A t-tautology (triangular tautology) is a propositional formula which is a tautology in all fuzzy logics deened by continuous triangular norms. In this paper we show that the problem of recognizing t-tautologies is coNP complete, and thus decidable.

This paper investigates association between portfolio returns and higher-order systematic co-moments at different timescales obtained through wavelet multiscalinga technique that decomposes a given return series into different timescales enabling investigation at different return intervals. For some portfolios, the relative risk positions indicated by systematic co-moments at higher timescales ...

Let O be an order of a quadratic number eld. In this paper we show that under the assumption of the generalized Riemann hypothesis the following decision problems are in NP \ co-NP:

Let R be an integral domain. Note some obvious facts. Every ele­ ment a of R divides 0. Indeed 0 = 0 · a. On the other hand, 0 only divides 0. Indeed if a = q · 0, then a = 0 (obvious!). Finally every unit u divides any other element a. Indeed if v ∈ R is the inverse of u, so that uv = 1 then a = a · 1 = (av)u. Lemma 19.3. Let R be an integral domain and let p ∈ R. Then p is prime if and only i...

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In the present paper we prove that relative to random oracle A (with respect to the uniform measure) the following three assertions hold: (1) there is a pair of disjoint NP A-sets which are separable by no P A-set, (2) there is a pair of disjoint Co-NP A-sets which are separable by no P A-set and (3) there is an innnite Co-NP A-set having no innnite NP A-subset