This paper classifies the even unimodular lattices that have a structure as a Hermitian OK-lattice of rank r ≤ 12 for rings of integers in imaginary quadratic number fields K of class number 1. The Hermitian theta series of such a lattice is a Hermitian modular form of weight r for the full modular group, therefore we call them theta lattices. For arbitrary imaginary quadratic fields we derive ...

The hydrostatic equilibrium is a prominent topic in fluid dynamics and astrophysics. Understanding the stability of perturbations near Boussinesq system helps gain insight into certain weather phenomena. 2D focused here anisotropic involves only horizontal dissipation thermal diffusion. Due to lack vertical dissipation, precise large-time behavior problem difficult. When spatial domain $${\math...

We show that for Lebesgue almost all $d$-tuples $(\theta\_1,\ldots,\theta\_d)$, with $|\theta\_j|>1$, any self-affine measure a homogeneous non-degenerate iterated function system ${Ax+a\_j}\_{j=1}^m$ in\~$\mathbb{R}^d$, where $A^{-1}$ is diagonal matrix the entries has power Fourier decay at infinity.

Motivated by the discovery that the eighth root of the theta series of the E8 lattice and the 24th root of the theta series of the Leech lattice both have integer coefficients, we investigate the question of when an arbitrary element f ∈ R (where R = 1 + xZ x ) can be written as f = gn for g ∈ R, n 2. Let Pn := {gn | g ∈R} and let μn := n∏p |n p. We show among other things that (i) for f ∈R, f ...

The weight $\theta$-sheaf $\underline{\mathbb{R}}_{X,\theta}$ helps us to reinterpret Morse-Novikov cohomologies via sheaf theory. We give several theorems of K\"{u}nneth and Leray-Hirsch types. As applications, we prove that the $\theta$-Lefschetz number is independent $\theta$ calculate projective bundles. Based on these results, two blow-up formulae (\emph{not necessarily compact}) complex m...


 Assume that \(f\) lies in the class of starlike functions order \(\alpha\in[0,1)\), is, which are regular and univalent for \(|z|<1\) such that
 Re\(\left(\frac{zf'(z)}{f(z)}\right)>\alpha\) \(|z|<1.\)
 In this paper we show each following sharp inequality holds:
 \(|f(re^{i\theta})|^{-1}\int_{0}^{r}|f'(ue^{i\theta})|\,du\leq\frac{\Gamma(\frac{1}{2})\Gamma(2-\alph...

We discuss the anomalous behavior of Faraday (transmission) and polar Kerr (reflection) rotation angles propagating light, in finite periodic parity-time ($\mathcal{P}\mathcal{T}$) symmetric structures, consisting $N$ cells. The unit cell potential is two complex $\delta$-potentials placed on both boundaries ordinary dielectric slab. It shown that, for a given set parameters describing system, ...

Let $(X, \omega)$ be a compact Kahler manifold of complex dimension n and $\theta$ smooth closed real $(1,1)$-form on $X$ such that its cohomology class $\{ \theta \}\in H^{1,1}(X, \mathbb{R})$ is pseudoeffective. $\varphi$ $\theta$-psh function, let $f$ continuous function with bounded distributional laplacian respect to $\omega$ $\varphi \leq f. $ Then the non-pluripolar measure $\theta_\va...