Our main result is that every graph G on n ≥ 10r vertices with minimum degree δ(G) ≥ (1−1/10r)n has a fractional Kr-decomposition. Combining this result with recent work of Barber, Kühn, Lo and Osthus leads to the best known minimum degree thresholds for exact (non-fractional) F -decompositions for a wide class of graphs F (including large cliques). For general k-uniform hypergraphs, we give a ...

This paper presents an approach to texture image segmentation using a family of fractional discrimination functions. In contrast to the conventional methods, the proposed functions provide uniform treatment of the existing functions and operators for selective feature extraction. The effectiveness of fractional discrimination functions for texture feature detection is demonstrated in the presen...

We present a novel frequency partitioning technique of fractional frequency reuse (FFR) that reduces the effect of co-channel interference and increases the capacity of OFDM systems. The usable sub-channel sets are classified into the common sub-channel sets for all cells and the dedicated sub-channel sets for specific cell types in FFR. The proposed fractional frequency reuse with ordering sch...

Extending the notion of (random) k-out graphs, we consider when the k-out hypergraph is likely to have a perfect fractional matching. In particular, we show that for each r there is a k = k(r) such that the k-out r-uniform hypergraph on n vertices has a perfect fractional matching with high probability (i.e., with probability tending to 1 as n → ∞) and prove an analogous result for r-uniform r-...

Background: Air pollution is a serious threat to children health. Given that children spend over 80% of their time indoors, understanding transport of pollutants from outdoor to indoor environments is important for assessing the impact of exposure to outdoor pollution on children health. The most common advice given during a smoke pollution episode is to stay indoors. How well this works depend...

As a generalization of the Fourier transform, the fractional Fourier transform was introduced and has been further investigated both in theory and in applications of signal processing. We obtain a sampling theorem on shift-invariant spaces associated with the fractional Fourier transform domain. The resulting sampling theorem extends not only the classical Whittaker-Shannon-Kotelnikov sampling ...

A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most O(n/ log n) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is provided for fractional partitioning both fo...

A new, constructive proof with a small explicit constant is given to the Erdős-Pyber theorem which says that the edges of a graph on n vertices can be partitioned into complete bipartite subgraphs so that every vertex is covered at most O(n/ logn) times. The theorem is generalized to uniform hypergraphs. Similar bounds with smaller constant value is provided for fractional partitioning both for...

BACKGROUND Numerous studies have shown associations between ambient air pollution and daily mortality. OBJECTIVES Our goal was to investigate the association of ambient air pollution and daily mortality in Erfurt, Germany, over a 10.5-year period after the German unification, when air quality improved. METHODS We obtained daily mortality counts and data on mass concentrations of particulate...