We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. ...

In this paper, we shall introduce $h$-expansiveness and asymptotical $h$-expansiveness for actions of sofic groups. By the definitions, each h-expansive action of sofic groups is asymptotically $h$-expansive. We show that ...

One of the most fruitful results from Minkowski’s geometric viewpoint on number theory is his so called 1st Fundamental Theorem. It provides an optimal upper bound for the volume of an o-symmetric convex body whose only ...

We prove the existence of periodic solutions of the differential delay equation $\varepsilon\dot{x}(t) + x(t)= f(x(t-1)), \varepsilon>0$ under the assumptions that the continuous nonlinearity $f(x)$ satisfies the negative ...

Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation $x'(t) = a(t)f(x([t-K]))$, where $f(x)$ is a continuous negative feedback function, $x \cdot ...

Given partitions $\alpha, \beta, \gamma$, the short exact sequences $0 \rightarrow N_\alpha \rightarrow N_\beta \rightarrow N_\gamma \rightarrow 0$ of nilpotent linear operators of Jordan types $\alpha, \beta, \gamma$, ...

This paper analyzes finite dimensional linear time-invariant systems with observation of a delay, where that delay satisfies a particular implicit relation with the state variables, rendering the entire problem nonlinear. ...

This work concerns random dynamics of hyperbolic entire and meromorphic functions of finite order and whose derivative satisfies some growth condition at infinity. This class contains most of the classical families of ...

We study generalized Killing spinors on the standard sphere $\mathbb{S}^3$, which turn out to be related to Lagrangian embeddings in the nearly Kähler manifold $S^3 \times S^3$ and to great circle flows on $\mathbb{S}^3$. ...