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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...
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...
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.
We prove some ”divergent” Ramanujan-type series for 1/ and 1/2 applying a Barnes-integrals strategy of the WZ-method.
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...
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...
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...
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...
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...
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...
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...
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 ...
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...

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