Search results for "Polygon"

showing 10 items of 282 documents

Some approximation properties of ( p , q ) $(p,q)$ -Bernstein operators

2016

This paper is concerned with the $(p,q)$ -analog of Bernstein operators. It is proved that, when the function is convex, the $(p,q)$ -Bernstein operators are monotonic decreasing, as in the classical case. Also, some numerical examples based on Maple algorithms that verify these properties are considered. A global approximation theorem by means of the Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem are proved.

MapleDiscrete mathematicsModulus of smoothnesslcsh:MathematicsApplied Mathematics010102 general mathematicsApproximation theoremRegular polygonMonotonic functionFunction (mathematics)Type (model theory)engineering.materialVoronovskaja type theoremlcsh:QA1-93901 natural sciences010101 applied mathematics( p q ) $(pq)$ -Bernstein operatorsengineeringDiscrete Mathematics and Combinatorics0101 mathematics( p q ) $(pq)$ -calculusK-functionalAnalysisMathematicsDitzian-Totik first order modulus of smoothnessJournal of Inequalities and Applications
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Cohesive delamination and frictional contact on joining surface via XFEM

2018

In the present paper, the complex mechanical behaviour of the surfaces joining two different bodies is analysed by a cohesive-frictional interface constitutive model. The kinematical behaviour is characterized by the presence of discontinuous displacement fields, that take place at the internal connecting surfaces, both in the fully cohesive phase and in the delamination one. Generally, in order to catch discontinuous displacement fields, internal connecting surfaces (adhesive layers) are modelled by means of interface elements, which connect, node by node, the meshes of the joined bodies, requiring the mesh to be conforming to the geometry of the single bodies and to the relevant connectin…

Materials scienceDiscretizationConstitutive equationGeometry02 engineering and technology01 natural sciencesdelaminationDiscontinuity (geotechnical engineering)0203 mechanical engineeringlcsh:TA401-492Polygon mesh0101 mathematicsjoined solidsExtended finite element methodCurvilinear coordinatescohesive-frictionalXFEMjoined solidjoined solids; interface; XFEM; cohesive-frictional; delaminationFinite element method010101 applied mathematics020303 mechanical engineering & transportsinterfacelcsh:Materials of engineering and construction. Mechanics of materialsAdhesiveSettore ICAR/08 - Scienza Delle CostruzioniAIMS Materials Science
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A grain boundary formulation for crystal plasticity

2016

Abstract A three-dimensional grain-boundary formulation for small strains crystal plasticity is presented for the first time. The method is developed and implemented for both single grains and polycrystalline aggregates and it is based on the use of a suitable set of boundary integral equations for modelling the individual grains, which are represented as anisotropic elasto-plastic domains. In the boundary integral framework, crystal plasticity is modelled resorting to an initial strains approach and specific aspects, related to the integration of strongly singular volume integrals in the anisotropic elasto-plastic grain-boundary equations, are discussed and suitably addressed for the first…

Materials scienceIterative methodCrystal plasticityCrystal plasticity Polycrystalline material02 engineering and technologyB. Polycrystalline materialNOVolume integralPolycrystalline material0203 mechanical engineeringGeneral Materials SciencePolygon meshMechanics of MaterialAnisotropyMechanical EngineeringMathematical analysis021001 nanoscience & nanotechnologyStrength of materialsCrystallography020303 mechanical engineering & transportsMechanics of MaterialsEmbeddingGrain boundaryCrystalliteMaterials Science (all)0210 nano-technologyB. Crystal plasticity
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Skeletizing 3D-Objects by Projections

2004

Skeletization is used to simplify an object and to give an idea of the global shape of an object. This paper concerns the continuous domain. While many methods already exist, they are mostly applied in 2D-space. We present a new method to skeletize the polygonal approximation of a 3D-object, based on projections and 2D-skeletization from binary trees.

Mathematical optimizationBinary treeDelaunay triangulationPolygonal chainSpace (commercial competition)Object (computer science)AlgorithmMathematicsDomain (software engineering)
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Nonmonotone Saturation Profiles for Hydrostatic Equilibrium in Homogeneous Porous Media

2012

Nonmonotonic saturation profiles (saturation overshoot) occur as travelling waves in gravity driven fingering. They seem important for preferential flow mechanisms and have found much attention recently. Here, we predict them even for hydrostatic equilibrium when all velocities vanish. We suggest that hysteresis suffices to explain the effect. Recently, the observation of nonmonotonicity of traveling wave solutions for saturation profiles during constant-flux infiltration experiments has highlighted the shortcomings of the traditional, seventy year old mathematical model for immiscible displacement in porous media. Several recent modifications have been proposed to explain these observation…

Mathematical optimizationChemistrySoil ScienceObservableMechanicsPreferential flowlaw.inventionMonotone polygonColumn experimentlawHomogeneousHydrostatic equilibriumPorous mediumSaturation (chemistry)Vadose Zone Journal
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A Proximal Solution for a Class of Extended Minimax Location Problem

2005

We propose a proximal approach for solving a wide class of minimax location problems which in particular contains the round trip location problem. We show that a suitable reformulation of the problem allows to construct a Fenchel duality scheme the primal-dual optimality conditions of which can be solved by a proximal algorithm. This approach permits to solve problems for which distances are measured by mixed norms or gauges and to handle a large variety of convex constraints. Several numerical results are presented.

Mathematical optimizationClass (set theory)Optimality criterionComputer scienceScheme (mathematics)1-center problemRegular polygonMinimax problemConstruct (python library)Variety (universal algebra)Minimax
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Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints

1994

In this paper, we establish some general metric regularity results for multivalued functions on Banach spaces. Then, we apply them to derive second-order necessary optimality conditions for the problem of minimizing a functionf on the solution set of an inclusion 0?F(x) withx?C, whenF has a closed convex second-order derivative.

Mathematical optimizationControl and OptimizationMultivalued functionApplied MathematicsTheory of computationSolution setRegular polygonBanach spaceMinificationManagement Science and Operations ResearchDirectional derivativeMathematicsJournal of Optimization Theory and Applications
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On Computational Properties of a Posteriori Error Estimates Based upon the Method of Duality Error Majorants

2004

In the present paper, we analyze computational properties of the functional type a posteriori error estimates that have been derived for elliptic type boundary-value problems by duality theory in calculus of variations. We are concerned with the ability of this type of a posteriori estimates to provide accurate upper bounds of global errors and properly indicate the distribution of local ones. These questions were analyzed on a series of boundary-value problems for linear elliptic operators of 2nd and 4th order. The theoretical results are confirmed by numerical tests in which the duality error majorant for the classical diffusion problem is compared with the standard error indicator used i…

Mathematical optimizationElliptic operatorDistribution (mathematics)Series (mathematics)Basis (linear algebra)Duality (mathematics)Applied mathematicsA priori and a posterioriPolygon meshCalculus of variationsMathematics
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Passivity-based output feedback control of Markovian jump systems with discrete and distributed time-varying delays

2013

In this article, we present a new method in designing mode-dependent passivity-based output feedback controllers for Markovian jump systems with time-varying delays. Both discrete and distributed delays are considered in the model. A Lyapunov–Krasovskii function is constructed to establish new required sufficient conditions for ensuring exponentially mean-square stability and the passivity criteria, simultaneously. The method produces linear matrix inequality formulation that allows obtaining controller gains based on a convex optimisation method. Finally, a numerical example is given to illustrate the effectiveness of our approach.

Mathematical optimizationExponential growthControl and Systems EngineeringControl theoryPassivityControl (management)Linear matrix inequalityRegular polygonFunction (mathematics)Stability (probability)Computer Science ApplicationsTheoretical Computer ScienceMathematicsInternational Journal of Systems Science
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Monotonic solution of flow and transport problems in heterogeneous media using Delaunay unstructured triangular meshes

2013

Transport problems occurring in porous media and including convection, diffusion and chemical reactions, can be well represented by systems of Partial Differential Equations. In this paper, a numerical procedure is proposed for the fast and robust solution of flow and transport problems in 2D heterogeneous saturated media. The governing equations are spatially discretized with unstructured triangular meshes that must satisfy the Delaunay condition. The solution of the flow problem is split from the solution of the transport problem and it is obtained with an approach similar to the Mixed Hybrid Finite Elements method, that always guarantees the M-property of the resulting linear system. The…

Mathematical optimizationFinite volume methodDiscretizationTransport problem porous media anisotropic diffusion tensor heterogeneous medium M-matrix Delaunay mesh edge swap numerical methods finite elementsDelaunay triangulationAnisotropic diffusionLinear systemMonotonic functionFinite element methodSettore ICAR/01 - IdraulicaApplied mathematicsPolygon meshWater Science and TechnologyMathematics
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