In this paper we study number fields which are Euclidean with respect to a function different from the absolute value of the norm. We also show that the Euclidean minimum with respect to weighted norms may be irrational and not isolated.

Let L be a time-periodic Tonelli Lagrangian on a closed manifold of dimension two. Then the β-function of L is differentiable in at least k directions at any k-irrational homology class. The same result holds when L is an autonomous mechanical Lagrangian with a C potential on a closed manifold of dimension three.

aim and background: infertility may cause various forms of emotional and psychosocial problems, especially among women. many studies have focused on the psychological problems, such as depression, anxiety, and marital adjustment, in infertile women. however, very little research has been published concerning women's perception of infertility. this study aimed to investigate the irrational perce...

Let {an}1 and {θn}0 be the sequences of partial quotients and approximation coefficients for the continued fraction expansion of an irrational number. We will provide a function f such that an+1 = f (θn±1,θn). In tandem with a formula due to Dajani and Kraaikamp, we will write θn±1 as a function of (θn∓1,θn), revealing an elegant symmetry in this classical sequence and allowing for its recovery...

The generalized Knizhnik-Zamolodchikov equations of irrational conformal field theory provide a uniform description of rational and irrational conformal field theory. Starting from the known high-level solution of these equations, we first construct the high-level conformal blocks and correlators of all the affine-Sugawara and coset constructions on simple g. Using intuition gained from these c...