We prove several results about groups of finite Morley rank without unipotent p-torsion: p-torsion always occurs inside tori, Sylow p-subgroups are conjugate, and p is not the minimal prime divisor of our approximation to the "Weyl group". These results are quickly finding extensive applications within the classification project.

We review the relation between spacetime geometries with trace-torsion fields, the so-called Riemann–Cartan–Weyl (RCW) geometries, and their associated Brownian motions. In this setting, the drift vector field is the metric conjugate of the trace-torsion one-form, and the laplacian defined by the RCW connection is the differential generator of the Brownian motions. We extend this to the state-space of non-relativistic quantum mechanics and discuss the relation between a non-canonical quantum RCW geometry in state-space associated with the gradient of the (...) quantum-mechanical expectation value of a self-adjoint operator given by the generalized laplacian operator defined by a RCW geometry. We discuss the reduction of the wave function in terms of a RCW quantum geometry in state-space. We characterize the Schroedinger equation in terms of the RCW geometries and Brownian motions. Thus, in this work, the Schroedinger field is a torsion generating field, both for the linear and non-linear cases. We discuss the problem of the many times variables and the relation with dissipative processes, and the role of time as an active field, following Kozyrev and a recent experiment in non-relativistic quantum systems. We associate the Hodge dual of the drift vector field with a possible angular-momentum source for the phenomenae observed by Kozyrev. (shrink)

We study Martsinkovsky–Russell torsion modules with pure embeddings as an abstract elementary class. We give a model-theoretic characterization of the pure-injective and the Σ-pure-injective modules relative to the class of torsion modules assuming that the torsion submodule is a pure submodule. Our characterization of relative Σ-pure-injective modules extends the classical characterization of Gruson and Jenson as well as Zimmermann. We study the limit models of the class and determine when the class is superstable assuming that the (...) class='Hi'>torsion submodule is a pure submodule. As a corollary, we show that the class of torsion abelian groups with pure embeddings is strictly stable (i.e., stable not superstable). (shrink)

The bulk of the DNA in eukaryotic chromatin behaves as if it is topologically relaxed; however, a subfraction can be shown to be under suercoil tension. Endonuclease S1 cuts at specific hypersentive sites in chromatin (in the promoter regions of active genes) and this enzyme cuts in the same region in supercoiled plasmids, but not in relaxed or linearized molecules. A subfraction of the minichromosomes formed after SV40 infection or microinjection of plasmid DNA into oocytes contains supercoil tension and this (...) subfraction is thought to play an important role in transcription. (shrink)

We study the R‐torsion‐free part of the Ziegler spectrum of an order Λ over a Dedekind domain R. We underline and comment on the role of lattices over Λ. We describe the torsion‐free part of the spectrum when Λ is of finite lattice representation type.

We show, for each computable ordinal α and degree $\alpha > {0^{\left( \alpha \right)}}$, the existence of a torsion-free abelian group with proper α th jump degree α.

Issuing from a geometry with nonmetricity and torsion we build up a generalized classical electrodynamics. This geometrically founded theory is coordinate covariant, as well as gauge covariant in the Weyl sense. Photons having arbitrary mass, intrinsic magnetic currents, (magnetic monopoles), and electric currents exist in this framework. The field equations, and the equations of motion of charged (either electrically or magnetically) particles are derived from an action principle. It is shown that the interaction between magnetic monopoles is transmitted by (...) massive photons. On the other hand, the photon is massive only in the presence of magnetic currents. We obtained a static spherically symmetric solution, describing either the Reissner-Nordstrom metric of an electric monopole, or the metric and field of a magnetic monopole. The latter must be massive. In the absence of torsion and in the Einstein gauge one obtains the Einstein-Maxwell theory. (shrink)

We prove that for any computable successor ordinal of the form α = δ + 2k there exists computable torsion-free abelian group that is relatively Δα0 -categorical and not Δα−10 -categorical. Equivalently, for any such α there exists a computable TFAG whose initial segments are uniformly described by Σαc infinitary computable formulae up to automorphism, and there is no syntactically simpler family of formulae that would capture these orbits. As far as we know, the problem of finding such optimal (...) examples of Δα0-categorical TFAGs for arbitrarily large α was first raised by Goncharov at least 10 years ago, but it has resisted solution 315–356]). As a byproduct of the proof, we introduce an effective functor that transforms a 0″-computable worthy labeled tree into a computable TFAG. We expect that this techni... (shrink)

In Anglophone educational research in the United States, the name Foucault has been more pointedly celebrated in some subfields such as curriculum studies relative to its more noticeable censorship in subfields such as history of education. This paper illustrates how such differential epistemological politics might be accounted for through reapproaching the challenges to historiography that Histoire de la Folie (Madness and Civilization) raised. Through the formalist lens of performative apophasis, and with attention to the dependencies of discourse that characterize narrative (...) prosthesis, this paper re‐engages the least referenced of Foucault's major histories in the educational field to bring into noticeability other ‘conditions of possibility’—ones that explicate how an apophatic turn might account for divergent reactions to less familiar philosophies of history and/or to ‘alternative’ approaches to documents through which history is now being narrated and critiqued in education and beyond. (shrink)

Conformal rescalings of spinors are considered, in which the factor Ω, inε AB ↦Ωε AB, is allowed to be complex. It is argued that such rescalings naturally lead to the presence of torsion in the space-time derivative▽ a. It is further shown that, in standard general relativity, a circularly polarized gravitational wave produces a (nonlocal) rotation effect along rays intersecting it similar to, and apparently consistent with, the local torsion of the Einstein-Cartan-Sciama-Kibble theory. The results of these deliberations (...) are suggestive rather than conclusive. (shrink)

Let G be a definably compact group in an o-minimal expansion of a real closed field. We prove that if dim(G\X) < dim G for some definable ${X \subseteq G}$ then X contains a torsion point of G. Along the way we develop a general theory for the so-called G-linear sets, and investigate definable sets which contain abstract subgroups of G.

We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree.

The Bianchi Identities relating asymmetric curvature to torsion are obtained as a new set of equations governing second-order curvature tensors. The usual contribution of symmetric curvature to the gravitational field is found to be a subset of these identities though with an added contribution due to torsion gradients. The antisymmetric curvature two-tensor is shown to be related to the divergence of the torsion. Using a model of particle-antiparticle pair production, identification of certain torsion components with electroweak (...) fields is proposed. These components obey equations, similar to Maxwell's, that are subsets of these linear Bianchi identities. These results are shown to be consistent with gauge and other previous analyses. (shrink)

En un momento de gran efervescencia feminista, se entremezclan las reclamaciones políticas del movimiento con las peligrosas reapropiaciones que de sus núcleos de lucha hace el neoliberalismo. Las tensiones que se presentan en este contexto son muchas y variadas, algunas evidentes y otras invisibles, pero todas contribuyen a la torsión actual del feminismo. En el presente artículo se abordarán algunas de estas tensiones que nacen en la intersección entre feminismo y neoliberalismo: desde la publicidad como posible herramienta feminista hasta los (...) discursos sobre el emprendimiento y el empleo, pasando por el diseño de políticas públicas, y la mercantilización de los cuerpos femeninos. También se abordarán algunas de las posibles rearticulaciones y respuestas políticas feministas ante esta realidad, mostrando la complejidad de los retos a los que tienen que hacer frente los feminismos hoy.In times of great feminist effervescence, the political claims of the movement are intermingled with the dangerous reappropriations that neoliberalism makes of its struggle nuclei. The tensions that appear in this context are many and varied, some obvious and some invisible, but all of them contribute to the torsion of feminism. This article will address some of the tensions that arise from the intersection between feminism and neoliberalism: from advertising as a possible feminist tool, to speeches on entrepreneurship and employment, through the design of public policies, and the commodification of female bodies. Some of the possible re-articulations and feminist political responses to this reality will be addressed, showing the great complexity of the challenges that feminisms face today. (shrink)

We show that in the presence of the torsion tensor \, the quantum commutation relation for the four-momentum, traced over spinor indices, is given by \. In the Einstein–Cartan theory of gravity, in which torsion is coupled to spin of fermions, this relation in a coordinate frame reduces to a commutation relation of noncommutative momentum space, \, where U is a constant on the order of the squared inverse of the Planck mass. We propose that this relation replaces (...) the integration in the momentum space in Feynman diagrams with the summation over the discrete momentum eigenvalues. We derive a prescription for this summation that agrees with convergent integrals: \^s}\rightarrow 4\pi U^{s-2}\sum _{l=1}^\infty \int _0^{\pi /2} d\phi \frac{\sin ^4\phi \,n^{s-3}}{[\sin \phi +U\varDelta n]^s}\), where \}\) and \ does not depend on p. We show that this prescription regularizes ultraviolet-divergent integrals in loop diagrams. We extend this prescription to tensor integrals. We derive a finite, gauge-invariant vacuum polarization tensor and a finite running coupling. Including loops from all charged fermions, we find a finite value for the bare electric charge of an electron: \. This torsional regularization may therefore provide a realistic, physical mechanism for eliminating infinities in quantum field theory and making renormalization finite. (shrink)

We show that an infinite field is interpretable in a stable torsion-free nilpotent groupG of classk, k>1. Furthermore we prove thatG/Z k-1 (G) must be divisible. By generalising methods of Belegradek we classify some stable torsion-free nilpotent groups modulo isomorphism and elementary equivalence.

A propósito de la revuelta chilena iniciada en 2019, detectamos la rápida puesta en marcha de iniciativas orientadas al registro y archivación de los acontecimientos ligados a las manifestaciones, intervenciones y ocupación de la calle. En este contexto, nos interesa analizar las desviaciones y torsiones propuestas por las prácticas de archivo vinculadas con las artes visuales. Para ello nos focalizamos en dos proyectos: la plataforma–archivo Antes del Olvido y el proyecto, archivo dinámico Inventario Iconoclasta de la Insurrección Chilena, ambos han (...) iniciado en 2019 y continúan en funcionamiento en la actualidad. En ellos detectamos propuesta que ensayan nuevas formas de registro documental y de valoración de la memoria, al mismo tiempo, que validan modos de selección, disponibilidad y acceso a los documentos signados por coordenadas visuales. El objetivo de este artículo, entonces, radica en deslindar estos aspectos en función de los debates actuales en torno a las activaciones del patrimonio y las desviaciones del archivo tradicional. (shrink)

A torsional-antenna and a log-periodic antenna are used as a source and an analyzer, respectively, to investigate the possible anomalies of an electro-magnetic field. An unexpected isotropic signal has been detected using those torsion angles, which correspond to a breakdown of the Local Lorentz Invariance, which was found in the past. This coincidence is interpreted as the recovery of a lost symmetry by torqueing the antenna, thus putting in evidence that this Lorentz violation is of angular nature. Introducing a (...) new physical dimension—not only a mathematical dimension as a way to rearrange some equations—is here proposed as a general rule to recover the lost symmetry. (shrink)

In this paper, we shall discuss some recent contributions to the project [15, 14, 2, 18, 22, 23] of explaining why no satisfactory system of complete invariants has yet been found for the torsion-free abelian groups of finite rank n ≥ 2. Recall that, up to isomorphism, the torsion-free abelian groups of rank n are exactly the additive subgroups of the n-dimensional vector space ℚn which contain n linearly independent elements. Thus the collection of torsion-free abelian groups (...) of rank at most n can be naturally identified with the set S of all nontrivial additive subgroups of ℚn. In 1937, Baer [4] solved the classification problem for the class Sof rank 1 groups as follows.Let ℙ be the set of primes. If G is a torsion-free abelian group and 0 ≠ x ϵ G, then the p-height of x is defined to behx = sup{n ϵ ℕ ∣ There exists y ϵ G such that pny = x} ϵ ℕ ∪{∞}; and the characteristic χ of x is defined to be the function. (shrink)

We extend the construction of bad fields of characteristic zero to the case of arbitrary prescribed divisible green torsion.

We study completely decomposable torsion-free abelian groups of the form $\mathcal{G}_S := \oplus_{n \in S} \mathbb{Q}_{p_n}$ for sets $S \subseteq \omega$. We show that $\mathcal{G}_S$has a decidable copy if and only if S is $\Sigma^0_2$and has a computable copy if and only if S is $\Sigma^0_3$.

We present the unification of Riemann–Cartan–Weyl (RCW) space-time geometries and random generalized Brownian motions. These are metric compatible connections (albeit the metric can be trivially euclidean) which have a propagating trace-torsion 1-form, whose metric conjugate describes the average motion interaction term. Thus, the universality of torsion fields is proved through the universality of Brownian motions. We extend this approach to give a random symplectic theory on phase-space. We present as a case study of this approach, the invariant Navier–Stokes (...) equations for viscous fluids, and the kinematic dynamo equation of magnetohydrodynamics. We give analytical random representations for these equations. We discuss briefly the relation between them and the Reynolds approach to turbulence. We discuss the role of the Cartan classical development method and the random extension of it as the method to generate these generalized Brownian motions, as well as the key to construct finite-dimensional almost everywhere smooth approximations of the random representations of these equations, the random symplectic theory, and the random Poincaré–Cartan invariants associated to it. We discuss the role of autoparallels of the RCW connections as providing polygonal smooth almost everywhere realizations of the random representations. (shrink)

ABSTRACTThe torsion balance, an instrument that was first developed to demonstrate the high precision of physical science in the laboratory became a different sort of demonstration instrument in its brief vogue in the 1920s. This article considers intersecting stories of acquiring and testing the torsion balance as a field instrument in Canada, Britain and Australia. It examines the purchasing trip and fieldwork of A. H. Miller of the Dominion Observatory in 1928–1931, testing conducted by the British Geological Survey (...) in 1926–1930, and finally the Imperial Geophysical Experimental Survey of 1928–1930 in Australia. These different stories produce a kind of collective biography, illustrating well the variety of material and textual records that accrete around instruments, especially expensive ones. But the trials and travels of the torsion balance also point to large themes. By comparing the different ways an instrument becomes valuable, and to whom, these micro-histories reveal significant features of the developing identity of geophysics. They also show the interaction of different forms of scientific internationalism in the inter-war period. (shrink)

[First paragraphs: This essay takes its practical orientation from my experiences as a member of a philosophy reading group on death row at Riverbend Maximum Security Penitentiary in Nashville, Tennessee. Its theoretical orientation comes from W. E. B. Du Bois’ lecture-turned-essay, “Criteria of Negro Art,” which argues that the realm of aesthetics is vitally important in the war against racial discrimination in the United States. And since, according to Michele Alexander’s critically-acclaimed The New Jim Crow: Mass Incarceration in the Age (...) of Colorblindness, the prison system should be the primary front today in this war, my essay’s ultimate aim is t/o articulate a new criterion of the present-day “Negro” art being created by a prison population that is still overwhelmingly constituted by persons of color. In my first section, I will show how Du Bois’ insights in “Criteria of Negro Art” remain relevant today, especially in the prison context, and argue that it is thus appropriate for my new criterion to be shaped by his distinctive conception of “propaganda.” In my second section, through a close reading of two texts by Michel Foucault (the pivotal thinker of modern imprisonment), I will flesh out this new criterion, “self-torsion,” defined as the effect of prisoners’ attempts at self-care within a prison system that distorts those attempts into further exploitation of both prisoners and the outside world that imprisons them. And my final section, in an attempt to illustrate this new criterion’s efficacy as a form of propagandistic resistance to contemporary racism, will deploy self-torsion as a critique of two artworks created by imprisoned members of my reading group at Riverbend penitentiary. (shrink)

On a macroscopic level we take general relativity as the appropriate theory of space-time and gravity. We will argue that, on a more microscopic level, in the Compton wavelength regime of elementary particles, there are good reasons for suspecting the presence of a torsion of space-time. A corresponding gaugetheoretical formalism related to the Poincaré group is reviewed, and the kinematical consequences of the presence of a torsion are worked out. In particular we discuss the operational meaning and the (...) measurability of torsion. The dynamics of torsion is left for a forthcoming article. (shrink)

An analysis of the extension of the Hawking-Penrose singularity theorem to Riemann-Cartan U4 space-times with torsion and spin density is undertaken. The minimal coupling principle in U4 is used to formulate a new expression for the convergence condition autoparallels in Einstein-Cartan theory. The Gödel model with torsion is given as an example.

Transient changes in DNA torsional tension are generated by environmental stimuli and transcriptional activity. In eukaryotic cells, these changes can only be accommodated by a chromatin structure that is flexible. This property of chromatin may be essential to the regulation of eukaryotic gene activity.

We prove that if p ≠ q are distinct primes, then the classification problems for p-local and q-local torsion-free abelian groups of rank two are incomparable with respect to Borel reducibility.

English title: Phenomenology of the pólis and torsion of Dasein: dialectic and hermeneutics in the early Gadamerian interpretation of Plato's ethics. Abstract: The aim of this paper is to present and analyse the main hypotheses of Hans-Georg Gadamer in his 1931 book Platos dialektische Ethik. Phänomenologische Interpretationen zum Philebos regarding the notions of pólis, aretḗ, tó agathṓn y Dasein. Then, it will be attempted to show that in this early book of Gadamer is his first relevant philosophical-political work, expressed (...) in the form of a critical dialogue with Martin Heidegger, departing from the new interpretative possibilities that philology and phenomenology opened to Gadamer’s studies on Plato’s philosophy. This early work, moreover, would have laid the foundations for the future developments of philosophical hermeneutics, in particular, regarding the characterization of the dialectical-dialogical structure of understanding and the relationship among éthos, práxis and lógos. -/- /// -/- Resumen: El objetivo de este artículo es presentar y analizar las principales hipótesis de Hans-Georg Gadamer en su libro de 1931 Platos dialektische Ethik. Phänomenologische Interpretationen zum Philebos en relación con las nociones de pólis, aretḗ, tó agathṓn y Dasein. Luego, se intentará demostrar que en este trabajo temprano de Gadamer se formula la primera producción filosófico-política de relevancia del autor, expresada en forma de diálogo crítico con Martin Heidegger, a partir de las nuevas posibilidades interpretativas que la filología y fenomenología le abrieron para el estudio de Platón y su filosofía. Esta obra temprana, además, habría sentado las bases de los futuros desarrollos de la hermenéutica filosófica, en particular, con relación a la caracterización de la estructura dialógico-dialéctica de la comprensión y al vínculo entre éthos, práxis y lógos. (shrink)

Contemporary scholars are engaged in a debate over whether Charles Augustin Coulomb’s results that he presented in his 1785 and 1787 memoirs to the Paris Academy of Sciences were attained experimentally or theoretically. In this paper, we study Coulomb’s famous 1785 electric torsion balance experiment through analysis of relevant texts and, more importantly, through a replication that is more faithful to Coulomb’s original design than previous attempts. We show that, despite recent claims, it has so far proved impossible to (...) obtain the same results reported by Coulomb in his paper of 1785, Coulomb’s published results are most likely atypical, and electric torsion balance experiments degenerate quickly when parameters are altered by small amounts. Acknowledgements: We wish to thank Jed Buchwald for generously making available the glass pieces of a torsion balance identical to that used by Alberto Martinez. Special thanks also to Paolo Palmieri for his important roles in replicating the electric torsion balance, discussing results and recording trials, as well as for the invaluable comments given on earlier drafts of this paper. A part of this paper was presented at the 2008 History of Science Society Annual Meeting in Pittsburgh, PA. We thank the participants of that meeting, especially Alberto A. Martinez, for helpful discussion and comments. Thank you also to Peter Heering for recent discussion and feedback. This research was supported by the Wesley C. Salmon fund, History and Philosophy of Science department, University of Pittsburgh. (shrink)

We consider a quadratic Lagrangian, in both curvature and torsion, with the aim of exploring the possibility that torsion and curvature behave as conjugate variables satisfying the commutation relations. For that proposal we first show that torsion represents a quantum correction to the classical equations of motion. We then observe that we have to introduce the spin in the Einstein theory with two spaces: a real space-time where we describe the curvature with tensors; and a complex space-time, (...) where we describe torsion with spinors. This is not satisfactory, and to overcome this contradiction we describe both mass and spin in a unique manifold, the real space-time, with the use of geometric algebra and geometric product. In that manner we are able to introduce a torsion trivector and curvature trivector that satisfy the commutation relations, opening the road for a quantum description of gravity theory. (shrink)

In this transdisciplinary article which stems from philosophical considerations (that depart from phenomenology—after Merleau-Ponty, Heidegger and Rosen—and Hegelian dialectics), we develop a conception based on topological (the Moebius surface and the Klein bottle) and geometrical considerations (based on torsion and non-orientability of manifolds), and multivalued logics which we develop into a unified world conception that surmounts the Cartesian cut and Aristotelian logic. The role of torsion appears in a self-referential construction of space and time, which will be further (...) related to the commutator of the True and False operators of matrix logic, still with a quantum superposed state related to a Moebius surface, and as the physical field at the basis of Spencer-Brown’s primitive distinction in the protologic of the calculus of distinction. In this setting, paradox, self-reference, depth, time and space, higher-order non-dual logic, perception, spin and a time operator, the Klein bottle, hypernumbers due to Musès which include non-trivial square roots of ±1 and in particular non-trivial nilpotents, quantum field operators, the transformation of cognition to spin for two-state quantum systems, are found to be keenly interwoven in a world conception compatible with the philosophical approach taken for basis of this article. The Klein bottle is found not only to be the topological in-formation for self-reference and paradox whose logical counterpart in the calculus of indications are the paradoxical imaginary time waves, but also a classical-quantum transformer (Hadamard’s gate in quantum computation) which is indispensable to be able to obtain a complete multivalued logical system, and still to generate the matrix extension of classical connective Boolean logic. We further find that the multivalued logic that stems from considering the paradoxical equation in the calculus of distinctions, and in particular, the imaginary solutions to this equation, generates the matrix logic which supersedes the classical logic of connectives and which has for particular subtheories fuzzy and quantum logics. Thus, from a primitive distinction in the vacuum plane and the axioms of the calculus of distinction, we can derive by incorporating paradox, the world conception succinctly described above. (shrink)