Let $G = (V_G, E_G)$ be an undirected graph, and $H$ be another graph. My goal is to encode the submultigraph isomorphism problem using integer multiplication. For the graph $G$, we encode connectivity as follows. For each edge $\{i,j\} \in G$ choose a unique pair of primes $p_{\varphi(i,j)}, p_...

I want to construct the chain map between two exact rows: Let $M$ be an $R$-module and $(A_{\bullet},f_\bullet), (B_\bullet,g_\bullet)$ be a chain complexes where $A_\bullet,B_\bullet$ are $R$-modules (Here, we define $A_{-1} = M = B_{-1}$). If two chains are exact i.e. $\cdots\to A_2\to A_1\to ...

Let $A\subseteq \mathbb{R}^n$ be open and $f:\mathbb{R}^n\to \mathbb{R}^m$ be $\mu$ locally integrable, where $\mu$ is a Radon measure (on $\mathbb{R}^n$). How to construct compactly supported continuous functions $\varphi_k:\mathbb{R}^n\to\mathbb{R}^m$ with $\text{spt}\varphi_k\subseteq A$ and $...