1,062 research outputs found
What did the COVID-19 crisis teach us about European solidarity? : incomplete integration, conflicts of sovereignty and the principle of solidarity in EU law
No full textThe main purpose of this chapter is to analyse and assess how the EU has reacted to the pandemic, considering that no Treaty reform has been undertaken and that a pivotal role has been played by the principle of solidarity. Solidarity can assume a special role in the governance of crises. Secondly, it is precisely through the prism of solidarity that I will look at the COVID-19 crisis as a governance crisis and at its meaning for European integration. Th is chapter will focus on the role played by the principle of solidarity, which is one of the vectors of flexibility of the European legal system, and on how it is used to mitigate the negative effects that competing sovereignties display on the functioning of the EU. Solidarity is invoked as the principle to fix integration fractures, precisely like in the Japanese kintsugi technique, where a gold fluid is used to put together the pieces of broken ceramics; solidarity is supposed to reconcile the EU and its Member States when conflicts emerge in a traumatic manner and, consequently, to boost the legitimacy of the EU, in the sense of capacity to deliver policy reforms and public goods when needed. Solidarity is also meant to supplement the capacity of the EU to deliver to citizens’ expectations irrespective of the limited or sectoral (depending on the context considered) competences it has been vested with – an expression of the incompleteness of the integration process, which finds expression in its similarly incomplete constitution. Having introduced the context of the research and its purpose and aim, the next section will expound on the conceptual framework underpinning it, namely discussing the incomplete integration and the conflicts of sovereignty which have emerged in a predominant manner in the last decade of integration and that are the consequences of the constitutional design of the EU. The chapter will then elaborate on the principle of solidarity as a core principle of European integration, and its function in managing crises, expounding on the challenges underpinning its achievement. In another section, the attention will turn on the solutions designed to fix the economic component of the COVID-19 crisis, focusing on the Next Generation EU to understand some lessons on how solidarity is used to ensure the achievement of a crucial target for the EU, namely recovery of the economies of the Member States, before concluding with some reflections learned on the principle of solidarity as a flexibility vector of the overall open and incomplete system of integration which is the EU
MR2569913: Rodríguez, José. Some examples in vector integration. Bull. Aust. Math. Soc. 80 (2009), no. 3, 384–392. (Reviewer: Luisa Di Piazza),
No full textThe paper deals with some classical examples in vector integration due to Phillips, Hagler and Talagrand, revisited from the point of view of the Birkhoff and McShane integrals. More precisely, the author considers:
- Phillips' example of a Pettis integrable function f which is not Birkhoff integrable [R. S. Phillips, Trans. Amer. Math. Soc. 47 (1940), 114--145; MR0002707 (2,103c)]. It is proved here that f is universally McShane integrable.
- Hagler's example of a scalarly measurable l∞-valued function g which is not strongly measurable. The function g is proved to be universally Birkhoff integrable.
- Talagrand's example of a bounded Pettis integrable function φ having no conditional expectation [M. Talagrand, Mem. Amer. Math. Soc. 51 (1984), no. 307, ix+224 pp.; MR0756174 (86j:46042)]. Here the author shows that φ is also Birkhoff integrable, giving a negative answer to the question whether conditional expectations exist within the Birkhoff theory.
Some interesting open problems are also stated.
Reviewed by Luisa Di Piazz
Fortuna, virtù e divinità nel caso di Alessandro il Grande
No full textThis paper looks at the partial apotheosis of Alexander the Great, providing a survey of his posthumous reception in Macedonia and Greece. Another key piece of evidence is Alexander's funeral organized in Egypt by Ptolemy son of Lagus. The main focus of the paper, however, is on what we know of Alexander's own behaviour and what we can conclude from it about the persona he sought to cultivate and convey. The author also aims to offer answers to some basic questions: firstly whether, towards the end of his life, Alexander deliberately acted in ways which suggested godhood, with careful consideration of his behaviour at Hephaistion's funeral; and, secondly, whether he took steps to establish an official apotheosis, with an analysis of the ancient very scanty tradition
MR3191427 Naralenkov, Kirill M., A Lusin type measurability property for vector- valued functions. J. Math. Anal. Appl. 417 (2014), no. 1, 293307. 28A20
No full textIn the paper under review the author introduces the notion of Riemann measurability for vector-valued
functions, generalizing the classical Lusin condition, which is equivalent to the Lebesgue measurability
for real valued functions. Let X be a Banach space, let f : [a; b] ! X and let E be a measurable subset of [a; b]. The function
f is said to be Riemann measurable on E if for each " > 0 there exist a closed set F E with
(E n F) < 0 (where is the Lebesgue measure) and a positive number such that
k XK
k=1
ff(tk) ?? f(t0
k)g (Ik)k < "
whenever fIkgKk
=1 is a nite collection of pairwise non-overlapping intervals with max1 k K (Ik) <
and tk; t0
k 2 Ik
T
F.
The Riemann measurability is more relevant to Riemann type integration theory, such as those of
McShane and Henstock, rather than the classical notion of Bochner or scalar measurability. In par-
ticular the author studies the relationship between the Riemann measurability and the M and the H
integrals that are obtained if we assume that the gauge in the de nitions of McShane and Henstock
integral can be chosen Lebesgue measurable.
The main results are the following
If f : [a; b] ! X is H-integrable on a measurable subset E of [a; b], then f is Riemann measurable
on E.
If f : [a; b] ! X is both bounded and Riemann measurable on a measurable subset E of [a; b], then
f is M-integrable on E.
If f : [a; b] ! X is both Riemann measurable and McShane (Henstock) integrable on a measurable
subset E of [a; b], then f is M-integrable (H-integrable) on E.
Suppose X separable. If f : [a; b] ! X is McShane (Henstock) integrable, then f is M-integrable
(H-integrable.)
The author concludes the paper with the following open problem: for which families of non-separable
Banach spaces does the McShane (or even the Pettis) integrability imply Riemann measurability?
Reviewed by (L. Di Piazza
Carta al Provincial de los Jesuitas en Nueva España avisándo el casamiento del rey con María Luisa de Borbón, 1679 octubre 1
No full textCarta al Padre Provincial de los Jesuitas en Nueva España avisándo el casamiento del rey Carlos II con la princesa María Luisa de Borbón, hija del Duque de Orleans. —— Letter to the Father Provincial of the Jesuits in New Spain informing him of the marriage of King Carlos II to Princess María Luisa de Borbón, daughter of the Duke of Orleans. 2 f. (4 p.
MR2657294 (2011h:28021) Bensimhoun, Michael Change of variable theorems for the KH integral. Real Anal. Exchange 35 (2010), no. 1, 167–194. (Reviewer: Luisa Di Piazza), 28B05 (26A42 46G10)
No full textFrom Reviews: 0
MR2657294 (2011h:28021)
Bensimhoun, Michael(IL-HEBR)
Change of variable theorems for the KH integral. (English summary)
Real Anal. Exchange 35 (2010), no. 1, 167–194.
28B05 (26A42 46G10)
PDF Clipboard Journal Article Make Link
Let ({\scr E},{\scr F}, {\scr G})(E,F,G) be a Banach triple and let f\colon [a,b] \subset \overline{\Bbb R} \rightarrow {\scr E}f:[a,b]⊂R−−→E, \varphi \colon [a,b] \rightarrow {\scr F}φ:[a,b]→F and ψ:[c,d]⊂R−−→[a,b] be given. The problem of change of variables in an integral consists in finding the best conditions under which the equality ∫dcf∘ψ⋅d(φ∘ψ)=∫ψ(d)ψ(c)f⋅dφ(1) holds, when one of these two integrals exists.
Here the context is that of the Kurzweil-Henstock-Stieltjes integral. The main result is Theorem 6.1:
Assume that ψ is continuous. If f∘ψ⋅d(φ∘ψ) is integrable in [c,d], then f⋅dφ is integrable in ψ([c,d]) and equality (1) holds.
Furthermore, if f∘ψ⋅d(φ∘ψ) is absolutely integrable in [c,d], then f⋅dφ is absolutely integrable in ψ([c,d]), with ∫dc∥f∘ψ⋅d(φ∘ψ)∥=∫ψ(d)ψ(c)∥f⋅dφ∥.
Without very specific additional conditions on f, the continuity of ψ is essential in order to get relation (1). As a corollary of Theorem 6.1, the author obtains, with an alternative proof, a formula for change of variables in [S. Leader, Real Anal. Exchange 29 (2003/04), no. 2, 905--920; MR2083825 (2005f:26023)], for the case φ=Id and ψ real-valued of bounded variation.
In the second part of the paper, necessary and sufficient conditions are given in order that the integrability of f⋅dφ implies that of f∘ψ⋅d(φ∘ψ) and the change of variable formula.
Reviewed by Luisa Di Piazz
MR2481817 (2010e:46040): Haluška, Ján; Hutník, Ondrej On vector integral inequalities. Mediterr. J. Math. 6 (2009), no. 1, 105–124. (Reviewer: Luisa Di Piazza),
No full textI. Dobrakov in his papers [Czechoslovak Math. J. 40(115) (1990), no. 1, 8--24; MR1032359 (90k:46097); Czechoslovak Math. J. 40(115) (1990), no. 3, 424--440; MR1065022 (91g:46052)] developed a theory for integrating vector-valued functions with respect to operator-valued measures:
Let X and Y be two Banach spaces, Δ be a δ-ring of subsets of a nonempty set T, L(X,Y) be the space of all continuous operators L:X→Y, and m:Δ→L(X,Y) be an operator-valued measure σ-additive in the strong operator topology of L(X,Y). A measurable function f:T→X is said to be integrable in the sense of Dobrakov if there exists a sequence of simple functions fn:T→X, n∈N, converging m-a.e. to f and the integrals ∫.fndm are uniformly σ-additive measures on σ(Δ) (i.e. the σ-algebra generated by Δ). The integral of the function f on E∈σ(Δ) is defined by the equality ∫Efdm=limn→∞∫Efndm.
The first author, in the papers [Math. Slovaca 43 (1993), no. 2, 185--192; MR1274601 (95f:46069); Rev. Roumaine Math. Pures Appl. 38 (1993), no. 4, 327--337; MR1258045 (95g:28008); Czechoslovak Math. J. 47(122) (1997), no. 2, 205--219; MR1452416 (98h:46044)], has generalized the Dobrakov integration to the complete bornological locally convex topological vector spaces (C.B.L.C.S., for short), developing a new technique for C.B.L.C.S. and operator-valued measures. The main novelty of such a theory is that instead of the "classical'' objects such as a submeasure, a norm, a metric, etc., he needs to work with lattices of submeasures, norms, etc.
In the present paper the authors first give a brief development of this new integration theory in C.B.L.C.S. (see Section 2). In Section 3 some inequalities, which are important tools in this Dobrakov-type integration technique, are proved.
Reviewed by Luisa Di Piazz
On a Functional Identity Involving Power Values of Generalized Skew Derivations on Lie Ideals
No full textLet R be a prime ring, Qr its right Martindale quotient ring and C its extended centroid. Suppose that F is a generalized skew derivation of R, L a non-central Lie ideal of R, m,n,s≥1 positive fixed integers. If F(u)n(F(u)m-um)s=0for all u∈L, then there exists λ∈C such that F(x)=λx, for any x∈R, with λm=1, unless when char(R)=2 and R⊆M2(K), the ring of 2×2 matrices over a field K. We will also provide a generalization of the previous result for semiprime rings. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024
Correction to: Integrative Robo-Ethics: Uncovering Roboticists’ Attitudes to Ethics and Moving Forward (International Journal of Social Robotics, (2023), 10.1007/s12369-023-00978-2)
No full textIn the original publication of this article, the affiliation information of two authors was inadvertently published incorrectly. Please find the correct affiliation information below: Antonio Fleres 1PhD School for Communication Studies, IULM University, via Carlo Bo 1, 20143 Milan, Italy Luisa Damiano 4Department of Communication, Arts and Media “Giampaolo Fabris”, IULM University, via Carlo Bo 1, 20143 Milan, Italy Springer wishes to apologize for the inconvenience caused.Intelligent SystemsInteractive Intelligenc
Supplemental Material - Application of Comprehensive Genomic Profiling-Based Next-Generation Sequencing Assay to Improve Cancer Care in a Developing Country
No full textSupplemental Material for Application of Comprehensive Genomic Profiling-Based Next-Generation Sequencing Assay to Improve Cancer Care in a Developing Country by Claudia Cifuentes, Milton Lombana, Henry Vargas, Paola Laguado, Alejandro Ruiz-Patiño, Leonardo Rojas, Uriel Navarro, Carlos Vargas, Luisa Ricaurte, Oscar Arrieta, Lucia Zatarain-Barron, Leandro Zapata, Guido González, Carlos Ortiz, Laura Bernal, Juan G. Restrepo, Lucia Viola, Fabio Grosso, Ricardo Zapata, William Mantilla, Hernán Carranza, Iván Bustillo, Néstor Llinas, Ricardo Duarte, July Rodríguez, Pilar Archila, Jenny Ávila, Maritza Bermúdez, Tatiana Gámez, Carolina Sotelo, Jorge Otero, Elkin Forero, Mauricio Lema, Catalina Limpias, Camila Ordóñez-Reyes, Sergio Mejía, Christian Rolfo, Rafael Rosell, Andrés F. Cardona; ONCOL Group and CLICaP in Cancer Control.</p
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