Physical properties (thermal,thermomechanical, magnetic,and adhesive) of some smart orthodontic wires

Thermal, thermomechanical, and caloric properties of commercial orthodontic wires (produced by Natural Orthodontics Corp., USA) with cylindrical and rectangular geometry were studied. Depending on the applied forces, there were identified the range of elasticity, the elasticity–viscoelasticity coexistence domain and the domain in which a maximum force of 18 N is applied, for the orthodontic wires. When increasing the thickness of orthodontic wires, deformation decreases. The Controlled Force Module, in the tension mode, was used for the determination of the orthodontic wires elongation at application of the stretching forces from 0 to 13 N, at 35 °C, maintaining each static force value for 3 min. The increase in the cross-sectional area of the orthodontic wires disfavors the process of elongation of the sample, at the same applied static force. Using the Multi-Frequency–Strain–Stress modulus, in the tension mode, DMA cyclic heating–cooling measurements were performed. The measured physical quantities for orthodontic wires were Storage Modulus, Loss Modulus, Tanδ and Stiffness, at heating and cooling. Thus, the characteristic temperatures of the phase transitions (A_s, A_f, M_s, M_f), of all the studied orthodontic wires were identified. Also, the values of the elasticity modulus (Young’s Modulus) of the orthodontic wires were calculated at 35 °C. With the DSC Q200 device, using temperature-modulated differential scanning calorimetry method, a multi-step temperature variation program, was applied to a rectangular wire, in three stages (cooling–heating–cooling). Through the interpretation of heat fluxes (reversible, irreversible and total), the phase transitions in the formation of martensite, austenite, but also of the rombohedral phase (R-phase), were identified. Formations of austenite and martensite were also evidenced by the classical DSC method, but the classical DSC method also enabled the R-phase identification. The adherence of some food dyes on the orthodontic wires, as well as the modification of the surface roughness of the orthodontic wire after the deposition of the food dye, was also studied. By magnetic measurements, it was established that the orthodontic wires had paramagnetic properties at room temperature, and nitinol was a mixture of 49.2% austenite and 50.8% martensite.

     

Discrete time Galerkin approximations to the nonlinear filtering solution

This paper concerns discrete time Galerkin approximations to the solution of the filtering problem for diffusions. Two families of schemes approximating the unnormalized conditional density, respectively, in an “average” and in a “pathwise” sense, are presented. L² error estimates are derived and it is shown that the rate of convergence is linear in the time increment or linear in the modulus of continuity of the sample path.     

Concavity maximum principle for viscosity solutions of singular equations

We prove a concavity maximum principle for the viscosity solutions of certain fully nonlinear and singular elliptic and parabolic partial differential equations. Our results parallel and extend those obtained by Korevaar and Kennington for classical solutions of quasilinear equations. Applications are given in the case of the singular infinity Laplace operator.     

On the Characterization of Harmonic and Subharmonic Functions via Mean-value Properties

We consider the different characterizations of harmonic and subharmonic functions in terms of their mean values in balls and on spheres. In particular, we prove a converse of an inequality of Beardon’s for subharmonic functions, and extend Rao’s integral inequalities of Harnack type between these two means in general domains.     

A hierarchical multi-label classification ant colony algorithm for protein function prediction

This paper proposes a novel ant colony optimisation (ACO) algorithm tailored for the hierarchical multi-label classification problem of protein function prediction. This problem is a very active research field, given the large increase in the number of uncharacterised proteins available for analysis and the importance of determining their functions in order to improve the current biological knowledge. Since it is known that a protein can perform more than one function and many protein functional-definition schemes are organised in a hierarchical structure, the classification problem in this case is an instance of a hierarchical multi-label problem. In this type of problem, each example may belong to multiple class labels and class labels are organised in a hierarchical structure—either a tree or a directed acyclic graph structure. It presents a more complex problem than conventional flat classification, given that the classification algorithm has to take into account hierarchical relationships between class labels and be able to predict multiple class labels for the same example. The proposed ACO algorithm discovers an ordered list of hierarchical multi-label classification rules. It is evaluated on sixteen challenging bioinformatics data sets involving hundreds or thousands of class labels to be predicted and compared against state-of-the-art decision tree induction algorithms for hierarchical multi-label classification.     

A spectral Bernstein theorem

We study the spectrum of the Laplace operator of a complete minimal properly immersed hypersurface M in \({\mathbb{R}^{n+1}}\). (1) Under a volume growth condition on extrinsic balls and a condition on the unit normal at infinity, we prove that M has only essential spectrum consisting of the half line [0, +∞). This is the case when \({{\rm lim}_{\tilde{r}\to +\infty}\,\tilde{r}\kappa_i=0}\), where \({\tilde{r}}\) is the extrinsic distance to a point of M and κ _i are the principal curvatures. (2) If the κ _i satisfy the decay conditions \({|\kappa_i|\leq 1/\tilde{r}}\) and strict inequality is achieved at some point \({y\in M}\), then there are no eigenvalues. We apply these results to minimal graphic and multigraphic hypersurfaces.