Indefinite causal order is a key feature involved in the study of quantum higher transformations. Recently, intense research has been focused on possible advantages related to lack definite processes. Quite often switch claimed provide information-theoretic and thermodynamic tasks. We address here question whether indefinite resource for thermodynamics. Inspired by previous results literature, ...

In this paper, we describe block matrix algorithms for the iterative solution of large scale linear-quadratic optimal control problems arising from the optimal control of parabolic partial differential equations over a finite control horizon. We describe three iterative algorithms. The first algorithm employs a CG method for solving a symmetric positive definite reduced linear system involving ...

It is known that in many functions of banded, and more generally, sparse Hermitian positive definite matrices, the entries exhibit a rapid decay away from the sparsity pattern. This is in particular true for the inverse, and based on results for the inverse, bounds for Cauchy–Stieltjes functions of Hermitian positive definite matrices have recently been obtained. We add to the known results by ...

We continue the complexity analysis of parametric definite and indefinite integration given by the authors in [2]. Here we consider anisotropic classes of functions, including certain classes with dominating mixed derivatives. Our analysis is based on a multilevel Monte Carlo method developed in [2] and we obtain the order of the deterministic and randomized n-th minimal errors (in some limit c...

Calculi of indefinite and definite descriptions are presented, and interpreted in Martin-Löf’s intensional type theory. The interpretations are formalizations of the implicit ideas found in the literature of constructive mathematics: if we have proved that an element with a certain property exists, we speak of ’the element such that the property holds’ and refer by that phrase to the element co...

Romanian is a language which exhibits differential object marking (DOM) using the particle pe and (in most cases) a clitic pronoun (Niculescu 1965, Pan -Dindelegan 1997, von Heusinger & Onea 2008, Stark & Sora 2008). Direct object case marking is optional with human indefinite direct objects, as in (1), and almost obligatory with postverbal human definite direct objects, as reflected in the con...

Let n > 4, and let Q ∈ Z[X1, . . . , Xn] be a non-singular quadratic form. When Q is indefinite we provide new upper bounds for the least non-trivial integral solution to the equation Q = 0, and when Q is positive definite we provide improved upper bounds for the greatest positive integer k for which the equation Q = k is insoluble in integers, despite being soluble modulo every prime power.

In recent years, the problem of symbolic summation has received much attention due to the exciting applications of Zeilberger’s method for definite hypergeometric summation. This lead to renewed interest in the central part of the algorithmic machinery, Gosper’s “classical” method for indefinite hypergeometric summation. We review some of the recent (partly unpublished as yet) work done in this...