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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...

A number of melting curves of various materials have recently been measured experimentally and calculated theoretically, but the agreement between different groups is not always good. We discuss here some of the problems which may arise in both experiments and theory. We also report the melting curves of Fe and Al calculated recently using quantum mechanics techniques, based on density function...

Th e study of self-regulation and autonomy has emerged as an important topic at the intersection of several areas in psychology. Developmental psychologists (e.g., Blair & Ursach, 2011 ; Carlson, 2005 ; Posner & Rothbart, 2007 ; Zelazo, Carlson, & Kesek, 2008 ) have identifi ed diff erent aspects of regulatory control and how these change over time. Social psychologists (e.g., Bandura, 1997 ; D...