The most popular algorithms for Nonnegative Matrix Factorization (NMF) belong to a class of multiplicative Lee-Seung algorithms which have usually relative low complexity but are characterized by slow-convergence and the risk of getting stuck to in local minima. In this paper, we present and compare the performance of additive algorithms based on three different variations of a projected gradie...

Sell’s approach [32] to the construction of attractors for the Navier– Stokes equations in 3-dimensions is extended to the 3-D stochastic equations with a general multiplicative noise.

In this paper, the linear quadratic regulation problem for discrete-time systems with state delays and multiplicative noise is considered. The necessary and sufficient condition for the problem admitting a unique solution is given. Under this condition, the optimal feedback control and the optimal cost are presented via a set of coupled difference equations. Our approach is based on the maximum...

abstract soil contamination by heavy metals is yet one of the most important environmental concerns. among heavy metals, nickel and cadmium have dangerous influences on human, animals and plants. the objective of this study was to derive a new model for simultaneous phytoextraction of ni and cd from contaminated soils. consequently, a macroscopic model was derived by combining yield reduction f...

Multiplicative noise, also known as speckle noise, is signal dependent and difficult to remove. Based on a fourth-order PDE model, this paper proposes a novel approach to remove the multiplicative noise on images. In practice, Fourier transform and logarithm strategy are utilized on the noisy image to convert the convolutional noise into additive noise, so that the noise can be removed by using...

Various scholars have lately employed a wide range of strategies to resolve specific types symmetrical fractional differential equations. In this paper, we propose new identity for multiplicatively differentiable functions; based on identity, establish some multiplicative Bullen-type inequalities convex functions. Some applications the obtained results are given.

Strongly multiplicative linear secret sharing schemes (LSSS) have been a powerful tool for constructing secure multi-party computation protocols. However, it remains open whether or not there exist efficient constructions of strongly multiplicative LSSS from general LSSS. In this paper, we propose the new concept of a 3-multiplicative LSSS, and establish its relationship with strongly multiplic...

We propose a simple approach, the multiplicative background correction, to solve a perplexing problem in spotted microarray data analysis: correcting the foreground intensities for the background noise, especially for spots with genes that are weakly expressed or not at all. The conventional approach, the additive background correction, directly subtracts the background intensities from foregro...