赋权图的w密度和w平衡性

The notion of w-density for the graphs with positive weights on vertices and nonnegative weights on edges is introduced. A weighted graph is called w-balanced if its w-density is no less than the w-density of any subgraph of it. In this paper,a good characterization of w-balanced weighted graphs is given. Applying this characterization ,many large w-balanced weighted graphs are formed by combining smaller ones. In the case where a graph is not w-balanced,a polynomial-time algorithm to find a subgraph of maximum w-density is proposed. It is shown that the w-density theory is closely related to the study of SEW(G,w) games.     

Global entropy solutions to the relativistic Euler equations for a class of large initial data

We are concerned with global entropy solutions to the relativistic Euler equations for a class of large initial data which involve the interaction of shock waves and rarefaction waves. We first carefully analyze the global behavior of the shock curves, the rarefaction wave curves, and their corresponding inverse curves in the phase plane. Based on these analyses, we use the Glimm scheme to construct global entropy solutions to the relativistic Euler equations for the class of large discontinuous initial data.Received: May 23, 2004     

Normally contracting Lie group actions

We show that there are no normally contracting actions of unimodular Lie groups on closed manifolds.     

On the existence of polyanalytic functions

We give a sharp estimate for the codimension of the poly‐Bergman space in the poly‐Bergman space over the punctured domain. It is established the behaviour at the infinity point of polyanalytic Bergman functions on the complement of closed disks. In the main result of the paper, we prove that for and the j‐polyanalytic Bergman space over the domain U is trivial precisely when the complement of U has at most one point and at most two points or three points lying in a circle, respectively. We point out the differences between the domains over which the Bergman space and the non‐analytic poly‐Bergman space are trivial.     

A General Tractable Density Concept for Graphs

In many applications it is an important algorithmic task to find a densest subgraph in an input graph. The complexity of this task depends on how density is defined. If density means the ratio of the number of edges and the number of vertices in the subgraph, then the algorithmic problem has long been known efficiently solvable. On the other hand, the task becomes NP-hard with closely related but somewhat modified concepts of density. To capture many possible tractable density concepts of interest in a common model, we define and analyze a general concept of density, called F-density. Here F is a family of graphs and we are looking for a subgraph of the input graph, such that this subgraph is the densest in terms of containing the highest number of graphs from F relative to the size of the subgraph. We show that for any fixed finite family F, a subgraph of maximum F-density can be found in polynomial time. As our main tool we develop an algorithm, that may be of independent interest, which can find an independent set of maximum independence ratio in a certain class of weighted graphs. The independence ratio is the weight of the independent set divided by the weight of its neighborhood. This work was supported in part by NSF grants ANI-0220001 and CCF-0634848.     

Dunford–Pettis properties, Hilbert spaces and projective tensor products

We study complete continuity properties of operators onto ℓ₂ and prove several results in the Dunford–Pettis theory of JB^*-triples and their projective tensor products, culminating in characterisations of the alternative Dunford–Pettis property for where E and F are JB^*-triples.     

A nonlinear functional for general scalar hyperbolic conservation laws

A generalized entropy functional was introduced in [T.-P. Liu, T. Yang, A new entropy functional for scalar conservation laws, Comm. Pure Appl. Math. 52 (1999) 1427-1442] for the scalar hyperbolic conservation laws with convex flux function. This functional was crucially used in the functional approach to the L¹ stability study on the system of hyperbolic conservation laws when each characteristic field is either genuinely nonlinear or linearly degenerate. However, how to construct the generalized entropy functional for scalar conservation laws with general flux, and then how to apply the functional approach to the L¹ study on general systems are still open. In this paper, we construct a new nonlinear functional which gives some partial answer to this question and we expect the analysis will shed some light on the future investigation in this direction.     

Fully-Dynamic Min-Cut*

We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic graph in worst-case time per edge insertion or deletion. Within logarithmic factors, this matches the best time bound for 1-edge connectivity. Previously, no o(n) bound was known for edge connectivity above 3, and even for 3-edge connectivity, the best update time was O(n^2/3), dating back to FOCS'92. Our algorithm maintains a concrete min-cut in terms of a pointer to a tree spanning one side of the cut plus ability to list the cut edges in O(log n) time per edge. By dealing with polylogarithmic edge connectivity, we immediately get a sampling based expected factor (1+o(1)) approximation to general edge connectivity in time per edge insertion or deletion. This algorithm also maintains a pointer to one side of a near-minimal cut, but if we want to list the cut edges in O(log n) time per edge, the update time increases to . * A preliminary version of this work was presented at the The 33rd ACM Symposium on Theory of Computing( STOC) [22], Crete, Greece, July 2001.     

Notwendige und hinreichende Strahlenschutzmessungen bei Arbeiten mit Quellen ionisierendcr Strahlung: Praktische Bemerkungen zu den §§ 23 und 24 der Strahlenschutzverordnung—Teil 1: Allgemeines

Bei Arbeiten mit Quellen ionisierender Strahlung oder mit Geräten und Anlagen, die solche Quellen als funktionsbedingte Bestandteile enthalten, sind im allgemeinen Strahlenschutzmessungen erforderlich. Im engeren Sinne dienen diese Messungen der Überwachung der Einhaltung vorgegebener Dosisleistungswerte, Aktivitätskonzentrationen sowie Kontaminationsgrößen. Im weiteren Sinne Iassen sich den Strahlenschutzmessungen drei Aspekte zuordnen [1]:

a) Ermittlung notwendiger Maßnahmen für einen wirksamen Strahlenschutz in einer gegebenen Situation;

b) Überprüfung der Wirksamkeit getroffener Strahlenschutzmaßnahmen in einer gegebenen Situation;

c) Beschränkung auf notwendige Maßnahmen.     

The Lebesgue measure of the algebraic difference of two random Cantor sets

In this paper we consider a family of random Cantor sets on the line. We give some sufficient conditions when the Lebesgue measure of the arithmetic difference is positive. Combining this with the main result of a recent joint paper of the second author with M. Dekking we construct random Cantor sets F₁, F₂ such that the arithmetic difference set F₂ − F₁ does not contain any intervals but ?eb(F₂ − F₁)> 0 almost surely, conditioned on non-extinction.