The small-ball method was introduced as a way of obtaining high probability, isomorphic lower bound on the quadratic empirical process, under weak assumptions indexing class. key assumption that class members satisfy uniform small-b

The famous results of Gross and Zagier compare the heights of Heegner points on modular curves with special values of the derivatives of related L-functions. When specialized to the level 1 case (i.e., the full modular curve H/Γ, where Γ = SL2(Z)), we recover an astounding formula for the differences of singular moduli (the Heegner points on the full modular curve) in terms of an explicit prime...

In this paper, we propose a method for constructing spline surfaces interpolating B-spline curve network, allowing the presence of free parameters, in order to model surface. We provide constructive algorithm its generation case biquadratic tensor product and bivariate on criss-cross triangulations. Finally, present graphical results.

Let B be a quaternion algebra over number field K : Assume that B satisfies the Eichler condition (i.e., there is at least one archimedean place which is unramified in B). Let O be an order in a quadratic extension L of K: The Eichler orders of B which admit an embedding of O are determined. This is a generalization of Chinburg and Friedman’s embedding theorem for maximal orders. r 2004 Elsevie...

Constructing a fast and efficient estimator for the B-mode power spectrum of cosmic microwave background (CMB) is critical importance CMB science. For general survey, Quadratic Maximum Likelihood (QML) polarization has been proved to be optimal with minimal uncertainties, but it computationally very expensive. In this article, we propose two new QML methods estimation. We use Smith–Zaldarriaga ...