4,246 research outputs found
Five Observations Concerning the Intended Meaning of the Intuitionistic Logical Constants
This paper contains five observations concerning the intended meaning of the intuitionistic logical constants: (1) if the explanations of this meaning are to be based on a non-decidable concept, that concept should not be that of 'proof'; (2) Kreisel's explanations using extra clauses can be significantly simplified; (3) the impredicativity of the definition of → can be easily and safely ameliorated; (4) the definition of → in terms of 'proofs from premises' results in a loss of the inductive character of the definitions of ∨ and ∃; and (5) the same occurs with the definition of ∀ in terms of 'proofs with free variables
Beauville structures in finite p-groups
We study the existence of (unmixed) Beauville structures in finite
-groups, where is a prime. First of all, we extend Catanese's
characterisation of abelian Beauville groups to finite -groups satisfying
certain conditions which are much weaker than commutativity. This result
applies to all known families of -groups with a good behaviour with respect
to powers: regular -groups, powerful -groups and more generally potent
-groups, and (generalised) -central -groups. In particular, our
characterisation holds for all -groups of order at most , which allows
us to determine the exact number of Beauville groups of order , for , and of order , for . On the other hand, we determine which
quotients of the Nottingham group over are Beauville groups, for
an odd prime . As a consequence, we give the first explicit infinite family
of Beauville -groups, and we show that there are Beauville -groups of
order for every
Outer commutator words are uniformly concise
We prove that outer commutator words are uniformly concise, i.e. if an outer
commutator word w takes m different values in a group G, then the order of the
verbal subgroup w(G) is bounded by a function depending only on m and not on w
or G. This is obtained as a consequence of a structure theorem for the subgroup
w(G), which is valid if G is soluble, and without assuming that w takes
finitely many values in G. More precisely, there is an abelian series of w(G),
such that every section of the series can be generated by values of w all of
whose powers are also values of w in that section. For the proof of this latter
result, we introduce a new representation of outer commutator words by means of
binary trees, and we use the structure of the trees to set up an appropriate
induction
Hausdorff dimension in -analytic profinite groups
We study the Hausdorff dimension of R-analytic subgroups in an R-analytic
profinite group, where R is a pro-p ring whose asso- ciated graded ring is an
integral domain. In particular, we prove that the set of such Hausdorff
dimensions is a finite subset of the rational numbers.Comment: 7 page
Run-time Support to Manage Architectural Variability Speci ed with CVL
The execution context in which pervasive systems or mobile
computing run changes continuously. Hence, applications for these systems
should be adapted at run-time according to the current context.
In order to implement a context-aware dynamic reconfiguration service,
most approaches usually require to model at design-time both the list of
all possible configurations and the plans to switch among them. In this
paper we present an alternative approach for the automatic run-time generation
of application configurations and the reconfiguration plans. The
generated configurations are optimal regarding di erent criteria, such as
functionality or resource consumption (e.g. battery or memory). This is
achieved by: (1) modelling architectural variability at design-time using
Common Variability Language (CVL), and (2) using a genetic algorithm
that finds at run-time nearly-optimal configurations using the information
provided by the variability model. We also specify a case study
and we use it to evaluate our approach, showing that it is efficient and
suitable for devices with scarce resources.Campus de Excelencia Internacional Andalucia Tech y proyectos de investigación TIN2008-01942, P09-TIC-5231 and INTER-TRUST FP7-317731
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