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A bstract We consider a class of 2d ? -models on products group spaces that provide new examples close connection between integrability and stability under the RG flow. first study integrable G × model derived from affine Gaudin construction (for which 1-loop ? -functions were found in arXiv:2010.07879 ) show its condition is preserved also by 2-loop then investigate flow gauged G/H model, part...

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

Let G be a flat finite-type group scheme over a scheme S, and X a noetherian S-scheme on which G-acts. We define and study G-prime and G-primary G-ideals on X and study their basic properties. In particular, we prove the existence of minimal G-primary decomposition and the well-definedness of G-associated G-primes. We also prove a generalization of Matijevic–Roberts type theorem. In particular,...

Given a plane graph G, we wish to nd a drawing of G in the plane such that the vertices of G are represented as grid points, and the edges are represented as straight-line segments between their endpoints without any edge-intersection. Such drawings are called planar straight-line drawings of G. An additional objective is to minimize the area of the rectangular grid in which G is drawn. In this...