Classification of nonoscillatory solutions of higher order neutral type difference equations

summary:The authors consider the difference equation $$\Delta ^{m} [y_{n} - p_{n} y_{n - k}] + \delta q_{n} y_{\sigma (n + m - 1)} = 0 \qquad \mathrm {(\ast )}$$ where $m \ge 2$, $\delta = \pm 1$, $k \in N_0 = \lbrace 0,1, 2, \dots \rbrace$, $\Delta y_{n} = y_{n + 1} - y_{n}$, $q_{n} > 0$, and $\lbrace \sigma (n)\rbrace$ is a sequence of integers with $\sigma (n) \le n$ and $\lim _{n \rightarrow \infty } \sigma (n) = \infty$. They obtain results on the classification of the set of nonoscillatory solutions of ($\ast$) and use a fixed point method to show the existence of solutions having certain types of asymptotic behavior. Examples illustrating the results are included

Human EHMT2/G9a activates p53 through methylation-independent mechanism

p53 is a critical tumor suppressor in humans. It functions mostly as a transcriptional factor and its activity is regulated by numerous post-translational modifications. Among different covalent modifications found on p53 the most controversial one is lysine methylation. We found that human G9a (hG9a) unlike its mouse orthologue (mG9a) potently stimulated p53 transcriptional activity. Both ectopic and endogenous hG9a augmented p53-dependent transcription of pro-apoptotic genes, including Bax and Puma, resulting in enhanced apoptosis and reduced colony formation. Significantly, shRNA-mediated knockdown of hG9a attenuated p53-dependent activation of Puma. On the molecular level, hG9a interacted with histone acetyltransferase, p300/CBP, resulting in increased histone acetylation at the promoter of Puma. The bioinformatics data substantiated our findings showing that positive correlation between G9a and p53 expression is associated with better survival of lung cancer patients. Collectively, this study demonstrates that depending on the cellular and organismal context, orthologous proteins may exert both overlapping and opposing functions. Furthermore, this finding has important ramifications on the use of G9a inhibitors in combination with genotoxic drugs to treat p53-positive tumors.Oncogene advance online publication, 25 July 2016; doi:10.1038/onc.2016.258

Existence of nonoscillatory solutions of a class of nonlinear difference equations with a forced term

summary:In this paper, necessary and sufficient conditions for the existence of nonoscillatory solutions of the forced nonlinear difference equation $$\Delta (x_{n}-p_{n} x_{\tau (n)})+f(n,x_{\sigma (n)})=q_{n}$$ are obtained. Examples are included to illustrate the results

Influence of Salinity Stress on Growth Parameters and Yield of Sugarcane

. Under salinity condition, the reduction in yield was less in C 92038 and Co 85004 (29.81 and 28.00 %) and it was found to be maximum in Co 85036 and Si 94050 (47.82 and 47.36 %

Oscillation of nonlinear third order perturbed functional difference equations

This paper deals with oscillatory and asymptotic behavior of all solutions of perturbed nonlinear third order functional difference equatio