|Bifurcations of periodic orbits are studied for two-dimensional diieomorphisms close to a diieomorphism with the quadratic homoclinic tangency to a saddle xed point whose Jacobian is equal to one. Problems of the coexistence of periodic orbits of various types of stability are considered. INTRODUCTION It is well known that homoclinic bifurcations of two-dimensional diieomorphisms generally giv...

BACKGROUND As dental implants receive masticatory stress, the distribution of stress is very important to peri-implant bone homeostasis and implant survival. In this report, we created a saddle-type implant and analyzed its stability and ability to distribute stress to the surrounding bone. METHODS The implants were designed as a saddle-type implant (SI) that wrapped around the alveolar bone,...

Bifurcation theory provides a classification of the expected ways in which the number and/or stability of invariant solutions (‘attractors’ and ‘repellors’) of nonlinear ordinary differential equations may change as parameter values are changed. The most common qualitative changes are ‘saddle-node’ bifurcations, ‘Hopf’ bifurcations, and ‘SNIPER’ bifurcations. At a saddle-node bifurcation, a pai...

Activated processes in materials are important for many of the properties that make them function. Batteries and catalysts are examples for which understanding how the component materials function on a timescale of milliseconds to seconds is critical to making improvements in a rational way. Modeling materials over these long timescales, relative to the timescale of atomic vibrations, is one of...

Here we prove a stability version of a Ramsey-type Theorem for paths. Thus in any 2-coloring of the edges of the complete graph Kn we can either find a monochromatic path substantially longer than 2n/3, or the coloring is close to the extremal coloring.

We present arguments for the existence of a new type of solutions of the Euclidean Einstein-YangMills-dilaton theory in d = 4 dimensions. Possesing nonvanishing nonabelian charges, these nonselfdual configurations have no counterparts on the Lorentzian section. They provide, however, new saddle points in the Euclidean path integral.

As a first approach to a derivation of the IBM from a microscopic nuclear hamiltonian, we bosonize the pairing hamiltonian in the framework of the path integral formalism respecting both the particle number conservation and the Pauli principle. We construct the saddle point expansion which reproduces the sector of the spectrum associated to the addition or removal of nucleon pairs.