Optimization of the Manufacturing Process by Molding Cobalt-Chrome Alloys in Assembled Dental Frameworks

In oral rehabilitation, the treatment of partial edentulism (PEd) is performed by removable partial dentures (RPD) or assembled prosthetic works (APW) composed of several components, fixed to the prosthetic field (Pa) and a removable one (Pb), in order to facilitate the daily hygiene but also the damping of the occlusal forces applied in mastication. Cobalt-Chromium alloys are materials used to manufacture modern prosthetic assembles. In order for this study to be relevant, it was necessary to standardize the design of the framework (Pa) in terms of shape and volume so that the experiment could be reproducible for the five Co-Cr alloys: 0-A (Co-Cr-Mo), 5-A and 10-A (Co-Cr-Mo-W), 15-A and 16.4-A (Co-Cr-W-Fe) and for the three fabrication methods of dental assembled prosthetic frameworks: refractory duplicate method (RD) resulting removable framework (Pb), direct construction method (DC) resulting removable framework (Pb-) and casting over metal method (CoM) resulting removable framework (Pb+). The time allocated to the adaptation process (AP), mechanical processing and sandblasting, in order to assemble the two components was between 43–70 min, even though the assembly between the Pa-framework and the complementary framework (Pb+) was not necessary, CoM-method hs been provide the elimination of AP step. By applying the arithmetic simple rule of three, the percentages for each of the three methods used were calculated, the values of the difference were obtained. The CoM method improves the joining precision between the components of the removable assembly of prosthetic frameworks by 91.7% compared to the RD method and by 80.62% compared to the DC method. According to the efficiency of the methods used in the precision of joining between frameworks components, their order is: casting over metal, direct construction and refractory duplicate method.

Conservation laws for partial differential equations based on the polynomial characteristic method

In this paper, the direct construction method combined with the differential polynomial characteristic set algorithm is used to complete conservation laws of PDE. The process of the direct construction method is to solve a system of linear determining equations, which is not easy to be solved. This paper uses the differential polynomial characteristic set algorithm to overcome the shortcoming, and constructs an explicit conservation law.

An Incremental Harmonic Balance Method With a General Formula of Jacobian Matrix and a Direct Construction Method in Stability Analysis of Periodic Responses of General Nonlinear Delay Differential Equations

A general formula of Jacobian matrix is derived in an incremental harmonic balance (IHB) method for general nonlinear delay differential equations (DDEs) with multiple discrete delays, where the fast Fourier transform is used to calculate Fourier coefficients of partial derivatives of residuals. It can be efficiently and automatically implemented in a computer program, and the only manual work is to derive the partial derivatives, which can be a much easier task than derivation of Jacobian matrix. An advantage of the IHB method in stability analysis is also revealed here. A direct construction method is developed for stability analysis of nonlinear differential equations with use of a relationship between Jacobian matrix in the IHB method and the system matrix of linearized equations. Toeplitz form of the system matrix can be directly constructed, and Hill’s method is used to calculate Floquet multipliers for stability analysis. Efficiency of stability analysis can be improved since no integration is needed to calculate the system matrix. Period-doubling bifurcations and period-p solutions of a delayed Mathieu–Duffing equation are studied to demonstrate use of the general formula of Jacobian matrix in the IHB method and the direct construction method in stability analysis. Its solution is the same as that from the numerical integration method using the spectral element method in the DDE toolbox in matlab, and it has a high convergence rate for solving a delayed Van der Pol equation.

Direct construction method for conservation laws of partial differential equations Part II: General treatment

This paper gives a general treatment and proof of the direct conservation law method presented in Part I (see Anco & Bluman [3]). In particular, the treatment here applies to finding the local conservation laws of any system of one or more partial differential equations expressed in a standard Cauchy-Kovalevskaya form. A summary of the general method and its effective computational implementation is also given.