Related papers: Oscillation Revisited

We investigate properties of ($\alpha,\beta$)-harmonic functions. First, we discuss the coefficient estimates for ($\alpha,\beta$)-harmonic functions. In particular, we obtain Heinz's inequality for ($\alpha,\beta$)-harmonic functions,…

Under certain conditions on an integrable function f having a real-valued Fourier transform Tf=F, we obtain a certain estimate for the oscillation of F in the interval [-C||f'||/||f||,C||f'||/||f||] with C>0 an absolute constant. Given q>0…

We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $\Omega \subseteq \mathbb{R}^n$. Specifically, we show that if…

We report on the possibilities of using the method of normal fundamental systems for solving some problems of oscillation theory. Large elastic dynamical systems with continuous and discrete parameters are considered, which have many…

Let $k$ be a perfect complete valued field with a nontrivial non-archimedean norm $|\cdot|$ and $\omega\in k$ with $0<|\omega|<1.$ Let $X$ be a reduced and normal $k$-analytic space. Then $O^{\circ}\simeq…

Motion of a point mass in gravitational fields of the Sun and of the galactic disk is studied. Fundamental features of the motion are found by investigating the time-averaged differential equations for orbital evolution. Several types of…

We generalize some classical results about quasicontinuous and separately continuous functions with values in metrizable spaces to functions with values in certain generalized metric spaces, called Maslyuchenko spaces. We establish…

We investigate the continuous function $f$ defined by $$x\mapsto \sum_{\sigma\le_L x }2^{-K(\sigma)}$$ as a variant of Chaitin's Omega from the perspective of analysis, computability, and algorithmic randomness. Among other results, we…

Let $\Omega$ be a metric space, $A^t$ denote the metric neighborhood of the set $A\subset\Omega$ of the radius $t$; ${\mathfrak O}$ be the lattice of open sets in $\Omega$ with the partial order $\subseteq$ and the order convergence. The…

Suppose that $f$ belongs to a suitably defined complete metric space $ {{\cal C}}^{{\alpha}}$ of H\"older $ {\alpha}$-functions defined on $[0,1]$. We are interested in whether one can find large (in the sense of Hausdorff, or lower/upper…

We give some further criteria for continuity or discontinuity of the Lempert funtion of the spectral ball $\Omega_n$, with respect to one or both of its arguments, in terms of cyclicity the matrices involved.

In the present study we highlight some results related to the oscillation for high order nonlinear generalized neutral difference equation in the following form \begin{equation*}…

We establish limit theorems for the fluctuations of the rescaled occupation time of a $(d,\alpha,\beta)$-branching particle system. It consists of particles moving according to a symmetric $\alpha$-stable motion in $\mathbb{R}^d$. The…

In this paper it is shown that if $\Omega \subset \mathbb{R}^N$ is an open, bounded Lipschitz set, and if $f: \Omega \times \mathbb{R}^{d \times N \times N} \rightarrow [0, \infty)$ is a continuous function with $f(x, \cdot)$ of linear…

We derive consistent equations for gravitational wave oscillations in bigravity. In this framework a second dynamical tensor field is introduced in addition to General Relativity and coupled such that one massless and one massive linear…

The shift map $\sigma$ on $\omega^*$ is the continuous self-map of $\omega^*$ induced by the function $n \mapsto n+1$ on $\omega$. Given a compact Hausdorff space $X$ and a continuous function $f: X \rightarrow X$, we say that $(X,f)$ is a…

In this paper the Bagley-Torvik Equation is considered with the order of the damping term allowed to range between one and two. The solution is found to be representable as a convolution of trigonometric and exponential functions with the…

Let $f$ be an exact area-preserving monotone twist diffeomorphism of the infinite cylinder and $P_{\omega,f}(\xi)$ be the associated Peierls barrier. In this paper, we give the H\"{o}lder regularity of $P_{\omega,f}(\xi)$ with respect to…

Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…

The work reported here originates in the discovery, four decades ago, of a previously unknown type of self-organizing interaction among oscillating systems -- so-called argumental interactions -- and of "quantized" modes of behavior in…