Search results for " Newton"

showing 10 items of 23 documents

Sharp capacity estimates for annuli in weighted R^n and in metric spaces

2017

We obtain estimates for the nonlinear variational capacity of annuli in weighted R^n and in metric spaces. We introduce four different (pointwise) exponent sets, show that they all play fundamental roles for capacity estimates, and also demonstrate that whether an end point of an exponent set is attained or not is important. As a consequence of our estimates we obtain, for instance, criteria for points to have zero (resp. positive) capacity. Our discussion holds in rather general metric spaces, including Carnot groups and many manifolds, but it is just as relevant on weighted R^n. Indeed, to illustrate the sharpness of our estimates, we give several examples of radially weighted R^n, which …

31C45 (Primary) 30C65 30L99 31B15 31C15 31E0 (Secondary)annulusmetric spacequasiconformal mappingMathematical Analysisexponent setsp-admissible weightSobolev spaceradial weightMathematics - Analysis of PDEsAnnulus; Doubling measure; Exponent sets; Metric space; Newtonian space; p-admissible weight; Poincare inequality; Quasiconformal mapping; Radial weight; Sobolev space; Variational capacityMatematisk analysPoincaré inequalitydoubling measureFOS: MathematicsNewtonian spacevariational capacityAnalysis of PDEs (math.AP)
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On strong solutions of the differential equations modeling the steady flow of certain incompressible generalized Newtonian fluids

2007

In this paper we discuss a system of partial differential equations describing the steady flow of an incompressible fluid and prove the existence of a strong solution under suitable assumptions on the data. In the 2D-case this solution turns out to be of class C^{1,\alpha}.

Algebra and Number TheoryPartial differential equationDifferential equationApplied MathematicsMathematical analysis510Physics::Fluid DynamicsStrong solutionsGeneralized Newtonian fluidFlow (mathematics)CompressibilityNewtonian fluidAnalysisMathematicsSt. Petersburg Mathematical Journal
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Oscillatory integrals and fractal dimension

2021

Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…

Box dimensionGeneral Mathematics010102 general mathematicsMathematical analysisPhase (waves)Resolution of singularitiesOscillatory integral ; Box dimension ; Minkowski content ; Critical points ; Newton diagramCritical points01 natural sciencesFractal dimensionCritical point (mathematics)Oscillatory integralAmplitudeDimension (vector space)Mathematics - Classical Analysis and ODEsMinkowski contentClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMinkowski contentOscillatory integralNewton diagram[MATH]Mathematics [math]fractal dimension; box dimension; oscillatory integrals; theory of singularitiesMathematics
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A Study on Engineering Freshman Conceptual Understanding of Newtonian Mechanics

2021

Force concept inventory is a multiple-choice questionnaire commonly used to assess students’ conceptual understanding of Newtonian mechanics. We here show that a cluster analysis method can be used to study student answers to the force concept inventory to investigate their understanding of Newtonian mechanics and provide new insights into the use of the force concept inventory. We identi- fied groups of students characterized by similar correct answers as well as by non- correct answers to the questionnaire, whose analysis allowed us to highlight student misconceptions/non-normative conceptions. Such an analysis of student answers gave us insights into the relationships between the student…

Classical mechanicsComputer scienceCluster analysis · Engineering freshmen · Force concept inventory · Newtonian mechanicsSettore FIS/08 - Didattica E Storia Della FisicaForce Concept InventoryAnalysis method
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Deficiencias epistemológicas en la enseñanza habitual de los conceptos de campo y potencial eléctrico

1997

This article intends to analyse up to what extent the scarce learning produced when introducing the basic concepts on electrostatics is due to deficiencies and inadequacies in its routine teaching. So, on the one hand, we analyse what have been the principal epistemological leaps forward in the making of electricity as a science. On the other hand, we analyse Physics books and the teachers’ opinions.

Corrent elèctricaElectricitatCàrregaPrincipal (computer security)ElectrocinèticaCosmologia newtonianaPotencial elèctricTeoria elèctricaCosmologia cartesianaLEAPSEducationEpistemologyEnseñanza de las Ciencias. Revista de investigación y experiencias didácticas
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The double cone: a mechanical paradox or a geometrical constraint?

2011

In the framework of the Italian National Plan ‘Lauree Scientifiche’ (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum and a couple of wooden rails.

Demonstration experiments and apparatuPhysicsEducation and communicationEducation and communication; Demonstration experiments and apparatus; Secondary schools; Newtonian mechanics;ComputationConstraint (computer-aided design)Mathematics educationGeneral Physics and AstronomyGeometryNewtonian mechanicSecondary schoolCone (formal languages)Education
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On the existence of weak solution to the coupled fluid-structure interaction problem for non-Newtonian shear-dependent fluid

2016

We study the existence of weak solution for unsteady fluid-structure interaction problem for shear-thickening flow. The time dependent domain has at one part a flexible elastic wall. The evolution of fluid domain is governed by the generalized string equation with action of the fluid forces. The power-law viscosity model is applied to describe shear-dependent non-Newtonian fluids.

Dilatant35D30General MathematicsConstant Viscosity Elastic (Boger) Fluidsfluid-structure interactionhemodynamics01 natural sciencesexistence of weak solutionPhysics::Fluid Dynamics76A0576D03Fluid–structure interactionshear-thinning fluids0101 mathematicsMathematicsWeak solution010102 general mathematicsMechanicsnon-Newtonian fluidsNon-Newtonian fluid010101 applied mathematicsShear rateCondensed Matter::Soft Condensed Matter74F10Shear (geology)Generalized Newtonian fluidshear-thickening fluids35Q30
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A new Cartan-type property and strict quasicoverings when p = 1 in metric spaces

2018

In a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality, we prove a new Cartan-type property for the fine topology in the case $p=1$. Then we use this property to prove the existence of $1$-finely open \emph{strict subsets} and \emph{strict quasicoverings} of $1$-finely open sets. As an application, we study fine Newton-Sobolev spaces in the case $p=1$, that is, Newton-Sobolev spaces defined on $1$-finely open sets.

Discrete mathematicsfine Newton–Sobolev spaceProperty (philosophy)General Mathematicsta111010102 general mathematicsOpen setfine topologystrict quasicoveringType (model theory)function of bounded variationmetriset avaruudet01 natural sciencesMeasure (mathematics)Complete metric spaceCartan propertyfunktioteoria010101 applied mathematicsMetric spacemetric measure spacepotentiaaliteoria0101 mathematicsFine topologyMathematicsAnnales Academiae Scientiarum Fennicae Mathematica
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Localization and separation of solutions for Fredholm integral equations

2020

[EN] In this paper, we establish a qualitative study of nonlinear Fredholm integral equations, where we will carry out a study on the localization and separation of solutions. Moreover, we consider an efficient algorithm to approximate a solution. To do this, we study the semilocal convergence of an efficient third order iterative scheme for solving nonlinear Fredholm integral equations under mild conditions. The novelty of our work lies in the fact that this study involves first order Frechet derivative and mild conditions. A numerical example involving nonlinear Fredholm integral equations, is solved to show the domains of existence and uniqueness of solutions. The applicability of the it…

Domain of existence of solutionApplied MathematicsFredholm integral equation010102 general mathematicsSeparation (statistics)Mathematical analysisFredholm integral equationTwo-steps Newton iterative schemeLipschitz continuity01 natural sciencesIntegral equation010101 applied mathematicssymbols.namesakesymbols0101 mathematicsDomain of uniqueness of solutionLipschitz conditionMATEMATICA APLICADAAnalysisMathematics
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Application of 5E model for learning Mechanics through inquiry in secondary education

2018

En este trabajo se examina el proceso de resolución de una actividad de indagación sobre las leyes de Newton que consiste en diseñar un montaje con el cuál averiguar qué superficie es la más adecuada para arrastrar cajas de ropa en un almacén. Los participantes son 23 estudiantes de 4º de ESO. Para la toma de datos se recogen sus respuestas escritas relativas al diseño del dispositivo, a la toma de datos, interpretación de resultados y establecimiento de conclusiones. Para el análisis se examinan utilizando como herramienta el modelo de instrucción 5E. Los resultados principales apuntan a ciertas dificultades en los desempeños del alumnado relativos a la elaboración del montaje y a la expli…

Educación secundariaFuerza de rozamientoInquiryLaboratorioIndagación:PEDAGOGÍA [UNESCO]Leyes de NewtonSecondary educationLaws of NewtonUNESCO::PEDAGOGÍAFriction forceLaboratory
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