The lack of stability in some matching problems suggests that alternative solution concepts to the core might be a step towards furthering our understanding of matching market performance. We propose absorbing sets as a solution for the class of roommate problems with strict preferences. This solution, which always exists, either gives the matchings in the core or predicts other matchings when ...

This represents a circle in the phase plane. Its plot is given in Fig. 2.1.b. __________________________________________________________________________________________ The nature of the system response corresponding to various initial conditions is directly displayed on the phase plane. In the above example, we can easily see that the system trajectories neither converge to the origin nor dive...

We consider a method for constructing uniformly stable spline approximations for scalar delay equations.

Small-gain statements play a key role in system analysis. These results state that the interconnection of two stable systems is stable provided that the closed loop gain is less than unity. This intuitively satisfying statement can be made rigorous in a number of ways depending on the notion of stability and the family of systems under consideration. Such results were originally given in the 19...

In this paper we consider the dynamics of solutions of impulsive differential equations with fixed time moments of impulsive effects on the basis of comparison methods and vector Lyapunov functions. We propose sufficient conditions on the following dynamic properties: stability, attractivity, and some combinations of them.

Let M<=R be a minimal surface. A domain Z><= M is an open connected set with compact closure D and such that its boundary dD is a finite union of piecewise smooth curves. We say that D is stable if D is a minimum for the area function of the induced metric, for all variations of D which keep dD fixed. In this note we announce the following estimate of the "size" of a stable minimal surface. We ...

Given a BIBD(v,k,A) we can construct a directed BIBD(v,k,A*) by writing each block of the BIBO twice, the second time in the reversed order. Here we prove the analagous expected but useful result that if a BIBD(v,b,r ks,k,A) exists, then a RCOBIBD(v,k,A *} also exists. A nonexistence result is also given.

In this paper an attempt is made to offer insights into local slope failure mechanisms from the perspective of hydrogeology. The hypothesis examined envisages that the hydraulic conductivity distribution in a weathered profile includes a relatively high hydraulic conductivity zone associated with the jointed rock mass near rockhead. There is evidence locally for such a condition. The groundwate...

The Barkhausen pattern from the amorphous alloy Fe21Co64B15 showed high sweep-to-sweep reproducibility for most sweeps when driven slowly over a minor hysteresis loop. Small changes in the maximum applied field led to completely different pulse patterns. When driven near saturation the sweep-to-sweep reproducibility was lost. Large features observed on rapid sweeps were also reproducible, but n...