We give two new characterizations of the notion Lyapunov regularity in terms lower and upper exponential growth rates singular values. These motivate introduction coefficients. In particular, we establish relations between these coefficients coefficient. Moreover, construct explicitly bounded sequences matrices attaining specific values

The irreducible ∗-representations of the Lie algebra su(1, 1) consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explici...

Recently presented explicit formulae for asymptotic expansions of Feynman diagrams in the Sudakov limit [1] are applied to typical two-loop diagrams. For a diagram with one non-zero mass these formulae provide an algorithm for analytical calculation of all powers and logarithms, i.e. coefficients in the corresponding expansion (Q) ∑ n,j=0 cnjt −n ln t, with t = Q/m and j ≤ 4. Results for the co...

The angular bispectrum of spherical random fields has recently gained an enormous importance, especially in connection with statistical inference on cosmological data. In this paper, we provide expressions for its moments of arbitrary order and we use these results to establish a multivariate central limit theorem and higher order approximations. The results rely upon combinatorial methods from...

We show that Kauffman brackets of colored framed graphs (also known as quantum spin networks) can be renormalized to a Laurent polynomial with integer coefficients by multiplying it by a coefficient which is a product of quantum factorials depending only on the abstract combinatorial structure of the graph. Then we compare the shadow-state sums and the state-sums based on R-matrices and Clebsch...

has the conditional distribution G(xjy) (unknown). We investigate the behavior of the extrema of sample functions of the form (x; G nk (xjy)), where G nk (xjy) is the k nearest neighbor (k-NN) estimator of G(xjy). Specii-cally, we rst study the properties of a multiparameter process Wn = k 1=2 (G nk (xjy) ?G(xjy)), (x; y) 2 R + C, where C is a compact set in R q. Then under some regular conditi...