Twisted Eguchi-Kawai reduced chiral models are shown to be formally equivalent a U(1) non-commutative parent theory. The non-commutative theory describes the vacuum dynamics of the non-commutative charged tachyonic field of a brane system. To make contact with the continuum non-commutative theory, a double scaling large N limit for the reduced model is required. We show a possible limiting proc...

Research on automatically solving mathematical word problems (MWP) has a long history. Most recent works adopt Seq2Seq approach to predict the result equations as sequence of quantities and operators. Although can be written sequence, it is essentially structure. More precisely, Direct Acyclic Graph (DAG) whose leaf nodes are quantities, internal root arithmetic or comparison In this paper, we ...

This is a further investigation of our approach to group actions in homological algebra the settings homology $$\Gamma $$ -simplicial groups, particularly -equivariant and cohomology -groups. new direction called -homological algebra. The abstract kernel non-abelian extensions its relationship with obstruction theory, second are extended case -extensions We compute rational (co)homology groups ...

The rings considered in this article are commutative rings with identity $1neq 0$. The aim of this article is to define and study the exact annihilating-ideal graph of commutative rings. We discuss the interplay between the ring-theoretic properties of a ring and graph-theoretic properties of exact annihilating-ideal graph of the ring.

The decomposition theorem for torsion abelian groups holds analogously for torsion commutative diassociative loops. With this theorem in mind, we investigate commutative diassociative loops satisfying the additional condition (trivially satisfied in the abelian group case) that all nth powers are central, for a fixed n. For n = 2, we get precisely commutative C loops. For n = 3, a prominent var...