Search results for "A priori and a posteriori"

Per una rilettura kantiana del principio di causalità

2018

There is no contradiction between Kant’s statement that the proposition, “every alteration has its cause,” is of no interest to the Critique of Pure Reason because of its dependence on empirical contents (KrV, B 3) and his use of the same proposition as an example of pure a priori knowledge (KrV, B 5). There is only the arduousness and sometimes also the ambiguity of a passage in which Kant attempts to establish a new basis for the validity of the principle of causality.

Technical support for a judge when assessing a priori odds

2015

A Challenge to Boghossian's Incompatibilist Argument

1998

The paradox arises as we realize that (3) is clearly not knowable a priori, but (1) and (2) are. (2) holds 'a priori' because, according to Boghossian, it "just is the view that I have called the doctrine of privileged self-knowledge" (p. 202). The core of the paper is devoted, though, to argue that an externalist (i.e., someone who holds the view that "... facts external to a thinker's skin are relevant to the individuation of (certain of) his mental contents" (p. 199). is bound to concede that (1) is knowable 'a priori'. It would follow that, contrary to intuition, (3) can be known a priori since is the conclusion of an inference that relies on two premises that are, in

Black holes in five-dimensional Palatinif(R)gravity and implications for the AdS/CFT correspondence

2014

We show that theories having second-order field equations in the context of higher-dimensional modified gravity are not restricted to the family of Lovelock Lagrangians, but can also be obtained if no a priori assumption on the relation between the metric and affine structures of space-time is made (the Palatini approach). We illustrate this fact by considering the case of Palatini $f(R)$ gravities in five dimensions. Our results provide an alternative avenue to explore new domains of the AdS/CFT correspondence without resorting to ad hoc quasitopological constructions.

Nonlocally-induced (fractional) bound states: Shape analysis in the infinite Cauchy well

2015

Fractional (L\'{e}vy-type) operators are known to be spatially nonlocal. This becomes an issue if confronted with a priori imposed exterior Dirichlet boundary data. We address spectral properties of the prototype example of the Cauchy operator $(-\Delta )^{1/2}$ in the interval $D=(-1,1) \subset R$, with a focus on functional shapes of lowest eigenfunctions and their fall-off at the boundaries of $D$. New high accuracy formulas are deduced for approximate eigenfunctions. We analyze how their shape reproduction fidelity is correlated with the evaluation finesse of the corresponding eigenvalues.

A posteriori estimates for a coupled piezoelectric model

2017

Erworben im Rahmen der Schweizer Nationallizenzen (http://www.nationallizenzen.ch)

A priori bounds and multiplicity of solutions for an indefinite elliptic problem with critical growth in the gradient

2019

Let $\Omega \subset \mathbb R^N$, $N \geq 2$, be a smooth bounded domain. We consider a boundary value problem of the form $$-\Delta u = c_{\lambda}(x) u + \mu(x) |\nabla u|^2 + h(x), \quad u \in H^1_0(\Omega)\cap L^{\infty}(\Omega)$$ where $c_{\lambda}$ depends on a parameter $\lambda \in \mathbb R$, the coefficients $c_{\lambda}$ and $h$ belong to $L^q(\Omega)$ with $q>N/2$ and $\mu \in L^{\infty}(\Omega)$. Under suitable assumptions, but without imposing a sign condition on any of these coefficients, we obtain an a priori upper bound on the solutions. Our proof relies on a new boundary weak Harnack inequality. This inequality, which is of independent interest, is established in the gener…

Maximal regularity via reverse Hölder inequalities for elliptic systems of n-Laplace type involving measures

2008

In this note, we consider the regularity of solutions of the nonlinear elliptic systems of n-Laplacian type involving measures, and prove that the gradients of the solutions are in the weak Lebesgue space Ln,∞. We also obtain the a priori global and local estimates for the Ln,∞-norm of the gradients of the solutions without using BMO-estimates. The proofs are based on a new lemma on the higher integrability of functions.

Toward a Quality Guide to Facilitate the Transference of Analytical Methods from Research to Testing Laboratories: A Case Study

2009

Abstract At present, there is no single viewpoint that defines QA strategies in analytical chemistry. On the other hand, there are no unique protocols defining a set of analytical tasks and decision criteria to be performed during the method development phase (e.g., by a single research laboratory) in order to facilitate the transference to the testing laboratories intending to adapt, validate, and routinely use this method. This study proposes general criteria, a priori valid for any developed method, recommended as a provisional quality guide containing the minimum internal tasks necessary to publish new analytical method results. As an application, the selection of some basic internal qu…

A Unified Approach to Measuring Accuracy of Error Indicators

2014

In this paper, we present a unified approach to error indication for elliptic boundary value problems. We introduce two different definitions of the accuracy (weak and strong) and show that various indicators result from one principal relation. In particular, this relation generates all the main types of error indicators, which have already gained high popularity in numerical practice. Also, we discuss some new forms of indicators that follow from a posteriori error majorants of the functional type and compare them with other indicators. Finally, we discuss another question related to accuracy of error indicators for problems with incompletely known data.