131,964 research outputs found
Enumerating finite class-2-nilpotent groups on 2 generators
No full textWe compute the numbers g(n,2,2) of nilpotent groups of order n, of class atmost 2 generated by at most 2 generators, by giving an explicit formula for theDirichlet generating function \sum_{n=1}^\infty g(n,2,2)n^{-s}
Functional equations for zeta functions of groups and rings
No full textWe introduce a new method to compute explicit formulae for various zeta functions associated to groups and rings. The specific form of these formulae enables us to deduce local functional equations. More precisely, we prove local functional equations for the subring zeta functions associated to rings, the subgroup, conjugacy and representation zeta functions of finitely generated, torsion-free nilpotent (or T -)groups, and the normal zeta functions of T -groups of class 2. In particular we solve the two problems posed in [9, Section 5]. We deduce our theorems from a ‘blueprint result’ on certain p-adic integrals which generalises work of Denef and others on Igusa’s local zeta function. The Malcev correspondence and a Kirillov-type theory developed by Howe are used to ‘linearise’ the problems of counting subgroups and representations in T -groups, respectively
Normal subgroup growth in free class-2-nilpotent groups
No full textLet F2,d denote the free class-2-nilpotent group on d generators. We compute the normal zeta functions zeta^\triangleleftF2,d(s), prove that they satisfy local functional equations and determine their abscissae of convergence and pole orders
A qualitative and quantitative post-mortem analysis: Studying free-radical initiation processes via soft ionization mass spectrometry
No full textThe current article contains a review of the electrospray ionization-mass spectrometry characterization of polymers prepared via thermal- and photoinitiation processes. The used analysis method permits direct access to detailed endgroup information. For a qualitative and quantitative endgroup analysis, sophisticated methods have been developed which provide a detailed image of the incorporation propensity of thermally as well as photolytically generated radicals at the polymer chain termini. Such a post-mortem analysis of polymeric materials specifically allows for the quantification of the ability of radical fragments to initiate polymerization processes. Herein, the most recent progress in the field of mass spectrometric radical reactivity mapping is outlined and open questions as well as future directions are discussed. © 2012 Wiley Periodicals, Inc
Representation zeta functions of compact p-adic analytic groups and arithmetic groups
No full textWe introduce new methods from p-adic integration into the study of representation zeta functions associated to compact p-adic analytic groups and arithmetic groups. They allow us to establish that the representation zeta functions of generic members of families of p-adic analytic pro-p groups obtained from a global, `perfect' Lie lattice satisfy functional equations. In the case of `semisimple' compact p-adic analytic groups, we exhibit a link between the relevant p-adic integrals and a natural filtration of the locus of irregular elements in the associated semisimple Lie algebra, defined by centraliser dimension.Based on this algebro-geometric description, we compute explicit formulae for the representation zeta functions of principal congruence subgroups of the groups SL_3(O), where O is a compact discrete valuation ring of characteristic 0, and of the corresponding unitary groups. These formulae, combined with approximative Clifford theory, allow us to determine the abscissae of convergence of representation zeta functions associated to arithmetic subgroups of algebraic groups of type A_2. Assuming a conjecture of Serre on the Congruence Subgroup Problem, we thereby prove a conjecture of Larsen and Lubotzky on lattices in higher-rank semisimple groups for algebraic groups of type A_2 defined over number fields
Gesundheit voll- und teilzeitbeschäftigter Lehrerinnen
No full textSeibt R, Dizinger V, Dutschke D, Scheuch K. Gesundheit voll- und teilzeitbeschäftigter Lehrerinnen. In: Baur X, Glensk E, eds. Ethische Fragen in der Arbeitsmedizin. Hamburg: DGAUM; 2008: 432-436
Representation zeta functions of some compact p-adic analytic groups
No full textUsing the Kirillov orbit method, novel methods from p-adic integration and Clifford theory, we study representation zeta functions associated to compact p-adic analytic groups. In particular, we give general estimates for the abscissae of convergence of such zeta functions. We compute explicit formulae for the representation zeta functions of some compact p-adic analytic groups, defined over a compact discrete valuation ring O of characteristic 0. These include principal congruence subgroups of SL_2(O), without any restrictions on the residue field characteristic of O, as well as the norm one group SL_1(D) of a non-split quaternion algebra D over the field of fractions of O and its principal congruence subgroups. We also determine the representation zeta functions of principal congruence subgroups of SL_3(O) in the case that O has residue field characteristic 3 and is unramified over Z_
MeSH term explosion and author rank improve expert recommendations
No full textInformation overload is an often-cited phenomenon that reduces the productivity, efficiency and efficacy of scientists. One challenge for scientists is to find appropriate collaborators in their research. The literature describes various solutions to the problem of expertise location, but most current approaches do not appear to be very suitable for expert recommendations in biomedical research. In this study, we present the development and initial evaluation of a vector space model-based algorithm to calculate researcher similarity using four inputs: 1) MeSH terms of publications; 2) MeSH terms and author rank; 3) exploded MeSH terms; and 4) exploded MeSH terms and author rank. We developed and evaluated the algorithm using a data set of 17,525 authors and their 22,542 papers. On average, our algorithms correctly predicted 2.5 of the top 5/10 coauthors of individual scientists. Exploded MeSH and author rank outperformed all other algorithms in accuracy, followed closely by MeSH and author rank. Our results show that the accuracy of MeSH term-based matching can be enhanced with other metadata such as author rank
Going Beyond Counting First Authors in Author Co-citation Analysis
No full textThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Enumerating graded ideals in graded rings associated to free nilpotent Lie rings
No full textLee S, Voll C. Enumerating graded ideals in graded rings associated to free nilpotent Lie rings. Mathematische Zeitschrift. 2018;290(3-4):1249-1276.We compute the zeta functions enumerating graded ideals in the graded Lie rings associated with the free d-generator Lie rings f(c,d) of nilpotency class c for all c <= 2 and for (c, d) is an element of{( 3, 3), ( 3, 2), ( 4, 2)}. We apply our computations to obtain information about p-adic, reduced, and topological zeta functions, in particular pertaining to their degrees and some special values
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