The semigroup-valued integral of M. Sion [S] is reformulated for a general notion of approximation by sums of values taken by a set function integrand. A convergence in measure theorem is established, which yields both his pointwise dominated convergence theorem as well as an integrability criterion which specializes to his existence theorem. In [S] M. Sion introduced and developed an "integral...

In this paper we proof the existence of digitally shifted polynomial lattice rules which achieve strong tractability results for Sobolev spaces of arbitrary high smoothness. The convergence rate is shown to be best possible up to a given degree of smoothness of the integrand. Indeed we even show the existence of polynomial lattice rules which automatically adjust themselves to the smoothness of...

Many techniques for the veri cation of reactive systems rely on the analysis of their reachable state spaces. In this paper, a new algorithm for the symbolic generation of the state spaces of asynchronous system models, such as Petri nets, is developed. The algorithm is based on previous work that employs Multi-valued Decision Diagrams for e ciently storing sets of reachable states. In contrast...

Devoted to multi-task learning and structured output learning, operator-valued kernels provide a flexible tool to build vector-valued functions in the context of Reproducing Kernel Hilbert Spaces. To scale up these methods, we extend the celebrated Random Fourier Feature methodology to get an approximation of operatorvalued kernels. We propose a general principle for Operator-valued Random Four...

Adaptive recursive linear equalizers present important advantages in terms of performance and robustness compared to more standard finite impulse response structures, and provide a means for blindly initializing the decision feedback structure. We present an analysis of a pair of algorithms for the adaptation of the recursive part of the equalizer, which are based on the second-order statistics...

in this paper we define intuitionistic fuzzy metric and normedspaces. we first consider finite dimensional intuitionistic fuzzy normed spacesand prove several theorems about completeness, compactness and weak convergencein these spaces. in section 3 we define the intuitionistic fuzzy quotientnorm and study completeness and review some fundamental theorems. finally,we consider some properties of...

We analyze convergence rates of quasi-Monte Carlo (QMC) quadratures for countablyparametric solutions of linear, elliptic partial differential equations (PDE) in divergence form with log-Gaussian diffusion coefficient, based on the error bounds in [James A. Nichols and Frances Y. Kuo: Fast CBC construction of randomly shifted lattice rules achieving O(N−1+δ) convergence for unbounded integrands...

Banach's contraction principle has been improved and extensively studied on several generalized metric spaces. Recently, complex-valued $S$-metric spaces have been introduced and studied for this purpose. In this paper, we investigate some generalized fixed point results on a complete complex valued $S$-metric space. To do this, we prove some common fixed point (resp. fixed point) theorems usin...