The CSP of a first-order theory $T$ is the problem of deciding for a given finite set $S$ of atomic formulas whether $T \cup S$ is satisfiable. Let $T_1$ and $T_2$ be two theories with countably infinite models and disjoint signatures. Nelson and Oppen presented conditions that imply decidability (or polynomial-time decidability) of $\mathrm{CSP}(T_1 \cup T_2)$ under the assumption that $\mathr...

The ADAM33 gene is associated with the pathophysiology of Chronic Obstructive Pulmonary Disease (COPD) and atherosclerosis. In this study we investigated all-cause, COPD and cardiovascular mortality, in relation to single nucleotide polymorphisms (SNPs) in ADAM33 (Q_1, S_1, S_2, T_1 and T_2) that were genotyped in 1,390 subjects from the Vlagtwedde/Vlaardingen cohort. Participants were examined...

This paper provides short proofs of two fundamental theorems of finite semigroup theory whose previous proofs were significantly longer, namely the two-sided Krohn-Rhodes decomposition theorem and Henckell's aperiodic pointlike theorem, using a new algebraic technique that we call the merge decomposition. A prototypical application of this technique decomposes a semigroup $T$ into a two-sided s...

suppose $f$ is a map from a non-empty finite set $x$ to a finite group $g$. define the map $zeta^f_g: glongrightarrow mathbb{n}cup {0}$ by $gmapsto |f^{-1}(g)|$. in this article, we show that for a suitable choice of $f$, the map $zeta^f_g$ is a character. we use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin g$) is a character, where $w(t_1,t...

 Suppose $f$ is a map from a non-empty finite set $X$ to a finite group $G$. Define the map $zeta^f_G: Glongrightarrow mathbb{N}cup {0}$ by $gmapsto |f^{-1}(g)|$. In this article, we show that for a suitable choice of $f$, the map $zeta^f_G$ is a character. We use our results to show that the solution function for the word equation $w(t_1,t_2,dots,t_n)=g$ ($gin G$) is a character, where $w(t_1,...

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Building on the weak CSR approach developed in a previous paper by Merlet, Nowak and Sergeev, we establish new bounds for periodicity threshold of powers tropical matrix. According to that approach, ultimate take form T=max(T_1,T_2), where T_1 is bound time after which expansion starts hold T_2 first term dominate. The established this make use cyclicity associated graph (tropical) factor rank ...