Lipschitz operator ideals and the approximation property

[EN] We establish the basics of the theory of Lipschitz operator ideals with the aim of recovering several classes of Lipschitz maps related to absolute summability that have been introduced in the literature in the last years. As an application we extend the notion and main results on the approximation property for Banach spaces to the case of metric spaces. (C) 2015 Elsevier Inc. All rights reserved.P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E.A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2012-36740-C02-02.Achour, D.; Rueda, P.; Sánchez Pérez, EA.; Yahi, R. (2016). Lipschitz operator ideals and the approximation property. Journal of Mathematical Analysis and Applications. 436(1):217-236. https://doi.org/10.1016/j.jmaa.2015.11.050S217236436

Integration of resilience and sustainability: from theory to application

Purpose – This study aims to explore the challenges associated with the integration of resilience and sustainability, and propose a workable solution that ensures resilient and sustainable buildings. Recent research outcomes suggest that the number of natural hazards, both environmental and geophysical, will increase due to the effect of global warming. Various approaches have been investigated to reduce environmental degradation and to improve the physical resilience to natural hazards. However, most of these approaches are fragmented and when combined with cultural barriers, they often result into less-efficient assessment tools. Design/methodology/approach – The primary source of information used to develop this paper has been research publications, policy papers, reports and tool guidelines. A set of questions were developed to guide the review which was complemented with information distilled from the HFA 2005-2015 to develop an integration process to evaluate 10 international sustainability appraisal tools. Findings – The major finding of this research is that, from a technical point of view, resilience and sustainability could be integrated. However, it requires a long and thorough process with a multidisciplinary stakeholder team including technical, strategic, social and political parties. A combination of incentives and policies would support this process and help people work towards the integration. The Japanese model demonstrates a successful case in engaging stakeholders in the process which led to the development of a comprehensive appraisal tool, CASBEE®, where resilience and sustainability are integrated. Practical implications – Although data have been sought through literature review (i.e. secondary data), the research is expected to have significant impact, as it provides a clear theoretical foundation and methods for those wishing to integrate resilience within current sustainability appraisal tools or develop new tools. Social implications – This paper provides original concepts that are required to reduce fragmentation in the way resilience and sustainability are addressed. It sets up a new research agenda which has the potential to have a strong impact due the fact that sustainability and resilience are getting higher on the political priority scale. Originality/value – This paper provides findings of an original idea to reduce fragmentation in the way resilience and sustainability are addressed. It sets up a new research agenda which has the potential to have a strong impact due the fact that sustainability and resilience are getting higher on the political priority scale

Tensor Characterizations of Summing Polynomials

[EN] Operators T that belong to some summing operator ideal, can be characterized by means of the continuity of an associated tensor operator T that is de¿ned between tensor products of sequences spaces. In this paper we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated ¿ten-sor¿ polynomial ¿which plays the role of T ¿, needs to be determined ¿rst. Examples of applications are shown.The third and fourth authors acknowledge with thanks the Ministerio de Economia, Industria y Competitividad and FEDER Grant MTM2016-77054-C2-1-P. The authors thank the referee for his valuable suggestions that improved the final presentation of the paper.Achour, D.; Alouani, A.; Rueda, P.; Sánchez Pérez, EA. (2018). Tensor Characterizations of Summing Polynomials. Mediterranean Journal of Mathematics. 15(3):127-139. https://doi.org/10.1007/s00009-018-1175-zS127139153Achour, D.: Multilinear extensions of absolutely (p;q;r)-summing operators. Rend. Circ. Mat. Palermo (2) 60(3), 337–350 (2011)Achour, D., Alouani, A.: On multilinear generalizations of the concept of nuclear operators. Colloq. Math. 120(1), 85–102 (2010)Achour, D., Saadi, K.: A polynomial characterization of Hilbert spaces. Collectanea. Math. 61(3), 291–301 (2010)Aron, R.M., Rueda, P.: p-Compact homogeneous polynomials from an ideal point of view. Function spaces in modern analysis, Contemp. Math., vol. 547. American Mathematical Society, Providence, RI, pp. 61–71 (2011)Botelho, G.: Ideals of polynomials generated by weakly compact operators. Note di Mat. 25, 69–102 (2005)Botelho, G.: Type, cotype and generalized Rademacher functions. Rocky Mt. J. Math. 28, 1227–1250 (1998)Botelho, G., Campos, J.: On the transformation of vector-valued sequences by linear and multilinear operators. Monatsh. Math. 183(2017), 415–435 (2015)Botelho, G., Campos, J., Santos, J.: Operator ideals related to absolutely summing and Cohen strongly summing operators. Pac. J. Math. 287, 1–17 (2017)Botelho, G., Pellegrino, D., Rueda, P.: Preduals of spaces of homogeneous polynomials on $$L_p$$ L p -spaces. Linear Multilinear Algebra 60(5), 565–571 (2012)Botelho, G., Pellegrino, D., Rueda, P.: Dominated polynomials on infinite dimensional spaces. Proc. Am. Math. Soc. 138(1), 209–216 (2010)Botelho, G., Pellegrino, D., Rueda, P.: Pietsch’s factorization theorem for dominated polynomials. J. Funct. Anal. 243(1), 257–269 (2007)Çalişkan, E., Pellegrino, D.M.: On the multilinear generalizations of the concept of absolutely summing operators. Rocky Mt. J. Math. 37(4), 1137–1154 (2007)Çalişkan, E., Rueda, P.: On distinguished polynomials and their projections. Ann. Acad. Sci. Fenn. Math. 37, 595–603 (2012)Cilia, R., Gutiérrez, J.: Dominated, diagonal polynomials on $$\ell _p$$ ℓ p spaces. Arch. Math. 84, 421–431 (2005)Cohen, J.S.: Absolutely p-summing, p-nuclear operators and their conjugates. Math. Ann. 201, 177–200 (1973)Defant, A., Floret, K.: Tensor norms and operator ideals. North-Holland Mathematics Studies, vol. 176. North-Holland Publishing Co., Amsterdam (1993)Diestel, J., Jarchow, H., Tonge, A.:, Absolutely summing operators. Cambridge Studies in Advanced Mathematics, vol. 43. Cambridge University Press, Cambridge (1995)Dimant, V.: Strongly p-summing multilinear operators. J. Math. Anal. Appl. 278, 182–193 (2003)Matos, M., Floret, K.: Application of a Khintchine inequality to holomorphic mappings. Math. Nachr. 176, 65–72 (1995)Mujica, J.: Complex Analysis in Banach spaces. Dover Publications Inc., New York (2010)Pérez-García, D.: Comparing different classes of absolutely summing multilinear operators. Arch. Math. 85, 258–267 (2005)Pellegrino, D., Rueda, P., Sánchez-Pérez, E.A.: Surveying the spirit of absolute summability on multilinear operators and homogeneous polynomials. Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM 110(1), 285–302 (2016)Pietsch, A.: Operator ideals. North-Holland Mathematical Library, vol. 20. North-Holland Publishing Co, Amsterdam-New York (1980)Rueda, P., Sánchez-Pérez, E.A.: Factorization of p-dominated polynomials through $$L_p$$ L p -spaces. Mich. Math. J. 63(2), 345–353 (2014)Rueda, P., Sánchez-Pérez, E.A., Tallab, A.: Traced tensor norms and multiple summing multilinear operators. Linear Multilinear Algebra 65(4), 768–786 (2017

Absolutely continuous multilinear operators

We introduce the new class of the (p;p1,...,pm; s)-absolutely continuous operators, that is defined using a summability property that provides the multilinear version of the (p, s)-absolutely continuous operators. We give an analogue of the Pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for (p, s)-absolutely continuous operators, obtaining in this way a rich factorization theory. We present also a tensor norm which represents this multi-ideal by trace duality. As an application, we show that (p; p1, . . . , pm; s)-absolutely continuous multilinear operators are compact under some requirements. Applications to factorization of linear maps on Banach function spaces through interpolation spaces are also given.EL-Hadj Dahia acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under grant 555/PGRS/C.U.K.M. (2011) for a short term stage. D. Achour acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under project PNR 8-U28-6543. E.A. Sanchez acknowledges with thanks the support of the Ministerio de Economia y Connpetitividad (Spain) under project #MTM2009-14483-C02-02.Dahia, E.; Achour, D.; Sánchez Pérez, EA. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications. 397:205-224. https://doi.org/10.1016/j.jmaa.2012.07.034S20522439

Learning lessons from the 2011 Van Earthquake to enhance healthcare surge capacity in Turkey

Historically, Turkey has adopted a reactive approach to natural hazards which resulted in significant losses. However, following the 1999 Kocaeli Earthquake, a more proactive approach has been adopted. This study aims to explore the way this new approach operates on the ground. A multi-national and multi-disciplinary team conducted a field investigation following the 2011 Van Earthquake to identify lessons to inform healthcare emergency planning in Turkey and elsewhere. The team interviewed selected stakeholders including, healthcare emergency responders, search and rescue services, ambulance services, and health authority representatives, in addition to conducting a focus group. Data were analysed according to an open coding process and SWOT analysis. The findings suggest that the approach succeeded in developing a single vision by consolidating official efforts in a more structured way, mobilising many governmental and non-governmental organisations, securing significant amounts of resources including physical and human, and increasing the resilience and flexibility of infrastructure to expand its capacity. However, more attention is required to the development of stronger management procedures and acquisition of further resources

Degenerate higher order scalar-tensor theories beyond Horndeski up to cubic order

We present all scalar-tensor Lagrangians that are cubic in second derivatives of a scalar field, and that are degenerate, hence avoiding Ostrogradsky instabilities. Thanks to the existence of constraints, they propagate no more than three degrees of freedom, despite having higher order equations of motion. We also determine the viable combinations of previously identified quadratic degenerate Lagrangians and the newly established cubic ones. Finally, we study whether the new theories are connected to known scalar-tensor theories such as Horndeski and beyond Horndeski, through conformal or disformal transformations

Factorization of strongly (p,sigma)-continuous multilinear operators

We introduce the new ideal of strongly-continuous linear operators in order to study the adjoints of the -absolutely continuous linear operators. Starting from this ideal we build a new multi-ideal by using the composition method. We prove the corresponding Pietsch domination theorem and we present a representation of this multi-ideal by a tensor norm. A factorization theorem characterizing the corresponding multi-ideal - which is also new for the linear case - is given. When applied to the case of the Cohen strongly -summing operators, this result gives also a new factorization theorem.D. Achour acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) under project PNR 8-U28-181. E. Dahia acknowledges with thanks the support of the Ministere de l'Enseignament Superieur et de la Recherche Scientifique (Algeria) [grant number 10/PG-FMI/2013] and the Universite de M'Sila (2013) for short term stage. P. Rueda acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) MTM2011-22417. E. A. Sanchez Perez acknowledges with thanks the support of the Ministerio de Economia y Competitividad (Spain) under project MTM2012-36740-C02-02.Achour, D.; Dahia, E.; Rueda, P.; Sánchez Pérez, EA. (2014). Factorization of strongly (p,sigma)-continuous multilinear operators. Linear and Multilinear Algebra. 62(12):1649-1670. doi:10.1080/03081087.2013.839677S164916706212Matter, U. (1987). Absolutely Continuous Operators and Super-Reflexivity. Mathematische Nachrichten, 130(1), 193-216. doi:10.1002/mana.19871300118Diestel, J., Jarchow, H., & Tonge, A. (1995). Absolutely Summing Operators. doi:10.1017/cbo9780511526138Pietsch, A. (1967). Absolut p-summierende Abbildungen in normierten Räumen. Studia Mathematica, 28(3), 333-353. doi:10.4064/sm-28-3-333-353Achour, D., & Mezrag, L. (2007). On the Cohen strongly p-summing multilinear operators. Journal of Mathematical Analysis and Applications, 327(1), 550-563. doi:10.1016/j.jmaa.2006.04.065Apiola, H. (1976). Duality between spaces ofp-summable sequences, (p, q)-summing operators and characterizations of nuclearity. Mathematische Annalen, 219(1), 53-64. doi:10.1007/bf01360858Sánchez PérezEA. Ideales de operadores absolutamente continuos y normas tensoriales asociadas [PhD Thesis]. Spain: Universidad Politécnica de Valencia; 1997.López Molina, J. A., & Sánchez Pérez, E. A. (2000). On operator ideals related to (p,σ)-absolutely continuous operators. Studia Mathematica, 138(1), 25-40. doi:10.4064/sm-138-1-25-40Cohen, J. S. (1973). Absolutelyp-summing,p-nuclear operators and their conjugates. Mathematische Annalen, 201(3), 177-200. doi:10.1007/bf01427941Mezrag, L., & Saadi, K. (2012). Inclusion and coincidence properties for Cohen strongly summing multilinear operators. Collectanea Mathematica, 64(3), 395-408. doi:10.1007/s13348-012-0071-2Achour, D., & Alouani, A. (2010). On multilinear generalizations of the concept of nuclear operators. Colloquium Mathematicum, 120(1), 85-102. doi:10.4064/cm120-1-7Mujica, X. (2008). τ(p;q)-summing mappings and the domination theorem. Portugaliae Mathematica, 211-226. doi:10.4171/pm/1806Campos, J. R. (2013). Cohen and multiple Cohen strongly summing multilinear operators. Linear and Multilinear Algebra, 62(3), 322-346. doi:10.1080/03081087.2013.779270Bu, Q., & Shi, Z. (2013). On Cohen almost summing multilinear operators. Journal of Mathematical Analysis and Applications, 401(1), 174-181. doi:10.1016/j.jmaa.2012.12.005Ryan, R. A. (2002). Introduction to Tensor Products of Banach Spaces. Springer Monographs in Mathematics. doi:10.1007/978-1-4471-3903-4Achour, D., & Belaib, M. T. (2011). Tensor norms related to the space of Cohen $p$-nuclear‎ ‎multilinear mappings. Annals of Functional Analysis, 2(1), 128-138. doi:10.15352/afa/1399900268Achour, D. (2011). Multilinear extensions of absolutely (p;q;r)-summing operators. Rendiconti del Circolo Matematico di Palermo, 60(3), 337-350. doi:10.1007/s12215-011-0054-2Dahia, E., Achour, D., & Sánchez Pérez, E. A. (2013). Absolutely continuous multilinear operators. Journal of Mathematical Analysis and Applications, 397(1), 205-224. doi:10.1016/j.jmaa.2012.07.034Botelho, G., Pellegrino, D., & Rueda, P. (2007). On Composition Ideals of Multilinear Mappings and Homogeneous Polynomials. Publications of the Research Institute for Mathematical Sciences, 43(4), 1139-1155. doi:10.2977/prims/1201012383Pellegrino, D., Santos, J., & Seoane-Sepúlveda, J. B. (2012). Some techniques on nonlinear analysis and applications. Advances in Mathematics, 229(2), 1235-1265. doi:10.1016/j.aim.2011.09.014Ramanujan, M. S., & Schock, E. (1985). Operator ideals and spaces of bilinear operators. Linear and Multilinear Algebra, 18(4), 307-318. doi:10.1080/03081088508817695Floret, K., & Hunfeld, S. (2002). Proceedings of the American Mathematical Society, 130(05), 1425-1436. doi:10.1090/s0002-9939-01-06228-

MBE grown GaAsBi/GaAs multiple quantum well structures: Structural and optical characterization

A series of GaAsBi/GaAs multiple quantum well p–i–n diodes were grown by molecular beam epitaxy. Nomarski images showed evidence of sub-surface damage in each diode, with an increase in the cross-hatching associated with strain relaxation for the diodes containing more than 40 quantum wells. X-ray diffraction ω–2θ scans of the (004) reflections showed that multiple quantum well regions with clearly defined well periodicities were grown. The superlattice peaks of the diodes containing more than 40 wells were much broader than those of the other diodes. The photoluminescence spectra showed a redshift of 56 meV and an attenuation of nearly two orders of magnitude for the 54 and 63 well diodes. Calculations of the quantum confinement and strain induced band gap modifications suggest that the wells in all diodes are thinner than their intended widths and that both loss of quantum confinement and strain probably contributed to the observed redshift and attenuation in the 54 and 63 well diodes. Comparison of this data with that gathered for InGaAs/GaAs multiple quantum wells, suggests that the onset of relaxation occurs at a similar average strain–thickness product for both systems. Given the rapid band gap reduction of GaAsBi with Bi incorporation, this data suggests that GaAsBi is a promising photovoltaic material candidate