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We present a new Min-Max theorem for an optimization problem closely connected to matchings and vertex covers in balanced hypergraphs. The result generalizes Kőnig’s Theorem (Berge and Las Vergnas in Ann N Y Acad Sci 175:32–40, 1970; Fulkerson et al. in Math Progr Study 1:120–132, 1974) and Hall’s Theorem (Conforti et al. in Combinatorica 16:325–329, 1996) for balanced hypergraphs.
The aim of this work was to perform a detailed investigation of the use of Selective Laser Melting (SLM) technology to process eutectic silver-copper alloy Ag 28 wt. % Cu (also called AgCu28). The processing occurred with a Realizer SLM 50 desktop machine. The powder analysis (SEM-topography, EDX, particle distribution) was reported as well as the absorption rates for the near-infrared (NIR) spectrum. Microscope imaging showed the surface topography of the manufactured parts. Furthermore, microsections were conducted for the analysis of porosity. The Design of Experiments approach used the response surface method in order to model the statistical relationship between laser power, spot distance and pulse time.
Bead-on-plate butt joints of 2.5 mm hot rolled DP600/DP600 and 1.2 mm cold rolled TRIP700/TRIP700 steel sheets were performed using 6 kW CO2 laser beam welding. The welding speed ranged from 1.5 to 3.0 and from 2.1 to 3.9 m/min in DP/DP and TRIP/TRIP steel weldments respectively. A top surface helium gas was used as a shielding gas at a flow rate of 20 l/min. Metallographic examinations and transverse tensile testing (DIN EN 895: 1995) were carried out to characterize the weldments. The formability of base metals and weldments were investigated by standard Erichsen test (DIN EN ISO 20482). It was found that the uniaxial plastic behavior of both DP600 and TRIP700 base metals was in agreement with Swift and modified Mecking–Kocks models respectively. In a perpendicular tensile test to the weld line, all specimens were fractured at the base metal however the strengths were somewhat higher than those of base metal. There was a significant reduction in formability caused by welding of both DP/DP and TRIP/TRIP steel weldments and the formability has been improved with the increase of the welding speed.