Root systems and elliptic curves
Inventiones Mathematicae, 1976 The Macdonald-Weyl formula \[ \prod_{w\in W_{\text{aff}}} \det(w)e^{2\pi is(w)(z)\tau}=C \prod_{a\in R^{+}_{\text{aff}}}(1-e^{2\pi ia(z)\tau}) \tag{*} \] where \(C = \prod\limits_{n=1}^\infty (1-e^{2\pi in \tau})\) is reproved here [cf. \textit{I. G. Macdonald}, Invent. Math. 15, 91--143 (1972; Zbl 0244.17005) and also \textit{M.
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Advanced Functional Materials, EarlyView.This study demonstrates a molecular strategy to enhance the stretchability of conjugated polymers by incorporating plasticizing molecular additives (PMAs). PMAs reduce the persistence length and promote chain entanglement, enabling deformable thin films with preserved electrical performance. A systematic analysis combining rheology, neutron scattering,
Sein Chung +11 more
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On Elliptic and Hyper-Elliptic Systems of Differential Equations and their Rational and Integral Algebraic Integrals, with a Discussion of the Periodicity of Elliptic and Hyper-Elliptic Functions [PDF]
, 1894 W. R. Westropp Roberts
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2D Borophene: In‐Plane Hyperbolic Polaritons in the Visible Spectral Range
Advanced Functional Materials, EarlyView.Researchers have synthesized the χ3 phase of borophene, a 2D metal, using chemical vapor deposition. Combining theory and deep‐subwavelength spectroscopy, they uncover borophene's unique anisotropic optical behavior in the visible range. This breakthrough paves the way for advanced optoelectronic devices using borophene‐based heterostructures ...
Yaser Abdi +5 more
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Maximum principle and existence results for elliptic systems on R^N
Electronic Journal of Differential Equations, 2010 In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on the whole $mathbb{R}^{N}$. This principle is then used to yield solvability for the cooperative
Liamidi Leadi, Aboubacar Marcos
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A note on the variational structure of an elliptic system involving critical Sobolev exponent
Journal of Applied Mathematics, 2003 We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by Fleckinger et al.
Mario Zuluaga
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On the System of a Binary Cubic and Quadratic and the Reduction of Hyperelliptic Integrals of Genus Two to Elliptic Integrals by a Transformation of the Fourth Order [PDF]
, 1901 J. H. McDonald
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Advanced Functional Materials, EarlyView.A thermoplastic elastomeric glue electrolyte featuring a strongly segregated PVA‐g‐PTFP bottlebrush copolymer exhibits a nanoscale domain architecture, dual‐ion transport pathways, and universal strong interfacial adhesion. The system delivers high ionic conductivity, wide electrochemical stability, and mechanical robustness, offering a versatile ...
Hyuk Jin Roh +4 more
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Maximum principle and existence results for nonlinear cooperative systems on a bounded domain
Electronic Journal of Differential Equations, 2011 In this work we give necessary and sufficient conditions for having a maximum principle for cooperative elliptic systems involving p-Laplacian operator on a bounded domain.
Liamidi Leadi, Aboubacar Marcos
doaj
Unique continuation theorem of elliptic systems of partial differential equations [PDF]
, 1962 Kazunari Hayashida
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