We define a Walsh space which contains all functions whose partial mixed derivatives up to order δ ≥ 1 exist and have finite variation. In particular, for a suitable choice of parameters, this implies that certain reproducing kernel Sobolev spaces are contained in these Walsh spaces. For this Walsh space we then show that quasi-Monte Carlo rules based on digital (t, α, s)-sequences achieve the ...

The possibility of embedding a quasi-periodic structure into a higher-dimensional superspace gives rise to an interpretation of certain dynamical excitations as motions in the additional space. These excitations then are called phason excitations. There is always infinite degeneracy of the ground state of an aperiodic quasi-periodic system, but this degeneracy leads only to zero frequency modes...

This paper analyzes the properties of a class of estimators, tests, and confidence sets (CSs) when the parameters are not identified in parts of the parameter space. Specifically, we consider estimator criterion functions that are sample averages and are smooth functions of a parameter θ . This includes log likelihood, quasi-log likelihood, and least squares criterion functions. We determine th...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

Discontinuous Galerkin (DG) finite element methods were studied by many researchers for second-order elliptic partial differential equations, and a priori error estimates were established when the solution of the underlying problem is piecewise H3/2+ smooth with > 0. However, elliptic interface problems with intersecting interfaces do not possess such a smoothness. In this paper, we establish a...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

This article is motivated by the following local-to-global question: is every variety with tame quotient singularities globally the quotient of a smooth variety by a finite group? We show that this question has a positive answer for all quasi-projective varieties which are expressible as a quotient of a smooth variety by a split torus (e.g. simplicial toric varieties). Although simplicial toric...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We prove that the perpetual American put option price of an exponential Lévy process whose jumps come from a compound Poisson process is the classical solution of its associated quasi-variational inequality, that it is C except at the stopping boundary and that it is C everywhere (i.e. the smooth pasting condition always holds). We prove this fact by constructing a sequence of functions, each o...

We study multiplicities of jumping numbers multiplier ideals in a smooth variety arbitrary dimension. prove that the multiplicity function is quasi-polynomial, hence proving Poincar\'e series rational function. further when various components quasi-polynomial have highest possible degree and relate it to contributed by Rees valuations. Finally, we special case monomial ideals.