Comparative study of the catalytic growth of patterned carbon nanotube films

Three different catalysts (Fe, Ni, Co nitrates dissolved in ethanol) were patterned on a SiO2/Si substrate and multi-wall carbon nanotubes were grown by catalytic decomposition of acetylene. We compare the growth of the carbon nanostructures in the temperature range between 580C and 1000C. With our experimental set-up the catalyst solutions of cobalt and nickel were found to be less efficient than the one of iron. An optimal production of multi-wall nanotubes was observed at temperatures between 650C and 720C with the iron solution as catalyst. We found a tendency towards thicker structures with higher temperatures. Finally, we suggest a mechanism for the growth of these carbon structures.Comment: 5 pages, 5 figure

Isoperimetric Functions of Finitely Generated Nilpotent Groups

We show that the isoperimetric function of a finitely generated nilpotent group of class c is bounded aboveby a polynomial of degree 2c

Online Association Rule Mining

We present a novel algorithm to compute large itemsets online. The user is free to change the support threshold any time during the first scan of the transaction sequence. The algorithm maintains a superset of all large itemsets and for each itemset a shrinking, deterministic interval on its support. After at most 2 scans the algorithm terminates with the precise support for each large itemset. Typically our algorithm is by an order of magnitude more memory efficient than Apriori or DIC

Integration into Prolog

We presentanintegration of Mathematica into Prolog using MathLink. We illustrate the interplaybetween the di#erent components byevaluating a simple example. The motivation based on algebraic modeling as well as an application from combinatorial group theory are brie#y sketched. 1 Introduction Many Prolog programming tasks need # besides the built-in predicates # access to additional functionalities such as those provided by relational databases, statistics packages or symbolic computation systems. While it is usually not feasible to implement these functionalities in Prolog itself, they are available as stand-alone applications. On one hand, these applications usually o#er means, like an external C-interface, to integrate them into other software tools. On the other hand, Prolog interpreters typically o#er an external interface as well, e.g. Modula Prolog #Mul86, Mul91# or SWI-Prolog #Wie92#. Hence we wanted to develop techniques to integrate stand-alone applications into Prolog c..

A Generalisation of the Cantor-Zassenhaus Algorithm

We generalise the Cantor-Zassenhaus algorithm for factoring polynomials over finite fields. The generalisation yields a class of factorisation algorithms. We compute their factorisation probability and their least upper bound. We then give a simple characterisation of the algorithms reaching the least upper bound. As an example we show the Cantor-Zassenhaus and the Ben-Or algorithms have a factorisation probability equal to the least upper bound. 1 Introduction The algorithm by Cantor & Zassenhaus (1981) computes the factorisation a univariate polynomial over a finite field using a probabilistic method. Let f be the univariate polynomial over the finite field F q of q elements which we want to factor. The general idea is to construct a non-trivial zero-divisor u in F q [X]=(f ). Computing the gcd of u and f then yields a proper factor of f . To illustrate the algorithm let q be odd. The case for q even is treated similarly. By the distinct degree factorisation, see Knuth (1981) x4...

Isoperimetric Functions of Amalgams of Finitely Generated Nilpotent Groups along a Cyclic Subgroup

We show that amalgams of finitely generated torsionfree nilpotent groups of class c along a cyclic subgroup satisfy a polynomial isoperimetric inequality of degree 4c 2 . The distortion of the amalgamated subgroup is bounded above by a polynomial of degree c. We also give an example of a non-cyclic amalgam of finitely generated torsionfree nilpotent groups along an abelian, isolated and normal subgroup having an exponential isoperimetric inequality

Isoperimetric Functions of Amalgamations of Nilpotent Groups

We consider amalgamations of finitely generated nilpotent groups of class c. We show that doubles satisfy a polynomial isoperimetric inequality of degree 2c 2 . Generalising doubles we introduce non-twisted amalgamations and show that they satisfy a polynomial isoperimetric inequality as well. We give a sufficient condition for amalgamations along abelian subgroups to be non-twisted and thereby to satisfy a polynomial isoperimetric inequality. We conclude by giving an example of a twisted amalgamation along an abelian subgroup having an exponential isoperimetric function

A Generalisation of the Cantor-Zassenhaus Algorithm

We generalise the Cantor-Zassenhaus algorithm for factoring polynomials over finite fields. The generalisation yields a set of factorisation algorithms. We compute their factorisation probability and their least upper bound. We also give a simple characterisation of the algorithms reaching the least upper bound. As an example we analyse the Cantor-Zassenhaus and the Ben-Or algorithms. 1 Introduction Let f be the univariate polynomial over the finite field F q of q elements which we want to factor. By the distinct degree factorisation, see Knuth (1981) x4.5.2 or von zur Gathen & Shoup (1992), we assume without loss of generality that f is the product of k pairwise distinct, irreducible, monic polynomials all of the same degree, i.e. f is an equal-degree polynomial. For 2 6 j q the algorithm by Cantor & Zassenhaus (1981) chooses a uniform random polynomial h 2 F q [X] and computes the gcd of f and h q\Gamma1 2 \Sigma 1 mod f yielding a proper factor of f with probability 1 \Gamma 1=2..

Potential- und Verteilungsmodelle für den schweizerischen Stückgutverkehr nach Regionen: (auf der Grundlage der Gütertransportstatistik 1974)

Nachdem das Institut für Verkehrsplanung und Transporttechnik (IVT) die Untersuchungen über Potential- und Verteilungsmodelle am Güterwagenladungsverkehr durchführte, wurde es vom Stab GVK-CH beauftragt, eine ähnliche Studie für den Stückgutverkehr zu erarbeiten

Isoperimetric Functions of Finitely Generated Nilpotent Groups

We show that the isoperimetric function of a finitely generated nilpotent group of class c is bounded above by a polynomial of degree 2c