We use a min-max procedure on the Allen–Cahn energy functional to construct geodesics closed, $2$‑dimensional Riemannian manifolds, as motivated by work of Guaraco [Gua18]. Borrowing classical blowup and curvature estimates from geometric analysis, well novel due Wang–Wei [WW19], we manage study fine structure potential singular points at diffuse level, show that problem reduces understanding “...

The set of min-max functions F : R n ! R n is the least set containing coordinate substitutions and translations and closed under pointwise max, min, and function composition. The Duality Conjecture asserts that the trajectories of a min-max function, considered as a dynamical system, have a linear growth rate (cycle time) and shows how this can be calculated through a representation of F as an...

conclusions the composition of unrecorded samples did not raise major toxicological concern beyond ethanol in alcohol products. however, concentration levels of methanol in some unrecorded alcohol samples made these samples detrimental for human consumption. results of 877 reports of alcohol samples, more than 50% were obtained from mashhad and the rest were from the suburbs. of the reports, 57...

Picture fuzzy relation is an important and powerful concept which suitable for describing correspondences between objects. It represents the strength of association elements picture sets. In this paper we have defined min-max composition relations some properties are explored based on definition. Also discussed max-min relations. Finally, application as illustration to show how applied in decis...