Search results for " convergence."

Existence of Unconditional Bases in Spaces of Polynomials and Holomorphic Functions

2002

Our main result shows that every Montel Kothe echelon or coechelon space E of order 1 < p ≤ ∞ is nuclear if and only if for every (some) m ≥ 2 the space ((mE), τ0) of m-homegeneus polynomials on E endowed with the compact-open topology τ0 has an unconditional basis if and only if the space (ℋ(E), τδ) of holomorphic functions on E endowed with the bornological topology τδ associated to τ0 has an unconditional basis (for coechelon spaces τδ equals τ0). The main idea is to extend the concept of the Gordon-Lewis property from Banach to Frechet and (DF) spaces. In this way we obtain techniques which are used to characterize the existence of unconditional basis in spaces of m-th (symmetric) tenso…

Countably compact weakly Whyburn spaces

2015

The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communica…

On approximation of a class of stochastic integrals and interpolation

2004

Given a diffusion Y = (Y_{t})_{t \in [0,T]} we give different equivalent conditions so that a stochastic integral has an L 2-approximation rate of n −η, {\rm \eta \in (0,1/2],} if one approximates by integrals over piece-wise constant integrands where equidistant time nets of cardinality n + 1 are used. In particular, we obtain assertions in terms of smoothness properties of g(Y T ) in the sense of Malliavin calculus. After optimizing over non-equidistant time-nets of cardinality n + 1 in case {\rm \eta > 0} , it turns out that one always obtains a rate of n^{ - 1/2}, which is optimal. This applies to all functions g obtained in an appropriate way by the real interpolation method between th…

On an iterative method for a class of integral equations of the first kind

1987

In this paper, we investigate an iterative method which has been proposed [1] for the numerical solution of a special class of integral equations of the first kind, where one of the essential assumptions is the positivity of the kernel and the given right-hand side. Integral equations of this special type occur in experimental physics, astronomy, medical tomography and other fields where density functions cannot be measured directly, but are related to observable functions via integral equations. In order to take into account the non-negativity of density functions, the proposed iterative scheme was defined in such a way that only non-negative solutions can be approximated. The first part o…

On the integration of Riemann-measurable vector-valued functions

2016

We confine our attention to convergence theorems and descriptive relationships within some subclasses of Riemann-measurable vector-valued functions that are based on the various generalizations of the Riemann definition of an integral.

Martingale Convergence Theorems and Their Applications

2020

We became familiar with martingales X=(X n ) n∈N0 as fair games and found that under certain transformations (optional stopping, discrete stochastic integral) martingales turn into martingales. In this chapter, we will see that under weak conditions (non-negativity or uniform integrability) martingales converge almost surely. Furthermore, the martingale structure implies L p -convergence under assumptions that are (formally) weaker than those of Chapter 7. The basic ideas of this chapter are Doob’s inequality (Theorem 11.4) and the upcrossing inequality (Lemma 11.3).

Social Dimension and Inequality Problems in the European Union

2017

The purpose of this paper is to introduce evaluation of social development convergence between EU-28 member states in the context of the EU cohesion policy. The main tasks of this study is to assess social dimension and inequalities problems in the European states by applying theory of convergence for real estimations social situations in EU countries. Additionally the development challenges are discussed for improvement of the socio-economic well-being of EU states and to avoid social disparities. The research methodology is based on the convergence theory, on the EU strategies, European Commission legitimate documents application, on the calculations and socio-economic forecasts analysis …

The response of calcareous nannoplankton to sea surface variability at Ceara Rise during the early Pleistocene glacial-interglacial cycles

2019

The Ceara Rise lies just beyond the edge of the Amazon River Fan and sediments from this site may record the complex interplay of different climatic systems and processes, including past changes in southern America monsoon activity, Intertropical Convergence Zone setting, different Atlantic Meridional Overturning Circulation (AMOC) strength and phytoplankton blooming triggered by Amazon River plumes. Here we investigate early Pleistocene calcareous nannoplankton at Ceara Rise, between about 1150 and 850 kiloyears ago. Our investigation shows abrupt variations in water column dynamics across glacial/interglacial cycles or, even better, linked with different AMOC modes. Dominant placoliths in…

Three essays on economic resilience and regional disparities

2017

Socio-economic Disparity problems and Convergence Policy in the EU States

2016

The purpose of this paper is to investigate socio-economic development condition and convergence evaluation in the EU-28 states in the context of the EU policy goals. The arm of this research is to estimate socioeconomic disparities and convergence problems in the European states by applying real valuations of well-being situations and economic development challenges in the EU member states. The research methodology is based on the European Commission legitimate documents application and socio-economic strategies, on the convergence theory and convergence scenario calculations and the socioeconomic forecasts analysis in the EU states. This research presents information about different socio…