In this paper, left derivations and Jordan left derivations in full and upper triangular matrix rings over unital associative rings are characterized.

This paper shows how derivations in the deep inference system SKS for classical propositional logic can be translated into proof nets. Since an SKS derivation contains more information about a proof than the corresponding proof net, we observe a loss of information which can be understood as “eliminating bureaucracy”. Technically this is achieved by cut reduction on proof nets. As an intermedia...

In this paper, we introduce and discuss the superstability of generalized module left derivations and generalized module derivations on a Banach module.

Q: Consider an uncorrelated (white) Gaussian signal s(t). Calculate its 3rd and 4th order moments, m3 = ⟨s(t1)s(t2)s(t3)⟩ and m4 = ⟨s(t1)s(t2)s(t3)s(t4)⟩. Confirm with simulation. The third moment m3 = ⟨s(t1)s(t2)s(t3)⟩ is zero. Namely, if t1 ̸= t2 ̸= t3 then m3 = ⟨s⟩ = 03 = 0. If t1 = t2 = t3, m3 = ⟨ s3 ⟩ = ́ N (0, σ2)x3dx = 0, as this is the integral over an odd function. For t1 = t2 ̸= t3, m3 = ...

A proof technique, called induction on failing derivations, is introduced. We wish to prove properties of judgments in deductive systems. Standard techniques exist for proving such properties on valid judgments; this note defines a technique for proving such properties on invalid (underivable) judgments.

When operating on cyclic data, programmers have to take care in assuring that their programs will terminate; in our opinion, this is a task for the interpreter. We present a Prolog meta-interpreter that checks for the presence of cyclic computations at runtime and returns a failure if this is the case, thus allowing inductive predicates to properly deal with cyclic terms.

The Akaike (1973, 1974) information criterion, AIC, and the corrected Akaike information criterion (Hurvich and Tsai, 1989), AICc, were both designed as estimators of the expected Kullback-Leibler discrepancy between the model generating the data and a tted candidate model. AIC is justiied in a very general framework, and as a result, ooers a crude estimator of the expected discrepancy: one whi...

This paper proves the Commuting Derivations Conjecture in dimension three: if D1 and D2 are two locally nilpotent derivations which are linearly independent and satisfy [D1, D2] = 0 then the intersection of the kernels, A1 ∩ A2 equals C[f ] where f is a coordinate. As a consequence, it is shown that p(X)Y + Q(X, Z, T ) is a coordinate if and only if Q(a, Z, T ) is a coordinate for every zero a ...

• Functor categories can combine with their arguments by the following rules: (2) Forward application (>) X/Y Y ⇒ X (3) Backward application (<) Y X\Y ⇒ X • Derivations are written as shown below, on the left side. Note the direct correspondence to the upside-down constituency tree shown on the right.