Search results for "ample"

showing 10 items of 2398 documents

Adjoint-based sampling methods for electromagnetic scattering

2010

In this paper we investigate the efficient realization of sampling methods based on solutions of certain adjoint problems. This adjoint approach does not require the explicit knowledge of the Green's function for the background medium, and allows us to sample for all points and all dipole directions simultaneously; thus, several limitations of standard sampling methods are relieved. A detailed derivation of the adjoint approach is presented for two electromagnetic model problems, but the framework can be applied to a much wider class of problems. We also discuss a relation of the adjoint sampling method to standard backprojection algorithms, and present numerical tests that illustrate the e…

Mathematical optimizationRelation (database)ScatteringApplied MathematicsSample (statistics)Function (mathematics)Inverse problemComputer Science ApplicationsTheoretical Computer ScienceAdjoint equationSignal ProcessingApplied mathematicsExplicit knowledgeRealization (systems)Mathematical PhysicsMathematicsInverse Problems
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Isometries of nilpotent metric groups

2016

We consider Lie groups equipped with arbitrary distances. We only assume that the distance is left-invariant and induces the manifold topology. For brevity, we call such object metric Lie groups. Apart from Riemannian Lie groups, distinguished examples are sub-Riemannian Lie groups and, in particular, Carnot groups equipped with Carnot-Carath\'eodory distances. We study the regularity of isometries, i.e., distance-preserving homeomorphisms. Our first result is the analyticity of such maps between metric Lie groups. The second result is that if two metric Lie groups are connected and nilpotent then every isometry between the groups is the composition of a left translation and an isomorphism.…

Mathematics - Differential GeometryIsometriesPure mathematicsA ne transformationsGeneral Mathematics22E25 53C30 22F30Group Theory (math.GR)01 natural sciencesisometriesMathematics - Metric GeometryetäisyysFOS: MathematicsMathematics (all)Mathematics::Metric GeometryA ne transformations; Isometries; Nilpotent groups; Nilradical; Mathematics (all)0101 mathematicsdistanceMathematicsLie groupsmatematiikkamathematicsta111010102 general mathematicsLie groupMetric Geometry (math.MG)nilpotent groupsnilradicalComposition (combinatorics)Manifoldaffine transformationsNilpotentDifferential Geometry (math.DG)Nilpotent groupsMetric (mathematics)IsometryNilradicalIsomorphismMathematics - Group TheoryCounterexampleJournal de l’École polytechnique — Mathématiques
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A reflection approach to the broken ray transform

2013

We reduce the broken ray transform on some Riemannian manifolds (with corners) to the geodesic ray transform on another manifold, which is obtained from the original one by reflection. We give examples of this idea and present injectivity results for the broken ray transform using corresponding earlier results for the geodesic ray transform. Examples of manifolds where the broken ray transform is injective include Euclidean cones and parts of the spheres $S^n$. In addition, we introduce the periodic broken ray transform and use the reflection argument to produce examples of manifolds where it is injective. We also give counterexamples to both periodic and nonperiodic cases. The broken ray t…

Mathematics - Differential GeometryPure mathematicsGeodesicmatematiikkaGeneral MathematicsAstrophysics::High Energy Astrophysical PhenomenaInjective functionManifold53C65 78A05 (Primary) 35R30 58J32 (Secondary)Mathematics - Analysis of PDEsReflection (mathematics)Differential Geometry (math.DG)Euclidean geometryFOS: MathematicsSPHERESMathematics::Differential GeometryCounterexampleMathematicsbroken ray transformAnalysis of PDEs (math.AP)
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DEVELOPING AN INTEGRATED FRAMEWORK FOR ANALYZING WAYS OF REASONING IN MATHEMATICS

2022

Mathematics education literature involves studies that sought a way of investigating the mode of reasoning in mathematics textbooks because textbooks are the main resource for teachers in planning their mathematics lessons. In this vein, this study aimed to analyze the ways of reasoning in mathematics textbooks that are currently used in five countries: Slovakia, Czech Republic, Italy, Norway, and Turkiye, as a part of a Horizon 2020 Project. We initially started with a framework that aimed to examine the effect of teachers’ participation in the lesson study on the improvement of students’ mathematical reasoning (Project LESSAM). However, as the textbook analysis of different countries proc…

Mathematics education ways of reasoning mathematics worked examples mathematics textbook analysisSettore MAT/04 - Matematiche Complementari
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Regularity of solutions to differential equations with non-Lipschitz coefficients

2008

AbstractWe study the ordinary and stochastic differential equations whose coefficients satisfy certain non-Lipschitz conditions, namely, we study the behaviors of small subsets under the flows generated by these equations.

Mathematics(all)Hölder continuousGeneral MathematicsMathematical analysisHausdorff dimensionNon-Lipschitz conditionMethod of undetermined coefficientsExamples of differential equationsStochastic partial differential equationDifferential equationCollocation methodC0-semigroupDifferential algebraic equationMathematicsSeparable partial differential equationNumerical partial differential equationsBulletin des Sciences Mathématiques
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Smart Sorption Materials in Green Analytical Chemistry

2019

The use of smart materials as alternative sorption materials for their use in greening sample preparation has been reviewed. It has been taking into consideration recent advances on the use of natural products, without any modification or purification, for making analyte extraction and pre-concentration and the use of specific materials in solid-phase extraction (SPE) and solid-phase microextraction (SPME) approaches. Inorganic materials, such as metal oxides, alumina-based, silica-based, and carbon-based materials together with biomimetic sorbents such as classical immunosorbents, aptamers, and molecularly imprinted polymers, have been reviewed as examples of these materials, stressing the…

Matrix (chemical analysis)AnalyteMaterials scienceAptamerMolecularly imprinted polymerNanotechnologySample preparationSorptionImmunosorbentsSmart material
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Evaluation of a Multidimensional Solid-Phase Extraction Platform for Highly Selective On-Line Cleanup and High-Throughput LC−MS Analysis of Triazines…

2001

A novel highly selective sample cleanup procedure based on the use of molecularly imprinted polymers (MIPs) as solid-phase extraction materials has been evaluated with respect to its applicability and routine use in environmental analysis. The method comprises the combination of a restricted access material (RAM) and a MIP allowing a selective sample preparation to be achieved in the online mode. This combination is called the size-selective sample separation and solvent switch (six-SPE). The RAM column combines size exclusion and adsorption chromatography, reducing the concentration of matrix molecules by a cutoff of 15 kDa. The MIP column selectively retains the triazine analytes whereas …

Matrix (chemical analysis)ChromatographyChemistryElutionSize-exclusion chromatographyExtraction (chemistry)Molecularly imprinted polymerAnalytical chemistrySample preparationSolid phase extractionHigh-performance liquid chromatographyAnalytical ChemistryAnalytical Chemistry
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Application of isotope-dilution laser ablation ICP-MS for direct determination of Pu concentrations in soils at pg g(-1) levels.

2003

The methods available for determination of environmental contamination by plutonium at ultra-trace levels require labor-consuming sample preparation including matrix removal and plutonium extraction in both nuclear spectroscopy and mass spectrometry. In this work, laser-ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) was applied for direct analysis of Pu in soil and sediment samples. Application of a LINA-Spark-Atomizer system (a modified laser ablation system providing high ablation rates) coupled with a sector-field ICP-MS resulted in detection limits as low as 3x10(-13) g g(-1) for Pu isotopes in soil samples containing uranium at a concentration of a few microg g(-1). …

Matrix (chemical analysis)Detection limitchemistryAnalytical chemistrychemistry.chemical_elementSample preparationIsotope dilutionUraniumMass spectrometryBiochemistryInductively coupled plasma mass spectrometryAnalytical ChemistryPlutoniumAnalytical and bioanalytical chemistry
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Systematic procedure for the preparation of sets of calibration standards for x-ray fluorescence analysis of ceramic materials

1998

A systematic procedure for the preparation of optimized sets of calibration solid standards for the x-ray fluorescence analysis of ceramic materials is described. The matrix of the contents of the N analytes in the n standards (n ≥ N) is calculated from an n x N experimental design matrix, and from the upper and lower limits of the calibration range for each of the N analytes. Two procedures, which are useful for taking into account analyte interactions, are proposed for constructing the experimental design matrix, i.e. the scroll procedure and the procedure of the centers. A program developed to help the analyst in designing and preparing the set of standards following the proposed procedu…

Matrix (chemical analysis)Set (abstract data type)AnalyteCertified reference materialsChemistryCalibrationAnalytical chemistryDesign matrixX-ray fluorescenceSample preparationCeramic materialsSpectroscopyX-Ray Spectrometry
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FIA—FT—IR determination of ibuprofen in pharmaceuticals

1992

A method has been developed for the determination of Ibuprofen (2-[4-isobutylphenyl]-propionic acid) in pharmaceuticals by FT-IR, using the carbonyl band which this compound presents at 1710 cm(-1) in carbon tetrachloride solutions. Samples are dissolved in carbon tetrachloride. In this solvent the excipients are not soluble and so the drug can be directly determined without any additional treatment. The use of a simple FIA manifold permits one to carry out this analysis with a low consumption of reagent and the FT-IR provides a continuous monitoring of the spectral base-line which permits an accurate determination of the maximum in the absorbance band. Also, the FIA system permits easy and…

Matrix (chemical analysis)SolventAbsorbancechemistry.chemical_compoundChromatographychemistryReagentAnalytical chemistryCarbon tetrachlorideInfrared spectroscopySample preparationFourier transform infrared spectroscopyAnalytical ChemistryTalanta
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