We investigate the problem of best simultaneous Diophantine approximation under a constraint on the denominator, as proposed by Jurkat. New lower estimates for optimal approximation constants are given in terms of critical determinants of suitable star bodies. Tools are results on simultaneous Diophantine approximation of rationals by rationals with smaller denominator. Finally, the approximati...

This paper presents a new decomposition technique for hierarchical Cayley graphs. This technique yields a very easy implementation of the divide & conquer paradigm for weak order problems on very complex architectures as the Star graph or the Pancake. As applications, we introduce asymptotically optimal algorithms for Broadcasting, Gossiping, and Semigroup operations for such interconnection ne...

We construct quasiequilibrium sequences of black hole-neutron star binaries for arbitrary mass ratios by solving the constraint equations of general relativity in the conformal thin-sandwich decomposition. We model the neutron star as a stationary polytrope satisfying the relativistic equations of hydrodynamics, and account for the black hole by imposing equilibrium boundary conditions on the s...

let $d$ be an integral domain and $star$ a semistar operation stable and of finite type on it. we define the semistar dimension (inequality) formula and discover their relations with $star$-universally catenarian domains and $star$-stably strong s-domains. as an application, we give new characterizations of $star$-quasi-pr"{u}fer domains and um$t$ domains in terms of dimension ine...

In Chapter 1 it was shown that Fisk's proof of the art gallery theorem can be converted into an algorithm that covers a polygon of n vertices with [n/3\ guards in O{n logn) time. Although [n/3\ is necessary in some cases, often this is far more guards than are needed to cover a particular polygon. For example, convex polygons only require one guard, but Avis and Toussaint's algorithm would stil...

By applying the combinatorial game theory notions of dominated move and reversible move, and by exploiting graph-theoretic properties of Hex board decompositions, we identify two new types of inferior Hex move.

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The peculiar pulsating variable XZ Ceti has a period of 0.8231 day, suggesting that it is a Bailey type ab RR Lyrae star, but it has a light curve shape and amplitude which is like that of the Bailey type c variables. Fourier decomposition analysis verifies that the parameters of its light curve match those of the type c variables, except for its unacceptably long period. We have obtained a new...

We present a quantitative analysis of the abundances of heavy elements in damped Lyα galaxies in the sample of Lu et al. (1996). In particular, we compare the observed gas-phase abundances with those expected when the intrinsic (i.e., nucleosynthetic) pattern is the same as that in either the Sun or in Galactic halo stars and when the depletion pattern is the same as that in the warm Galactic i...

This paper is concerned with the Poincaré-Steklov operator that is widely used in domain decomposition methods. It is proved that the inverse of the Poincaré-Steklov operator can be expressed explicitly by an integral operator with a kernel being the Green’s function restricted to the interface. As an application, for the discrete Poincaré-Steklov operator with respect to either a line (edge) o...