A new perspective on some approximations used in neutron transport modeling

Hanuš, Milan

Displaying similar documents to “A new perspective on some approximations used in neutron transport modeling”

A new kind of augmentation of filtrations

Joseph Najnudel, Ashkan Nikeghbali (2011)

ESAIM: Probability and Statistics

Similarity:

Let (Ω, $ℱ$ , ( $ℱ_{t}$ ), $ℙ$ ) be a filtered probability space satisfying the usual assumptions: it is usually not possible to extend to $ℱ_{\infty}$ (the-algebra generated by ( $ℱ_{t}$ )) a coherent family of probability measures ( $ℚ_{t}$ ) indexed by , each of them being defined on $ℱ_{t}$ . It is known that for instance, on the Wiener space, this extension problem has a positive answer if one takes the filtration generated by the coordinate process, made right-continuous, but can have a negative...

Multi-Harnack smoothings of real plane branches

Pedro Daniel González Pérez, Jean-Jacques Risler (2010)

Annales scientifiques de l'École Normale Supérieure

Similarity:

Let $Δ \subset 𝐑^{2}$ be an integral convex polygon. G. Mikhalkin introduced the notion of, a class of real algebraic curves, defined by polynomials supported on $Δ$ and contained in the corresponding toric surface. He proved their existence, viamethod, and that the topological type of their real parts is unique (and determined by $Δ$ ). This paper is concerned with the description of the analogous statement in the case of a smoothing of a real plane branch $(C, 0)$ . We introduce the class ofsmoothings of $(C, 0)$ by...

On a certain generalization of spherical twists

Yukinobu Toda (2007)

Bulletin de la Société Mathématique de France

Similarity:

This note gives a generalization of spherical twists, and describe the autoequivalences associated to certain non-spherical objects. Typically these are obtained by deforming the structure sheaves of $(0, - 2)$ -curves on threefolds, or deforming $ℙ$ -objects introduced by D.Huybrechts and R.Thomas.

Optional splitting formula in a progressively enlarged filtration

Shiqi Song (2014)

ESAIM: Probability and Statistics

Similarity:

Let $𝔽_{}^{}$ F be a filtration andbe a random time. Let $𝔾_{}^{}$ G be the progressive enlargement of $𝔽_{}^{}$ F with. We study the following formula, called the optional splitting formula: For any $𝔾_{}^{}$ G-optional process, there exists an $𝔽_{}^{}$ F-optional process and a function defined on [0∞] × (ℝ × ) being $ℬ [0, \infty] \otimes 𝒪 (𝔽_{}^{})$ ℬ[0,∞]⊗x1d4aa;(F) measurable, such that $Y = Y^{'} 1_{[0, τ)}^{} + Y^{''} (τ) 1_{[τ, \infty)}^{} .$ Y=Y′1[0,τ)+Y′′(τ)1[τ,∞). (This formula can also be formulated for multiple random times ...

Necessary and sufficient condition for the existence of a Fréchet mean on the circle

Benjamin Charlier (2013)

ESAIM: Probability and Statistics

Similarity:

Let ( $𝕊^{1}, d_{𝕊^{1}}$ S 1 , d S 1 ) be the unit circle in ℝ endowed with the arclength distance. We give a sufficient and necessary condition for a general probability measure to admit a well defined Fréchet mean on ( $𝕊^{1}, d_{𝕊^{1}}$ S 1 , d S 1 ). We derive a new sufficient condition of existence() with no restriction on the support of the measure. Then, we study the convergence of the empirical Fréchet mean to the Fréchet mean and we give an algorithm to compute it.

Constructive quantization: approximation by empirical measures

Steffen Dereich, Michael Scheutzow, Reik Schottstedt (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

In this article, we study the approximation of a probability measure $μ$ on $ℝ^{d}$ by its empirical measure ${\hat{μ}}_{N}$ interpreted as a random quantization. As error criterion we consider an averaged $p$ th moment Wasserstein metric. In the case where $2 p l t; d$ , we establish fine upper and lower bounds for the error, a. Moreover, we provide a universal estimate based on moments, a . In particular, we show that quantization by empirical measures is of optimal order under weak assumptions.

Estimate of the pressure when its gradient is the divergence of a measure. Applications

Marc Briane, Juan Casado-Díaz (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper, a $W^{- 1, N^{'}}$ estimate of the pressure is derived when its gradient is the divergence of a matrix-valued measure on $ℝ^{N}$ , or on a regular bounded open set of $ℝ^{N}$ . The proof is based partially on the Strauss inequality [Strauss, 23 (1973) 207–214] in dimension two, and on a recent result of Bourgain and Brezis [ 9 (2007) 277–315] in higher dimension. The estimate is used to derive a representation result for divergence free distributions which read as the divergence of a measure, and...

Curvature measures, normal cycles and asymptotic cones

Xiang Sun, Jean-Marie Morvan (2013)

Actes des rencontres du CIRM

Similarity:

The purpose of this article is to give an overview of the theory of the and to show how to use it to define a on singular surfaces embedded in an (oriented) Euclidean space $𝔼^{3}$ . In particular, we will introduce the notion of associated to a Borel subset of $𝔼^{3}$ , generalizing the defined at each point of a smooth surface. For simplicity, we restrict our singular subsets to polyhedra of the $3$ -dimensional Euclidean space $𝔼^{3}$ . The coherence of the theory lies in a convergence theorem: If a...

A proof of Reidemeister-Singer’s theorem by Cerf’s methods

François Laudenbach (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

Similarity:

Heegaard splittings and Heegaard diagrams of a closed 3-manifold $M$ are translated into the language of Morse functions with Morse-Smale pseudo-gradients defined on $M$ . We make use in a very simple setting of techniques which Jean Cerf developed for solving a famous problem. In passing, we show how to cancel the supernumerary local extrema in a generic path of functions when $dim M > 2$ . The main tool that we introduce is an which could be useful elsewhere.

Numerical analysis of a transmission problem with Signorini contact using mixed-FEM and BEM

Gabriel N. Gatica, Matthias Maischak, Ernst P. Stephan (2011)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Similarity:

This paper is concerned with the dual formulation of the interface problem consisting of a linear partial differential equation with variable coefficients in some bounded Lipschitz domain Ω in $ℝ^{n}$ ( ≥ 2) and the Laplace equation with some radiation condition in the unbounded exterior domain Ω:= $ℝ^{n} ∖ \bar{Ω}$ . The two problems are coupled by transmission and Signorini contact conditions on the interface Γ = ∂Ω. The exterior part of the interface problem is rewritten using a Neumann to Dirichlet mapping...

An inequality for spherical Cauchy dual tuples

Sameer Chavan (2013)

Colloquium Mathematicae

Similarity:

Let T be a spherical 2-expansive m-tuple and let $T^{}$ denote its spherical Cauchy dual. If $T^{}$ is commuting then the inequality $\binom{\sum_{| β | = k} {(β!)}^{- 1} {(T^{})}^{β} (T^{}) *^{β} \leq (k + m - 1}{k) \sum_{| β | = k} {(β!)}^{- 1} (T^{}) *^{β} {(T^{})}^{β}}$ holds for every positive integer k. In case m = 1, this reveals the rather curious fact that all positive integral powers of the Cauchy dual of a 2-expansive (or concave) operator are hyponormal.

A priori bounds for some infinitely renormalizable quadratics: II. Decorations

Jeremy Kahn, Mikhail Lyubich (2008)

Annales scientifiques de l'École Normale Supérieure

Similarity:

A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we prove bounds. They imply local connectivity of the corresponding Julia...

On some identities involving spherical means

Gianfranco Cimmino (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Similarity:

For every positive definite quadratic form in $n$ variables the reciprocal of the square root of the discriminant is equal to the arithmetic mean of the values assumed by the form on the $n-1$ sphere centered at $0$ and with radius $1$ raised to the ( $-\frac{n}{2}$ )-th. power. Various consequences are deduced from this, in particular a simplification of some calculations from which one obtains the possibility of solving linear systems using spherical means rather than determinants.

The jacobian map, the jacobian group and the group of automorphisms of the Grassmann algebra

Vladimir V. Bavula (2010)

Bulletin de la Société Mathématique de France

Similarity:

There are nontrivial dualities and parallels between polynomial algebras and the Grassmann algebras (e.g., the Grassmann algebras are dual of polynomial algebras as quadratic algebras). This paper is an attempt to look at the Grassmann algebras at the angle of the Jacobian conjecture for polynomial algebras (which is the question/conjecture about the Jacobian set– the set of all algebra endomorphisms of a polynomial algebra with the Jacobian...

Waring’s problem for Beatty sequences and a local to global principle

William D. Banks, Ahmet M. Güloğlu, Robert C. Vaughan (2014)

Journal de Théorie des Nombres de Bordeaux

Similarity:

We investigate in various ways the representation of a large natural number $N$ as a sum of $s$ positive $k$ -th powers of numbers from a fixed Beatty sequence. , a very general form of the local to global principle is established in additive number theory. Although the proof is very short, it depends on a deep theorem of M. Kneser.

Some problems in automata theory which depend on the models of set theory

Olivier Finkel (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Similarity:

We prove that some fairly basic questions on automata reading infinite words depend on the models of the axiomatic system ZFC. It is known that there are only three possibilities for the cardinality of the complement of an -language $L (𝒜)$ (x1d49c;) accepted by a Büchi 1-counter automaton $𝒜$ x1d49c;. We prove the following surprising result: there exists a 1-counter Büchi automaton $𝒜$ x1d49c; such that the cardinality of the complement $L {(𝒜)}^{-}$ (𝒜) of the -language...

On some identities involving spherical means

Gianfranco Cimmino (1989)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti

Similarity:

Limit theorems for stationary Markov processes with L2-spectral gap

Déborah Ferré, Loïc Hervé, James Ledoux (2012)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

Let ${(X_{t}, Y_{t})}_{t \in 𝕋}$ be a discrete or continuous-time Markov process with state space $𝕏 \times ℝ^{d}$ where $𝕏$ is an arbitrary measurable set. Its transition semigroup is assumed to be additive with respect to the second component, i.e. ${(X_{t}, Y_{t})}_{t \in 𝕋}$ is assumed to be a Markov additive process. In particular, this implies that the first component ${(X_{t})}_{t \in 𝕋}$ is also a Markov process. Markov random walks or additive functionals of a Markov process are special instances of Markov additive processes. In this paper, the process ${(Y_{t})}_{t \in 𝕋}$ is shown...

On the optimality of the empirical risk minimization procedure for the convex aggregation problem

Guillaume Lecué, Shahar Mendelson (2013)

Annales de l'I.H.P. Probabilités et statistiques

Similarity:

We study the performance of (ERM), with respect to the quadratic risk, in the context of , in which one wants to construct a procedure whose risk is as close as possible to the best function in the convex hull of an arbitrary finite class $F$ . We show that ERM performed in the convex hull of $F$ is an optimal aggregation procedure for the convex aggregation problem. We also show that if this procedure is used for the problem of model selection aggregation, in which one wants to mimic the...