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<i>Lysimachia barcae</i> (Primulaceae), a new endemic shrub from Wainiha, Kaua'i, Hawaiian Islands. [PDF]
PhytoKeysWood KR +3 more
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A new synonym of <i>Mussaenda</i> (Rubiaceae) from Vietnam. [PDF]
PhytoKeysHuang WY +4 more
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Canonicalizing Zeta Generators: Genus Zero and Genus One. [PDF]
Commun Math PhysDorigoni D +7 more
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An efficient elliptic curve-based deterministic measurement matrix for micro-seismic data acquisition. [PDF]
PLoS OneLiu H, Ge G, Jiang Z, Chen X.
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Phylotranscriptomics and genome-size evidence clarify the Taiwanese Cirsium japonicum complex and delimit C. brevicaule and allied East Asian thistles. [PDF]
BMC Plant BiolChang CY +5 more
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ELLIPTIC CURVES AND -ADIC ELLIPTIC TRANSCENDENCE
Bulletin of the Australian Mathematical Society, 2021AbstractWe prove a necessary and sufficient condition for isogenous elliptic curves based on the algebraic dependence ofp-adic elliptic functions. As a consequence, we give a short proof of thep-adic analogue of Schneider’s theorem on the linear independence ofp-adic elliptic logarithms of algebraic points on two nonisogenous elliptic curves defined ...
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Theory of Probability & Its Applications, 1986
Let \(E_ n=(\xi_{pl})^ n_{p,l=1}\) denote random complex (n\(\times n)\)-matrices. Random vectors \((\xi^ n_{pl},\xi^ n_{lp})\), \(p\geq l\), \(p,l=\overline{s,n}\) are independent, \(M\xi^ n_{pl}=0\), \(M| \xi^ n_{pl}|^ 2=n^{-1}\), \(M\xi^ n_{pl}\xi^ n_{lp}=n^{-1}\rho\), \(l\neq p\), random variables Re \(\xi\) \({}^ n_{pl}\), Im \(\xi\) \({}^ n_{pl}\)
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Let \(E_ n=(\xi_{pl})^ n_{p,l=1}\) denote random complex (n\(\times n)\)-matrices. Random vectors \((\xi^ n_{pl},\xi^ n_{lp})\), \(p\geq l\), \(p,l=\overline{s,n}\) are independent, \(M\xi^ n_{pl}=0\), \(M| \xi^ n_{pl}|^ 2=n^{-1}\), \(M\xi^ n_{pl}\xi^ n_{lp}=n^{-1}\rho\), \(l\neq p\), random variables Re \(\xi\) \({}^ n_{pl}\), Im \(\xi\) \({}^ n_{pl}\)
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Mathematische Nachrichten, 1999
AbstractIf G is the structure group of a manifold M it is shown how a certain ideal in the character ring of G corresponds to the set of geometric elliptic operators on M. This provides a simple method to construct these operators. For classical structure groups like G = O(n) (Riemannian manifolds), G = SO(n) (oriented Riemannian manifolds), G = U(m ...
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AbstractIf G is the structure group of a manifold M it is shown how a certain ideal in the character ring of G corresponds to the set of geometric elliptic operators on M. This provides a simple method to construct these operators. For classical structure groups like G = O(n) (Riemannian manifolds), G = SO(n) (oriented Riemannian manifolds), G = U(m ...
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