Relaxation of Residual Stresses in Brush-Plated Gold and Silver Coatings on Copper and on Brass Substrates

The investigated brush-plated gold and silver coatings are used for repairing the commutators of generators and sliding contacts. Tensile residual stresses generated in the plated coatings were determined by the curvature method and by instrumented indentation testing of a thin-walled open ring substrate, as described in our earlier papers. These stresses relax over time and their dependence on relaxation time was approximated by a linear-fractional function. The Young ́s modulus and nanohardness of the coatings were determined. The surface structure and cross section of the coated substrates were studied.

Comparative Analysis of Residual Stresses Determined by Various Methods in Brush-Plated Hard Gold and Silver Coatings

The investigated brush-plated silver and gold coatings are used for refining the surface properties of electric apparatuses. Tensile residual stresses generated in the plated coatings were determined with a thin-walled ring substrate using the curvature and instrumented indentation techniques. These stresses relax over time; the dependence of relaxation time was approximated by a linear-fractional function. The modulus of elasticity and the nanohardness of the coatings were determined by nanoindentation. The surface morphology and structure in cross-section of the coated substrates are presented.

An Approach for Solving Linear Fractional Programming Problems

Linear fractional programming problems are useful tools in production planning, financial and corporate planning, health care and hospital planning and as such have attracted considerable research interest. The paper presents a new approach for solving a fractional linear programming problem in which the objective function is a linear fractional function, while the constraint functions are in the form of linear inequalities. The approach adopted is based mainly upon solving the problem algebraically using the concept of duality and partial fractions and an example is given to clarify the developed method.

DEGENERATE BIFURCATIONS AND BORDER COLLISIONS IN PIECEWISE SMOOTH 1D AND 2D MAPS

We recall three well-known theorems related to the simplest codimension-one bifurcations occurring in discrete time dynamical systems, such as the fold, flip and Neimark–Sacker bifurcations, and analyze these bifurcations in presence of certain degeneracy conditions, when the above mentioned theorems are not applied. The occurrence of such degenerate bifurcations is particularly important in piecewise smooth maps, for which it is not possible to specify in general the result of the bifurcation, as it strongly depends on the global properties of the map. In fact, the degenerate bifurcations mainly occur in piecewise smooth maps defined in some subspace of the phase space by a linear or linear-fractional function, although not necessarily only by such functions. We also discuss the relation between degenerate bifurcations and border-collision bifurcations.