Understanding the three and four-leg inverter Space Vector

This paper shows a new point of view of the classical voltage space vectors and its implications on three and four-leg converters. It is easy to find in the literature, authors using bi-dimensional and threedimensional representations of the converter states. Nonetheless, the literature rarely specifies what these spaces represent. Therefore, this paper proposes a wide analysis of the state voltages and its references for three-leg, three-leg four-wire and four-leg inverters, in favour of understanding the space vector behaviour under three and four-wire scenarios.Postprint (published version

Smart grid architecture for rural distribution networks: application to a Spanish pilot network

This paper presents a novel architecture for rural distribution grids. This architecture is designed to modernize traditional rural networks into new Smart Grid ones. The architecture tackles innovation actions on both the power plane and the management plane of the system. In the power plane, the architecture focuses on exploiting the synergies between telecommunications and innovative technologies based on power electronics managing low scale electrical storage. In the management plane, a decentralized management system is proposed based on the addition of two new agents assisting the typical Supervisory Control And Data Acquisition (SCADA) system of distribution system operators. Altogether, the proposed architecture enables operators to use more effectively—in an automated and decentralized way—weak rural distribution systems, increasing the capability to integrate new distributed energy resources. This architecture is being implemented in a real Pilot Network located in Spain, in the frame of the European Smart Rural Grid project. The paper also includes a study case showing one of the potentialities of one of the principal technologies developed in the project and underpinning the realization of the new architecture: the so-called Intelligent Distribution Power Router.Postprint (published version

Corrigendum to Cluster values for algebras of analytic functions

[EN] While the article was in publication process, we found a mistake in a key tool for the proof one of the main results. As a consequence, our result on the ball A(u)(B-X) algebra remains open. For the algebra H-b(X) we obtain a weaker statement, which still extends previous work in the subject. In this note we enumerate those results which should be omitted or modified. (C) 2018 Elsevier Inc. All rights reserved.This work was partially supported by projects CONICET PIP 11220130100329CO, ANPCyT PICT 2015-2299, ANPCyT PICT-2015-3085, ANPCyT PICT-2015-2224, UBACyT 20020130300057BA, UBACyT 20020130300052BA, UBACyT 20020130100474BA and MINECO and FEDER Project MTM2014-57838-C2-2-P.Carando, D.; Galicer, D.; Muro, S.; Sevilla Peris, P. (2018). Corrigendum to Cluster values for algebras of analytic functions. Advances in Mathematics. 329:1307-1309. https://doi.org/10.1016/j.aim.2018.03.019S1307130932

Some polynomial versions of cotype and applications

[EN] We introduce non-linear versions of the classical cotype of Banach spaces. We show that spaces with l.u.st. and cotype, and spaces having Fourier cotype enjoy our non-linear cotype. We apply these concepts to get results on convergence of vector-valued power series in infinite many variables and on l(1)-multipliers of vector-valued Dirichlet series. Finally we introduce cotype with respect to indexing sets, an idea that includes our previous definitions. (C) 2015 Elsevier Inc. All rights reserved.The first author was partially supported by CONICET-PIP 11220130100329CO, UBACyT 20020130100474BA and ANPCyT PICT 2011-1456. The third author was also supported by UPV-SP20120700. All three authors were supported by project MTM2014-57838-C2-2-P.Carando, D.; Defant, A.; Sevilla Peris, P. (2016). Some polynomial versions of cotype and applications. Journal of Functional Analysis. 270(1):68-87. https://doi.org/10.1016/j.jfa.2015.09.017S6887270

Limit orders and multilinear forms on l(p) spaces

[EN] Since the concept of limit order is a useful tool to study operator ideals, we propose an analogous definition for ideals of multilinear forms. From the limit orders of some special ideals (of nuclear, integral, r-dominated and extendible multilinear forms) we derive some properties of them and show differences between the bilinear and n-linear cases (n ¿ 3).The third author was supported by the MCYT and FEDER Project BFM2002-01423 and grant GV-GRUPOS04/45Carando, D.; Dimant, V.; Sevilla Peris, P. (2006). Limit orders and multilinear forms on l(p) spaces. Publications of the Research Institute for Mathematical Sciences. 42(2):507-522. http://hdl.handle.net/10251/166258S50752242

Asymptotic estimates on the von Neumann inequality for homogeneous polynomials

[EN] By the von Neumann inequality for homogeneous polynomials there exists a positive constant C-k,C-q(n) such that for every k-homogeneous polynomial p in n variables and every n-tuple of commuting operators (T-1, ..., T-n with Sigma(n)(i=1) parallel to T-i parallel to(q) <= 1 we have parallel to P (T-1, ..., T-n)parallel to L(H) <= C-k,C-q(n) sup {vertical bar p(z(1), ..., z(n))vertical bar: Sigma(n)(i=1) vertical bar(q) <= 1}. For fixed k and q, we study the asymptotic growth of the smallest constant C-k,C-q(n) as n (the number of variables/operators) tends to infinity. For q = infinity, we obtain the correct asymptotic behavior of this constant (answering a question posed by Dixon in the 1970s). For 2 <= q < infinity we improve some lower bounds given by Mantero and Tonge, and prove the asymptotic behavior up to a logarithmic factor. To achieve this we provide estimates of the norm of homogeneous unimodular Steiner polynomials, i.e. polynomials such that the multi-indices corresponding to the nonzero coefficients form partial Steiner systems.The first two named authors were supported by CONICET projects PIP 0624 and PICT 2011-1456, and by UBACyT projects 20020130300057BA and 20020130300052BA. The third named author was supported by MICINN project MTM2014-57838-C2-2-P.Galicer, D.; Muro, S.; Sevilla Peris, P. (2018). Asymptotic estimates on the von Neumann inequality for homogeneous polynomials. Journal für die reine und angewandte Mathematik (Crelles Journal). 743:213-227. https://doi.org/10.1515/crelle-2015-0097S213227743Defant, A., Garcia, D., & Maestre, M. (2004). MAXIMUM MODULI OF UNIMODULAR POLYNOMIALS. Journal of the Korean Mathematical Society, 41(1), 209-229. doi:10.4134/jkms.2004.41.1.209Bayart, F. (2010). MAXIMUM MODULUS OF RANDOM POLYNOMIALS. The Quarterly Journal of Mathematics, 63(1), 21-39. doi:10.1093/qmath/haq026Crabb, M. J., & Davie, A. M. (1975). Von Neumann’s Inequality for Hilbert Space Operators. Bulletin of the London Mathematical Society, 7(1), 49-50. doi:10.1112/blms/7.1.49Alon, N., Kim, J.-H., & Spencer, J. (1997). Nearly perfect matchings in regular simple hypergraphs. Israel Journal of Mathematics, 100(1), 171-187. doi:10.1007/bf02773639Defant, A., Frerick, L., Ortega-Cerdà, J., Ounaïes, M., & Seip, K. (2011). The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive. Annals of Mathematics, 174(1), 485-497. doi:10.4007/annals.2011.174.1.13Maurizi, B., & Queffélec, H. (2009). Some Remarks on the Algebra of Bounded Dirichlet Series. Journal of Fourier Analysis and Applications, 16(5), 676-692. doi:10.1007/s00041-009-9112-yCarando, D., & Dimant, V. (2006). Extension of polynomials and John’s theorem for symmetric tensor products. Proceedings of the American Mathematical Society, 135(6), 1769-1773. doi:10.1090/s0002-9939-06-08666-7Blei, R. C. (1979). Multidimensional extensions of the Grothendieck inequality and applications. Arkiv för Matematik, 17(1-2), 51-68. doi:10.1007/bf02385457Schütt, C. (1984). Entropy numbers of diagonal operators between symmetric Banach spaces. Journal of Approximation Theory, 40(2), 121-128. doi:10.1016/0021-9045(84)90021-2Mantero, A., & Tonge, A. (1980). The Schur multiplication in tensor algebras. Studia Mathematica, 68(1), 1-24. doi:10.4064/sm-68-1-1-24Varopoulos, N. T. (1974). On an inequality of von Neumann and an application of the metric theory of tensor products to operators theory. Journal of Functional Analysis, 16(1), 83-100. doi:10.1016/0022-1236(74)90071-8Rödl, V. (1985). On a Packing and Covering Problem. European Journal of Combinatorics, 6(1), 69-78. doi:10.1016/s0195-6698(85)80023-