57 research outputs found
Concept and development of an autonomous wearable micro-fluidic platform for real time pH sweat analysis
No full textIn this work the development of an autonomous, robust and wearable micro-fluidic platform capable of performing on-line analysis of pH in sweat is discussed. Through the means of an optical detection system based on a surface mount light emitting diode (SMD LED) and a light photo sensor as a detector, a wearable system was achieved in which real-time monitoring of sweat pH was performed during 55 minutes of cycling activity. We have shown how through systems engineering, integrating miniaturised electrical components, and by improving the micro-fluidic chip characteristics, the wearability, reliability and performance of the micro-fluidic platform was significantly improved
A posteriori error estimates in the finite element method for elliptic BVP with degeneration
No full textWe consider a class of elliptic boundary value problems with degenerating coefficients for which we construct FEM schemes with optimal convergence on the basis of multiplicative extraction of the singularity. For a scale of weighted Sobolev norms including the energy norm of the differential operator, we prove a posteriori estimates for the error of the discrete solutions. © 2014 Pleiades Publishing, Ltd
A posteriori error estimates in the finite element method for elliptic BVP with degeneration
No full textWe consider a class of elliptic boundary value problems with degenerating coefficients for which we construct FEM schemes with optimal convergence on the basis of multiplicative extraction of the singularity. For a scale of weighted Sobolev norms including the energy norm of the differential operator, we prove a posteriori estimates for the error of the discrete solutions. © 2014 Pleiades Publishing, Ltd
Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients
No full textIn this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides. © Allerton Press, Inc., 2011
A Hardy inequality with a point-singular weight inside a domain
No full textSobolev spaces with weights taking infinite values at some interior points of a two-dimensional domain are considered. For functions from these spaces, a Hardy inequality is obtained. Embedding theorems for weighted Lebesgue spaces and equivalent renorming theorems are proved. © 2013 Pleiades Publishing, Ltd
Schemes of the finite element method with separation of singularity for a two-point boundary-value problem of the 4th order with degenerate coefficients
No full textIn this paper we construct a high accuracy variant of the finite element method for an ordinary differential equation of the fourth order whose coefficients are degenerate on the boundary. The proposed technique is based on the multiplicative and additive-multiplicative separation of singularity. We prove that the convergence rate of the proposed technique is optimal in a given class of smoothness of right-hand sides. © Allerton Press, Inc., 2011
High-Order Accuracy Approximation for a Two-Point Boundary Value Problem of Fourth Order with Degenerate Coefficients
No full text© 2018, Pleiades Publishing, Ltd. High-order accurate finite element schemes for a fourth-order ordinary differential equation with degenerate coefficients on the boundary are constructed. The method for solving the problem is based on multiplicative and additive-multiplicative separation of singularities. For right-hand sides of the given class of smoothness, an optimal convergence rate is proved
Rasskazy o bylom vospominanija o peregovorach po nerasprostraneniju i razoruženiju i o mnogom drugom
No full textSharp estimates for the polynomial approximation in weighted Sobolev spaces
No full text© 2015, Pleiades Publishing, Ltd. We obtain sharp estimates for the accuracy of the best approximation of functions by algebraic polynomials on an interval, the half-line, and the entire line in weighted Sobolev spaces with Jacobi, Laguerre, and Hermite weights, respectively. We show that the orthogonal polynomials associated with these weights form orthogonal bases in the respective weighted Sobolev spaces. We obtain sharp estimates of Markov–Bernstein type
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