Finding the convex hull of a simple polygon

It is well known that the convex hull of a set of n points in the plane can be found by an algorithm having worst-case complexity O(n log n). A short linear-time algorithm for finding the convex hull when the points form the (ordered) vertices of a simple (i.e., non-self-intersecting) polygon is given.     

Local energy decay for scattering of elastic waves

We show that if $\text{B}$ is a star-shaped body in $\text{R}$³ and u is a solution of the equation of linearized homogeneous isotropic elasticity in the exterior of $\text{B}$ which vanishes on ?$\text{B}$ and has initially compact support, then the rate of decay of the total elastic energy in any sphere of finite radius is bounded by t^? for large values of the time t.     

Nonequilibrium Time Reversibility with Maps and Walks

Time-reversible dynamical simulations of nonequilibrium systems exemplify both Loschmidt’s and Zermélo’s paradoxes. That is, computational time-reversible simulations invariably produce solutions consistent with the irreversible Second Law of Thermodynamics (Loschmidt’s) as well as periodic in the time (Zermélo’s, illustrating Poincaré recurrence). Understanding these paradoxical aspects of time-reversible systems is enhanced here by studying the simplest pair of such model systems. The first is time-reversible, but nevertheless dissipative and periodic, the piecewise-linear compressible Baker Map. The fractal properties of that two-dimensional map are mirrored by an even simpler example, the one-dimensional random walk, confined to the unit interval. As a further puzzle the two models yield ambiguities in determining the fractals’ information dimensions. These puzzles, including the classical paradoxes, are reviewed and explored here.     

Oriented local entropies for expansive actions by commuting automorphisms

Given an expansive action α of ?² by automorphisms of a compact connected metrizable abelian groupX, we show how the entropy of the action may be decomposed into local contributions, 1 $$h(\alpha ) = \sum\limits_{p \leqslant \infty } {h_p^{(a,b)} } (\alpha )$$ in which the summandh _p ^(a,b) (α) represents thep-adic entropy due to arithmetic or geometric hyperbolicity in the direction (a, b). We recognize thep-adic contribution as an integral over thep-adic unit circle, in analogy with the global counterpart. As (a, b) changes, the decomposition (1) changes only when the line through (a, b) passes through one of a finite collection of critical directions, which are explicitly identified.     

Oscillatory light loss within the cladding of a straight optical fiber: comparison with whispering-gallery modes

Light propagating within the cladding of a straight optical fiber exhibits wavelength-dependent oscillatory loss that resembles the whispering-gallery modes of a bent fiber. This novel observation can be explained by interference of light only within the cladding and the buffer without any influence of the fiber core. The technique promises applications similar to those that are due to whispering-gallery modes but without the additional requirement of having a bent fiber.     

Edward Teller ninety

Edward Teller is a member of a very fortunate great generation. He was born into this exciting 20th century. As a university student he witnessed the birth of quantum mechanics, one of the boldest cultural venture of human spirit, and he actively participated in widening the realm of physics to chemistry and astrophysics. And he was one of the main actors in shaping the history of this century by realizing the potential power of modern physics. We greet him from his native country in the name of Hungarian physicists.     

Poincaré like inequalities for semigroups, cosine and sine operator functions

Here we present Poincaré type general L _p inequalities regarding semigroups, cosine and sine operator functions.     

A new synthetic strategy for the synthesis of bioactive stilbene dimers. A direct synthesis of amurensin H

2,3-Diarylbenzofurans are efficiently generated by the cyclization of ortho-benzyloxybenzophenones using the hindered phosphazene base P₄-t-Bu.