valdis laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. in this paper we introduce a new property of acts over monoids, called u-wpf which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. we also show that regu...

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Shape-based metrics measure how faithfully a drawing D represents the structure of graph G, using proximity S D. While some limited classes admit drawings (i.e., optimally shape-faithful drawings, where $$S = G$$ ), algorithms for general graphs have not been investigated. In this paper, we present first study graphs. First, conduct extensive comparison experiments popular layouts shape-based m...

A typical concept in quantum state analysis is based on the idea that states vicinity of some pure entangled share same properties, implying with a high fidelity must be entangled. States whose entanglement can detected this way are also called faithful. We prove structural result corresponding fidelity-based witnesses, resulting simple condition for faithfulness two-party state. For simplest c...