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Beznea L.,Simion Stoilow Institute of Mathematics of the Romanian Academy | Rockner M.,Bielefeld University | Rockner M.,Purdue University
Complex Analysis and Operator Theory | Year: 2011

We establish relations between the existence of the -superharmonic functions that have compact level sets ( being the generator of a right Markov process), the path regularity of the process, and the tightness of the induced capacities. We present several examples in infinite dimensional situations, like the case when is the Gross-Laplace operator on an abstract Wiener space and a class of measure-valued branching process associated with a nonlinear perturbation of . © 2010 Springer Basel AG.

Ionescu-Kruse D.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Journal of Mathematical Fluid Mechanics | Year: 2015

By taking into account the $${\beta}$$β-plane effects, we provide an exact nonlinear solution to the geophysical edge-wave problem within the Lagrangian framework. This solution describes trapped waves propagating eastward or westward along a sloping beach with the shoreline parallel to the Equator. © 2015, Springer Basel.

Ionescu-Kruse D.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Journal of Nonlinear Mathematical Physics | Year: 2015

In this paper we present a dynamical study of the exact nonlinear Pollard wave solution to the geophysical water-wave problem in the f-plane approximation. We deduce an exact dispersion relation and we discuss some properties of this solution. © 2015 the authors.

Kohlenbach U.,TU Darmstadt | Leustean L.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences | Year: 2012

This paper addresses new developments in the ongoing proof mining programme, i.e. the use of tools from proof theory to extract effective quantitative information from prima facie ineffective proofs in analysis. Very recently, the current authors developed a method of extracting rates of metastability (as defined by Tao) from convergence proofs in nonlinear analysis that are based on Banach limits and so (for all that is known) rely on the axiom of choice. In this paper, we apply this method to a proof due to Shioji and Takahashi on the convergence of Halpern iterations in spaces X with a uniformly Gâteaux differentiable norm. We design a logical metatheorem guaranteeing the extractability of highly uniform rates of metastability under the stronger condition of the uniform smoothness of X. Combined with our method of eliminating Banach limits, this yields a full quantitative analysis of the proof by Shioji and Takahashi. We also give a sufficient condition for the computability of the rate of convergence of Halpern iterations. This journal is © 2012 The Royal Society.

Diaconescu R.,Simion Stoilow Institute of Mathematics of the Romanian Academy
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

Computer Science has been long viewed as a consumer of mathematics in general, and of logic in particular, with few and minor contributions back. In this article we are challenging this view with the case of the relationship between specification theory and the universal trend in logic. © Springer International Publishing Switzerland 2014.

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