Search results for "first"

Agde, dépôt de la Motte (Hérault)

2013

Cardinal estimates involving the weak Lindelöf game

2021

AbstractWe show that if X is a first-countable Urysohn space where player II has a winning strategy in the game $$G^{\omega _1}_1({\mathcal {O}}, {\mathcal {O}}_D)$$ G 1 ω 1 ( O , O D ) (the weak Lindelöf game of length $$\omega _1$$ ω 1 ) then X has cardinality at most continuum. This may be considered a partial answer to an old question of Bell, Ginsburg and Woods. It is also the best result of this kind since there are Hausdorff first-countable spaces of arbitrarily large cardinality where player II has a winning strategy even in the weak Lindelöf game of countable length. We also tackle the problem of finding a bound on the cardinality of a first-countable space where player II has a wi…

Forcing for First-Order Languages from the Perspective of Rasiowa–Sikorski Lemma

2017

The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski [9]. The central idea, developed in this paper, consists in constructing first-order models from individual variables. The key notion of a Rasiowa–Sikorski set of formulas for an arbitrary countable language L is examined. Each Rasiowa–Sikorski set defines a countable model for L . Conversely, every countable model for L is determined by a Rasiowa–Sikorski set. The focus is on constructing Rasiowa–Sikorski sets by applying forcing techniques restricted to Boolean algebras arising from the subsets of the set of atomic formulas of L .

The Classical Theory of Real Functions

1998

The first class of real functions we deal with in this chapter is the class of functions of locally finite variation. These functions are closely related to the real measures on B. Exploiting this connection would allow us to obtain the properties of these functions from the general results in Chapter 4. But the path we follow here is a more direct one which applies the theory of vector lattices. The link with the measures on B will be established in the next section.

On Inductive Generalization in Monadic First-Order Logic With Identity

1966

Publisher Summary The chapter examines the results obtained by means of a system when the relation of identity is used in addition to monadic predicates. The chapter compares the new system of inductive logic sketched by Jaakko Hintikka with Carnap's system. The main advantage of Hintikka's system is that it gives natural degrees of confirmation to inductive generalizations, whereas Carnap's confirmation function c * enables one to deal satisfactorily with singular inductive inference only. According to Carnap's system, general sentences that are not logically true receive nonnegligible degrees of confirmation only if the evidence contains a large part of the individuals in the whole univer…

A constructive semantics for non-deducibility

2008

This paper provides a constructive topological semantics for non-deducibility of a first order intuitionistic formula. Formal topology theory, in particular the recently introduced notion of a binary positivity predicate, and co-induction are two needful tools. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

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…

Semi-physiologic model validation and bioequivalence trials simulation to select the best analyte for acetylsalicylic acid

2015

Abstract The objective of this paper is to apply a previously developed semi-physiologic pharmacokinetic model implemented in NONMEM to simulate bioequivalence trials (BE) of acetyl salicylic acid (ASA) in order to validate the model performance against ASA human experimental data. ASA is a drug with first-pass hepatic and intestinal metabolism following Michaelis–Menten kinetics that leads to the formation of two main metabolites in two generations (first and second generation metabolites). The first aim was to adapt the semi-physiological model for ASA in NOMMEN using ASA pharmacokinetic parameters from literature, showing its sequential metabolism. The second aim was to validate this mod…

Computer simulations for bioequivalence trials: Selection of analyte in BCS class II and IV drugs with first-pass metabolism, two metabolic pathways …

2018

A semi-physiological two compartment pharmacokinetic model with two active metabolites (primary (PM) and secondary metabolites (SM)) with saturable and non-saturable pre-systemic efflux transporter, intestinal and hepatic metabolism has been developed. The aim of this work is to explore in several scenarios which analyte (parent drug or any of the metabolites) is the most sensitive to changes in drug product performance (i.e. differences in in vivo dissolution) and to make recommendations based on the simulations outcome. A total of 128 scenarios (2 Biopharmaceutics Classification System (BCS) drug types, 2 levels of KM Pgp, in 4 metabolic scenarios at 2 dose levels in 4 quality levels of t…

Structure and Phase Transitions in Ethylenediammonium Dichloride and its Salts with Antimony Trichloride

2000

During the mixing of ethylenediammonium dichloride and antimony trichloride except of reported earlier [NH3(CH2)2NH3]5(Sb2Cl11)2 · 4 H2O a new salt [NH3(CH2)2NH3](SbCl4)2 was obtained. The crystals are monoclinic at 295 K, space group C2/m, a = 13.829(3), b = 7.408(1), c = 7.588(2) A; β = 103.18(3)°; V = 756.9(3) A3; Z = 2; dc = 2.585, dm = 2.56(2) g · cm–3. The structure consists of anionic sublattice built of Sb2Cl82– units composed of two SbCl52– square pyramids connected by edge. The ethylenediammonium cations are located in anionic cavities. The cations are disordered. Each methylene carbon atom is split between two positions. The X-ray diffraction, DSC, TGA and dilatometric methods we…