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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...
Nuclear and type I crossed products of C*-algebras by group and compact quantum group actions
Direct proofs Feigin-Fuchs character formula unitary representations Virasoro algebra
2011/3/1
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary
discrete series of the Virasoro algebra with 0 < c < 1. The proof showed directly that the mutliplicity sp...
Direct proofs of the Feigin-Fuchs character formula for unitary representations of the Virasoro algebra
Direct proofs of the Feigin-Fuchs character unitary representations Virasoro algebra
2011/3/1
Previously we gave a proof of the Feigin–Fuchs character formula for the irreducible unitary
discrete series of the Virasoro algebra with 0 < c < 1.
WZ-proofs of "divergent" Ramanujan-type series
Hypergeometric series WZ-method Ramanujan-type series for 1/ and 1/2 Barnes Integrals
2011/1/21
We prove some ”divergent” Ramanujan-type series for 1/ and 1/2 applying a Barnes-integrals strategy of the WZ-method.
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 counterexample to a Penrose inequality conjectured by Gibbons
counterexample Penrose inequality Gibbons
2011/3/3
We show that the Brill-Lindquist initial data provides a counterexample to a Riemannian Penrose inequality with charge conjectured by G. Gibbons. The observation illustrates a sub-additive characteris...
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...
On Kadell's two Conjectures for the $q$-Dyson Product
Dyson conjecture Dyson product Kadell’s conjecture constant term q-analog
2010/12/1
By extending Lv-Xin-Zhou’s first layer formulas of the q-Dyson product, we prove Kadell’s conjecture for the Dyson product and show the error of his q-analogous conjec-ture. With the extended formulas...
In this note, we describe motivic cell structures arising from the Bia lynicki-Birula decomposition. This provides a description of stable A1-homotopy types of smooth projective Gm-varieties where the...
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...
Discussion on Lechicki and Spakowski's counterexample
Lechicki Spakowski's counterexample
2010/11/29
It is well-known that intersection of continuous correspondences can lost the continuity
property. Lechicki and Spakowski’s theorem says that intersection of H-lsc functions remains
H-lsc if the int...
On Einstein metrics, normalized Ricci flow and smooth structures on $3\mathbb{CP}^2 # k \bar{\mathbb{CP}}^2$
Einstein metrics normalized Ricci flow and smooth structures
2010/11/30
Recent years have witnessed a drastic increase in our understanding of the topology and geometry of 4-manifolds and complex surfaces. The newest developments can be exemplified by the construction of ...
Versal Deformations and Versality in Central Extensions of Jacobi's Schemes
Versal Deformations Versality in Central Extensions of Jacobi's Schemes
2010/11/29
Let Lm be the scheme of the laws defined by the Jacobi’s iden-tities on Km with K a field. A deformation of g ∈ Lm, parametrized by a local K-algebra A, is a local K-algebra morphism from the local ri...