Irreducibility of Random Hilbert Schemes

We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the set of nonempty Hilbert schemes as a probability space, we transform this set into a disjoint union of infinite binary trees, reinterpreting Macaulay's classification of admissible Hilbert polynomials. Choosing discrete probability distributions with infinite support on the trees establishes our notion of random Hilbert schemes. To bound the probability that random Hilbert schemes are irreducible and nonsingular, we show that at least half of the vertices in the binary trees correspond to Hilbert schemes with unique Borel-fixed points.

Introduction: resilience and the Anthropocene: the stakes of ‘renaturalising’ politics

The Anthropocene marks a new geological epoch in which human activity (and specifically Western production and consumption practices) has become a geological force. It also profoundly destabilizes the grounds of Western political philosophy. Visions of a dynamic earth system wholly indifferent to human survival liquefy modernity’s division between nature and politics. Critical thought has only begun to scratch the surface of the Anthropocene’s re-naturalization of politics. This special issue of Resilience: International Policies, Practices and Discourses explores the politics of resilience within the wider cultural and political moment of the Anthropocene. It is within the field of resilience thinking that the implications of the Anthropocene for forms of governance are beginning to be sketched out and experimental practices are undertaken. Foregrounding the Anthropocene imaginary’s re-naturalization of politics enables us to consider the political possibilities of resilience from a different angle, one that is irreducible to neoliberal post-political rule.

Beamforming and interference cancellation in D2D communication underlaying cellular networks

This paper presents an analytical performance investigation of both beamforming (BF) and interference cancellation (IC) strategies for a device-to-device (D2D) communication system underlaying a cellular network with an M-antenna base station (BS). We first derive new closed-form expressions for the ergodic achievable rate for BF and IC precoding strategies with quantized channel state information (CSI), as well as, perfect CSI. Then, novel lower and upper bounds are derived which apply for an arbitrary number of antennas and are shown to be sufficiently tight to the Monte-Carlo results. Based on these results, we examine in detail three important special cases including: high signal-to-noise ratio (SNR), weak interference between cellular link and D2D link, and BS equipped with a large number of antennas. We also derive asymptotic expressions for the ergodic achievable rate for these scenarios. Based on these results, we obtain valuable insights into the impact of the system parameters, such as the number of antennas, SNR and the interference for each link. In particular, we show that an irreducible saturation point exists in the high SNR regime, while the ergodic rate under IC strategy is verified to be always better than that under BF strategy. We also reveal that the ergodic achievable rate under perfect CSI scales as log2M, whilst it reaches a ceiling with quantized CSI.

Integrability for Relativistic Spin Networks

The evaluation of relativistic spin networks plays a fundamental role in the Barrett-Crane state sum model of Lorentzian quantum gravity in 4 dimensions. A relativistic spin network is a graph labelled by unitary irreducible representations of the Lorentz group appearing in the direct integral decomposition of the space of L^2 functions on three-dimensional hyperbolic space. To `evaluate' such a spin network we must do an integral; if this integral converges we say the spin network is `integrable'. Here we show that a large class of relativistic spin networks are integrable, including any whose underlying graph is the 4-simplex (the complete graph on 5 vertices). This proves a conjecture of Barrett and Crane, whose validity is required for the convergence of their state sum model.

SYSTEMS OF DIFFERENTIAL EQUATIONSTHAT ARE COMPETITIVE OR COOPERATIVE II:CONVERGENCE ALMOST EVERYWHERE*MORRIS W. HIRSCH

A vector field in n-space determines a competitive (or cooperative) system of differential equations provided all of the off-diagonal terms of its Jacobian matrix are nonpositive (or nonnegative). The main results in this article are the following. A cooperative system cannot have nonconstant attracting periodic solutions. In a cooperative system whose Jacobian matrices are irreducible the forward orbit converges for almost every point having compact forward orbit closure. In a cooperative system in 2 dimensions, every solution is eventually monotone.  Applications are made to generalizations of positive feedback loops.

Classical Invariants for Principal Series and Isomorphisms of Root Data

We develop some new techniques to calculate the Schur indicator for self-dual irreducible Langlands quotients of the principal series representations. Using these techniques we derive some new formulas for the Schur indicator and the real-quaternionic indicator. We make progress towards developing an algorithm to decide whether or not two root data are isomorphic. When the derived group has cyclic center, we solve the isomorphism problem completely. An immediate consequence is a clean and precise classification theorem for connected complex reductive groups whose derived groups have cyclic center.

Estudo paramétrico da recuperação de petróleo pesado por aquecimento eletromagnético resistivo

Electrical resistive heating (ERH) is a thermal method used to improve oil recovery. It can increase oil rate and oil recovery due to temperature increase caused by electrical current passage through oil zone. ERH has some advantage compared with well-known thermal methods such as continuous steam flood, presenting low-water production. This method can be applied to reservoirs with different characteristics and initial reservoir conditions. Commercial software was used to test several cases using a semi-synthetic homogeneous reservoir with some characteristics as found in northeast Brazilian basins. It was realized a sensitivity analysis of some reservoir parameters, such as: oil zone, aquifer presence, gas cap presence and oil saturation on oil recovery and energy consumption. Then it was tested several cases studying the electrical variables considered more important in the process, such as: voltage, electrical configurations and electrodes positions. Energy optimization by electrodes voltage levels changes and electrical settings modify the intensity and the electrical current distribution in oil zone and, consequently, their influences in reservoir temperature reached at some regions. Results show which reservoir parameters were significant in order to improve oil recovery and energy requirement in for each reservoir. Most significant parameters on oil recovery and electrical energy delivered were oil thickness, presence of aquifer, presence of gas cap, voltage, electrical configuration and electrodes positions. Factors such as: connate water, water salinity and relative permeability to water at irreducible oil saturation had low influence on oil recovery but had some influence in energy requirements. It was possible to optimize energy consumption and oil recovery by electrical variables. Energy requirements can decrease by changing electrodes voltages during the process. This application can be extended to heavy oil reservoirs of high depth, such as offshore fields, where nowadays it is not applicable any conventional thermal process such as steam flooding

Étude du nombre de polynômes irréductibles dans les corps finis avec certaines contraintes imposées aux coefficients

L'objectif de ce mémoire est de dénombrer les polynômes irréductibles unitaires sur un corps fini en prescrivant des contraintes sur les coefficients. Dans les prochaines pages, il sera question de fixer simplement des coefficients, ou simplement de fixer leur signe, leur cubicité ou leur quarticité.

Étude du nombre de polynômes irréductibles dans les corps finis avec certaines contraintes imposées aux coefficients

L'objectif de ce mémoire est de dénombrer les polynômes irréductibles unitaires sur un corps fini en prescrivant des contraintes sur les coefficients. Dans les prochaines pages, il sera question de fixer simplement des coefficients, ou simplement de fixer leur signe, leur cubicité ou leur quarticité.

Semigrupos numéricos

Um semigrupo numérico é um submonoide de (N, +) tal que o seu complementar em N é finito. Neste trabalho estudamos alguns invariantes de um semigrupo numérico S tais como: multiplicidade, dimensão de imersão, número de Frobenius, falhas e conjunto Apéry de S. Caracterizamos uma apresentação minimal para um semigrupo numérico S e descrevemos um método algorítmico para determinar esta apresentação. Definimos um semigrupo numérico irredutível como um semigrupo numérico que não pode ser expresso como intersecção de dois semigrupos numéricos que o contenham propriamente. A finalizar este trabalho, estudamos os semigrupos numéricos irredutíveis e obtemos a decomposição de um semigrupo numérico em irredutíveis. ABSTRACT: A numerical semigroup is a submonoid of (N, +) such that its complement of N is finite. ln this work we study some invariants of a numerical semigroup S such as: multiplicity, embedding dimension, Frobenius number, gaps and Apéry set of S. We characterize a minimal presentation of a numerical semigroup S and describe an algorithmic procedure which allows us to compute a minimal presentation of S. We define an irreducible numerical semigroup as a numerical semigroup that cannot be expressed as the intersection of two numerical semigroups properly containing it. Concluding this work, we study and characterize irreducible numerical semigroups, and describe methods for computing decompositions of a numerical semigroup into irreducible numerical semigroups.

The Worldhood of the Cinematic Image

A close analysis of the specifically cinematographic procedure in Akira Kurosawa’s ‘Dream’ Crows reveals it as an articulated and insightful philosophical statement, endowed with general relevance concerning ‘natural’ perception, phenomenological Erlebnis, mechanical image and aesthetic rapture. The antagonism between the Benjaminian lineage of a mechanical irreducibility of the cinematic image to anthropocentric categories, and the Cartesian tradition of a film-philosophy still relying on the equally irreducible structure of the intentional act, be it the one of a deeply embodied and enworlded counsciousness, in accounting for the essential structure of film and spectator (and their relation), i.e., the antagonism between the decentering primacy of the image and the self-centered primacy of perception, cannot be settled through a simple Phenomenological shift from occularcentric, intentional counsciousness to its embodyment ‘in-the-world’ as yet another carrier of intentionality. Still it remains to be explained what is it in the mechanical image that is able to so deeply affect the human flesh, and conversely, to what features in the human bodily experience is its mechanical other, the fascinating image, so successfuly adressing? It should be expected from the anti-Cartesianism of both the early and the late Merleau-Ponty the textual support for an approach to the essential condition of passivity in movie watching, that would be convergent with Benjamin. The Chapter ‘Le sentir’, in Phénoménologie de la perception, will offer us the proper guide to elucidate what we are already perceiving and conceiving in Kurosawa’s film, where the ex-static phenomenological body of the aesthetical contemplator ‘enters the frame’ like the Benjaminian surgeon enters the body and like the painter - and always already like our deepest level of ‘sensing’, previously to any act of cousciousness - ‘just looses himself in the scene before him’. The Polichinello secret of cinema watching is nonetheless too evident to be seen, and that is where Phenomenological description and reduction are still required.