Search results for "Mathematics"
showing 10 items of 22031 documents
Dual attachment pairs in categorically-algebraic topology
2011
[EN] The paper is a continuation of our study on developing a new approach to (lattice-valued) topological structures, which relies on category theory and universal algebra, and which is called categorically-algebraic (catalg) topology. The new framework is used to build a topological setting, based in a catalg extension of the set-theoretic membership relation "e" called dual attachment, thereby dualizing the notion of attachment introduced by the authors earlier. Following the recent interest of the fuzzy community in topological systems of S. Vickers, we clarify completely relationships between these structures and (dual) attachment, showing that unlike the former, the latter have no inh…
Ficción y compromiso ontológico
2014
En este trabajo me ocupo de la semántica de los términos de ficción, en el marco de una posición de tipo abstractista (KRIPKE 2011 y 2013, VAN INWAGEN 1977, SALMON 1998 y 2002, THOMASSON 1999, PREDELLI 1997, 2002 y 2005 y VOLTOLINI 2011). En particular, me concentro en dos problemas que afectan a este tipo de posiciones: el primero de ellos es dar cuenta de la verdad intuitiva de enunciados como "Ulises duerme en la playa de Ithaca"; el segundo es explicar la aceptación, también intuitiva, de que "Ulises no existe" es un enunciado verdadero. In this paper I am concerned with a variant of Kripke´s abstractist theory of fiction, namely, the semantic theory according to which proper names and …
Two-dimensional Banach spaces with polynomial numerical index zero
2009
We study two-dimensional Banach spaces with polynomial numerical indices equal to zero.
Common fixed points of g-quasicontractions and related mappings in 0-complete partial metric spaces
2012
Abstract Common fixed point results are obtained in 0-complete partial metric spaces under various contractive conditions, including g-quasicontractions and mappings with a contractive iterate. In this way, several results obtained recently are generalized. Examples are provided when these results can be applied and neither corresponding metric results nor the results with the standard completeness assumption of the underlying partial metric space can. MSC:47H10, 54H25.
Variable time amplitude amplification and quantum algorithms for linear algebra problems
2012
Quantum amplitude amplification is a method of increasing a success probability of an algorithm from a small epsilon>0 to Theta(1) with less repetitions than classically. In this paper, we generalize quantum amplitude amplification to the case when parts of the algorithm that is being amplified stop at different times. We then apply the new variable time amplitude amplification to give two new quantum algorithms for linear algebra problems. Our first algorithm is an improvement of Harrow et al. algorithm for solving systems of linear equations. We improve the running time of the algorithm from O(k^2 log N) to O(k log^3 k log N) where k is the condition number of the system of equations. …
Derivation of a Homogenized Two-Temperature Model from the Heat Equation
2014
This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential equations governing the evolution of the temperature of each phase at a macroscopic level of description. The coupling terms describing the exchange of heat between the phases are obtained by using homogenization techniques originating from [D. Cioranescu, F. Murat: Coll\`ege de France Seminar vol. 2. (Paris 1979-1980) Res. Notes in Math. vol. 60, pp. 98-138. Pitman, Boston, London, 1982.]
Extensions and corona decompositions of low-dimensional intrinsic Lipschitz graphs in Heisenberg groups
2020
This note concerns low-dimensional intrinsic Lipschitz graphs, in the sense of Franchi, Serapioni, and Serra Cassano, in the Heisenberg group $\mathbb{H}^n$, $n\in \mathbb{N}$. For $1\leq k\leq n$, we show that every intrinsic $L$-Lipschitz graph over a subset of a $k$-dimensional horizontal subgroup $\mathbb{V}$ of $\mathbb{H}^n$ can be extended to an intrinsic $L'$-Lipschitz graph over the entire subgroup $\mathbb{V}$, where $L'$ depends only on $L$, $k$, and $n$. We further prove that $1$-dimensional intrinsic $1$-Lipschitz graphs in $\mathbb{H}^n$, $n\in \mathbb{N}$, admit corona decompositions by intrinsic Lipschitz graphs with smaller Lipschitz constants. This complements results that…
Инфинитезимальная проблема центра на нулевых циклах и гипотеза композиции
2021
Изучается аналог классической инфинитезимальной проблемы центра на плоскости для нулевых циклов. Для этого случая определяется функция смещения и доказывается, что она тождественно равна нулю тогда и только тогда, когда деформация имеет композиционный фактор. Иными словами, гипотеза композиции верна в этом случае, в отличие от тангенциальной проблемы центра для нулевых циклов. Приводятся примеры применения результатов.
Basics of Post-quantum Calculus
2018
A Model for High-Cycle Fatigue in Polycrystals
2018
A grain-scale formulation for high-cycle fatigue inter-granular degradation in polycrystalline aggregates is presented. The aggregate is represented through Voronoi tessellations and the mechanics of individual bulk grains is modelled using a boundary integral formulation. The inter-granular interfaces degrade under the action of cyclic tractions and they are represented using cohesive laws embodying a local irreversible damage parameter that evolves according to high-cycle continuum damage laws. The consistence between cyclic and static damage, which plays an important role in the redistribution of inter-granular tractions upon cyclic degradation, is assessed at each fatigue solution jump,…