Abstract: A mechanism for providing equation-level diagnostic error messages for system models undergoing circuit simulations is discussed. The components in a model of a system being simulated are converted into multiple numerical equations where each equation corresponds to a component in the system being simulated or a topology equation for the system model. Each numerical equation is numerically analyzed in order to identify illegal configurations in the system. Upon detection of an error, an error message listing the components associated with the illegal configuration is generated for the user.

Abstract: A mechanism for providing equation-level diagnostic error messages for system models undergoing circuit simulations is discussed. The components in a model of a system being simulated are converted into multiple numerical equations where each equation corresponds to a component in the system being simulated or a topology equation for the system model. Each numerical equation is numerically analyzed in order to identify illegal configurations in the system. Upon detection of an error, an error message listing the components associated with the illegal configuration is generated for the user.

Abstract: This invention relates to a mild oral hygiene composition such as a toothpaste, dental gel, mouthrinse or tooth powder containing a mild surfactant, protein fatty acid condensate or acid hydrolyzed, hydrolyzed animal protein or the mixtures thereof, and in combination therewith, mild high foaming surfactant, e.g., disodium cocoamido MIPA sulfosuccinate or disodium oleamido PEG-2 sulfosuccinate or disodium lauryl sulfosuccinate or the mixtures thereof; or a natural emulsifier, e.g., lecithin, or both a mild surfactant and a nautral emulsifier.