The Optimal Rubbling Number of Ladders, Prisms and M\"obius-ladders

A pebbling move on a graph removes two pebbles at a vertex and adds one pebble at an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed. In this new move, one pebble each is removed at vertices $v$ and $w$ adjacent to a vertex $u$, and an extra pebble is added at vertex $u$. A vertex is reachable from a pebble distribution if it is possible to move a pebble to that vertex using rubbling moves. The optimal rubbling number is the smallest number $m$ needed to guarantee a pebble distribution of $m$ pebbles from which any vertex is reachable. We determine the optimal rubbling number of ladders ($P_n\square P_2$), prisms ($C_n\square P_2$) and M\"oblus-ladders

A KKK-rendszer és az OKKR viszonya

A magyar felsőoktatásban az ezredfordulót követően már történtek nagy áttörések: a képzés rendszerében akkor, amikor áttért a bolognai struktúrára, az oktatás szabályozásában pedig akkor, amikor a korábbi bemenet- és folyamatszabályozásról áttért a képzési és kimeneti követelmények (KKK) formájú szabályozásra. Az Európai Képesítési Keretrendszer (EKKR) most egy újabb nagy kihívást jelent: az eddigi, valóban áttörést jelentő, mégis csak felemás fordulatot – az alapvetően input jellegű szabályozás kiegészítését output jellegű elemekkel – az EKKR teljessé akarja tenni azzal, hogy kizárólag kimeneti jellemzőkkel kívánja beazonosítani, definiálni az egyes képzési szinteket

Poisson Reductions of Master Integrable Systems on Doubles of Compact Lie Groups

We consider three 'classical doubles' of any semisimple, connected and simply connected compact Lie group $G$: the cotangent bundle, the Heisenberg double and the internally fused quasi-Poisson double. On each double we identify a pair of 'master integrable systems' and investigate their Poisson reductions. In the simplest cotangent bundle case, the reduction is defined by taking quotient by the cotangent lift of the conjugation action of $G$ on itself, and this naturally generalizes to the other two doubles. In each case, we derive explicit formulas for the reduced Poisson structure and equations of motion and find that they are associated with well known classical dynamical $r$-matrices. Our principal result is that we provide a unified treatment of a large family of reduced systems, which contains new models as well as examples of spin Sutherland and Ruijsenaars--Schneider models that were studied previously. We argue that on generic symplectic leaves of the Poisson quotients the reduced systems are integrable in the degenerate sense, although further work is required to prove this rigorously.Comment: 33 pages, minor edits in v2, correction of small typos in v

Phase field theory of interfaces and crystal nucleation in a eutectic system of fcc structure: II. Nucleation in the metastable liquid immiscibility region

The official version of this Article can be accessed from the link below - Copyright @ 2007 American Institute of PhysicsIn the second part of our paper, we address crystal nucleation in the metastable liquid miscibility region of eutectic systems that is always present, though experimentally often inaccessible. While this situation resembles the one seen in single component crystal nucleation in the presence of a metastable vapor-liquid critical point addressed in previous works, it is more complex because of the fact that here two crystal phases of significantly different compositions may nucleate. Accordingly, at a fixed temperature below the critical point, six different types of nuclei may form: two liquid-liquid nuclei: two solid-liquid nuclei; and two types of composite nuclei, in which the crystalline core has a liquid "skirt," whose composition falls in between the compositions of the solid and the initial liquid phases, in addition to nuclei with concentric alternating composition shells of prohibitively high free energy. We discuss crystalline phase selection via exploring/identifying the possible pathways for crystal nucleation.This work has been supported by the Hungarian Academy of Sciences under contract No. OTKA-K-62588 and by the ESA PECS Nos. 98021 and 98043

Poisson limit of an inhomogeneous nearly critical INAR(1) model

An inhomogeneous first--order integer--valued autoregressive (INAR(1)) process is investigated, where the autoregressive type coefficient slowly converges to one. It is shown that the process converges weakly to a Poisson or a compound Poisson distribution.Comment: Latex2e pdfeTex Version 3, 22 pages, submitted to ACTA Sci. Math. (Szeged

Constructions for the optimal pebbling of grids

In [C. Xue, C. Yerger: Optimal Pebbling on Grids, Graphs and Combinatorics] the authors conjecture that if every vertex of an infinite square grid is reachable from a pebble distribution, then the covering ratio of this distribution is at most $3.25$. First we present such a distribution with covering ratio $3.5$, disproving the conjecture. The authors in the above paper also claim to prove that the covering ratio of any pebble distribution is at most $6.75$. The proof contains some errors. We present a few interesting pebble distributions that this proof does not seem to cover and highlight some other difficulties of this topic