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    Semi-algebraic geometry and generic Hamiltonian stability

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    The steepness property is a local geometric transversality condition on the gradient of a -function which proves fundamental in order to ensure the stability of sufficiently-regular nearly-integrable Hamiltonian systems over long timespans. Steep functions were originally introduced by Nekhoroshev, who also proved their genericity. Namely, given a pair of positive integers , with r high enough, and a point , the Taylor polynomials of those functions which are not steep around are contained in a semi-algebraic set of positive codimension in the space of polynomials of n variables and degree bounded by r. The demonstration of this result was originally published in 1973 and has been hardly studied ever since, probably due to the fact that it involves no arguments of dynamical systems: it makes use of quantitative reasonings of real-algebraic geometry and complex analysis. The aim of the present work is two-fold. In the first part, the original proof of the genericity of steepness is rewritten by making use of modern tools of real-algebraic geometry: this allows to clarify the original reasonings, that were obscure or sketchy in many parts. In particular, Yomdin's Lemma on the analytic reparameterization of semi-algebraic sets, together with non trivial estimates on the codimension of certain algebraic varieties, turns out to be the fundamental ingredients to prove the genericity of steepness. The second part of this work is entirely new and is devoted to the formulation of explicit algebraic criteria to check steepness of any given sufficiently regular function, which constitutes a very important result for applications, as the original definition of steepness is not constructive. These criteria involve both the derivatives of the studied function up to any given order and external real parameters that, generically, belong to compact setsIn the months preceding the end of the redaction of this work, S.B. has been funded by the ERC project 757802 Haminstab; therefore, he wish to acknowledge both the ERC and the PI of the project (M. Guàrdia) for their support. Open Access funding provided thanks to the CRUE-CSIC agreement with Elsevie

    The follicular fluid regulates sperm capacitation and the acrosome reaction in the donkey while alleviating oxidative stress

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    The follicular fluid (FF) is a complex and dynamic biological medium that surrounds the oocytes during their development and growth. This fluid provides the necessary nutrients to both the oocyte and the surrounding cells, enabling the proper maturation of the oocyte. Additionally, the FF is involved in key sperm function processes, such as capacitation, which occurs when sperm reach the oviduct and are exposed to this fluid. Nevertheless, how this happens in donkeys has not been investigated. For this reason, the present study aimed to evaluate the influence of the FF on sperm capacitation in the donkey. Preovulatory FF was obtained from five different Catalan jennies (two follicles per animal), and nine ejaculates from fertile Catalan donkeys were collected. Sperm were resuspended in four different treatments: non-capacitating medium (TBM), non-capacitating medium supplemented with 20 % FF (TBM+FF), capacitating medium (TCM), and capacitating medium supplemented with 20 % FF (TCM+FF). Samples were incubated at 38 °C for 120 min, and at 60 min, progesterone was added to induce the acrosome reaction. After 0, 60, 70, and 120 min of incubation, sperm motility, membrane lipid disorder, acrosome integrity, mitochondrial membrane potential (MMP), and intracellular concentrations of calcium, reactive oxygen species (ROS) and superoxides were evaluated. These results suggest that the preovulatory FF promotes sperm capacitation in donkeys, as it increases intracellular calcium, membrane lipid disorder, and acrosome exocytosis, while maintaining sperm motility and reducing ROS concentration. Although the results are not entirely conclusive and further tests are needed, this study supports that the FF modulates sperm capacitation and alleviates the oxidative stress associated with this processJ.C. was funded by the Ministry of Science, Innovation and Universities, Spain (MCIN/AEI/10.13039/501100011033) and the European Union NextGenerationEU/PRTR (Juan de la Cierva Scheme: JDC2022–049684-I). The authors also acknowledge the support from the Ministry of Science and Innovation, Spain (Grants: PID2020–113320RB-I00 and PID2023–149853OB-I00); the Catalan Agency for the Management of University and Research Grants, Regional Government of Catalonia, Spain (Grant: 2021-SGR-00900); and the Catalan Institution for Research and Advanced Studies, Spain (ICREA). Open Access funding provided thanks to the CRUE-CSIC agreement with Elsevie

    El Rif. El Derecho Consuetudinario Rifeño y su consideración en el Protectorado Español en Marruecos

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    This paper addresses the issue of Riffian customary law by means of a systematic analysis of this legal system, in order to subsequently analyse its value or consideration in the administration of justice in the temporal context of the Spanish Protectorate of Morocco, with special reference to the “interventor” as a key element of the Spanish system of intervention. First, we will proceed to analyse pre-colonial Riffian society through an anthropological and ethnographic approach, taking into account the main characteristics of this community, in order to better understand and comprehend its legal system. This system is deeply rooted in the most central aspects of their existence, making it difficult to distinguish between the legal element and the factual element in an essentially tribal society. Once this approach has been made, we will proceed to explain the historical context of the establishment of the protectorate, briefly examining the colonial administrative structures created by the Spanish administration to control the territory and the population. In the following chapters, we will delve into the core of this work, i.e., the study of Rif customary law, the figure of the Spanish “interventor”, and the impact of the Spanish administration on the existence, conservation or disappearance of the Rif normative tradition, through the figure of the “interventor”En el presente trabajo se aborda la cuestión del derecho consuetudinario rifeño, mediante un ensayo sistemático de este sistema jurídico, para analizar, posteriormente, su valor o consideración en la administración de justicia en el contexto temporal del Protectorado español de Marruecos, con especial referencia al interventor como elemento clave del sistema de intervención español. En primer lugar, se procederá a analizar la sociedad rifeña precolonial mediante una aproximación antropológica y etnográfica, que tenga en cuenta las características principales de esta comunidad, a efectos de entender y comprender mejor su sistema jurídico. Sistema que está profundamente enraizado en los aspectos más centrales de su existencia, dificultando la distinción entre el elemento jurídico y el elemento fáctico, en una sociedad esencialmente tribal. Una vez realizada dicha aproximación, se procederá a explicar el contexto histórico de la instauración del protectorado, examinando de forma sucinta las estructuras administrativas coloniales creadas por la administración española para el control del territorio y de la población. En los siguientes capítulos, se ahondará en el núcleo de este trabajo, es decir, en el estudio del derecho consuetudinario del Rif, la figura del interventor español, y el impacto de la administración española en la existencia, conservación o desaparición de la tradición normativa rifeña, a través de la figura del interventorEn aquest treball s'aborda la qüestió del dret consuetudinari rifeny, mitjançant un assaig sistemàtic d'aquest sistema jurídic, per analitzar-ne, posteriorment, el valor o la consideració en la administració de justícia en el context temporal del Protectorat espanyol del Marroc, amb especial referència a l'interventor com a element clau del sistema espanyol. En primer lloc, es procedirà a analitzar la societat rifenya precolonial mitjançant una aproximació antropològica i etnogràfica, que tingui en compte les característiques principals d'aquesta comunitat, a efectes d'entendre i comprendre millor el sistema jurídic. Sistema que està profundament arrelat als aspectes més centrals de la seva existència, dificultant la distinció entre l'element jurídic i l'element fàctic, en una societat essencialment tribal. Un cop realitzada aquesta aproximació, es procedirà a explicar el context històric de la instauració del protectorat, examinant de forma succinta les estructures administratives colonials creades per l'administració espanyola per al control del territori i de la població. En els capítols següents, s'aprofundirà al nucli d'aquest treball, és a dir, a l'estudi del dret consuetudinari del Rif, la figura de l'interventor espanyol, i l'impacte de l'administració espanyola en l'existència, conservació o desaparició de la tradició normativa rifenya, a través de la figura de l'interventor1

    El visual merchandising a La Roca Village. Comparativa de tres grans marques i els seus aparadors

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    En aquest treball fi nal de grau, s’investiga i es dona a conèixer una nova eina de màrqueting i publicitat subliminar i indirecta, una eina que no es necessita una gran inversió i que molts professionals utilitzen en el sector de la moda i dels centres comercials: el visual merchandising, és a dir, mostrar els productes d’una forma molt atractiva a través de diferents suports (aparadors, elements digitals, colors, llum, etc.) per aconseguir infl uir en la decisió de compra dels consumidors i millorar alhora l’experiència de compra perquè el client torni. La millor manera per investigar si realment aquest visual merchandising infl ueix en la decisió de compra, és observant les tècniques que s’utilitzen en els grans centres comercials, plens de marques i de sensacions de compra. En aquest cas, s’aplica en un context molt més específi c, en un centre comercial d’outlet de luxe: La Roca Village. A través de l’observació de tres marques totalment diferents però enllaçades per la seva localització en aquest centre comercial: Prada, Nude Project i Vans Off The Wall. S’ha pogut investigar com treballen l’estratègia del visual merchandising en cada cas, l’aplicació, i si els resultats obtinguts han estat favorables gràcies al visual merchandising. Finalment, també s’ha analitzat l’època de Nadal i la campanya que aquesta comporta en els aparadors i les botigues físiques del centre comercial i també durant les rebaixes, per observar com potencien i treuen el màxim rendiment a aquesta eina segons la temporada.1

    La incidència del co-branding en la percepció de marca

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    Aquest Treball de Final de Grau analitza la col·laboració entre el FC Barcelona, Spotify i artistes internacionals com Drake, Rosalía, Karol G o Coldplay, a través del llançament de samarretes d’edició limitada que s’han utilitzat en els partits de El Clàssic. En un moment on les marques busquen maneres més creatives i emocionals de connectar amb el públic, aquesta combinació entre el futbol i la música s’ha convertit en una aposta forta dins del màrqueting col·laboratiu o també anomenat co-branding. L’objectiu del treball és entendre com els usuaris perceben aquestes col·laboracions i quins són els motius que poden portar una persona a comprar aquestes samarretes: si és per la vinculació amb el club, per la presència de l’artista, pel disseny, pel sentiment d’exclusivitat o per una suma de tots aquests elements, entre altres. Per donar resposta a aquestes qüestions, s’ha aplicat una metodologia mixta. Per una banda, s’ha dissenyat una enquesta oberta a persones de totes les edats i perfils, amb l’objectiu d’obtenir una visió àmplia i diversa sobre com es viu aquesta estratègia. Per l’altra, s’han realitzat entrevistes a especialistes en màrqueting esportiu per obtenir una visió més profunda i professional. El treball es basa en diverses hipòtesis que plantegen que factors com l’artista col·laborador, l’exclusivitat del producte o la vinculació emocional amb el club poden influir tant en la decisió de compra com en la percepció general d’aquestes accions. Els resultats obtinguts mostren tendències clares i ofereixen una mirada enriquidora sobre com aquest tipus d’aliances poden influir en la percepció de marca i en el comportament dels consumidors dins del món esportiu i de l’entreteniment.1

    Prueba y regla general antiabuso en los convenios de doble imposición : Cuestiones a partir del Principal Purpose Test de la OCDE

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    Este trabajo realiza un minucioso análisis del PPT introducido por el artículo 29(9) del Modelo de Convenio de Doble Imposición de la OCDE, que constituye una regla general antia-buso en los convenios de doble imposición. Se profundiza en la distribución de la carga probatoria y los estándares de prueba exigidos para su aplicación, destacando la relevancia del PPT reflejada en su adopción a través del Instrumento Multilateral. El estudio evalúa el impacto de la implemen-tación del PPT en los derechos procesales de los contribuyentes, especificando las obligaciones de demostrar la concurrencia de los elementos subjetivo y objetivo, que fundamentan su aplicación. Se examina cómo la formulación de esta cláusula en los convenios y los Comentarios de la OCDE influyen en la definición del estándar probatorio adecuado, considerando las funciones y particula-ridades de las normas que establecen los niveles de corroboración requeridos para que una hipótesis se considere suficientemente probadaThis essay conducts a thorough analysis of the Principal Purpose Test (PPT) introduced by Article 29(9) of the OECD Model Tax Convention on Income and Capital, which establis-hes a general anti-abuse rule in double taxation conventions. It delves into the distribution of the burden of proof and the standards of evidence required for its application, highlighting the growing significance of the PPT as reflected in its adoption through the Multilateral Instrument. The study assesses the impact of the PPT’s implementation on the procedural rights of taxpayers, specifying the obligations to demonstrate the presence of both subjective and objective elements that underpin its application. It examines how the drafting of this clause in the agreements and the OECD Commentary influence the definition of the appropriate standard of proof, considering the functions and particularities of the rules that establish the levels of corroboration required for a hypothesis to be considered sufficiently proven1

    Enhancing the Statistical Probability Factor in Triplet Fusion Upconversion via TIPS Functionalization.

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    We investigated the effect of triisopropylsilyl (TIPS) functionalization of annihilators in triplet-triplet annihilation photon upconversion on their spin statistical probability factor. A new green annihilator 3,9-bis((triisopropylsilyl)ethynyl)perylene (TIPS-PY) displaying record red-to-green TTA-UC quantum yield of 13.7% (50% theoretical maximum) is synthesized. This remarkable efficiency was achieved due to the following features of the TIPS functionalization of PY: 1) high fluorescence quantum yield of 95%, 2) reduced triplet energy to 1.29 eV enabling efficient triplet energy transfer (~100%) from the sensitizer, PdTPBP (T1= 1.5 eV), and 3) a high efficiency of singlet generation after triplet coupling, indicated by the statistical probability factor, f = 39.2% ± 2.4%. Notably, the f value of TIPS-PY surpasses other annihilators in the 470-540 nm emission range by ≥1.5-fold. DFT and TDDFT calculations revealed that TIPS-functionalized chromophores (TIPS-PY, TIPS-naphthalene, and TIPS-anthracene), exhibit singlet-like character in their triplet dimer state which can enhance the coupling of the triplet-pair state with the excited singlet-state, thereby increasing the efficiency of singlet generation a phenomenon undisclosed before. Furthermore, the suitable T1 of TIPS-PY enables upconversion of 730 nm light when sensitized with Os(m-peptpy)2(TFSI)2 (T1 = 1.63 eV), demonstrating the broad upconversion range of TIPS-PY in the phototherapeutic window desired for biological applicationsL. N. acknowledges the Erasmus + Traineeship Program, P. B. and M. M. acknowledge financial support from the La-Caixa junior research leadership-post doctoral program (ID: 100010434, fellowship code: LCF/BQ/P122/11910023) the State Investigation Agency, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2023-001263-S) and project PID2021-123873NB-I00 for financial support. L. N. and A. B. P. acknowledge the start-up funds provided by the University of California San Diego and the use of facilities and instrumentation supported by NSF through the UC San Diego Materials Research Science and Engineering Center (UCSD MRSEC), grant # DMR-2011924. K. M. P. acknowledges funding from the European Research Council (No. 101002131), the Swedish Energy Agency, the Göran Gustafsson Foundation, the Swedish Research Council, Swedish Research Council Formas, the European Research Council (ERC) under grant agreement CoG, PHOTHERM – 101002131, the Catalan Institute of Advanced Studies (ICREA), and the European Union's Horizon 2020 Framework Programme under grant agreement no. 951801. M. D., G. K., K. K., acknowledge the “Universities” Excellence Initiative” programme by the Ministry of Education, Science and Sports of the Republic of Lithuania under the agreement with the Research Council of Lithuania (project No. S-A-UEI-23-6). M. S. is grateful for financial support from the Agencia Española de Investigación (MCIN/AEI/10.13039/501100011033) for projects RED2024-154178-T and PID2023-147424NB-I00 and from the Generalitat de Catalunya for Project 2021SGR623 and ICREA Academia 2025 prize to M. S. N. Y. ackn

    AI Authoritarianism: Towards an Analytical Framework

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    This intervention offers a call for investigating the deepening alignment of artificial intelligence and authoritarian politics. The paper highlights three key features of AI that inflect the workings and logics of authoritarianism: (selective) inhumanisation, the cult of intelligence and scaling. We argue that AI, through these features, is not simply extending, but actively modulating, key dynamics of authoritarianism. To account for this, we propose a flexible analytical framework designed to grapple with the rapidly changing materialisations of the confluence of AI and authoritarianism and suggest focusing on how what we call 'authoritarian tendencies' are introduced on the level of the techno-material, the ideological and the everyday. The framework recognises that both AI and authoritarianism are relational practices and thus requires geographers to trace these relations across multiple sites and actors while being attentive to the ways AI and authoritarianism mutually shape one another in ever-shifting waysResearch funding: Australian Research Council. Grant Number: DP250101885. Spain's Ministry of Science, Innovation and Universities -State Research Agency and the European Social Fund Plus. Grant Number: RYC2023-043382-

    Policubos para una 'polimatemática' en el aula

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    Polycubes are presented as a manipulative that, rather than helping to understand a single mathematical concept at a given level ('monomathematics'), serves as a support for understanding mathematical concepts from all areas of mathematics throughout the stages of early childhood and primary education ('polymathematics'). From this perspective, the aim of this article is to provide an inventory of activities organised by content blocks (number, algebra, geometry, measurement, statistics and probability) and by age (3-6 years, 6-8 years, 8-10 years, 10-12 years), along with developing 10 activities to illustrate how to plan and manage activities with polycubes in the mathematics classroomSe presentan los policubos como un material manipulativo que, en lugar de ayudar a comprender un único contenido matemático de un determinado nivel ("monomatemática"), sirve de apoyo para comprender contenidos matemáticos de todoslos bloques de contenido matemático a lo largo de las etapas de educación infantil y primaria (“polimatemática”). Desde esta perspectiva, el objetivo de este artículo es ofrecer un inventario de actividades organizadas por bloques de contenido (numeración y cálculo, álgebra, geometría, medida, estadística y probabilidad) y por edades (3-6 años, 6-8 años, 8-10 años, 10-12 años), junto con desarrollar 10 actividades para ejemplificar como planificar y gestionar actividades con policubos en el aula de matemática

    The BARD Standard : from Historical Sources to New Challenges. A Comment on Della Torre

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    The work comments on Della Torre’s essay about the evolution of the reasonable doubt criminal standard of proof. By going through the main claims of the essay, which is both historical and theoretical, the work contends that the essay clarifies (and hopefully soothes) some badly framed discussions on that standard, furthermore that it provides valuable reasons to prefer the reasonable doubt formulation over some revolutionary ambitions, and that it sheds light on the reasons for taking the standard not only in the strict reading of an evidentiary threshold but also in the broad one of a method or even a principle of criminal justice. Finally, the work suggests some refinements to Della Torre’s arguments and addresses the tension between the reasonable doubt safeguards and the efficiency of the criminal justice system1

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