Geometric Generalization of the Exponential Law

For the multivariate ℓ₁-norm symmetric distributions, which are generalizations of the n-dimensional exponential distribution with independent marginals, a geometric representation formula is given, together with some of its basic properties. This formula can especially be applied to a new developed and statistically well motivated system of sets. From that the distribution of a t-statistic adapted for the two-parameter exponential distribution and its generalizations is determined. Asymptotic normality of this adapted t-statistic is shown under certain conditions.     

In-situ observation of MOVPE epitaxial growth

Metal organic vapour phase epitaxy (MOVPE) is nowadays one of the leading techniques for epitaxial growth. While the processes in the gas phase of MOVPE are reasonably well understood, the processes on the growing surface are not. This situation is in contrast to molecular beam epitaxy (MBE), where considerable knowledge about growth processes on the surface could be gained. The main reason is that all the UHV-based classical surface-science tools (using electrons and ions), especially reflection high-energy electron diffraction, can be applied in the vacuum-based MBE but not under the gas-phase conditions of MOVPE. This situation has changed in the last decade since optical surface-science tools have been developed. Especially, with the linear optical techniques like reflectance anisotropy spectroscopy and spectroscopic ellipsometry, there is now a quasi-standard tool at hand which allows for the study of all kinds of pregrowth and growth situations in MOVPE (in MBE of course, as well). These optical methods give, moreover, chemical information also. In this article we will describe shortly the features of these optical techniques and then concentrate on III-V-semiconductor growth. The spectral definition of surface reconstructions and time-resolved studies of phase transitions between them (adsorption/desorption kinetics of group-III and group-V elements) are discussed next. Under growth, the surfaces can be classified and defined according to their optical surface response into a pressure versus temperature phase diagram. The regions of such a phase diagram correspond to different geometrical and chemical surface structures and consequently lead to different growth modes. Finally, as an example of modern nanogrowth, monitoring of the growth of quantum-dot structures is presented. Received: 2 August 2001 / Accepted: 23 October 2001 / Published online: 3 April 2002     

Heteroaryl substituted ansa‐titanocene anti‐cancer drugs derived from fulvenes and titanium dichloride

Starting from 2‐furylfulvene (1a) , 2‐thiophenylfulvene (1b) , and 1‐methyl‐2‐pyrrolylfulvene (1c), [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐furyl)ethanediyl] titanium dichloride (2a) , [1,2‐di(cyclopentadienyl)‐1,2‐di‐(2‐thiophenyl)ethanediyl] titanium dichloride (2b) , and [1,2‐di(cyclopentadienyl)‐1,2‐bis‐(1‐methyl‐2‐pyrrolyl)ethanediyl] titanium dichloride (2c) were synthesized. When titanocenes (2a–c) were tested against pig kidney carcinoma cells (LLC‐PK), inhibitory concentrations (50%) of 4.5 × 10^?4 M , 2.9 × 10^?4 M and 2.0 × 10^?4 M respectively were observed. Copyright © 2005 John Wiley & Sons, Ltd.     

On the Floer homology of cotangent bundles

This paper concerns Floer homology for periodic orbits and for a Lagrangian intersection problem on the cotangent bundle T* M of a compact orientable manifold M. The first result is a new L^∞ estimate for the solutions of the Floer equation, which allows us to deal with a larger—and more natural—class of Hamiltonians. The second and main result is a new construction of the isomorphism between the Floer homology and the singular homology of the free loop space of M in the periodic case, or of the based loop space of M in the Lagrangian intersection problem. The idea for the construction of such an isomorphism is to consider a Hamiltonian that is the Legendre transform of a Lagrangian on T M and to construct an isomorphism between the Floer complex and the Morse complex of the classical Lagrangian action functional on the space of W^1,2 free or based loops on M. © 2005 Wiley Periodicals, Inc.     

The Galois representations associated to a Drinfeld module in special characteristic—III: Image of the group ring

Let K be a finitely generated field of transcendence degree 1 over a finite field, and set G_K?Gal(K^sep/K). Let φ be a Drinfeld A-module over K in special characteristic. Set E?End_K(φ) and let Z be its center. We show that for almost all primes p of A, the image of the group ring A_p[G_K] in End_A(T_p(φ)) is the commutant of E. Thus, for almost all p it is a full matrix ring over Z⊗_AA_p. In the special case E=A it follows that the representation of G_K on the p-torsion points φ[p] is absolutely irreducible for almost all p.     

On the complexity of recognizing perfectly orderable graphs

The question whether a polynomial time recognition algorithm for the class of perfectly orderable graphs exists was posed by Chvátal in 1981 when he introduced the notion of perfect orders. Since then several classes of perfectly orderable graphs have been identified. In this note we prove that recognizing perfectly orderable graphs is NP-complete.     

On the cardinality of the Pareto set in bicriteria shortest path problems

Computing shortest paths with two or more conflicting optimization criteria is a fundamental problem in transportation and logistics. We study the problem of finding all Pareto-optimal solutions for the multi-criteria single-source shortest-path problem with nonnegative edge lengths. The standard approaches are generalizations of label-setting (Dijkstra) and label-correcting algorithms, in which the distance labels are multi-dimensional and more than one distance label is maintained for each node. The crucial parameter for the run time and space consumption is the total number of Pareto optima. In general, this value can be exponentially large in the input size. However, in various practical applications one can observe that the input data has certain characteristics, which may lead to a much smaller number—small enough to make the problem efficiently tractable from a practical viewpoint. For typical characteristics which occur in various applications we study in this paper whether we can bound the size of the Pareto set to a polynomial size or not. These characteristics are also evaluated (1) on a concrete application scenario (computing the set of best train connections in view of travel time, fare, and number of train changes) and (2) on a simplified randomized model. It will turn out that the number of Pareto optima on each visited node is restricted by a small constant in our concrete application, and that the size of the Pareto set is much smaller than our worst case bounds in the randomized model. A preliminary short version of this paper appeared in the Proceedings of the 5th Workshop on Algorithm Engineering (WAE 2001), LNCS 2141, Springer Verlag, pp. 185–197 (2001) under the title “Pareto shortest paths is often feasible in practice.”