In this paper, we prove some analogues of Payne-Polya-Weinberger, HileProtter and Yang’s inequalities for Dirichlet (discrete) Laplace eigenvalues on any subset in the integer lattice Z. This partially answers a question posed by Chung and Oden [CO00].

We examine a number of generalized and extended versions of concentration inequalities and martingale inequalities. These inequalities are effective for analyzing processes with quite general conditions as illustrated in an example for an infinite Polya process and webgraphs.

Actin is a major cytoskeletal protein in eukaryotes. Recent studies suggest more diverse functional roles for this protein. Actin mRNA is known to be localized to neuronal synapses and undergoes rapid deadenylation during early developmental stages. However, its 3’-untranslated region (UTR) is not characterized and there are no experimentally determined polyadenylation (polyA) sites in actin mR...

The polyA tails of mRNAs are monitored by the exosome as a quality control mechanism. We find that fission yeast, Schizosaccharomyces pombe, adopts this RNA quality control mechanism to regulate a group of 30 or more meiotic genes at the level of both splicing and RNA turnover. In vegetative cells the RNA binding protein Mmi1 binds to the primary transcripts of these genes. We find the novel mo...

All ribosome profiling experiments analyzed involve attaching a known sequence to the 3′ end of RNA footprints to which a reverse transcription primer can be annealed. Some experiments use polyA tailing for this purpose, while others attach an oligonucleotide linker sequence. For experiments using polyA tailing, reads were trimmed from the end back to the first base that wasn’t an A or an N. Fo...

Polynucleotides are anionic macromolecules which are expected to transfer into the targeted cells through specific uptake mechanisms. So, we developed polynucleotides coating complexes of plasmid DNA (pDNA) and polyethylenimine (PEI) for a secure and efficient gene delivery system and evaluated their usefulness. Polyadenylic acid (polyA), polyuridylic acid (polyU), polycytidylic acid (polyC), a...

Motivated by recent studies of big samples, this work aims at constructing a parametric model which is characterized the following features: (i) "local" reinforcement, i.e. reinforcement mechanism mainly based on last observations, (ii) random persistent fluctuation predictive mean, and (iii) long-term convergence empirical mean to deterministic limit, together with chi-squared goodness fit res...