Dynamic frictionless contact with adhesion

A model for the dynamic, adhesive, frictionless contact between a viscoelastic body and a deformable foundation is described. The adhesion process is modeled by a bonding field on the contact surface. The contact is described by a modified normal compliance condition. The tangential shear due to the bonding field is included. The problem is formulated as a coupled system of a variational equality for the displacements and a differential equation for the bonding field. The existence of a unique weak solution for the problem is established, together with a partial regularity result. The existence proof proceeds by construction of an appropriate mapping which is shown to be a contraction on a Hilbert space.     

On the Hyers-Ulam-Rassias stability of functional equations in n-variables

In this paper we investigate a generalization of the Hyers-Ulam-Rassias stability for a functional equation of the form f(φ(X))=?(X)f(X)+ψ(X) and the stability in the sense of Ger for the functional equation of the form f(φ(X))=?(X)f(X), where X lie in n-variables. As a consequence, we obtain a stability result in the sense of Hyers-Ulam-Rassias, Gǎvruta, and Ger for some well-known equations such as the gamma, beta, and G-function type's equations.     

The Hochschild class of the Chern character for semifinite spectral triples

We provide a proof of Connes’ formula for a representative of the Hochschild class of the Chern character for (p,∞)-summable spectral triples. Our proof is valid for all semifinite von Neumann algebras, and all integral p?1. We employ the minimum possible hypotheses on the spectral triples.     

Complete caps in projective spaces PG (n, q)

A computer search in the finite projective spaces PG(n, q) for the spectrum of possible sizes k of complete k-caps is done. Randomized greedy algorithms are applied. New upper bounds on the smallest size of a complete cap are given for many values of n and q. Many new sizes of complete caps are obtained.     

Optimal control of the obstacle in a quasilinear elliptic variational inequality

In this paper we consider an obstacle control problem where the state satisfies a quasilinear elliptic variational inequality and the control function is the obstacle. The state is chosen to be close to the desire profile while the H² norms of the obstacle is not too large. Existence and necessary conditions for the optimal control are established.     

Fock Theories and Quantum Logics

The notion of Fock theory is introduced in the framework of quantum logics, which are here orthomodular atomic lattices satisfying the covering property. It is shown that there are some fundamental facts concerning particles, which may be successfully discussed in this general context. One of these facts is to establish the theoretical conditions for considering particles as sharply defined entities. The other refers to the theoretical circumstances, which almost impose to consider that some particles have a structure, meaning they are composed from other particles. This last problem is strongly related with the conservative time evolutions.     

Contractibility of Efficient Frontier of Simply Shaded Sets

In finite dimensional Euclidean space, we prove the contractibility of the efficient frontier of simply shaded sets. This work extends the result of Peleg [7], which confirms the contractibility of the efficient frontier in the convex case.     

Fracture strength of class II slot cavities restored with polymerizable restorative materials

This study compared the fracture strength of Class II slot cavities restored with polymerizable restorative materials. Sixty, caries-free, posterior teeth were divided into five groups of 12 teeth. The Class II slot cavities were prepared. The teeth were restored with two packable composites (Filtek P60, Surefil), a microhybrid composite (Filtek Z250)and two ormocer (Definite, Admira). The restorations were then subjected to fracture resistance tests. The marginal ridges of the restorations were loaded at an angle of 13.5° to the long axis of the tooth in an Universal Testing Machine until failure. Analysis of mean forces indicated that, Filtek P60, Surefil and Filtek Z250 exhibited better performance than Definite and Admira. The tested resin composites differed in their mechanical properties. This study suggested that fracture behavior were highly influenced by the filler system. Overall, Filtek P60, Surefil, Filtek Z250, demonstrated good fracture resistance. Copyright © 2003 John Wiley & Sons, Ltd.     

Pressure-induced polymorphism in enstatite (MgSiO3) at room temperature: clinoenstatite and orthoenstatite

The phase transition of a synthetic clinoenstatite in a diamond-anvil cell has been studied by using Raman spectroscopy at various pressures and room temperature. The phenomena observed in clinoenstatite have been compared with that observed in orthoenstatite. It is found that the pressure-induced phase transitions in the two enstatites are reversible, but with different transition pressures and transition behavior. An analysis of Raman spectra has revealed that the two enstatites have different high-pressure polymorphs. This result suggests that the space group of the high-pressure polymorph of orthoenstatite is not of C2/c, and that orthoenstatite and orthoferrosilite have different transition routes at room temperature and high pressure. The compressional behavior of the high-PC2/c enstatite is also discussed according to the pressure dependences of Raman frequencies.     

Constructions of rank five geometries for the Mathieu group M 22

We construct nine rank five incidence geometries that are firm and residually connected and on which the Mathieu group M²² acts flag-transitively. The constructions use mainly objects arising from the Steiner systemS(3, 6, 22). One of these geometries was constructed by Meixner and Pasini in [10]. Three of them are obtained from the geometry of Meixner and Pasini using doubling (see [8] or [12]) or similar constructions. The remaining five are new and four of them have a star diagram. These latter four geometries are constructed using special partitions of the 22 points of the Steiner system S(3, 6, 22).