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...

1Introduction: The generalized linear signal processing systems have been introduced and extensively studied by Oppenheim et al. [5] at the end of the 1960s. A generalized linear signal processing system consists of vector spaces for the input and output signal sets and a linear mapping, called the system transformation [5]. In their research, Oppenheim et al. have mainly focused on the impleme...

for fr$acute{mathbf{text{e}}}$chet algebras $(a, (p_n))$ and $(b, (q_n))$, a linear map $t:arightarrow b$ is textit{almost multiplicative} with respect to $(p_n)$ and $(q_n)$, if there exists $varepsilongeq 0$ such that $q_n(tab - ta tb)leq varepsilon p_n(a) p_n(b),$ for all $n in mathbb{n}$, $a, b in a$, and it is called textit{weakly almost multiplicative} with respect to $(p_n)$ and $(q_n)$,...

A simple one-dimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behavior observed along the transition line changes from a directed-percolation type to a multiplicative-noise type. Numerical simulations allow for a quantitative study of the multicritical point separ...

In the current study, we investigate stochastic Benjamin–Bona–Mahony equation with beta derivative (SBBME-BD). The considered term is multiplicative noise in Itô sense. By combining F-expansion approach two separate equations, such as Riccati and elliptic new hyperbolic, trigonometric, rational, Jacobi solutions for SBBME-BD can be generated. to are useful understanding various scientific pheno...

We prove that a class of stochastic differential equations with multiplicative noise has a unique solution in a noncommutative L2 space associated with a von Neumann algebra. As examples we consider usual L2 on a measure space, Hilbert-Schmidt operators and a hyperfinite II1-factor. A problem of finding an inverse of the solution is then discussed. Finally, we explain how a stochastic different...

A novel feed forward multiplicative neural network architecture with optimum number of nodes is used for adaptive channel equalization in this paper.The replacement of summation at each node by multiplication results in more powerful mapping because of its capability of processing higher-order information from training data. Performance comparison with Chebyshev neural network show that the pro...

BACKGROUND The effect of urbanization on age-adjusted lung cancer mortality rates in US counties is investigated. The data come from National Cancer Institute, and urban trends are estimated in time periods 1970-1979 and 1980-1987, for both white males and white females. To account for possibly different gradients in different parts of the country, the 48 contiguous states are divided into seve...

Factored Edge-Valued Binary Decision Diagrams form an extension to Edge-Valued Binary Decision Diagrams. By associating both an additive and a multiplicative weight with the edges, FEVBDDs can be used to represent a wider range of functions concisely. As a result, the computational complexity for certain operations can be significantly reduced compared to EVBDDs. Additionally, the introduction ...

In this paper, at first the elemantary and basic concepts of multiplicative discrete and continous differentian and integration introduced. Then for these kinds of differentiation invariant functions the general solution of discrete and continous multiplicative differential equations will be given. Finaly a vast class of difference equations with variable coefficients and nonlinear difference e...