Bifurcation analysis on ion sound and Langmuir solitary waves solutions to the stochastic models with multiplicative noises.

This article explores on a stochastic couple models of ion sound as well as Langmuir surges propagation involving multiplicative noises. We concentrate on the analytical stochastic solutions including the travelling and solitary waves by using the planner dynamical systematic approach. To apply the method, First effort is to convert the system of equations into the ordinary differential form and present it in form of a dynamic structure. Next analyze the nature of the critical points of the system and obtain the phase portraits on various conditions of the corresponding parameters. The analytic solutions of the system in an account of distinct energy states for each phase orbit are performed. We also show how the results are highly effective and interesting to realize their exciting physical as well as the geometrical phenomena based on the demonstration of the stochastic system involving ion sound as well as Langmuir surges. Descriptions of effectiveness of the multiplicative noise on the obtained solutions of the model, and its corresponding figures are demonstrated numerically.

Fracture Resistance of Primary Zirconia Crowns: An In Vitro Study.

In this study, we evaluated the fracture resistance of three commercially available prefabricated primary zirconia crowns and their correlation with dimensional variance. METHODS: a total of 42 zirconia crowns were selected from three companies, (1) NuSmile primary zirconia crowns, (2) Cheng Crowns zirconia, and (3) Sprig EZ crowns. The crowns were divided into two groups based on their location in the oral cavity and further divided into subgroups based on the brand. All of the samples were subjected to fracture tests using a universal testing machine. RESULTS: the mean load observed was highest with Cheng Crowns zirconia anterior crowns (1355 ± 484) and the least load was seen with Sprig EZ anterior crowns with a mean load of 339 ± 94. The mean load observed was highest with Cheng Crowns zirconia posterior crowns (1990 ± 485) followed by NuSmile posterior crowns and the least load was seen with Sprig EZ posterior crowns with a mean load of 661 ± 184. CONCLUSION: the Cheng crowns showed the highest fracture resistance amongst all three groups. Overall, the zirconia crowns (anterior and posterior) tested showed optimum mechanical properties to withstand the masticatory forces.