On the construction of a nonlinear recursive predictor

In this paper, we present a novel approach for constructing a nonlinear recursive predictor. Given a limited time series data set, our goal is to develop a predictor that is capable of providing reliable long-term forecasting. The approach is based on the use of an artificial neural network and we propose a combination of network architecture, training algorithm, and special procedures for scaling and initializing the weight coefficients. For time series arising from nonlinear dynamical systems, the power of the proposed predictor has been successfully demonstrated by testing on data sets obtained from numerical simulations and actual experiments.     

Relaxation Results for Nonlinear Evolution Inclusions with One-sided Perron Right-hand Side

In a Banach space X, we study the evolution inclusion of the form x ^′(t)∈A x(t)+F(t,x(t)), where A is an m-dissipative operator and F is an almost lower semicontinuous multifunction with nonempty closed values. If F is one-sided Perron with sublinear growth, then, we establish the relation between the solutions of the considered differential inclusion and the solutions of the relaxed one, i.e., \(x^{\prime} (t)\in Ax (t)+\overline{co}F (t,x (t) )\) . A variant of the well known Filippov-Pli? lemma is also proved.     

Matrix-dependent cooperativity in spin crossover Fe(pyrazine)Pt(CN)4 nanoparticles

Anisotropic nanoparticles of the Fe(pyrazine)Pt(CN)(4) network were prepared embedded in various matrices that revealed to have a dramatic effect on the cooperative spin crossover phenomena. By a judicious choice of the nature of the matrix and the control of interparticle distances, a hysteresis of 15 K was achieved close to room temperature for such nano-objects.     

CONTRA: improving the performance of dynamic investigations in natural abundance organic solids by mirror-symmetric constant-time CODEX

We present a minor but essential modification to the CODEX 1D-MAS exchange experiment. The new CONTRA method, which requires minor changes of the original sequence only, has advantages over the previously introduced S-CODEX, since it is less sensitive to artefacts caused by finite pulse lengths. The performance of this variant, including the finite pulse effect, was confirmed by SIMPSON calculations and demonstrated on a number of dynamic systems.     

Investigation of slow dynamic processes in natural abundance polymeric systems by novel 1D-MAS exchange NMR methods

We introduce a recently developed class of SolidState NMR experiments for the investigation of slow dynamic processes in organic solids. These 1D-MAS exchange experiments do not require selective isotopic labeling and can be performed with standard solid-state NMR hardware. The data are easy to analyze and provide selective information about the correlation times as well as about the topology (jump angles etc.) of dynamic processes in different sub-units of the molecules. We present data for Poly(n-butylmethacrylate), PBMA, between the glass transition temperature T_g and the αβ splitting temperature, in order to demonstrate the advantages of these 1D-MAS methods.     

Contact points with integer frequencies in the thin obstacle problem

For the thin obstacle problem, we develop a unified approach that leads to rates of convergence to blow-up profiles at contact points with integer frequencies. For these points, we also obtain a stratification result.