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Constructive Proof of Global Lyapunov Function as Potential Function
Constructive Proof Global Lyapunov Function Potential Function
2011/3/2
We provide a constructive proof on the equivalence of two fundamental concepts: the global
Lyapunov function in engineering and the potential function in physics, establishing a bridge be-tween these...
On a proof of the Labastida-Marino-Ooguri-Vafa conjecture
proof Labastida-Marino-Ooguri-Vafa conjecture
2011/1/21
We outline a proof of a remarkable conjecture of Labastida-Mari˜no-Ooguri-Vafa about certain new algebraic structures of quantum link invariants and the integrality of infinite family of new topo...
A standard Hilbert-space proof of Dirichlet’s principle is simplified, using an observation that a certain form of min-problem has unique solution, at a specified point. This solves Dirichlet’s proble...
A proof of the continuous Dyson-Maleev representation
proof continuous Dyson-Maleev representation
2011/2/24
Recently Ivanov and Skvortsov introduced continuous Dyson-Maleev (DM) representations of supersymmetric non-linear sigma models and motivated that these representations are non-perturbatively exact. B...
A simple proof of a generalization of the Chu-Vandermonde identity
simple proof generalization Chu-Vandermonde identity
2011/1/18
We provide a simple proof of a generalization of the multivariate Chu-Vandermonde identity recently derived in Favaro et al. (2010a). Exploiting known results for rising factorials and fourth Lauricel...
Reduced Gröbner Bases of Certain Toric Varieties; A New Short Proof
Reduced Grö bner Bases Certain Toric Varieties New Short Proof
2010/11/30
Let K be a field and let m0, ...,mn be an almost arithmetic sequence of positive integers. Let C be a toric variety in the affine (n + 1)-space,defined parametrically by x0 = tm0 , . . . , xn = tmn. I...
A simple proof of the isoperimetric theorem for the hyperbolic plane
isoperimetric theorem hyperbolic plane
2010/11/30
В этой методической заметке приводятся четкая формулировка и короткое доказа-тельство основного результата работы [A] (см. ниже), а также проясняется его связь с изопериметрической теоремой для плоско...
A proof of Wahl's conjecture in the symplectic case
proof of Wahl's conjecture symplectic case
2010/11/29
Let X denote a flag variety of type A or type C. We construct a canonical Frobenius splitting of X ×X which vanishes with maximal multiplicty along the diagonal. This way we verify a conjecture by Lak...
Let S be a complex smooth projective surface and L be a line bundle on S. G¨ottsche conjectured that for every integer r, the number of r-nodal curves in |L is a universal polynomial of four topologic...