Parenthetical Meaning

Abstract

This book investigates the semantics and pragmatics of a representative sample of parenthetical constructions. These constructions are argued to fall into two major classes: pure and impure. Pure parentheticals comment on some part of the descriptive content of the root sentence but are otherwise relatively independent of it. Impure parentheticals modify components of the illocutionary force and affect the felicity or the truth of the root sentence. The book studies parentheticals from three theoretical viewpoints: illocutionary effects, scopal properties, and discourse status. It establishes and explicates the notion of parenthetical meaning in a formally precise and predictive dynamic semantic model. As a result, parentheticality is brought to bear on linguistic phenomena such as entailment and presupposition, binding and anaphora, evidentiality and modality, illocutionary force, and polarity.

High relative accuracy with some special matrices related to Γ and β functions

“…The matrix  n corresponds to the matrix  n 𝜆,𝜇 for 𝜆 k = 𝜇 k = k for all k = 1, … , n. In remark 2.7 of Reference 13 the strict total positivity of  n was shown. Now we consider generalized matrices  n 𝜆,𝜇 for any real sequences 𝜆, 𝜇 satisfying ( 9) and (11). The following result will provide a bidiagonal decomposition of these matrices.…”

“…𝜆,𝜇 the matrix given by (15) for real positive sequences 𝜆 = (𝜆 i ) n i=1 and 𝜇 = (𝜇 i ) n i=1 satisfying ( 9) and (11). Then, it is STP and its bidiagonal decomposition is given by…”

“…We have implemented in the Matlab functions TNGammaBD and TNBetaBD the bidiagonal decompositions ( 14) and (18) of Γ n 𝜆,𝜇 and  n 𝜆,𝜇 , respectively, to HRA given the integer sequences 𝜆 and 𝜇 satisfying ( 9) and (11). Algorithms 1 and 2 show the pseudocode of those functions.…”

Accurate computations with totally positive matrices applied to the computation of Gaussian quadrature formulae

“…Of course, there exist positive definite symmetric tridiagonal matrices with negative off-diagonal entries, but in the case of Jacobi matrices (as it will be seen in Section 2) the off-diagonal entries are √ b i and so they are also positive. In this case, as recalled in [28] (p. 110), the Jacobi matrix is totally nonnegative (totally positive in the classical terminology of Pinkus [38]), and so we can use the algorithms of Plamen Koev [20] for totally nonnegative matrices. In addition, as we will see, we are in the positive case considered in [37], which should imply a better behavior of the corresponding algorithms.…”

“…which means the columns of V (i.e., the right singular vectors of R) are the eigenvectors of J (and, of course, the eigenvalues of J are the squares of the singular values of R). In fact, Laurie in Section 5 of [24] gives the alternative of using the function svd of Matlab to compute the eigenvalues of J, and the same use of svd is included in the algorithm TNEigenValues of P. Koev for computing the eigenvalues of a totally positive matrix [18,20].…”