A Note about the Appearance of Non-Hyperbolic Solutions in a Mechanical Pendulum System

The investigation of the behavior of a nonlinear system consists in theanalysis of different stages of its motion, where the complexity varieswith the proximity of a resonance region. Near this region the stabilitydomain of the system undergoes sudden changes due basically tocompetition and interaction between periodic and saddle solutions insidethe phase portrait, leading to the occurrence of the most differentphenomena. Depending of the domain of the chosen control parameter,these events can reveal interesting geometric features of the system sothat the phase portrait is not capable to express all them, since theprojection of these solutions on the two-dimensional surface can hidesome aspects of these events. In this work we will investigate thenumerical solutions of a particular pendulum system close to a secondaryresonance region, where we vary the control parameter in a restrictdomain in order to draw a preliminary identification about what happenswith this system. This domain includes the appearance of non-hyperbolicsolutions where the basin of attraction in the center of the phaseportrait diminishes considerably, almost disappearing, and afterwardsits size increases with the direction of motion inverted. Thisphenomenon delimits a boundary between low and high frequency of theexternal excitation.     

An Overview on Non-Ideal Vibrations

We analyze the dynamical coupling between energy sources and structural response that must not be ignored in real engineering problems, since real motors have limited output power.     

Production of the Enzyme Cyclodextringlycosyltransferase from Bacillus firmus Alkalophilic

Different culture media have been testedfor the production of the enzyme CGTase (cyclodextringlycosyltransferase) from Bacillus firmus (strain #37). The concentration of different carbon and nitrogen sources have been varied and the enzyme activity, cell concentration, reducing sugars, total reducing sugars, soluble protein and pH have been followed during cultivation. Results indicate that higher concentrations of yeast extract and polypeptone lead to increased synthesis of CGTase, whereas when starch is substituted by glucose there is a drastic inhibition of CGTase production.