Space-times admitting an r-parameter Lie group of homotheties are studied for r > 2 devoting a special attention to those representing perfect fluid solutions to Einstein's field equations. 1 Basic facts about homotheties Throughout this paper (M, g) will denote a space-time: M then being a Haus-dorff, simply connected, four-dimensional manifold, and g a Lorentz metric of signature (-,+,+,+). A...

We consider L-graphs, that is contact graphs of axis-aligned L-shapes in the plane, all with the same rotation. We provide several characterizations of Lgraphs, drawing connections to Schnyder realizers and canonical orders of maximally planar graphs. We show that every contact system of L’s can always be converted to an equivalent one with equilateral L’s. This can be used to show a stronger v...

We study harmonic morphisms by placing them into the context of conformal foli-ations. Most of the results we obtain hold for bres of dimension one and codomains of dimension not equal to two. We consider foliations which produce harmonic mor-phisms on both compact and noncompact Riemannian manifolds. By using integral formulae, we prove an extension to one-dimensional foliations which produce ...

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. When these consumers trade in a sequence of markets, their time-inconsistency may introduce a non-convexity that gives them an incentive to trade lotteries. If there are many consumers, competitive equilibria with and without lotteries exist. The existence of symmetric equilibria may req...

Motivated by notions of aversion to Knightian uncertainty, this paper develops the theory of competitive asset pricing and consumption/portfolio choice with homothetic recursive preferences that allow essentially any homothetic uncertainty averse certainty-equivalent form. The market structure is scale invariant but otherwise general, allowing any trading constraints that scale with wealth. Tec...

the present paper is concerned with the generalization of the holditch theorem under oneparameterhomothetic motion on lorentzian planes. in this paper, for the homothetic lorentzian motion, weexpressed the steiner formula. furthermore, we present the holditch-type theorems.

For positive integers s and t, let f (sÒ t) denote the smallest positive integer N such that every 2-colouring of [1ÒN] = f1Ò 2Ò    ÒNg has a monochromatic homothetic copy of f1Ò 1 + sÒ 1 + s + tg. We show that f (sÒ t) = 4(s + t) + 1 whenever sÛg and tÛg are not congruent to 0 (modulo 4), where g = gcd(sÒ t). This can be viewed as a generalization of part of van der Waerden’s theorem on ari...

Abstract For all positive integers s and t, Brown et. al [1] defined f(s, t) to be the smallest positive integer N such that every 2-coloring of [1, N ] has a monochromatic homothetic copy of {1, 1+ s, 1+ s+ t}. They proved that f(s, t) ≤ 4(s + t) + 1 for all s, t and that the equality holds in the case where both s/g 6≡ 0 (mod 4) and t/g 6≡ 0 (mod 4) with g = gcd(s, t) and in many other cases....

We show how to use graphics hardware for tackling optimization problems arising in the field of computational geometry. We exemplarily discuss three problems, where combinatorial algorithms are inefficient or hard to implement. Given a set S of n point in the plane, the first two problems are to determine the smallest homothetic scaling of a star shaped polygon P enclosing S and to find the lar...

A novel method of texture primitive description using morphological skeleton is proposed. The skeleton of an object has the property that it is reduced to one point when the structuring element used for the skeletonization is exactly homothetic to the object. This method applies this property. This method minimizes the number of pixels contained in the skeleton. If we assume that the texture is...