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G is the real points of a linear connected reductive group. - g0 := Lie(G),  Cartan involution, g0 = k0 + s0, g := (g0)C, K maximal compact subgroup, g = k + s, - P = MAN minimal parabolic subgrou...
The full unitary dual for the complex classical groups viewed as real Lie groups is computed in [B1]. This was close to 20 years ago. Since then there have been many advances, but the general proble...
1.1. Positive de nite functions. We start with the classical notion of positive de nite functions. De nition. A continuous function f : R 􀀀! C is called positive de nite if it satis es (1...
The course is a short introduction to some aspects of the simplest non-integrable three body problem, the study of which goes back to the seminal works of Hill, Poincar′e and Birkhoff. After Goursat (...
On the sums of two cubes      sums  two cubes        2011/2/28
We solve the equation f(x, y)3 + g(x, y)3 = x3 + y3 for homogeneous f, g ∈ C(x, y), completing an investigation begun by Vi`ete in 1591. The usual addition law for elliptic curves and composition give...
The generalized wreath product of permutation groups is intro-duced. By means of it we study the schurity problem for S-rings over a cyclic group G and the automorphism groups of them.
Noncommutative field theories are a class of theories beyond the standard model of elementary particle physics. Their importance may be summarized in two facts.Firstly as field theories on noncommutat...
In this paper, we give the expressions for the bounded spherical functions, or equivalently the spherical functions of positive type, for the free two-step nilpotent Lie groups endowed with the action...
Bernardi and Tirabassi show the existence of a full strong excep-tional collection consisting of line bundles on smooth toric Fano 3-folds under assuming Bondal’s conjecture, which states that the Fro...
Let (N, Φ) be a circular Ferrero pair. We define the disk with center b and radius a, D(a; b), as D(a; b) = {x ∈ Φ(r) +c | r 6= 0, b ∈ Φ(r) +c, |(Φ(r) +c) ∩ (Φ(a)+b)| = 1}.We prove that in the field-g...
In this paper, we obtain the counting formulaes of convex pentagons and convex hexagons, respectively, in an n-triangular net by solving the corresponding recursive formulaes.
We study the covariantly constant Savvidy-type chromomagnetic vacuum in finite-temperature Yang-Mills theory on the four-dimensional curved spacetime. Motivated by the fact that a positive spatial cu...
For an elliptic problem with two space dimensions, we propose to formulate the finite volume method with the help of Petrov-Galerkin mixed finite elementsthat are based on the building of a dual Ravia...
We study a class of fourth order curvature flows on a compact Riemannian manifold, which includes the gradient flows of a number of quadratic geometric functionals, as for instance the L2 norm of th...

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