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[EN] This article presents a remote laboratory to carry out identification and control experiments of two real parallel robots over the Internet. The remote laboratory has a client-server architecture. The client is a Java control interface that allows the user to command experiments and visualize the results in the form of graphs and live feed of the robots. The server is an industrial computer that controls both robots through a dSPACE 1103 control board programmed with Matlab/Simulink, and also runs Jimserver and other programs that allow the users to reserve and safely use the robots. The article describes and illustrates various laboratory practices and experiments that can be carried out with the presented remote laboratory, such as the identification of the linearized state-space model of the robots, the design of integral regulators with state feedback, or study how singularities of parallel robots decrease their controllability., [ES] En este artículo se presenta un laboratorio remoto para realizar prácticas de identificación y control de dos robots paralelos reales mediante Internet. El laboratorio remoto tiene una arquitectura cliente-servidor. El cliente es una interfaz de control Java que permite comandar experimentos y visualizar los resultados en forma de gráficas y de imágenes de video en tiempo real de los robots. Por su parte, el servidor es un computador industrial que controla a los robots mediante una tarjeta de control dSPACE 1103 programada con Matlab/Simulink, y además ejecuta Jimserver y otros programas de gestión que permiten reservar y utilizar los robots de forma segura. El artículo describe e ilustra varias prácticas y experimentos que pueden realizarse con el laboratorio remoto presentado, como la identificación del modelo de estado linealizado de los robots, el diseño de reguladores integrales con realimentación del estado, o estudiar cómo las singularidades de los robots paralelos disminuyen su controlabilidad.

[EN] This article presents a remote laboratory to carry out identification and control experiments of two real parallel robots over the Internet. The remote laboratory has a client-server architecture. The client is a Java control interface that allows the user to command experiments and visualize the results in the form of graphs and live feed of the robots. The server is an industrial computer that controls both robots through a dSPACE 1103 control board programmed with Matlab/Simulink, and also runs Jimserver and other programs that allow the users to reserve and safely use the robots. The article describes and illustrates various laboratory practices and experiments that can be carried out with the presented remote laboratory, such as the identification of the linearized state-space model of the robots, the design of integral regulators with state feedback, or study how singularities of parallel robots decrease their controllability., [ES] En este artículo se presenta un laboratorio remoto para realizar prácticas de identificación y control de dos robots paralelos reales mediante Internet. El laboratorio remoto tiene una arquitectura cliente-servidor. El cliente es una interfaz de control Java que permite comandar experimentos y visualizar los resultados en forma de gráficas y de imágenes de video en tiempo real de los robots. Por su parte, el servidor es un computador industrial que controla a los robots mediante una tarjeta de control dSPACE 1103 programada con Matlab/Simulink, y además ejecuta Jimserver y otros programas de gestión que permiten reservar y utilizar los robots de forma segura. El artículo describe e ilustra varias prácticas y experimentos que pueden realizarse con el laboratorio remoto presentado, como la identificación del modelo de estado linealizado de los robots, el diseño de reguladores integrales con realimentación del estado, o estudiar cómo las singularidades de los robots paralelos disminuyen su controlabilidad.

[EN] This article presents a remote laboratory to carry out identification and control experiments of two real parallel robots over the Internet. The remote laboratory has a client-server architecture. The client is a Java control interface that allows the user to command experiments and visualize the results in the form of graphs and live feed of the robots. The server is an industrial computer that controls both robots through a dSPACE 1103 control board programmed with Matlab/Simulink, and also runs Jimserver and other programs that allow the users to reserve and safely use the robots. The article describes and illustrates various laboratory practices and experiments that can be carried out with the presented remote laboratory, such as the identification of the linearized state-space model of the robots, the design of integral regulators with state feedback, or study how singularities of parallel robots decrease their controllability., [ES] En este artículo se presenta un laboratorio remoto para realizar prácticas de identificación y control de dos robots paralelos reales mediante Internet. El laboratorio remoto tiene una arquitectura cliente-servidor. El cliente es una interfaz de control Java que permite comandar experimentos y visualizar los resultados en forma de gráficas y de imágenes de video en tiempo real de los robots. Por su parte, el servidor es un computador industrial que controla a los robots mediante una tarjeta de control dSPACE 1103 programada con Matlab/Simulink, y además ejecuta Jimserver y otros programas de gestión que permiten reservar y utilizar los robots de forma segura. El artículo describe e ilustra varias prácticas y experimentos que pueden realizarse con el laboratorio remoto presentado, como la identificación del modelo de estado linealizado de los robots, el diseño de reguladores integrales con realimentación del estado, o estudiar cómo las singularidades de los robots paralelos disminuyen su controlabilidad.

[EN] This article presents a remote laboratory to carry out identification and control experiments of two real parallel robots over the Internet. The remote laboratory has a client-server architecture. The client is a Java control interface that allows the user to command experiments and visualize the results in the form of graphs and live feed of the robots. The server is an industrial computer that controls both robots through a dSPACE 1103 control board programmed with Matlab/Simulink, and also runs Jimserver and other programs that allow the users to reserve and safely use the robots. The article describes and illustrates various laboratory practices and experiments that can be carried out with the presented remote laboratory, such as the identification of the linearized state-space model of the robots, the design of integral regulators with state feedback, or study how singularities of parallel robots decrease their controllability., [ES] En este artículo se presenta un laboratorio remoto para realizar prácticas de identificación y control de dos robots paralelos reales mediante Internet. El laboratorio remoto tiene una arquitectura cliente-servidor. El cliente es una interfaz de control Java que permite comandar experimentos y visualizar los resultados en forma de gráficas y de imágenes de video en tiempo real de los robots. Por su parte, el servidor es un computador industrial que controla a los robots mediante una tarjeta de control dSPACE 1103 programada con Matlab/Simulink, y además ejecuta Jimserver y otros programas de gestión que permiten reservar y utilizar los robots de forma segura. El artículo describe e ilustra varias prácticas y experimentos que pueden realizarse con el laboratorio remoto presentado, como la identificación del modelo de estado linealizado de los robots, el diseño de reguladores integrales con realimentación del estado, o estudiar cómo las singularidades de los robots paralelos disminuyen su controlabilidad.

© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works., It is well known that the singularities of a Gough-Stewart platform arise when the determinant of the Plücker coordinates of the robot leg lines vanish. The direct expansion of this determinant in terms of the configuration of the moving platform leads to an intimidating algebraic expression which is difficult to organize in a manner that facilitates extracting geometric conditions for singularities to occur. The use of Grassmann-Cayley algebra has permitted expressing this determinant as a bracket polynomial which is easier to manipulate symbolically. Each monomial in this polynomial is the product of three brackets, 4×4 determinants involving the homogeneous coordinates of four leg attachments. In this paper, we show how to derive, using elementary linear algebra arguments, bracket polynomials where all brackets can be interpreted as reciprocal products between lines. Contrarily to what one might expect, these new bracket polynomials are simpler in general than those previously obtained using Grassmann-Cayley algebra., This work was partially supported by the Spanish Government through project PID2020-117509GB-I00/AEI/10.13039/50110001103., Peer Reviewed, Postprint (author's final draft)

This study, whose theme is romantic love, for being it is a timeless theme in all cultures and literatures, aims to demonstrate the correspondences in the loving lyric of Oswaldo Osório and Vinicius de Moraes, and has as a background The Four Loves,by C. S. Lewis, whose terms, storge, philia, erosand agape constitute the axes of approach to the loving aesthetics of the two authors, especially in the construction of the female figure, emphasizing their passion, sensuality, gentleness, delicacy and strength. In this sense, the research is based on a theoretical perspective - which is linked to the orientation of Comparative Literature, with a multidisciplinary dimension, in a dialogue close to the studies of Mikhail Bakhtin, Julia Kristeva, Harold Bloom, Earl Miner or Tania Carvalhal - as well as a brief presentation of the context of the temporal, dialogism and intertextuality between life and the work of the two authors, taking into account the identity and literary systems of each one. It is observed that the romantic loving aesthetics of vinician and osorian texts present plural senses constructed under the objective reality and ideal of these poetic subjects - each one in his space and in his time - converging in the way they exalt love, femininity and eroticism., Este estudio, cuyo tema es el amor romántico, por ser un tema atemporal en todas las culturas y literaturas, tiene como objetivo demostrar las similitudes y singularidades en la poesia de amor de Oswaldo Osório y Vinícius de Moraes, teniendo como telón de fondo la obra Loss Cuatro Amores, de C. S. Lewis, cuyos términos, storge, philia, eros y agape constituyen ejes de aproximación a la estética amorosa de los dos autores, especialmente en la construcción de la figura femenina, destacando su pasión, sensualidad, suavidad, delicadeza y fuerza. En este sentido, la investigación parte de una perspectiva teórica -que se vincula con la orientación de la Literatura Comparada, con una dimensión multidisciplinar, en estrecho diálogo con los estudios de Mikhail Bakhtin, Julia Kristeva, Harold Bloom, Earl Miner o Tania Carvalhal - así como sobre una breve presentación del contexto temporal, dialogismo e intertextualidad entre la vida y obra de los dos autores, teniendo en cuenta la identidad y los sistemas literarios de cada uno. Parece que la estética del amor romántico de los textos vinicianos y osorianos presenta significados plurales construidos bajo la realidad objetiva e ideal de estos sujetos poéticos - cada uno en su propio espacio y tiempo- confluyendo en la forma en que exaltan el amor, la feminidad y el erotismo., Escuela de Doctorado, Doctorado en Español: Lingüística, Literatura y Comunicación

Producción Científica, The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of these rings is related to some invariants used in algorithmic resolution of singularities., Ministerio de Ciencia, Innovación y Universidades (PGC2018-095392-B-I00), Ministerio de Economía y Competitividad, a través del Programa “Severo Ochoa” para Centros de Excelencia en I+D+i (SEV-2015-0554), Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

Producción Científica, The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of these rings is related to some invariants used in algorithmic resolution of singularities., Ministerio de Ciencia, Innovación y Universidades (PGC2018-095392-B-I00), Ministerio de Economía y Competitividad, a través del Programa “Severo Ochoa” para Centros de Excelencia en I+D+i (SEV-2015-0554), Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

Producción Científica, The asymptotic Samuel function generalizes to arbitrary rings the usual order function of a regular local ring. In this paper, we use this function to introduce the notion of the Samuel slope of a Noetherian local ring, and we study some of its properties. In particular, we focus on the case of a local ring at singular point of a variety, and, among other results, we prove that the Samuel slope of these rings is related to some invariants used in algorithmic resolution of singularities., Ministerio de Ciencia, Innovación y Universidades (PGC2018-095392-B-I00), Ministerio de Economía y Competitividad, a través del Programa “Severo Ochoa” para Centros de Excelencia en I+D+i (SEV-2015-0554), Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE

This thesis delves into the intricacies of coupled cavity magnonic systems, aiming to construct higher orders of complexity with multiple components. It sheds light on the dissipative photon-magnon coupling by introducing dissipation and subsequently broadening the scope of the dissipatively coupled system across time and space. Initially, this thesis offers a comprehensive review of coherent coupling in closed systems, emphasizing the consideration of energy. Progressing further, the incorporation of dissipation in open systems is elucidated, laying out both the theoretical foundation and experimental validation for energy level attraction in dissipative coupling. The interplay with coherent coupling showcases the potential of nonreciprocity in applications like isolators and circulators. Two non-Hermitian singularities, namely exceptional points (EPs) and bound states in the continuum (BICs), are explored in dissipative coupling with anti-parity-time (PT ) symmetry, underscoring practical applications like eigenmodes control, sensors and slow light. Moreover, by incorporating time as a third layer of complexity, this thesis employs Floquet theory to an open dissipatively-coupled cavity magnonic system. This approach paves the way for controlling previously elusive hybrid systems, like the higher-order EP. Finally, spatial distance is integrated as a fourth component to complete our hierarchical structure, by achieving remarkable long-distance coupling exceeding 1 meter. Notably, BIC emerges in long-distance coherent coupling, facilitating high-efficiency, long-range BIC transfers between discrete systems, hinting at promising possibilities for future networks. In summary, this thesis broadens the understanding of cavity magnonics by venturing beyond energy to explore dissipation, time, and spatial distance as additional components. The insights gleaned from this exploration not only enrich the field of cavity magnonics with wide-ranging applications, but also lay

Physical reasons suggested in [J.B. Hartle, S.W. Hawking, Wave function of the universe, Phys. Rev. D41 (1990) 1815-1834] for the Quantum Gravity Problem lead us to study type-changing metrics on a manifold. The most interesting cases are Transverse Rieniann-Lorentz Manifolds. Here we study the conformal geometry of such manifolds., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

We study the b-completion of the three Friedmann models of the Universe, having as models for 3-space the sphere, the Euclidean space or the hyperbolic space. We show that in the first case there is just one singularity, having the full completion as only neighborhood. In the other two cases there is one essential singularity, which is the limit of all past causal geodesics; again, it has a single neighborhood. This extends results by Bosshard [On the b-boundary of the closed Friendmann Model, Commun. Math. Phys. 46 (1976) 263-268] and Johnson [The bundle boundary in some special cases, J. Math. Phys. 18 (5) (1977) 898-902] on the closed Friedmann model. (C) 1999 Elsevier Science B.V. All rights reserved., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

In this paper we give a positive answer to a question of Nash, concerning the arc space of a singularity, for the class of quasi-ordinary hypersurface singularities, extending to this case previous results and techniques of Shihoko Ishii., Ministerio de Educación y Ciencia (MEC), Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Given a real analytic function f(x, y) with one critical point P-0, we Study deformations f(1) of f such that, for any t not equal 0, the analytic function f(t) has no critical points in a neighborhood of P-0. We give explicitly a deformation without real critical points for any function which has only one real branch with characteristic exponents (4, 2q, r)., Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

© World Scientific Publishing Company. The present work has been supported by Dirección General de Enseñanza Superior Project PB98-0772. The authors wish to thank F.J. Chinea and F. Navarro-Lérida for valuable discussions., In this paper we analyse the possibility of constructing singularity-free inhomogeneous cosmological models with a pure radiation field as matter content. It is shown that the conditions for regularity are very easy to implement and therefore there is a huge number of such spacetimes., Dirección General de Enseñanza Superior, Depto. de Física Teórica, Fac. de Ciencias Físicas, TRUE, pub

CRUE-CSIC (Acuerdos Transformativos 2022), A classical problem in real geometry concerns the representation of positive semidefinite elements of a ring A as sums of squares of elements of A. If A is an excellent ring of dimension ≥3, it is already known that it contains positive semidefinite elements that cannot be represented as sums of squares in A. The one dimensional local case has been afforded by Scheiderer (mainly when its residue field is real closed). In this work we focus on the 2-dimensional case and determine (under some mild conditions) which local excellent henselian rings A of embedding dimension 3 have the property that every positive semidefinite element of A is a sum of squares of elements of A., Ministerio de Economía, Industria y Competitividad (MINECO), Universidad Complutense de Madrid, Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

This thesis presents the conceptual development of an innovative parallel manipulator that leverages the beneficial attributes of parallel kinematic structures. These attributes include increased stiffness, uniform load distribution, and reduced moving mass, which are strategically incorporated into the design to enhance resource efficiency. This approach aims to yield more robust, cost-effective, and reliable alternatives to conventional serial manipulators. The concept is synthesized from various literature sources, leading to a detailed kinematic analysis through inverse kinematics. This analysis provides valuable insights into the mechanism's functionality and facilitates iterative design improvements. Additionally, a dynamic behavior simulation of the mechanism is conducted using Simulink's Simscape. Based on these insights, a prototype is constructed to empirically validate the design concept. The final design demonstrates a compact, fully accessible workspace with a kinematic structure conducive to robust manipulation. The load distribution is optimized across all motors, maximizing motor capacity utilization and enabling efficient handling of peak loads., Mechanical Engineering

In this article we introduce and analyze in detail singular contact structures, with an emphasis on bm -contact structures, which are tangent to a given smooth hypersurface Z and satisfy certain transversality conditions. These singular contact structures are determined by the kernel of non-smooth differential forms, called bm -contact forms, having an associated critical hypersurface Z. We provide several constructions, prove local normal forms, and study the induced structure on the critical hypersurface. The topology of manifolds endowed with such singular contact forms are related to smooth contact structures via desingularization. The problem of existence of bm -contact structures on a given manifold is also tackled in this paper. We prove that a connected component of a convex hypersurface of a contact manifold can be realized as a connected component of the critical set of a bm -contact structure. In particular, given an almost contact manifold M with a hypersurface Z, this yields the existence of a b2k -contact structure on M realizing Z as a critical set. As a consequence of the desingularization techniques in [21], we prove the existence of folded contact forms on any almost contact manifold., Eva Miranda and Cédric Oms are partially supported by the AEI grant PID2019-103849GB-I00 of MCIN/AEI/10.13039/501100011033, Peer Reviewed, Objectius de Desenvolupament Sostenible::14 - Vida Submarina, Objectius de Desenvolupament Sostenible::13 - Acció per al Clima, Postprint (published version)

This thesis delves into the intricacies of coupled cavity magnonic systems, aiming to construct higher orders of complexity with multiple components. It sheds light on the dissipative photon-magnon coupling by introducing dissipation and subsequently broadening the scope of the dissipatively coupled system across time and space. Initially, this thesis offers a comprehensive review of coherent coupling in closed systems, emphasizing the consideration of energy. Progressing further, the incorporation of dissipation in open systems is elucidated, laying out both the theoretical foundation and experimental validation for energy level attraction in dissipative coupling. The interplay with coherent coupling showcases the potential of nonreciprocity in applications like isolators and circulators. Two non-Hermitian singularities, namely exceptional points (EPs) and bound states in the continuum (BICs), are explored in dissipative coupling with anti-parity-time (PT ) symmetry, underscoring practical applications like eigenmodes control, sensors and slow light. Moreover, by incorporating time as a third layer of complexity, this thesis employs Floquet theory to an open dissipatively-coupled cavity magnonic system. This approach paves the way for controlling previously elusive hybrid systems, like the higher-order EP. Finally, spatial distance is integrated as a fourth component to complete our hierarchical structure, by achieving remarkable long-distance coupling exceeding 1 meter. Notably, BIC emerges in long-distance coherent coupling, facilitating high-efficiency, long-range BIC transfers between discrete systems, hinting at promising possibilities for future networks. In summary, this thesis broadens the understanding of cavity magnonics by venturing beyond energy to explore dissipation, time, and spatial distance as additional components. The insights gleaned from this exploration not only enrich the field of cavity magnonics with wide-ranging applications, but also lay

We consider the one-phase Muskat problem modeling the dynamics of the free boundary of a single fluid in porous media. In the stable regime, we prove local well-posedness for fluid interfaces that are general curves and can have singularities. In particular, the free boundary can have acute angle corners or cusps. Moreover, we show that isolated corners/cusps on the interface must be rigid, meaning the angle of the corner is preserved for a finite time, there is no rotation at the tip, the particle at the tip remains at the tip and the velocity of that particle at the tip points vertically downward.

CRUE-CSIC (Acuerdos Transformativos 2021), In this paper we give a complete answer to a question posed by Dimca and Greuel about the quotient of the Milnor and Tjurina numbers of a plane curve singularity. We put this question into a general framework of the study of the difference of Milnor and Tjurina numbers for isolated complete intersection singularities showing its connection with other problems in singularity theory., Ministerio de Ciencia e Innovación (MICINN), Depto. de Álgebra, Geometría y Topología, Fac. de Ciencias Matemáticas, TRUE, pub

Legendre’s equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of the first and second kind. In physics, however, commonly the only acceptable members of this set are Legendre polynomials. The quantization of the eigenvalues of Legendre’s operator is a consequence of this. We present and explain a stand-alone and in-depth argument for rejecting all solutions of Legendre’s equation in physics apart from the polynomial ones. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre’s equation are quintessential to the argument. We demonstrate that the evenness or oddness of Legendre polynomials is a consequence of the same premises., Mathematical Physics

In this thesis we study singularities of Hilbert schemes and show that there are many (components) of Hilbert schemes that are smooth or mildly singular and use them to explore phenomena in birational geometry and commutative algebra. Specifically, we study the Hilbert scheme compactification of a pair of linear spaces, describe all the sub- schemes parameterized by this component and show that it is a smooth Mori dream space. We study Hilbert schemes with two Borel-fixed points and prove that they are reduced, and that their irreducible components have normal and Cohen-Macaulay singularities. We study the Hilbert scheme of points on a threefold and extend results on the Hilbert scheme of points of a surface to this case; we also provide bounds on the dimension of this Hilbert scheme. Finally, we generalize the Hilbert and Quot schemes to construct the fiber-full scheme, which is a fine moduli space that controls all the cohomological data of a variety instead of just the Hilbert polynomial.

In low-dimensional topology one often decomposes a space into pieces that can be individually understood then put back together, yielding a combinatorial description, and such descriptions can be used for diagrammatic reasoning, computations of algebraic invariants, constructions of new objects, and so on. A powerful tool for this is singularity theory, where a classification of the types of singularities that generically might be present (for example, Morse critical points) leads to systematic approaches to decompositions, and in the ideal case the classification reduces to analyzing singularities of polynomial functions. We develop singularity theory relevant to "n-categorical" decompositions of smooth manifolds, in which pieces each have a recursive decomposition of their boundaries. In particular, we study smooth functions from manifolds to flag-foliated R^n, which serves as a model for the composition laws of an n-category. We use a refinement of the jet transversality techniques for the Thom--Boardman singularity types to define dense sets of functions that are suitably generic with respect to the foliations. We show how to compute codimensions of the submanifolds that correspond to a singularity type. For a few situations, for instance surfaces with embedded curves, we carry out a classification of the germs that appear in this dense set up to structure-preserving diffeomorphism. To this end, we prove stability results that aid in proving equivalence of germs and in finding polynomial representatives.We explain how to use this classification of singularities to give a presentation of the symmetric monoidal 2-category of curves with embedded curves. As an application, we give a way to compute the Krushkal polynomial, which is a combinatorial invariant of graphs in surfaces, using an extended TQFT on the symmetric monoidal 2-category of surfaces that are decomposed into black and white regions.

Let G be a connected, reductive, complex affine algebraic group, and let Xr denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in Xr resolving conjectures of Florentino-Lawton. In particular, we compute the codimension of the orbifold singular locus using facts about Borel-de Siebenthal groups. We then use this codimension to calculate some higher homotopy groups of the smooth locus of Xr, proving conjectures of Florentino-Lawton-Ramras. Lastly, using the earlier analysis of Borel-de Siebenthal groups, we prove a conjecture of Sikora about CI Lie groups.

Let G be a connected, reductive, complex affine algebraic group, and let Xr denote the moduli space of G-valued representations of a rank r free group. We first characterize the singularities in Xr resolving conjectures of Florentino-Lawton. In particular, we compute the codimension of the orbifold singular locus using facts about Borel-de Siebenthal groups. We then use this codimension to calculate some higher homotopy groups of the smooth locus of Xr, proving conjectures of Florentino-Lawton-Ramras. Lastly, using the earlier analysis of Borel-de Siebenthal groups, we prove a conjecture of Sikora about CI Lie groups.

Manifolds with boundary, with corners, b-manifolds and foliations model configuration spaces for particles moving under constraints and can be described as E-manifolds. E-manifolds were introduced in [NT01] and investigated in depth in [MS20]. In this article we explore their physical facets by extending gauge theories to the E-category. Singularities in the configuration space of a classical particle can be described in several new scenarios unveiling their Hamiltonian aspects on an E-symplectic manifold. Following the scheme inaugurated in [Wei78], we show the existence of a universal model for a particle interacting with an E-gauge field. In addition, we generalize the description of phase spaces in Yang-Mills theory as Poisson manifolds and their minimal coupling procedure, as shown in [Mon86], for base manifolds endowed with an E-structure. In particular, the reduction at coadjoint orbits and the shifting trick are extended to this framework. We show that Wong's equations, which describe the interaction of a particle with a Yang-Mills field, become Hamiltonian in the E-setting. We formulate the electromagnetic gauge in a Minkowski space relating it to the proper time foliation and we see that our main theorem describes the minimal coupling in physical models such as the compactified black hole., Preprint

In this work, we aim to discuss, qualitatively, possible associations between biological diversity and cultural diversity in the formation of biology teachers. These reflections can broaden the understanding of the relationship between society and nature, as well as the construction of curricula for the degree in biology. We approach some ecological perspectives of biodiversity and cultural diversity; in this one, we demarcate the perceptions of individual and collective singularities as a possible descriptor of a contemporary sociocultural profile. Seeking to approximate diversities, we present the biocultural and biocentric approaches, and the possibility of inserting integrating, disintegrating, biocentric and anthropocentric elements to analyze the perceptions of undergraduates. We conclude that the recognition of the relationships between particularities/collectivities and the themes related to the variability of living beings helps in the process of social emancipation of the teacher in training. Furthermore, we consider that a biocentric approach, based on equity, enables the recognition of the interspecific alterities of living beings, providing (re)connection, (re)integration and diplomatic coexistence., Neste trabalho, objetivamos discutir, qualitativamente, possíveis associações entre diversidade biológica e diversidade cultural na formação de professores de biologia. Essas reflexões podem ampliar o entendimento das relações entre sociedade e natureza, bem como a construção de currículos para a licenciatura em biologia. Abordamos, algumas perspectivas ecológicas de biodiversidade e diversidade cultural; nesta, demarcamos as percepções das singularidades individuais e coletivas como possível descritor de perfil sociocultural contemporâneo. Buscando aproximar as diversidades, apresentamos as abordagens biocultural e biocêntrica, e a possibilidade de inserção de elementos integradores, desintegradores, biocêntricos e antropocêntricos para análise das percepções de licenciandos. Concluímos que o reconhecimento das relações entre particularidades/coletividades e as temáticas relacionadas à variabilidade dos seres vivos auxilia no processo de emancipação social do professor/professora em formação. Ademais, consideramos que uma abordagem biocêntrica, baseada na equidade, possibilita o reconhecimento das alteridades interespecíficas dos seres vivos, proporcionando a (re)conexão, a (re)integração e a convivência diplomática., En este trabajo, pretendemos discutir, cualitativamente, posibles asociaciones entre diversidad biológica y diversidad cultural en la formación de profesores de biología. Estas reflexiones pueden ampliar la comprensión de la relación entre sociedad y naturaleza, así como la construcción de currículos para la carrera de biología. Abordamos algunas perspectivas ecológicas de la biodiversidad y la diversidad cultural; en éste, delimitamos las percepciones de las singularidades individuales y colectivas como posible descriptor de un perfil sociocultural contemporáneo. Buscando aproximar las diversidades, presentamos los enfoques biocultural y biocéntrico, y la posibilidad de insertar elementos integradores, desintegradores, biocéntricos y antropocéntricos para analizar las percepciones de los estudiantes de grado. Concluimos que el reconocimiento de las relaciones entre particularidades/colectividades y los temas relacionados con la variabilidad de los seres vivos ayuda en el proceso de emancipación social del profesor en formación. Además, consideramos que un enfoque biocéntrico, basado en la equidad, posibilita el reconocimiento de las alteridades interespecíficas de los seres vivos, propiciando la (re)conexión, la (re)integración y la convivencia diplomática.

[Resumen] Este artículo presenta un laboratorio remoto para realizar prácticas de control en el espacio de estados con dos robots paralelos reales, a través de Internet. Se presenta la arquitectura cliente-servidor de este laboratorio, en la que el cliente es una interfaz Java de control usada por el estudiante para comandar experimentos y visualizar resultados, mientras que el servidor es un PC industrial que controla ambos robots paralelos mediante una tarjeta de control dSPACE 1103 y una serie de componentes software que incluyen Matlab, Jimserver, y un gestor de reservas y de credenciales para garantizar un acceso seguro a los robots remotos. Se describen varias prácticas que pueden realizarse con este laboratorio remoto, como la identificación del modelo dinámico multivariable de los robots paralelos, el diseño de controladores integrales con estado realimentado, o el estudio de la pérdida de controlabilidad de dichos robots a medida que se aproximan a singularidades., [Abstract] This paper presents a remote laboratory for doing practices of state-space control with two real parallel robots over the Internet. The client-server architecture of this laboratory is presented, where the client is a Java control interface used by the student to command experiments and visualize results, whereas the server is an industrial PC that controls both parallel robots through a dSPACE 1103 control board and a series of software components including Matlab, Jimserver and a book manager that guarantees safe access to the remote robots. Different lab practices that can be done with this remote laboratory are described, such as the identification of the multivariate dynamic model of the parallel robots, the design of integral controllers with state feedback, or the study of loss of controllability of the robots when they approach singularities.

This is an expository survey on the theory of Bernstein-Sato polynomials with special emphasis in its recent developments and its importance in commutative algebra, Peer Reviewed, Postprint (author's final draft)

Legendre’s equation is key in various branches of physics. Its general solution is a linear function space, spanned by the Legendre functions of the first and second kind. In physics, however, commonly the only acceptable members of this set are Legendre polynomials. The quantization of the eigenvalues of Legendre’s operator is a consequence of this. We present and explain a stand-alone and in-depth argument for rejecting all solutions of Legendre’s equation in physics apart from the polynomial ones. We show that the combination of the linearity, the mirror symmetry and the signature of the regular singular points of Legendre’s equation are quintessential to the argument. We demonstrate that the evenness or oddness of Legendre polynomials is a consequence of the same premises., Mathematical Physics

This dissertation concerns the Inverse Mean Curvature Flow of closed hypersurfaces in Euclidean Space, and its relationship with minimal surfaces. Inverse Mean Curvature Flow is an extrinsic geometric flow which has become prominent in differential geometry because of its applications to geometric inequalities and general relativity, but deep questions persist about its analytic and geometric structure. The first four chapters of this dissertation focus on singularity formation in the flow, the flow behavior near singularities, and the dynamical stability of round spheres under mean-convex perturbations.On the topic of singularities, I establish the formation of a singularity for all embedded flow solutions which do not have spherical topology within a prescribed time interval. I later show that mean-convex, rotationally symmetric tori undergo a flow singularity wherein the flow surfaces converge to a limit surface without rescaling, contrasting sharply with the singularities of other extrinsic geometric flows. On the topic of long-time behavior, I show that all flow solutions whichexist and remain embedded for some minimal time depending only on initial data must exist for all time and asymptotically converge to round spheres at large times. In the fourth chapter, I utilize this characterization to establish dynamical stability of the round sphere under certain mean-convex, axially symmetric perturbations that are not necessarily star-shaped. In the last chapter, I relate questions of singularities and dynamical stability for the InverseMean Curvature Flow to the mathematics of soap films. Specifically, I show that certain families of solutions to Plateau’s problem do not self-intersect and remain contained within a given region of Euclidean space. I accomplish this using a barrier method arising from global embedded solutions of Inverse Mean Curvature Flow. Conversely, I also use minimal disks to establish that a singularity likely forms in the flow of a specific

[EN] We study foliations F on Hirzebruch surfaces Sd and prove that, similarly to those on the projective plane, any F can be represented by a bi-homogeneous polynomial affine 1-form. In case F has isolated singularities, we show that, for delta = 1, the singular scheme of F does determine the foliation, with some exceptions that we describe, as is the case of foliations in the projective plane. For delta not equal 1, we prove that the singular scheme of F does not determine the foliation. However, we prove that, in most cases, two foliations F and F' given by sections s and s' have the same singular scheme if and only if s' = Phi(s), for some global endomorphism F of the tangent bundle of S-delta.

How can we understand the relations between economic things and different forms of exchange – commodities, assets, gifts and singularities – in the contemporary economy? The decline of industrial capitalism and the emergence of new types of intangible valuables challenge our understanding of what economic life is about. Analysing economies through one dominant form of exchange risks overlooking the interplay between different types of valuables, their materiality and interactions that form the basis of value creation and exchange. In contrast, this special issue highlights the mutability of things – their capacity to take on and abandon different forms – as a precondition for economic activity. Drawing on a variety of empirical case studies of markets for seeds, grains, fish, carbon emissions and cattle, the contributions set out to trace the social biographies of economic things in, between and beyond multiple economic forms. We argue that it is the very ability of economic things to shift in and out of particular forms of exchange that enables the complex globalised economies of our time.

This dissertation concerns the Inverse Mean Curvature Flow of closed hypersurfaces in Euclidean Space, and its relationship with minimal surfaces. Inverse Mean Curvature Flow is an extrinsic geometric flow which has become prominent in differential geometry because of its applications to geometric inequalities and general relativity, but deep questions persist about its analytic and geometric structure. The first four chapters of this dissertation focus on singularity formation in the flow, the flow behavior near singularities, and the dynamical stability of round spheres under mean-convex perturbations.On the topic of singularities, I establish the formation of a singularity for all embedded flow solutions which do not have spherical topology within a prescribed time interval. I later show that mean-convex, rotationally symmetric tori undergo a flow singularity wherein the flow surfaces converge to a limit surface without rescaling, contrasting sharply with the singularities of other extrinsic geometric flows. On the topic of long-time behavior, I show that all flow solutions whichexist and remain embedded for some minimal time depending only on initial data must exist for all time and asymptotically converge to round spheres at large times. In the fourth chapter, I utilize this characterization to establish dynamical stability of the round sphere under certain mean-convex, axially symmetric perturbations that are not necessarily star-shaped. In the last chapter, I relate questions of singularities and dynamical stability for the InverseMean Curvature Flow to the mathematics of soap films. Specifically, I show that certain families of solutions to Plateau’s problem do not self-intersect and remain contained within a given region of Euclidean space. I accomplish this using a barrier method arising from global embedded solutions of Inverse Mean Curvature Flow. Conversely, I also use minimal disks to establish that a singularity likely forms in the flow of a specific

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

How can we understand the relations between economic things and different forms of exchange – commodities, assets, gifts and singularities – in the contemporary economy? The decline of industrial capitalism and the emergence of new types of intangible valuables challenge our understanding of what economic life is about. Analysing economies through one dominant form of exchange risks overlooking the interplay between different types of valuables, their materiality and interactions that form the basis of value creation and exchange. In contrast, this special issue highlights the mutability of things – their capacity to take on and abandon different forms – as a precondition for economic activity. Drawing on a variety of empirical case studies of markets for seeds, grains, fish, carbon emissions and cattle, the contributions set out to trace the social biographies of economic things in, between and beyond multiple economic forms. We argue that it is the very ability of economic things to shift in and out of particular forms of exchange that enables the complex globalised economies of our time.

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

How can we understand the relations between economic things and different forms of exchange – commodities, assets, gifts and singularities – in the contemporary economy? The decline of industrial capitalism and the emergence of new types of intangible valuables challenge our understanding of what economic life is about. Analysing economies through one dominant form of exchange risks overlooking the interplay between different types of valuables, their materiality and interactions that form the basis of value creation and exchange. In contrast, this special issue highlights the mutability of things – their capacity to take on and abandon different forms – as a precondition for economic activity. Drawing on a variety of empirical case studies of markets for seeds, grains, fish, carbon emissions and cattle, the contributions set out to trace the social biographies of economic things in, between and beyond multiple economic forms. We argue that it is the very ability of economic things to shift in and out of particular forms of exchange that enables the complex globalised economies of our time.

In this work, we present results of a social research, whose main objective is to analyze the stories, meanings and practices around rights and the public sphere, present in the experiences of young people and adults in educational institutions that train for work on others. Considering this objective, we developed a qualitative research methodology, conducting participant observations and semistructured interviews with students, teachers, managers and non-teaching workers in five nonuniversity higher education institutes of state management, located in different neighborhoods of the Metropolitan Area of Buenos Aires, Argentina. To unfold the problem, we take up conceptual tools from contemporary social sciences, especially the works of Danilo Martuccellion the contemporary experience of the modern social condition, and François Dubet’s, on the decline of the institutional program and the feelings of injustice. Following the guidelines of the grounded theory, we identify in the narratives and experiences analyzed the main institutional grammars around justice / injustice and the public sphere, strongly presented and articulated among themselves. Through these grammars, these institutions and their subjects are (re)built in a permanent tension between deinstitutionalization and reinstitutionalization, between singularities and life in common. Both in their everyday interactions, and their demands and demonstrations and virtual scenarios, people who participate in these institutes try out forms of access and exercise of rights in our contemporary society: meanings and practices about the public sphere with a sensitivity that makes it possible to singularize the common., En este trabajo presentamos resultados de una investigación social, cuyo objetivo principal es analizar los relatos, los sentidos y las prácticas en torno a los derechos y lo público presentes en las experiencias de personas jóvenes y adultas en instituciones educativas que forman para el trabajo sobre los otros. Con dicho objetivo, desarrollamos una estrategia metodológica cualitativa, realizando observaciones y entrevistas semiestructuradas a estudiantes, docentes, directivas/os y personal no docente en cinco institutos de educación superior no universitaria de gestión estatal, ubicados en distintos barrios del Área Metropolitana de Buenos Aires, Argentina. Para el despliegue del problema, retomamos herramientas conceptuales de las ciencias sociales contemporáneas, especialmente los trabajos de Danilo Martuccelli en torno a la experiencia contemporánea de la condición social moderna, y de François Dubet, sobre el declive del programa institucional y los sentimientos de injusticia. Siguiendo los lineamientos de la teoría fundamentada, identificamos en los relatos y experiencias analizadas las principales gramáticasinstitucionales en torno a las justicias/injusticias y lo público, presentes con fuerza y articuladas entre sí. Mediante dichas gramáticas, estas instituciones y sus sujetos se (re)construyen en una permanente tensión entre desinstitucionalización y reinstitucionalización, entre singularidades y vida en común. Tanto en sus interacciones cotidianas, como en sus demandas y manifestaciones en escenarios presenciales y virtuales, las personas que participan en estos institutos ensayan formas del acceso y ejercicio de derechos en nuestra sociedad contemporánea: sentidos y prácticas sobre lo público con una sensibilidad que posibilita singularizar lo común.

How can we understand the relations between economic things and different forms of exchange – commodities, assets, gifts and singularities – in the contemporary economy? The decline of industrial capitalism and the emergence of new types of intangible valuables challenge our understanding of what economic life is about. Analysing economies through one dominant form of exchange risks overlooking the interplay between different types of valuables, their materiality and interactions that form the basis of value creation and exchange. In contrast, this special issue highlights the mutability of things – their capacity to take on and abandon different forms – as a precondition for economic activity. Drawing on a variety of empirical case studies of markets for seeds, grains, fish, carbon emissions and cattle, the contributions set out to trace the social biographies of economic things in, between and beyond multiple economic forms. We argue that it is the very ability of economic things to shift in and out of particular forms of exchange that enables the complex globalised economies of our time.

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

A general equation of state is considered for analyzing the possible behaviors for (Early) dark energy that alleviates the Hubble parameter tension problem. By departing from the possible evolution for the (Early) dark energy density and the corresponding dynamical equations, the equation of state is obtained, which allow us to analyze qualitatively the cosmological evolution and the dominance of each term in the equation of state along the cosmic expansion, which show some interesting consequences as the occurrence of (past) future singularities. Then, by considering two general models, their free parameters are fit with different sources of data, showing the goodness of the fits in comparison to more standard models. Results might be considered as a promising starting point to get a better understanding of the cosmological evolution as a whole.

Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider n-RRR robot prototype.

Black holes are unique among astrophysical sources: they are the simplest macroscopic objects in the Universe, and they are extraordinary in terms of their ability to convert energy into electromagnetic and gravitational radiation. Our capacity to probe their nature is limited by the sensitivity of our detectors. The LIGO/Virgo interferometers are the gravitational-wave equivalent of Galileo’s telescope. The first few detections represent the beginning of a long journey of exploration. At the current pace of technological progress, it is reasonable to expect that the gravitational-wave detectors available in the 2035-2050s will be formidable tools to explore these fascinating objects in the cosmos, and space-based detectors with peak sensitivities in the mHz band represent one class of such tools. These detectors have a staggering discovery potential, and they will address fundamental open questions in physics and astronomy. Are astrophysical black holes adequately described by general relativity? Do we have empirical evidence for event horizons? Can black holes provide a glimpse into quantum gravity, or reveal a classical breakdown of Einstein’s gravity? How and when did black holes form, and how do they grow? Are there new long-range interactions or fields in our Universe, potentially related to dark matter and dark energy or a more fundamental description of gravitation? Precision tests of black hole spacetimes with mHz-band gravitational-wave detectors will probe general relativity and fundamental physics in previously inaccessible regimes, and allow us to address some of these fundamental issues in our current understanding of nature., SCOPUS: ar.j, info:eu-repo/semantics/published

Parallel robots with configurable platforms are a class of robots in which the end-effector has an inner mobility, so that its overall shape can be reconfigured: in most cases, the end-effector is thus a closed-loop kinematic chain composed of rigid links. These robots have a greater flexibility in their motion and control with respect to rigid-platform parallel architectures, but their kinematics is more challenging to analyze. In our work, we consider n-RRR planar configurable robots, in which the end-effector is a chain composed of n links and revolute joints, and is controlled by n rotary actuators located on the base of the mechanism. In particular, we study the geometrical design of such robots and their direct and inverse kinematics for n = 4, n = 5 and n = 6; we employ the bilateration method, which can simplify the kinematic analysis and allows us to generalize the approach and the results obtained for the 3-RRR mechanism to n-RRR robots (with n > 3). Then, we study the singularity configurations of these robot architectures. Finally, we present the results from experimental tests that have been performed on a 5–RRR robot prototype., This research was funded by the Spanish Ministry of Economy and Competitiveness grants number DPI2017-88282-P and MDM-2016-0656. The APC was funded by Marco Carricato., Peer Reviewed, Postprint (published version)

A unified approach is developed for the analysis of singularities of the scattered field and vanishing of scattering harmonics. Rigorous proofs are presented of the existence of complex resonance singularities of the solution to the problem of the plane wave scattering by a circular homogeneous dielectric cylinder. The method employs a mathematically correct approach of the spectral theory of open structures involving generalized conditions at infinity when complex resonance frequencies may be considered. The result is obtained by verifying the existence of complex singularities of the series solution coefficients considered as functions of the problem parameters. The recently developed theory of generalized cylindrical polynomials (GCPs) is used that enables one to reduce determination of singularities (resonances) to finding zeros (real or complex) of a particular subfamily of GCPs.

How can we understand the relations between economic things and different forms of exchange – commodities, assets, gifts and singularities – in the contemporary economy? The decline of industrial capitalism and the emergence of new types of intangible valuables challenge our understanding of what economic life is about. Analysing economies through one dominant form of exchange risks overlooking the interplay between different types of valuables, their materiality and interactions that form the basis of value creation and exchange. In contrast, this special issue highlights the mutability of things – their capacity to take on and abandon different forms – as a precondition for economic activity. Drawing on a variety of empirical case studies of markets for seeds, grains, fish, carbon emissions and cattle, the contributions set out to trace the social biographies of economic things in, between and beyond multiple economic forms. We argue that it is the very ability of economic things to shift in and out of particular forms of exchange that enables the complex globalised economies of our time.

In this article we give a universal model for geometric quantization associated to a real polarization given by an integrable system with non-degenerate singularities. This universal model goes one step further than the cotangent models in [13] by both considering singular orbits and adding to the cotangent models a model for the prequantum line bundle. These singularities are generic in the sense that are given by Morse-type functions and include elliptic, hyperbolic and focus-focus singularities. Examples of systems admitting such singularities are toric, semitoric and almost toric manifolds, as well as physical systems such as the coupling of harmonic oscillators, the spherical pendulum or the reduction of the Euler’s equations of the rigid body on T *(SO(3)) to a sphere. Our geometric quantization formulation coincides with the models given in [11] and [21] away from the singularities and corrects former models for hyperbolic and focus-focus singularities cancelling out the infinite dimensional contributions obtained by former approaches. The geometric quantization models provided here match the classical physical methods for mechanical systems such as the spherical pendulum as presented in [4]. Our cotangent models obey a local-to-global principle and can be glued to determine the geometric quantization of the global systems even if the global symplectic classification of the systems is not known in general., Peer Reviewed, Postprint (published version)