• 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.

Let A be a Banach algebra and M be a Banach left A-module. A linear map δ : M → M is called a generalized derivation if there exists a derivation d : A → A such that δ(ax) = aδ(x) + d(a)x (a ∈ A,x ∈ M). In this paper, we associate a triangular Banach algebra T to Banach A-module M and investigate the relation between generalized derivations on M and derivations on T . In particular, we prove th...

We recall the definition of strong homotopy derivations of A∞ algebras and introduce the corresponding definition for L∞ algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.

EEG spectral analysis allows a quantitative analysis of changes in the frequency bands during disease progression in Alzheimer's disease (AD) and could be used to monitor treatment and disease progression. Eighteen patients with probable AD were evaluated by Folstein Mini Mental State Examination (MMSE) and EEG spectral analysis before donepezil treatment, 2 months after 5 mg/day and 4 months a...

Thermodynamics entails a set of mathematical conditions on quantum Markovian dynamics. In particular, strict energy conservation between the system and environment implies that dissipative dynamical map commutes with unitary propagator. Employing spectral analysis we prove general form ensuing master equation. We compare this result to equations obtained from standard microscopic derivations. T...

The sleep electroencephalogram (EEG) was recorded from anterior (Fz/Cz) and posterior (Pz/Oz) bipolar derivations in two developmental groups: 20 pre- or early pubertal (Tanner 1/2, mean age 11.4 +/- 1.1 years, 11 boys) and 20 late pubertal or mature adolescents (Tanner 4/5, 14.1 +/- 1.3 years, 8 boys). A sleep-state independent reduction of EEG power over almost the entire frequency range was ...

We study a class of matrix function algebras, here denoted T (Cn). We introduce a notion of point derivations, and classify the point derivations for certain finite dimensional representations of T (Cn). We use point derivations and information about n×n matrices to show that every T (Cn)-valued derivation on T (Cn) is inner. Certain matrix function algebras arise in some standard constructions...

This paper focuses on certain finite dimensional point derivations for the non-selfadjoint operator algebras corresponding to directed graphs. We begin by analyzing the derivations corresponding to full matrix representations of the tensor algebra of a directed graph. We determine when such a derivation is inner, and describe situations that give rise to non-inner derivations. We also analyze t...

This paper shows how derivations in (a variation of) SKS 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 intermediate step between the two extremes, SKS deriv...

This paper is a study of derivations on unbounded operator algebras in connection with those in operator algebras. In particular we study spatiality of derivations in several situations. We give the characterization of derivations on general «-algebras by using positive linear functionals. We also show that a derivation with some range-property on a left ■EW*-algebra induced by an unbounded Hub...