Normal forms for a class of formulas

Orbital Normal Forms for a family of-zero Singularity

Consider a Dynamical system x'=F(x,µ) such that its linear part has a pair of imaginary eigenvalues and one zero eigenvalue (Hopf zero singularity). Recently, the simplest normal form for this singular system has been obtained by sl(2) Lie algebra theory and the decomposition of space into three invariant subspaces. The normal form of this singular system is divided into three general cases. In...

Exact Formulas for Coefficients of Jacobi Forms

In previous work, we introduced harmonic Maass-Jacobi forms. The space of such forms includes the classical Jacobi forms and certain Maass-Jacobi-Poincaré series, as well as Zwegers’ real-analytic Jacobi forms, which play an important role in the study of mock theta functions and related objects. Harmonic Maass-Jacobi forms decompose naturally into holomorphic and non-holomorphic parts. In this...

Asymptotic formulas for partial sums of class numbers of indefinite binary quadratic forms

Sarnak obtained the asymptotic formula of the sum of the class numbers of indefinite binary quadratic forms from the prime geodesic theorem for the modular group. In the present paper, we show several asymptotic formulas of partial sums of the class numbers by using the prime geodesic theorems for the congruence subgroups of the modular group.

Efficacy of commercial formulas in comparison with home-made formulas for enteral feeding: A critical review

Background: In several disease conditions, patients must inevitably be nourished by enteral feeding (EF). Though in many countries, commercial formulas are routinely used for EF, in Iran still home-made formulas are commonly employed as commercial formulas are not covered by insurance. This may pose patients to malnutrition and bring about further costs.  The aim of this study was to evalu...

Smooth and Analytic Normal Forms: A Special Class of Strict Feedforward Forms