New Ore‐Type Conditions for H‐Linked Graphs

For a fixed (multi)graph H, a graph G is H‐linked if any injection f: V(H)→V(G) can be extended to an H‐subdivision in G. The notion of an H ‐linked graph encompasses several familiar graph classes, including k‐linked, k‐ordered and k‐connected graphs. In this article, we give two sharp Ore‐type degree sum conditions that assure a graph G is H ‐linked for arbitrary H. These results extend and refine several previous results on H ‐linked, k‐linked, and k‐ordered graphs. © 2011 Wiley Periodicals, Inc. J Graph Theory 71:69–77, 2012     

Shunting yard operations: Theoretical aspects and applications

Almost ever since freight has been transported via rail, shunting yards (also called classification or marshaling yards) are operated in order to separate freight trains and reassemble new trains. The efficient use of shunting yards has a deep impact on the efficiency and reliability of rail freight services. Thus, much research on shunting yards has been published, starting from the 1950s. Lately, several publications mostly focusing on the sorting procedures have livened up research on shunting yards. This paper reviews the literature on the operational processes at shunting yards over the last 40 years and discusses the operational challenges of freight transshipment. The approaches are classified according to different sorting strategies which allows an easy access to the models for both, researchers and practitioners. The paper concludes with an overview on future research challenges.     

In-situ Raman spectroscopy used to study and control the initial growth phase of microcrystalline absorber layers for thin-film silicon solar cells

The continuous deposition of microcrystalline silicon has been monitored with in-situ Raman spectroscopy. The process and measurement settings were chosen such that one spectrum was taken during approximately 9 nm of layer growth. This allows observing the crystallinity in the initial growth phase of microcrystalline silicon absorber layers. The influence of different p-doped seed layers has been studied. Under constant deposition conditions, an initial decrease in crystallinity was observed over the first tens of nanometers. By profiling the process gas flows during the initial phase it was possible to reduce the amount of amorphous material that was detected during the initial phase of deposition.     

On the largest prime factor of numerators of Bernoulli numbers

We prove that for almost all $n$, the numerator of the Bernoulli number $B_{2n}$ is divisible by a large prime.     

A performance analysis of channel fragmentation in dynamic spectrum access systems

Dynamic Spectrum Access systems offer temporarily available spectrum to opportunistic users capable of spreading transmissions over a number of non-contiguous subchannels. Such methods can be highly beneficial in terms of spectrum utilization, but excessive fragmentation degrades performance and hence off-sets the benefits. To get some insight into acceptable levels of fragmentation, we present experimental and analytical results derived from a mathematical model. According to the model, a system operates at capacity serving requests for bandwidth by assigning a collection of one or more gaps of unused bandwidth to each request as bandwidth becomes available. Our main result is a proof that, even if fragments can be arbitrarily small, the system remains stable in the sense that the average total number of fragments remains bounded. Within the class of dynamic fragmentation models, including models of dynamic storage allocation that have been around for many decades, this result appears to be the first of its kind. In addition, we provide extensive experimental results that describe behavior, at times unexpected, of fragmentation as parameter values are varied. Different scanning rules for searching gaps of available spectrum, all covered by the above stability result, are also studied. Our model applies to dynamic linked-list storage allocation, and provides a novel analysis in that domain. We prove that, interestingly, a version of the 50?% rule of the classical, non-fragmented allocation model holds for the new model as well. Overall, the paper provides insights into the behavior of practical fragmentation algorithms.     

Two-Component Two-Compressible Flow in a Porous Medium

We prove existence of solutions of a two-compressible (liquid and gas) phase flow model in porous media with two components (water and hydrogen). This model is obtained by writing the mass conservation for each component in each phase. We suppose that the mass exchange between dissolved hydrogen and hydrogen in the gas phase is supposed finite. This mass exchange is modeled by a source term on each mass conservation equations.     

On the number of nonzero digits of the partition function

Let p(n) be the function that counts the number of partitions of n. Let b ≥ 2 be a fixed positive integer. In this paper, we show that for almost all n the sum of the digits of p(n) in base b is at least log n/(7log log n). Our proof uses the first term of Rademacher’s formula for p(n).