183 research outputs found
Improved bounds for the inverses of diagonally dominant tridiagonal matrices
No full textWe obtain new bounds for the entries of the inverse of a diagonally-dominant tridiagonal matrix which improve the best previous ones, due to H.-B. Li et al. We apply our bounds to the tridiagonal matrices arising in the second-order finite-difference discretization of certain boundary-value problems of parabolic type, establishing asymptotically optimal bounds.Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Análisis matemático : un enfoque constructivo
No full textEl presente texto está orientado fundamentalmente a estudiantes de profesorado de matemática de escuela media, aunque también puede ser adoptado en cursos de análisis matemático de estudiantes de licenciatura. En tal sentido, algunos temas de importancia en la matemática de la escuela media, como los números reales y las funciones polinomiales y trascendentes elementales , reciben un tratamiento que les otorga tal vez mayor preponderancia que en textos de análisis para estudiantes de licenciaturas en matemática. Asimismo, presuponemos que los lectores conocen las nociones básicas del cálculo diferencial e integral para funciones en una variable, a la vez que poseen familiaridad con el razonamiento matemático y un manejo fluido del lenguaje algebraico.Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina
Newton's method and a mesh independence principle for certain semilinear boundary value problems
No full textWe exhibit an algorithm which computes an ϵ-approximation of the positive solutions of a family of boundary-value problems with Neumann boundary conditions. Such solutions arise as the stationary solutions of a family of semilinear parabolic equations with Neumann boundary conditions. The algorithm is based on a finite-dimensional Newton iteration associated with a suitable discretized version of the problem under consideration. To determine the behavior of such a discrete iteration we establish an explicit mesh-independence principle. We apply a homotopy-continuation algorithm to compute a starting point of the discrete Newton iteration, and the discrete Newton iteration until an ϵ-approximation of the stationary solution is obtained. The algorithm performs roughly O((1/ϵ)1/2 ) flops and function evaluations.Fil: Dratman, Ezequiel. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
The number of reducible space curves over a finite field
No full text"Most" hypersurfaces in projective space are irreducible, and rather precise estimates are known for the probability that a random hypersurface over a finite field is reducible. This paper considers the parametrization of space curves by the appropriate Chow variety, and provides bounds on the probability that a random curve over a finite field is reducible.Fil: Cesaratto, Eda. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Von zur Gathen, Joachim. No especifíca;Fil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
On the bit complexity of polynomial system solving
No full textWe describe and analyze a randomized algorithm which solves a polynomial system over the rationals defined by a reduced regular sequence outside a given hypersurface. We show that its bit complexity is roughly quadratic in the Bézout number of the system and linear in its bit size. The algorithm solves the input system modulo a prime number p and applies p-adic lifting. For this purpose, we establish a number of results on the bit length of a “lucky” prime p, namely one for which the reduction of the input system modulo p preserves certain fundamental geometric and algebraic properties of the original system. These results rely on the analysis of Chow forms associated to the set of solutions of the input system and effective arithmetic Nullstellensätze.Fil: Gimenez, Nardo Ariel. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
On the computation of rational points of a hypersurface over a finite field
No full textWe design and analyze an algorithm for computing rational points of hypersurfaces defined over a finite field based on searches on vertical strips, namely searches on parallel lines in a given direction. Our results show that, on average, less than two searches suffice to obtain a rational point. We also analyze the probability distribution of outputs, using the notion of Shannon entropy, and prove that the algorithm is somewhat close to any ideal equidistributed algorithm.Fil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Pérez, Mariana. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentin
Explicit estimates for polynomial systems defining irreducible smooth complete intersections
No full textThis paper deals with properties of the algebraic variety defined as the set of zeros of a “typical” sequence of polynomials. We consider various types of “nice” varieties: set-theoretic and ideal-theoretic complete intersections, absolutely irreducible ones, and nonsingular ones. For these types, we present a nonzero “genericity” polynomial of explicitly bounded degree in the coefficients of the sequence that vanishes if its variety is not of the type. Here, the number of polynomials and their degrees are fixed. Over finite fields, this yields bounds on the number of such sequences. We also show that most sequences (of at least two polynomials) define a degenerate variety, namely an absolutely irreducible nonsingular hypersurface in some linear projective subspace.Fil: Von zur Gathen, Joachim. Universitat Bonn; AlemaniaFil: Matera, Guillermo. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
Matera Countrymen Capital
No full textIn the 1950s, Italy recovered from the trauma of the Second World War. However, in the deep South of the country, a city remained alien to this progress. Indeed, isolated for a long time, it was unable to challenge new immigration movements and ended up exceeding its saturation limit. That town was Matera, the ‘Shame of Italy’. In a country projected towards the new millennium, it was unacceptable that almost 20.000 people were living together with animals in dirty and cramped caves. Matera seemed to blame the national political class for not having taken steps to eradicate this age-old misery. The city had to be decongested, so to move part of its population and allow the caves to regain the human scale they always had. However, it did generalize: all the caves had to be cleared and the delicate countrymen life had to be transferred to a galaxy of model rural villages. In the end, few of these were made, none properly. Those same people who lived in poverty were moved to modern dormitory districts, which yet had all the comforts allowed by modern times, but which were not suitable to hosting a community shaped by consolidated urban and interpersonal relationships. Only in the 1990s, it was realized that that life, those people, could not survive outside of those same narrow caves. The human and the architectural and natural components were inseparable. They did begin to realize what should have been done long before: restoring the architectural value of the caves, which today is even beginning to attract mass tourism.AR2A011Architecture, Urbanism and Building Science
A Hidden Water-Harvesting System: The Sassi de Matera
No full textThe water-harvesting system of the ancient Sassi di Matera, in the Basilicata region of southern Italy, represents a clever way of living with water in an arid climate. The terrain, with its soft rocks (Calcarenite di Gravina), provided the foundation for the water-harvesting system that shaped the cave dwellings of Sassi physically, socially and culturally. People caught, guided and stored water in private and public spaces, mostly underground, ensuring its availability for all. In 1993 UNESCO declared the cave village a World Heritage Site. Unfortunately, the water-harvesting system of Sassi di Matera is no longer functioning. Its historic ingenuity is not as visible as the system deserves and its cultural and social values are almost forgotten. Using layered visual analysis – the illustrative method – knowledge can be collected and communicated in drawings to get insight regarding more resilient, circular, and people-related approaches (Bobbink, Chourairi and Di Nicola 2022). This article and the included drawings focus on the water system’s value, from which we can learn today.Landscape Architectur
Singularities of Symmetric Hypersurfaces and Reed-Solomon Codes
No full textWe determine conditions on q for the nonexistence of deep holes of the standard Reed-Solomon code of dimension k over Fq generated by polynomials of degree k + d. Our conditions rely on the existence of q-rational points with nonzero, pairwise-distinct coordinates of a certain family of hypersurfaces defined over Fq. We show that the hypersurfaces under consideration are invariant under the action of the symmetric group of permutations of the coordinates. This allows us to obtain critical information concerning the singular locus of these hypersurfaces, from which the existence of q-rational points is established.Fil: Cafure, Antonio Artemio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Matera, Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; ArgentinaFil: Privitelli, Melina Lorena. Universidad Nacional de General Sarmiento. Instituto del Desarrollo Humano; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin
- …
