Search results for "Equivalence"
showing 10 items of 301 documents
Remarks on G-Metric Spaces
2013
In 2005, Mustafa and Sims (2006) introduced and studied a new class of generalized metric spaces, which are called G-metric spaces, as a generalization of metric spaces. We establish some useful propositions to show that many fixed point theorems on (nonsymmetric) G-metric spaces given recently by many authors follow directly from well-known theorems on metric spaces. Our technique can be easily extended to other results as shown in application.
Butterflies in a Semi-Abelian Context
2011
It is known that monoidal functors between internal groupoids in the category Grp of groups constitute the bicategory of fractions of the 2-category Grpd(Grp) of internal groupoids, internal functors and internal natural transformations in Grp, with respect to weak equivalences (that is, internal functors which are internally fully faithful and essentially surjective on objects). Monoidal functors can be equivalently described by a kind of weak morphisms introduced by B. Noohi under the name of butterflies. In order to internalize monoidal functors in a wide context, we introduce the notion of internal butterflies between internal crossed modules in a semi-abelian category C, and we show th…
New Results on Identifiability of Nonlinear Systems
2004
Abstract In this paper, we recall definition of identifiability of nonlinear systems. We prove equivalence between identifiability and smooth identifiability. This new result justifies our definition of identifiability. In a previous paper (Busvelle and Gauthier, 2003), we have established that • If the number of observations is three or more, then, systems are generically identifiable. • If the number of observations is 1 or 2, then the situation is reversed. Identifiability is not at all generic. Also, we have completely classified infinitesimally identifiable systems in the second case, and in particular, we gave normal forms for identifiable systems. Here, we will give similar results i…
A Note on Algebraic Sums of Subsets of the Real Line
2002
AbstractWe investigate the algebraic sums of sets for a large class of invari-ant ˙-ideals and ˙- elds of subsets of the real line. We give a simpleexample of two Borel subsets of the real line such that its algebraicsum is not a Borel set. Next we show a similar result to Proposition 2from A. Kharazishvili paper [4]. Our results are obtained for ideals withcoanalytical bases. 1 Introduction We shall work in ZFC set theory. By !we denote natural numbers. By 4wedenote the symmetric di erence of sets. The cardinality of a set Xwe denoteby jXj. By R we denote the real line and by Q we denote rational numbers. IfAand Bare subsets of R n and b2R , then A+B= fa+b: a2A^b2Bgand A+ b= A+ fbg. Simila…
On Finite Satisfiability of the Guarded Fragment with Equivalence or Transitive Guards
2007
The guarded fragment of first-order logic, GF, enjoys the finite model property, so the satisfiability and the finite satisfiability problems coincide. We are concerned with two extensions of the two-variable guarded fragment that do not possess the finite model property, namely, GF2 with equivalence and GF2 with transitive guards. We prove that in both cases every finitely satisfiable formula has a model of at most double exponential size w.r.t. its length. To obtain the result we invent a strategy of building finite models that are formed from a number of multidimensional grids placed over a cylindrical surface. The construction yields a 2NEXPTIME-upper bound on the complexity of the fini…
Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces
2012
In this paper, we introduce cyclic weak $\phi-$contractions in fuzzy metric spaces and utilize the same to prove some results on existence and uniqueness of fixed point in fuzzy metric spaces. Some related results are also proved besides furnishing illustrative examples.
Biowaiver Monographs for Immediate-Release Solid Oral Dosage Forms: Codeine Phosphate
2014
The present monograph reviews data relevant to applying the biowaiver procedure for the approval of immediate-release multisource solid dosage forms containing codeine phosphate. Both biopharmaceutical and clinical data of codeine were assessed. Solubility studies revealed that codeine meets the "highly soluble" criteria according to World Health Organization (WHO), the European Medicines Agency (EMA), and the United States Food and Drug Administration (US FDA). Codeine's fraction of dose absorbed in humans was reported to be high (>90%) based on cumulative urinary excretion of drug and drug-related material following oral administration. The permeability of codeine was also assessed to be …
Biowaiver Monograph for Immediate-Release Solid Oral Dosage Forms: Sitagliptin Phosphate Monohydrate
2021
Sitagliptin is an antihyperglycemic drug used in adults for the treatment of diabetes Type 2. Literature data and in-house experiments were applied in this monograph to assess whether methods based on the Biopharmaceutics Classification System (BCS) could be used to assess the bioequivalence of solid immediate-release (IR) oral dosage forms containing sitagliptin phosphate monohydrate, as an alternative to a pharmacokinetic study in human volunteers. The solubility and permeability characteristics of sitagliptin were reviewed according to the BCS, along with dissolution, therapeutic index, therapeutic applications, pharmacokinetics, pharmacodynamic characteristics, reports of bioequivalence…
Biowaiver Monographs for Immediate-Release Solid Oral Dosage Forms: Ketoprofen
2012
Literature and experimental data relevant to the decision to allow a waiver of in vivo bioequivalence (BE) testing for the approval of immediate-release (IR) solid oral dosage forms containing ketoprofen are reviewed. Ketoprofen's solubility and permeability, its therapeutic use and therapeutic index, pharmacokinetic properties, data related to the possibility of excipient interactions, and reported BE/bioavailability (BA)/dissolution data were taken into consideration. The available data suggest that according to the current Biopharmaceutics Classification System (BCS) and all current guidances, ketoprofen is a weak acid that would be assigned to BCS Class II. The extent of ketoprofen abso…
Biowaiver Monographs for Immediate Release Solid Oral Dosage Forms: Levetiracetam.
2015
Literature and experimental data relevant for the decision to allow a waiver of in vivo bioequivalence (BE) testing for the approval of immediate release (IR) solid oral dosage forms containing levetiracetam are reviewed. Data on solubility and permeability suggest that levetiracetam belongs to class I of the biopharmaceutical classification system (BCS). Levetiracetam's therapeutic use, its wide therapeutic index, and its favorable pharmacokinetic properties make levetiracetam a valid candidate for the BCS-based biowaiver approach. Further, no BE studies with levetiracetam IR formulations in which the test formulation failed to show BE with the comparator have been reported in the open lit…