This paper is mainly concerned with whether the almost sure exponential stability of stochastic differential equations (SDEs) is shared with that of a numerical method. Under the global Lipschitz condition, we first show that the SDE is pth moment exponentially stable (for p ∈ (0, 1)) if and only if the stochastic theta method is pth moment exponentially stable for a sufficiently small step siz...

In this note, we introduce the notion of almost unramified representations quasi-split unitary groups even ranks with respect to an quadratic extension local fields, and study their behavior under theta correspondence. These are in some sense least ramified that have root number −1.

In this work, we derive a goal-oriented a posteriori error estimator for the error due to time discretization. As time discretization scheme we consider the fractional step theta method, that consists of three subsequent steps of the one-step theta method. In every sub-step, the full incompressible system has to be solved (in contrast to time integrators of operator splitting type). The resulti...

for any lacunary sequence $theta = (k_{r})$, we define the concepts of $s_{theta}-$limit point and $s_{theta}-$cluster point of a sequence of fuzzy numbers $x = (x_{k})$. we introduce the new sets  $lambda^{f}_{s_{theta}}(x)$, $gamma^{f}_{s_{theta}}(x)$ and prove some inclusion relaions between these and the sets $lambda^{f}_{s}(x)$, $gamma^{f}_{s}(x)$ introduced in ~cite{ayt:slpsfn} by aytar [...

The current applications of non-Hermitian but ${\cal PT}-$symmetric Hamiltonians $H$ cover several, mutually not too closely connected subdomains quantum physics. Mathematically, the split between open and closed systems can be characterized by respective triviality non-triviality an auxiliary inner-product metric $\Theta=\Theta(H)$. With our attention restricted to latter, mathematically more ...

We theoretically study the energy and optical absorption spectra of alternating twist multilayer graphene (ATMG) under a perpendicular electric field. obtain analytically low-energy effective Hamiltonian ATMG up to pentalayer in presence interlayer bias by means first-order degenerate-state perturbation theory, present general rules for constructing an arbitrary number layers. Our analytical re...

This study investigated tennis players' speed before, during and after the split-step, deceleration before and acceleration after the split-step in four different stroke groups in three age categories. Seven male professional, eleven male and ten female junior tennis players were recorded with video cameras at official tournaments. Using the SAGIT system, we gathered data on 8,545 split-steps. ...

We introduce a one-dimensional random walk, which at each step performs reinforced dynamics with probability $\theta$ and $1 - \theta$, the walk independent of past. analyse its asymptotic behaviour, showing law large numbers characterizing diffusive superdiffusive regions. prove central limit theorems iterated logarithm based on martingale approach.