Classification of rotational special Weingarten surfaces of minimal type in {\mathbb{S}^2 \times \mathbb{R}} and {\mathbb{H}^2 \times \mathbb{R}}

In this paper we classify the complete rotational special Weingarten surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ ; i.e. rotational surfaces in ${\mathbb{S}^2 \times \mathbb{R}}$ and ${\mathbb{H}^2 \times \mathbb{R}}$ whose mean curvature H and extrinsic curvature K _e satisfy H = f(H ² ? K _e ), for some function ${f \in \mathcal{C}^1([0,+\infty))}$ such that f(0) = 0 and 4x(f′(x))² < 1 for any x ≥ 0. Furthermore we show the existence of non-complete examples of such surfaces.     

Incremental displacement-correction schemes for incompressible fluid-structure interaction

In this paper we introduce a class of incremental displacement-correction schemes for the explicit coupling of a thin-structure with an incompressible fluid. These methods enforce a specific Robin–Neumann explicit treatment of the interface coupling. We provide a general stability and convergence analysis that covers both the incremental and the non-incremental variants. Their stability properties are independent of the added-mass effect. The superior accuracy of the incremental schemes (with respect to the original non-incremental variant) is highlighted by the error estimates, and then confirmed in a benchmark by numerical experiments.     

Infinitesimal Carleson Property for Weighted Measures Induced by Analytic Self-Maps of the Unit Disk

We prove that, for every $\alpha > -1$ , the pull-back measure $\varphi ({\mathcal A }_\alpha )$ of the measure $d{\mathcal A }_\alpha (z) = (\alpha + 1) (1 - |z|^2)^\alpha \, d{\mathcal A } (z)$ , where ${\mathcal A }$ is the normalized area measure on the unit disk $\mathbb D $ , by every analytic self-map $\varphi :\mathbb D \rightarrow \mathbb D $ is not only an $(\alpha \,{+}\, 2)$ -Carleson measure, but that the measure of the Carleson windows of size $\varepsilon h$ is controlled by $\varepsilon ^{\alpha + 2}$ times the measure of the corresponding window of size $h$ . This means that the property of being an $(\alpha + 2)$ -Carleson measure is true at all infinitesimal scales. We give an application by characterizing the compactness of composition operators on weighted Bergman–Orlicz spaces.     

Characterization of UMD Banach Spaces by Imaginary Powers of Hermite and Laguerre Operators

In this paper we characterize the Banach spaces with the UMD property by means of L ^p -boundedness properties for the imaginary powers of the Hermite and Laguerre operators. In order to do this we need to obtain pointwise representations for the Laplace transform type multipliers associated with Hermite and Laguerre operators.     

Some New Hermite–Hadamard and Related Inequalities for Convex Functions via (p,q)-Integral

In this investigation, for convex functions, some new (p,q)–Hermite–Hadamard-type inequalities using the notions of (p,q)π2 derivative and (p,q)π2 integral are obtained. Furthermore, for (p,q)π2-differentiable convex functions, some new (p,q) estimates for midpoint and trapezoidal-type inequalities using the notions of (p,q)π2 integral are offered. It is also shown that the newly proved results for p=1 and q→1− can be converted into some existing results. Finally, we discuss how the special means can be used to address newly discovered inequalities.     

Gromov hyperbolicity of planar graphs

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ?² with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ?² such that every tile is a triangle and a partial answer to this question is given. A weaker version of this conjecture stating that every tessellation graph of ?² with rectangular tiles is non-hyperbolic is given and partially answered. If this conjecture were true, many tessellation graphs of ?² with tiles which are parallelograms would be non-hyperbolic.     

Characterization of Banach valued BMO functions and UMD Banach spaces by using Bessel convolutions

In this paper we consider the space ${{{BMO}_o(\mathbb{R}, X)}}$ of bounded mean oscillations and odd functions on ${{\mathbb{R}}}$ taking values in a UMD Banach space X. The functions in ${{{BMO}_o(\mathbb{R}, X)}}$ are characterized by Carleson type conditions involving Bessel convolutions and γ-radonifying norms. Also we prove that the UMD Banach spaces are the unique Banach spaces for which certain γ-radonifying Carleson inequalities for Bessel–Poisson integrals of ${{{BMO}_o(\mathbb{R}, X)}}$ functions hold.     

Quaternion solution for the rock’n’roller: Box orbits, loop orbits and recession

We consider two types of trajectories found in a wide range of mechanical systems, viz. box orbits and loop orbits. We elucidate the dynamics of these orbits in the simple context of a perturbed harmonic oscillator in two dimensions. We then examine the small-amplitude motion of a rigid body, the rock’n’roller, a sphere with eccentric distribution of mass. The equations of motion are expressed in quaternionic form and a complete analytical solution is obtained. Both types of orbit, boxes and loops, are found, the particular form depending on the initial conditions. We interpret the motion in terms of epi-elliptic orbits. The phenomenon of recession, or reversal of precession, is associated with box orbits. The small-amplitude solutions for the symmetric case, or Routh sphere, are expressed explicitly in terms of epicycles; there is no recession in this case.     

Vibrational resonance in a time-delayed genetic toggle switch

Biological oscillators can respond in a surprising way when they are perturbed by two external periodic forcing signals of very different frequencies. The response of the system to a low-frequency signal can be enhanced or depressed when a high-frequency signal is acting. This is what is known as vibrational resonance (VR). Here we study this phenomenon in a simple time-delayed genetic toggle switch, which is a synthetic gene-regulatory network. We have found out how the low-frequency signal changes the range of the response, while the high-frequency signal influences the amplitude at which the resonance occurs. The delay of the toggle switch has also a strong effect on the resonance since it can also induce autonomous oscillations.