Contribution of “unusual” domain walls to the magnetoresistance of multilayer magnetic structures

The contribution to electrical resistance due to scattering of charge carriers by domain walls is analyzed. It is revealed that “unusual” domain walls are created by frustrations in ferromagnet-antiferromagnet multilayer magnetic structures. The thickness of an unusual domain wall is substantially less than that of a usual domain wall. It is shown that scattering of charge carriers by unusual domain walls can contribute significantly to the magnetoresistance of ferromagnet-antiferromagnet multilayer magnetic structures. An analysis of the contribution made by the Levy-Zhang mechanism to the magnetoresistance demonstrates that the initial estimate obtained for this contribution is considerably exaggerated.     

On removable even circuits in graphs

Let G be a connected graph with minimum degree at least 3. We prove that there exists an even circuit C in G such that G−E(C) is either connected or contains precisely two components one of which is isomorphic to a 1-bond. We further prove sufficient conditions for there to exist an even circuit C in a 2-connected simple graph G such that G−E(C) is 2-connected. As a consequence of this, we obtain sufficient conditions for there to exist an even circuit C in a 2-connected graph G for which G−E(C) is 2-connected.     

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On the Application of the Auxiliary Problem Principle

The auxiliary problem principle (APP) derives from a general theory on decomposition-coordination methods establishing a comprehensive framework for both one-level and two-level methods. In this paper, the results of the two-level methods of APP are specialized for an efficient application to some engineering problems.     

Investigating buyer and seller strategies in online auctions

The annual turnover of online auctions is already in tens of billions of dollars and this amount is predicted to grow substantially over the next few years. Hence, it is important to know how buyers and sellers can influence their chances of success. Therefore, data were collected from eBay auctions for three different categories of collectible items, namely those with a published guide price, those with a rough guide price and those having no easily obtainable guide price. The options available to buyers and sellers of items were then analysed. It was found that it was hard for the seller to influence an item's achieved price significantly, apart from items with no guide price where the starting price could have an effect. Most bidders bid close to the current value and so there were insufficient data to determine the consequences of timing on the placing of high bids. For low bids, delaying a bid was found to improve significantly the chances of winning for one of the data sets.