The adsorption and growth of Cu n clusters on highly reducible CeO 2 (110).

Let $p$ be an odd prime and $q$ a power of $p$. We examine the deformation theory reducible indecomposable Galois representations $\bar{\rho}:G_{\mathbb{Q}}\rightarrow \text{GSp}_{2n}(\mathbb{F}_q)$ that are unramified outside finite set primes $S$ whose image lies in Borel subgroup. show under some additional hypotheses, such have geometric lifts to Witt vectors $\text{W}(\mathbb{F}_q)$. The m...

We present a family of reducible cyclic codes constructed as the direct sum of two different semiprimitive two-weight irreducible cyclic codes. This family generalizes the class of reducible cyclic codes that was reported in the main result of B. Wang, et al. [11]. Moreover, despite of what was stated therein, we show that, at least for the codes studied here, it is still possible to compute th...

This paper presents the prediction-preserving reducibility with membership queries (pwm-reducibility) on formal languages, in particular, simple CFGs and finite unions of regular pattern languages. For the former, we mainly show that DNF formulas are pwm-reducible to CFGs that is sequential or that contains at most one nonterminal. For the latter, we show that both bounded finite unions of regu...