Extremal Vector Valued Inequalities for Hankel Transforms

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Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, I

36 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.-- Part II of this paper published in: Approx. Theory Appl. 18(2): 1-32 (2002), available at: http://e-archivo.uc3m.es/handle/10016/6483MR#: MR2047389 (2005k:42062)Zbl#: Zbl 1081.42024In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first (J.M.R.), third (E.R.) and fourth (D.P.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Approximation theory for weighted Sobolev spaces on curves

17 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR1882649 (2003c:42002)In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete. We also prove the density of the polynomials in these spaces for non-closed compact curves and, finally, we find conditions under which the multiplication operator is bounded on the completion of polynomials. These results have applications to the study of zeroes and asymptotics of Sobolev orthogonal polynomials.Research of V. Álvarez, D. Pestana and J.M. Rodríguez partially supported by a grant from DGI, BFM2000-0206-C04-01, Spain.Publicad

Weighted Sobolev spaces on curves

45 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.MR#: MR1934626 (2003j:46038)Zbl#: Zbl 1019.46026In this paper we present a definition of weighted Sobolev spaces on curves and find general conditions under which the spaces are complete for non-closed compact curves. We also prove the density of the polynomials in these spaces and, finally, we find conditions under which the multiplication operator is bounded in the space of polynomials.Research of second (D.P.), third (J.M.R.) and fourth (E.R.) authors was partially supported by a grant from DGI (BFM 2000-0206-C04-01), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials, II

32 pages, no figures.-- MSC1987 codes: 41A10, 46E35, 46G10.-- Part I of this paper published in: Acta Appl. Math. 80(3): 273-308 (2004), available at: http://e-archivo.uc3m.es/handle/10016/6482MR#: MR1928169 (2003h:42034)Zbl#: Zbl 1095.42014^aWe present a definition of general Sobolev spaces with respect to arbitrary measures, $W^{k,p}(\Omega,\mu)$ for $1\leq p\leq\infty$. In Part I [Acta Appl. Math. 80(3): 273-308 (2004), http://e-archivo.uc3m.es/handle/10016/6482] we proved that these spaces are complete under very mild conditions. Now we prove that if we consider certain general types of measures, then $C^\infty_c({\bf R})$ is dense in these spaces. As an application to Sobolev orthogonal polynomials, we study the boundedness of the multiplication operator. This gives an estimation of the zeroes of Sobolev orthogonal polynomials.Research partially supported by a grant from DGES (MEC), Spain.Publicad

Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials: a survey

6 pages, no figures.-- MSC2000 codes: 41A10, 46E35, 46G10.MR#: MR2219917 (2006k:42051)Zbl#: Zbl 1146.42005In this paper we present a definition of Sobolev spaces with respect to general measures, prove some useful technical results, some of them generalizations of classical results with Lebesgue measure and find general conditions under which these spaces are complete. These results have important consequences in approximation theory. We also find conditions under which the evaluation operator is bounded.Research by first author (J.M.R.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain. Research by second author (V.A.) was partially supported by grants from MCYT (MTM 2004-00078) and Junta de Andalucía (FQM-210), Spain. Research by third author (E.R.) was partially supported by a grant from DGI (BFM 2003-06335-C03-02), Spain. Research by fourth author (D.P.) was partially supported by grants from DGI (BFM 2003-06335-C03-02 and BFM 2003-04870), Spain.Publicad

Agent-based model for the effect of curing temperature on cement hydration

The agent-based model presented here, comprises an algorithm that computes the degree of hydration, the water consumption and the layer thickness of C-S-H gel as functions of time for different temperatures and different w/c ratios. The results are in agreement with reported experimental studies, demonstrating the applicability of the model. As the available experimental results regarding elevated curing temperature are scarce, the model could be recalibrated in the future. Combining the agent-based computational model with TGA analysis, a semiempirical method is achieved to be used for better understanding the microstructure development in ordinary cement pastes and to predict the influence of temperature on the hydration process

Agent-based modelling for cement hydration

The Agent-Based Modelling and simulation (ABM) is a rather new approach for studying complex systems withinteracting autonomous agents that has lately undergone great growth in various fields such as biology, physics, social science, economics and business. Efforts to model and simulate the highly complex cement hydration process have been made over the past 40 years, with the aim of predicting the performance of concrete and designing innovative and enhanced cementitious materials. The ABM presented here - based on previous work - focuses on the early stages of cement hydration by modelling the physical-chemical processes at the particle level. The model considers the cement hydration process as a time and 3D space system, involving multiple diffusing and reacting species of spherical particles. Chemical reactions are simulated by adaptively selecting discrete stochastic simulation for the appropriate reaction, whenever that is necessary. Interactions between particles are also considered. The model has been inspired by reported cellular automata?s approach which provides detailed predictions of cement microstructure at the expense of significant computational difficulty. The ABM approach herein seeks to bring about an optimal balance between accuracy and computational efficiency