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 ...

We study the problem of intergenerational equity for utility streams and a countable set of agents. A numerical social welfare function is invariant to ordinal transformation, satis…es a weak monotonicity condition, and an invariance with respect to concatenation of utility streams if and only if it is either the sup, inf, lim sup, or lim inf.

Let b k := (C 2 A)(M b;k), then lim k!1 a k = lim k!1 b k. The proof is complete. 2 From the preceding lemmas, we obtain the following theorem. As fhg ? ; M k(m) ig is a Cauchy sequence, hg ? ; M m;1 i 0 hg ? ; M k(m) i ! 0 (as m ! 1): We obtain that lim m!1 b m = lim m!1 a k(m). The proof is complete. 2 Lemma 23 We obtain Proof It suces to prove that for a Cauchy sequence fa k g F such that li...