Related papers: Functions preserving slowly oscillating double seq…

In this paper, we consider a long-time behavior of stable-like processes. A stable-like process is a Feller process given by the symbol $p(x,\xi)=-i\beta(x)\xi+\gamma(x)|\xi|^{\alpha(x)},$ where $\alpha(x)\in(0,2)$, $\beta(x)\in\R$ and…

Let $U=\{U_{j,k},j,k\in \overline {\mathbb N}\}$ be the potential of a transient symmetric Borel right process $X$ with state space $\overline {\mathbb N}$. For any excessive function $f=\{f_{k,k\in \overline {\mathbb N}}\}$ for $X$ ,…

It is known that the M\"obius function in number theory is higher order oscillating. In this paper we show that there is another kind of higher order oscillating sequences in the form $(e^{2\pi i \alpha \beta^{n}g(\beta)})_{n\in \N}$, for a…

Large $N$ conformal field theories often admit unitary renormalization group flows triggered by double-trace deformations. We compute the change in scalar four-point functions under double-trace flow, to leading order in $1/N$. This has a…

Double $L$-functions are the generalization of Dirichlet $L$-functions to two variable functions. We investigate the order estimation of double $L$-functions, and give upper bounds which are explicit in conductor aspect.

In the continuous setting, we expect the product of two oscillating functions to oscillate even more (generically). On a graph $G=(V,E)$, there are only $|V|$ eigenvectors of the Laplacian $L=D-A$, so one oscillates `the most'. The purpose…

Suppose that $d\ge 1$ and $0<\beta<\alpha<2$. We establish the existence and uniqueness of the fundamental solution $q^b(t, x, y)$ to a class of (possibly nonsymmetric) non-local operators $L^b=\Delta^{\alpha/2}+S^b$, where $$ S^bf(x):=A(d,…

An explicit expression is obtained for the sectional curvature in the plane spanned by two stationary flows, cos(k, x) and cos(l, x). It is shown that for certain values of the wave vectors k and l the curvature becomes positive for alpha >…

Let $X=\{X_n: n\in\mathbb{N}\}$ be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an $\alpha$-stable law…

In this paper, we introduce and investigate a concept of Abel statistical continuity. A real valued function $f$ is Abel statistically continuous on a subset $E$ of $\R$, the set of real numbers, if it preserves Abel statistical convergent…

A function is called quasiperiodic if its fundamental frequencies are linearly independent over the rationals. With appropriate parameters, the sliding window point clouds of such functions can be shown to be dense in tori with dimension…

We find all factorized duality functions for a class of interacting particle systems. The functions we recover are self-duality functions for interacting particle systems such as zero-range processes, symmetric inclusion and exclusion…

In this paper we continue the work that we began in arXiv:1912.07537. Given $1<p<N$, two measurable functions $V\left(r \right)\geq 0$ and $K\left(r\right)> 0$, and a continuous function $A(r) >0\ (r>0)$, we consider the quasilinear…

Multiplicity fluctuations are studied both globaly (in terms of high-order moments) and locally (in terms of small phase-space intervals). The ratio of cumulant factorial to factorial moments of the charged-particle multiplicity…

We study the continuity properties of trajectories for some random series of functions $\sum a\_kf(\alpha X\_k(\omega))$ where $a\_k$ is a complex sequence, $X\_k$ a sequence of real independent random variables, $f$ is a real valued…

This paper discusses the frequency function of multiple-valued Dirichlet minimizing functions in the special case when the domain and range are both two dimensional. It shows that the frequency function must be of value k/2 for some…

It is shown generally that any oscillation probability in matter with approximately constant density coincides with that in vacuum to the first two nontrivial orders in $\Delta m^2_{jk}L/E$ if $|\Delta m^2_{jk}L/E|\ll 1$ and $|G_F N_e L|\ll…

A real valued function $f$ defined on a subset $E$ of $\textbf{R}$, the set of real numbers, is statistically upward continuous if it preserves statistically upward half quasi-Cauchy sequences, is statistically downward continuous if it…

In this paper we analyze the behavior of solutions of the Neumann problem posed in a thin domain of the type $R^\epsilon = \{(x_1,x_2) \in \R^2 \; | \; x_1 \in (0,1), \, - \, \epsilon \, b(x_1) < x_2 < \epsilon \, G(x_1,…

We study sustained oscillations in two-dimensional oscillator systems driven by Rayleigh-type negative friction. In particular we investigate the influence of mismatch of the two frequencies. Further we study the influence of external noise…