Search results for "Complete"
showing 10 items of 490 documents
Iterationsverfahren höherer Ordnung in Banach-Räumen
1969
The Newton process for operator equations in say a linear normed complete space converges under certain hypothesis about the Frechet-derivatives of the operator with at least the order two. There are different ways to improve this Newton process. For instance you obtain a process of order three if you add a correction element containing the second Frechet-derivative of the operator [1]. In the following note we will generalize this idea. In a recursive manner -- by adding higher derivatives -- we will construct iterative processes of any orderk (k > 1). A general theorem due toCollatz provides us error estimates for this processes. Last we will illustrate the processes by several examples.
Lambda substitution algebras
1993
In the paper an algebraic metatheory of type-free λ-calculus is developed. Our version is based on lambda substitution algebras (λSAs), which are just SAs introduced by Feldman (for algebraizing equational logic) enriched with a countable family of unary operations of λ-abstraction and a binary operation of application. Two representation theorems, syntactical and semantic, are proved, what directly provides completeness theorems.
An Integral Version of Ćirić’s Fixed Point Theorem
2011
We establish a new fixed point theorem for mappings satisfying a general contractive condition of integral type. The presented theorem generalizes the well known Ciric's fixed point theorem [Lj. B. Ciric, Generalized contractions and fixed point theorems, Publ. Inst. Math. 12 (26) (1971) 19-26]. Some examples and applications are given.
Unification in first-order transitive modal logic
2019
We introduce unification in first-order transitive modal logics, i.e. logics extending Q–K4, and apply it to solve some problems such as admissibility of rules. Unifiable formulas in some extensions of Q–K4 are characterized and an explicit basis for the passive rules (those with non-unifiable premises) is provided. Both unifiability and passive rules depend on the number of logical constants in the logic; we focus on extensions of Q–K4 with at most four constants ⊤,⊥,□⊥,◊⊤. Projective formulas, defined in a way similar to propositional logic, are used to solve some questions concerning the disjunction and existence properties. A partial characterization of first-order modal logics with pr…
Electronic excitations of 1,4-disilyl-substituted 1,4-disilabicycloalkanes: a MS-CASPT2 study of the influence of cage size.
2007
We present a multistate complete active space second-order perturbation theory computational study aimed to predict the low-lying electronic excitations of four compounds that can be viewed as two disilane units connected through alkane bridges in a bicyclic cage. The analysis has focused on 1,4-disilyl-1,4-disilabicyclo[2.2.1]heptane (1a), 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.2.1]heptane (1b), 1,4-disilyl-1,4-disilabicyclo[2.1.1]hexane (2a), and 1,4-bis(trimethylsilyl)-1,4-disilabicyclo[2.1.1]hexane (2b). The aim has been to find out the nature of the lowest excitations with significant oscillator strengths and to investigate how the cage size affects the excitation energies and the…
Association of derived neutrophil-to-lymphocyte ratio (dNLR) with pathological complete response (pCR) after neoadjuvant chemotherapy (CT)
2019
Abstract Background dNLR is a novel biomarker associated with clinical outcome in solid tumors including early stage breast cancer (BC). Here we report the association of dNLR with pCR in triple-negative (TN) and luminal BC patients (pts) treated with neoadjuvant CT. Methods This was a retrospective analysis of two randomized studies (GEICAM/2006-03 - NCT00432172 and ETNA - NCT01822314) involving 821 pts with early stage (>2cm) or locally advanced TN or luminal BC receiving anthracycline/taxane-based CT +/- carboplatin (GEICAM/2006-03) or nab-paclitaxel/paclitaxel followed by anthracycline regimen (ETNA). dNLR was calculated as the ratio of neutrophils and the difference between total leuko…
Visible parts and dimensions
2003
We study the visible parts of subsets of n-dimensional Euclidean space: a point a of a compact set A is visible from an affine subspace K of n, if the line segment joining PK(a) to a only intersects A at a (here PK denotes projection onto K). The set of all such points visible from a given subspace K is called the visible part of A from K. We prove that if the Hausdorff dimension of a compact set is at most n−1, then the Hausdorff dimension of a visible part is almost surely equal to the Hausdorff dimension of the set. On the other hand, provided that the set has Hausdorff dimension larger than n−1, we have the almost sure lower bound n−1 for the Hausdorff dimensions of visible parts. We al…
Ab initio study of the C60+Na system
2004
Abstract In this work we present the first CAS-CI calculation of the potential-electronic curves for the lowest states of the C 60 +Na system using a set of local orbitals. These orbitals permit to select a small active space describing the ionic interaction between the C 60 and the Na atom. A binding energy of about 3 eV has been found, a value substantially larger than previous theoretical results.
Theoretical spectroscopy of organic systems
1999
Abstract The complete active space (CAS) SCF method in conjunction with the multiconfigurational second-order perturbation theory (CASPT2) has been applied to study the electronically excited states of basic organic compounds. As shown in the lecture with a number of examples, the CASPT2 method is capable of yielding accurate results for relative energies and other properties of excited states, provided that flexible one-electron basis sets are employed. The applications comprise an ample range of systems and problems, including polyenes, conjugated and unconjugated dienes, alternant and nonalternant hydrocarbons, polyenals, etc. As a whole these studies enable both qualitative and quantita…
Theoretical absorption and emission spectra of 1H- and 2H-benzotriazole
2003
Excitation energies, dipole moments, and transition properties for the lowest-lying 1(π, π*) and 1(n, π*) electronic states of two benzotriazole tautomers have been studied at the complete active space (CAS) SCF and multiconfigurational second-order perturbation (CASPT2) levels. With these results, the UV absorption spectra of 1H- and 2H-benzotriazole were first described individually, and then they were considered simultaneously in order to better understand the experimental, observed spectrum of benzotriazole. Aspects of the fluorescence of the compound have been also analyzed. The spectrum of benzotriazole is finally related to those of other azo-compounds.