Tur\'an Graphs, Stability Number, and Fibonacci Index

The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.Comment: 11 pages, 3 figure

Trees with Given Stability Number and Minimum Number of Stable Sets

We study the structure of trees minimizing their number of stable sets for given order $n$ and stability number $\alpha$. Our main result is that the edges of a non-trivial extremal tree can be partitioned into $n-\alpha$ stars, each of size $\lceil \frac{n-1}{n-\alpha} \rceil$ or $\lfloor \frac{n-1}{n-\alpha}\rfloor$, so that every vertex is included in at most two distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate

Metallography of Al-Si Alloys with Alloying By Fe up to 1%

Metallographic analysis of aluminum-silicon alloys with different silicon content from 0 to 12% carried out. All alloys were differed in 2% by silicon amount from each other and all of them were additionally alloyed with iron in an amount of up to 1% in order to improve the technological properties in a die casting process. The paper shows the distribution of structural components of alloys made by electronic microscopy.     Keywords: aluminum-silicon alloys, metallography analysis, eutectic, structure, cast alloy, alloying, electron microscop

Fast Algorithm for Partial Covers in Words

A factor $u$ of a word $w$ is a cover of $w$ if every position in $w$ lies within some occurrence of $u$ in $w$. A word $w$ covered by $u$ thus generalizes the idea of a repetition, that is, a word composed of exact concatenations of $u$. In this article we introduce a new notion of $\alpha$-partial cover, which can be viewed as a relaxed variant of cover, that is, a factor covering at least $\alpha$ positions in $w$. We develop a data structure of $O(n)$ size (where $n=|w|$) that can be constructed in $O(n\log n)$ time which we apply to compute all shortest $\alpha$-partial covers for a given $\alpha$. We also employ it for an $O(n\log n)$-time algorithm computing a shortest $\alpha$-partial cover for each $\alpha=1,2,\ldots,n$

Current distribution and giant magnetoimpedance in composite wires with helical magnetic anisotropy

The giant magnetoimpedance effect in composite wires consising of a non-magnetic inner core and soft magnetic shell is studied theoretically. It is assumed that the magnetic shell has a helical anisotropy. The current and field distributions in the composite wire are found by means of a simultaneous solution of Maxwell equations and the Landau-Lifshitz equation. The expressions for the diagonal and off-diagonal impedance are obtained for low and high frequencies. The dependences of the impedance on the anisotropy axis angle and the shell thickness are analyzed. Maximum field sensitivity is shown to correspond to the case of the circular anisotropy in the magnetic shell. It is demonstrated that the optimum shell thickness to obtain maximum impedance ratio is equal to the effective skin depth in the mahnetic material.Comment: 23 pages, 7 figure

Evolution of community structure in the world trade web

In this note we study the bilateral merchandise trade flows between 186 countries over the 1948-2005 period using data from the International Monetary Fund. We use Pajek to identify network structure and behavior across thresholds and over time. In particular, we focus on the evolution of trade "islands" in the a world trade network in which countries are linked with directed edges weighted according to fraction of total dollars sent from one country to another. We find mixed evidence for globalization.Comment: To be submitted to APFA 6 Proceedings, 8 pages, 3 Figure

Catalytic conversion of methanol to larger organic molecules over crystalline forsterite: laboratory study and astrophysical implications

Laboratory catalytic reactions of methanol over heated crystalline silicates (forsterite) lead to the formation of gas-phase olefinic and polycyclic aromatic hydrocarbon (PAH) molecules, and are of potential importance in astrophysical environments including hot molecular cores, protoplanetary disks and shocks. In our experiments the methanol reagent, together with intermediate and product gas-phase molecular species were detected using time-of-flight mass-spectrometry (TOF-MS). A solid deposited on the crystalline forsterite surface was examined subsequently using high-resolution transmission electron microscopy and thermal gravimetric techniques and found to comprise amorphous and graphitic carbon. The chemical players in this work – gas-phase methanol, crystalline silicates and PAHs, have been identified spectroscopically in a range of astrophysical environments including young and evolved stars, protoplanetary disks, comets, captured dust particles and meteorites. It is envisaged that reactions on bare dust grains as studied here both experimentally and theoretically through DFT calculations, can have implications for chemical transformations and conversions, in forming PAH molecules and potentially in the synthesis of prebiotic molecules

Information entropy in fragmenting systems

The possibility of facing critical phenomena in nuclear fragmentation is a topic of great interest. Different observables have been proposed to identify such a behavior, in particular, some related to the use of information entropy as a possible signal of critical behavior. In this work we critically examine some of the most widespread used ones comparing its performance in bond percolation and in the analysis of fragmenting Lennard Jones Drops.Comment: 3 pages, 3 figure

An integrated information management model for proactive prevention of struck-by-falling-object accidents on construction sites

The construction industry is one of the most hazardous industries in many countries. Struck-by-falling-object accidents are not given adequate attention even though they are of great importance on construction sites. The objective of this paper is to analyze the proactively preventive information requirement of struck-by-falling-object accidents and propose an integrated information management model using a ZigBee RFID sensor network to fulfill these requirements. First, the frequency of particular type of objects is analyzed based on vast historical accident cases. Next, this paper analyzes the proactively preventive information requirement of struck-by-falling-object accidents and brought forth an integrated information management model. Furthermore, considering the crucial and controllable objects, an integrated information management model is proposed. This study would provide a possible approach for tracking struck-by-falling-object accidents based on real-time information for proactive prevention and could serve as a foundation for further study. © 2012 Elsevier B.V. All rights reserved