Separated Transcriptomes of Male Gametophyte and Tapetum in Rice: Validity of a Laser Microdissection (LM) Microarray

In flowering plants, the male gametophyte, the pollen, develops in the anther. Complex patterns of gene expression in both the gametophytic and sporophytic tissues of the anther regulate this process. The gene expression profiles of the microspore/pollen and the sporophytic tapetum are of particular interest. In this study, a microarray technique combined with laser microdissection (44K LM-microarray) was developed and used to characterize separately the transcriptomes of the microspore/pollen and tapetum in rice. Expression profiles of 11 known tapetum specific-genes were consistent with previous reports. Based on their spatial and temporal expression patterns, 140 genes which had been previously defined as anther specific were further classified as male gametophyte specific (71 genes, 51%), tapetum-specific (seven genes, 5%) or expressed in both male gametophyte and tapetum (62 genes, 44%). These results indicate that the 44K LM-microarray is a reliable tool to analyze the gene expression profiles of two important cell types in the anther, the microspore/pollen and tapetum

Approximate identities and Young type inequalities in Musielak-Orlicz spaces

summary:We discuss the convergence of approximate identities in Musielak-Orlicz spaces extending the results given by Cruz-Uribe and Fiorenza (2007) and the authors F.-Y. Maeda, Y. Mizuta and T. Ohno (2010). As in these papers, we treat the case where the approximate identity is of potential type and the case where the approximate identity is defined by a function of compact support. We also give a Young type inequality for convolution with respect to the norm in Musielak-Orlicz spaces

Trudinger's inequality for double phase functionals with variable exponents

summary:Our aim in this paper is to establish Trudinger's inequality on Musielak-Orlicz-Morrey spaces $L^{\Phi ,\kappa }(G)$ under conditions on $\Phi$ which are essentially weaker than those considered in a former paper. As an application and example, we show Trudinger's inequality for double phase functionals $\Phi (x,t) = t^{p(x)} + a(x) t^{q(x)}$, where $p(\cdot )$ and $q(\cdot )$ satisfy log-Hölder conditions and $a(\cdot )$ is nonnegative, bounded and Hölder continuous