We present a type theory with some proof-irrelevance built into the conversion rule. We argue that this feature is useful when type theory is used as the logical formalism underlying a theorem prover. We also show a close relation with the subset types of the theory of PVS. We show that in these theories, because of the additional extentionality, the axiom of choice implies the decidability of ...

Vasil'ev posed Problem 16.26 in [The Kourovka Notebook: Unsolved Problems in Group Theory, 16th ed.,Sobolev Inst. Math., Novosibirsk (2006).] as follows:Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphicnonabelian finite simple groups with the same graphs of primes? Conjecture: $k = 5$.In [Zvezdina, On nonabelian simple groups having the same prime graph a...

The representation or order reduction of a rational transfer function by a linear combination of orthogonal rational functions offers several advantages, among which the possibility to work with prescribed poles and hence the guarantee of system stability. Also for multidimensional linear shift-invariant systems with infinite-extent impulse response, stability can be guaranteed a priori by the ...

A computable structure A is x-computably categorical for some Turing degree x, if for every computable structure B ∼= A there is an isomorphism f : B → A with f ≤T x. A degree x is a degree of categoricity if there is a computable structure A such that A is x-computably categorical, and for all y, if A is y-computably categorical then x ≤T y. We construct a Σ2 set whose degree is not a degree o...

We present an approach to directly study mutual relationships between audio and video signals for multimedia applications. The presented approach is mathematically based on information theory and is closely related to information theoretic classification. We show that very simple features of the audioresp. video-channel can already contain lots of mutual information between both modalities. The...

This paper provides a short and transparent solution for the covering cost of white–grey trees which play a crucial role in the algorithm of Bergeron et al. to compute the rearrangement distance between two multichromosomal genomes in linear time (Theor. Comput. Sci., 410:5300– 5316, 2009). In the process it introduces a new center notion for trees, which seems to be interesting on its own.

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