Veech groups uniformize Teichmüller geodesics in Riemann moduli space. We gave examples of infinitely generated Veech groups; see Duke Math. J. 123 (2004), 49–69. Here we show that the associated Teichmüller geodesics can even have both infinitely many cusps and infinitely many infinite ends.

In this note we exhibit a condition under which a sequence of elements a19 , an in a commutative noetherian local ring A form an Asequence, and derive a number of corollaries. Recall that if M is an A-module, then a19 , an is an M-sequence if 1) ai+1 is a nonzerodivisor on M/(a19 9a1)M for i = 0, 9n — 1,. and 2) M Φ (al9 . . . , α n ) M . If a19 , an is an A-sequence and / is the ideal generate...

Audiovisual devices such as satellite and conventional televisions can offer easy access to authentic programs which are considered to be a rich source of language input for SLA (Second Language Acquisition). The immediacy of various audiovisual programs ensures that language learners’ exposure is up-to-date and embedded in the real world of native speakers. In the same line, in the present pap...

Audiovisual devices such as satellite and conventional televisions can offer easy access to authentic programs which are considered to be a rich source of language input for SLA (Second Language Acquisition). The immediacy of various audiovisual programs ensures that language learners’ exposure is up-to-date and embedded in the real world of native speakers. In the same line, in the present pap...

This paper fortifies and defends the so called Sufficiency Argument (SA) against Classical Invariantism. In Sect. 2, I explain the version of the SA formulated but then rejected by Brown (2008a). In Sect. 3, I show how cases described by Hawthorne (2004), Brown (2008b), and Lackey (forthcoming) threaten to undermine one or the other of the SA’s least secure premises. In Sect. 4, I buttress one ...

We introduce a recurrent architecture having a modular structure and we formulate a training procedure based on the EM algorithm. The resulting model has similarities to hidden Markov models, but supports recurrent networks processing style and allows to exploit the supervised learning paradigm while using maximum likelihood estimation.

Two things are striking about this medieval definition. The first is that it is very close to the modern conception of formal consequence one finds in Bolzano and Tarski3. The second is that although Buridan and the other fourteenth-century logicians state these distinctions with a great deal of precision, they say almost nothing about the point of the distinctions. Why are these distinctions d...

Derived varieties were invented by P. Cohn in [4]. Derived varieties of a given type were invented by the authors in [10]. In the paper we deal with the derived variety Vσ of a given variety, by a fixed hypersubstitution σ. We introduce the notion of the dimension of a variety as the cardinality κ of the set of all proper derived varieties of V included in V. We examine dimensions of some varie...