We prove some inequalities related to the concepts of C1(st) -conservative matrices, C1(st) lim sup and C1(st) lim inf which are natural analogues of (c, st ∩ l∞) -matrices, st lim sup and st lim inf respectively.

Several theorems, inspired by the Krasovskii-LaSalle invariance principle, to establish “lim inf” convergence results are presented in a unified framework. These properties are useful to “describe” the oscillatory behavior of the solutions of dynamical systems. The theorems resemble “lim inf” Matrosov and Smallgain theorems and are based on a “lim inf” Barbalat’s Lemma. Additional technical ass...

lim-7 is one of seven Caenorhabditis elegans LIM-homeodomain (LIM-HD)-encoding genes and the sole Islet ortholog. LIM-HD transcription factors, including Islets, function in neuronal and non-neuronal development across diverse phyla. Our results show that a lim-7 deletion allele causes early larval lethality with terminal phenotypes including uncoordination, detached pharynx, constipation and m...

The LIM/homeodomain transcription factor Lim-1 has been shown to play an essential role in early embryonic patterning during vertebrate development. Here we report the spatial and temporal expression patterns of Lim-1 during retinal development as detected by immunohistochemistry using a specific anti-Lim-1 antibody. By double-immunostaining, we have demonstrated for the first time that Lim-1 i...

We describe here the functional analysis of the C. elegans LIM homeobox gene lim-6, the ortholog of the mammalian Lmx-1a and b genes that regulate limb, CNS, kidney and eye development. lim-6 is expressed in a small number of sensory-, inter- and motorneurons, in epithelial cells of the uterus and in the excretory system. Loss of lim-6 function affects late events in the differentiation of two ...

The simultaneous flow of immiscible fluids in porous media occurs in a wide variety of applications. The equations governing these flows are inherently nonlinear, and the geometries and material properties characterizing many problems in petroleum and groundwater engineering can be quite irregular. As a result, numerical simulation often offers the only viable approach to the mathematical model...

The Mumford-Shah model has been one of the most powerful models in image segmentation and denoising. The optimization of the multiphase Mumford-Shah energy functional has been performed using level sets methods that optimize the Mumford-Shah energy by evolving the level sets via the gradient descent. These methods are very slow and prone to getting stuck in local optima due to the use of the gr...

This paper provides a full numerical tool set for modeling and predicting an effective apparent dielectric constant of multiphase microporous media, which includes a multiparameter random generation-growth algorithm for generating microstructures of multiphase porous media and a lattice Boltzmann solver for the electric potential transport equations through porous structures. After being valida...

We are concerned with robust and accurate forecasting of multiphase flow rates in wells and pipelines during oil and gas production. In practice, the possibility to physically measure the rates is often limited; besides, it is desirable to estimate future values of multiphase rates based on the previous behavior of the system. In this work, we demonstrate that a Long Short-Term Memory (LSTM) re...

Cavitation is an intricate multiphase phenomenon that interplays with turbulence in fluid flows. It exhibits clear duality in characteristics, being both destructive and beneficial in our daily lives and industrial processes. Despite the multitude of occurrences of this phenomenon, highly dynamic and multiphase cavitating flows have not been fundamentally well understood in guiding the effort t...