We show that nonlinear Liouville theorems does not hold in general for indefinite problems on half spaces. Thus, in order to use blow-up method to obtain a priori estimates of indefinite elliptic equations, one has to impose assumptions on the nodal set of nonlinearity. The counter example is constructed by shooting method in one-dimensional case and then extended to higher dimensions.

Gaussian processes (GPs) enable probabilistic kernel-machines with remarkable modeling efficacy and GPML toolbox facilitates a widespread use by practitioners and researchers. Many modern applications demand non-metric (dis)similarities. As a result, Mercer’s condition for positive semidefiniteness is violated. Through a simple text categorization example that involves a KL-divergence based ker...

In this paper, we view planning as a special case of reasoning about indefinite actions. We treat actions as predicates defined over a linear temporal order. This formalism permits the representation of concurrent activity. Suppose we have a set of abstract actions defined by Horn clauses from a set of basic actions. Let us assume that an abstract action ψ has occurred, and ask whether a given ...

Stein’s higher Riesz transforms are translation invariant operators on L2(Rn) built from multipliers whose restrictions to the unit sphere are eigenfunctions of the Laplace–Beltrami operators. In this article, generalizing Stein’s higher Riesz transforms, we construct a family of translation invariant operators by using discrete series representations for hyperboloids associated to the indefini...

We will use the variational approach to (0.1) as described in [2] and we will stick to the notations of that paper. Given the complex n-dimensional Hermitian space (C, 〈·, ·〉), for any m ∈ N let H m := H(J,C) be the Sobolev space of all H-maps from J := [0, 1] into C. A derivative dependent Hermitian form is the form Ω(x)[u] = Pm i,j=0〈D u(x), ωi,j(x)D u(x)〉, where, each ωi,j is a smooth path o...

In 1986 Bruckner, Fleissner and Foran [2] obtained a descriptive definition of a minimal extension of the Lebesgue integral which integrates the derivative of any differentiable function. Recently, Bongiorno, Di Piazza and Preiss [1] showed that this minimal integral can be obtained from McShane’s definition of the Lebesgue integral [4] by imposing a mild regularity condition on McShane’s parti...

From the time of Bertrand Russell, the semantics of the English definite article has been the object of continued semantic analysis. Most analyses make some use of the notions of uniqueness, or familiarity, however defined more precisely (see for instance Roberts, 2003, for one recent analysis and review). In this paper, though, we wish to motivate through both experimental and non-experimental...

When an indefinite newly introduces or reintroduces an accessible referent into the discourse, it is called specific. Thus, in (1a), it can be coreferential with a lion in the previous sentence, which indicates a particular lion in the relevant situation. By contrast, a nonspecific indefinite has no specific referent at all, as is illustrated in (1b), where a lion can be any lion. In that case,...

We analyze the behavior of indefinite type functionals depending on a real parameter ? over its Nehari set. A special attention is paid to extremal ? , which plays an important role. The main difficulty arises when > as energy functional may be unbounded from below In such situation we prove existence local minimizers constrained this unify and extend previous multiplicity results for critical ...