The debate on the properties and use of additive and multiplicative partitioning of species diversity exemplified in this forum reflects the broader challenge of quantifying and interpreting alpha, beta, and gamma diversity at multiple scales of sampling. As noted by Wilsey and Ricotta in their contributions, ecologists use a wide range of measures of beta diversity, partly because of differenc...

To analyze the stability of Itô stochastic differential equations with multiplicative noise, we introduce the stochastic logarithmic norm. The logarithmic norm was originally introduced by G. Dahlquist in 1958 as a tool to study the growth of solutions to ordinary differential equations and for estimating the error growth in discretization methods for their approximate solutions. We extend the ...

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy, and in the unpinned case also conserves the momentum. We obtain a time-inhomogeneous OrnsteinUhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit...

Following classical work by Freidlin [Trans. Amer. Math. Soc. (1988) 305 665–657] and subsequent works by Sowers [Ann. Probab. (1992) 20 504–537] and Peszat [Probab. Theory Related Fields (1994) 98 113–136], we prove large deviation estimates for the small noise limit of systems of stochastic reaction–diffusion equations with globally Lipschitz but unbounded diffusion coefficients, however, ass...

The characteristics of impulse bursts in remote sensing images are analyzed and a model for this noise is proposed. The model also takes into consideration other noise types, for example, the multiplicative noise present in radar images. As a case study, soft morphological filters utilizing a training-based optimization scheme are used for the noise removal. Different approaches for the trainin...

Let $\{x_{\alpha}\}_{\alpha \in \mathbb{Z}}$ and $\{y_{\alpha}\}_{\alpha be two independent collections of zero mean, unit variance random variables with uniformly bounded moments all orders. Consider a nonsymmetric Toeplitz matrix $X_n = ((x_{i - j}))_{1 \le i, j n}$ Hankel $Y_n ((y_{i + n}$, let $M_n X_n \odot Y_n$ their elementwise/Schur-Hadamard product. In this article, we show that almost...

‎In this work‎, ‎we investigate admitting center map on multiplicative metric space‎ ‎and establish some fixed point theorems for such maps‎. ‎We modify the Banach contraction principle and‎ ‎the Caristi's fixed point theorem for M-contraction admitting center maps and we prove some‎ ‎useful theorems‎. ‎Our results on multiplicative metric space improve and modify‎ ‎s...

In this paper we obtain an upper bound and also a lower bound for maximum edges of strongly 2 multiplicative graphs of order n. Also we prove that triangular ladder the graph obtained by duplication of an arbitrary edge by a new vertex in path and the graphobtained by duplicating all vertices by new edges in a path and some other graphs are strongly 2 multiplicative

We study the impact of applying stochastic forcing to Ghil-Sellers energy balance climate model in form a fluctuating solar irradiance. Through numerical simulations, we explore noise-induced transitions between competing warm and snowball states. consider multiplicative driven by Gaussian $\alpha$-stable L\'evy - $\alpha\in(0,2)$ noise laws, examine statistics transition times, estimate most p...