In this report, we investigate phenomena on the edge of spatially uniform chaotic mode and spatial temporal chaos in a lattice of chaotic 1-D maps with only local connections. It is shown that in autonomous lattice with local connections, spatially uniform chaotic mode cannot exist if the Lyapunov exponent λ of the isolated chaotic map is greater than some critical value λcr > 0. We proposed a ...

We establish various uniformity properties of the harmonic map heat ow, including uniform convergence in L 2 exponentially as t ! 1, and uniqueness of the positions of bubbles at innnite time. Our hypotheses are that the ow is between 2-spheres, and that the limit map and any bubbles share the same orientation.

The uniform distribution of the trace map lends itself very well to the construction of binary and non-binary codes from Galois fields and Galois rings. In this paper we study the distribution of the trace map with the argument ax over the Galois field GF (p, 2). We then use this distribution to construct two-weight, self-orthogonal, trace codes.

A recent publication [1] introduced a growth procedure for planar maps, whose almost sure limit is “the uniform infinite 3-connected planar map”. A classical construction of Brooks, Smith, Stone and Tutte [7] associates a squaring of a rectangle (i.e. a tiling of a rectangle by squares) to any finite, edge-rooted planar map with nonseparating root edge. We use this construction together with th...

Suppose $G$ is a connected complex semisimple group and $W$ its Weyl group. The lifting of an element to semisimple. This induces well-defined map from the set elliptic conjugacy classes $G$. In this paper, we give uniform algorithm compute map. We also consider twisted case.

Mucoadhesive particles (MAP) have been widely explored for pulmonary drug delivery because of their perceived benefits in improving particle residence in the lungs. However, retention of particles adhesively trapped in airway mucus may be limited by physiologic mucus clearance mechanisms. In contrast, particles that avoid mucoadhesion and have diameters smaller than mucus mesh spacings rapidly ...

Theorem A. Let g : [0, T ]× IR 7→ IR be a bounded function. (i) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is continuous for each t, then the Cauchy problem (1.1) has at least one solution. (ii) If the map t 7→ g(t, x) is measurable for each x and the map x 7→ g(t, x) is Lipschitz continuous for each t, with a uniform Lipschitz constant, then the Cauchy problem (1...