, and differentiation on orbit orientation seems to be more functional than inherited. Thus, despite the apparent homogeneity on didelphid morphology, there is subtle morphological variability that may be directly related to feeding behavior.展开更多
文摘Suppose that the outer mapping function of domain D has its second continuous derivatives. In this paper, the order proximation by (0,1,…,q) Hermite-Fejer interpolating polynomials at nearly Fejer's points of function of class A(D) are presented. Moreover in general the order of approximation is sharp.
基金National Natural Science Foundation of China (Grant No. 11071074)
文摘Let {fn} be a sequence of meromorphic functions on a plane domain D, whose zeros and poles have multiplicity at least 3. Let {hn} be a sequence of meromorphic functions on D, whose poles are multiple, such that {hn} converges locally uniformly in the spherical metric to a function h which is meromorphic and zero-free on D.If fn≠hn, then {fn} is normal on D.
基金supported by National Research Foundation of Korea(No.2012-011755)a stipend from the Humboldt foundation
文摘A real Liouville domain is a Liouville domain with an exact anti-symplectic involution. The authors call a real Liouville domain uniruled if there exists an invariant finite energy plane through every real point. Asymptotically, an invariant finite energy plane converges to a symmetric periodic orbit. In this note, they work out a criterion which guarantees uniruledness for real Liouville domains.
文摘Usually considered a morphologically conservative group, didelphid marsupials present consider- able variation in ecology and body size, some of which were shown to relate to morphological structures. Thus, changes on orbit morphology are likely and could be related to that variation. We calculated orbit orientation in 873 specimens of 16 Didelphidae genera yielding estimates of orbits convergence （their position relative to midsagittal line） and verticality （their position relative to frontal plane）. We then compared similarities in these variables across taxa to ecological, morpho- logical and phylogenetic data to evaluate the influencing factors on orbit orientation in didelphids. We found an inverse relation between convergence and verticality. Didelphids orbits have low ver- ticality but are highly convergent, yet orbit orientation differs significantly between taxa, and that variation is related to morphological aspects of the cranium. Rostral variables are the only morpho- logical features correlated with orbit orientation： increasing snout length yields more convergent orbits, whereas increase on snout breadth imply in more vertical orbits. Size and encephalization quotients are uncorrelated with orbit orientation. Among ecological data, diet showed significant correlation whereas locomotion is the factor that less affects the position of orbits. Phylogeny is uncorrelated to any orbital parameters measured. Ecological factors seemingly play a more import- ant role on orbit orientation than previously expected, and differentiation on orbit orientation seems to be more functional than inherited. Thus, despite the apparent homogeneity on didelphid morphology, there is subtle morphological variability that may be directly related to feeding behavior.
