When is the stability of a nonlinear input-output system robust?

We consider a general nonlinear input-output system governed by operator equations that relate the system's input, state, and output, all of which are in extended spaces. It is assumed that the system variables are separated. Our results give conditions under which the stability of the nominal system is robust; i.e., it is not destroyed by any sufficiently small admissible perturbation of the system. Theorem 1 deals with the case when by stability we mean theincremental stability. Theorem 3 concerns the^*-stability; i.e., the case when the stability is essentially the boundedness of the transmission operator. Moreover, in Theorem 2 it is shown that, under certain conditions, the incremental stability of the nominal system implies insensitivity. Basically, our results show that if the operators describing the nominal system are well behaved, and the transition from the nominal system to the perturbed system is not abrupt, then the nominal system stability is robust. The applications of the results are illustrated by several examples.     

Generalized solutions of semistate equations and stability

In this paper, solvability and stability of nonlinear, time-varying semistate equations is discussed. It is shown that generalized solutions exist in a vicinity of an equilibrium. Moreover, results on a Liapunov-like (uniform, asymptotic) stability are given.     

Some practical stability criteria for semistate equations

In this paper various conditions guaranteeing the ordinary, uniform, and asymptoticA-stability of semistate equations are given. These results are based on and given in terms of the semi-explicit form of a semistate equation.     

Surface morphology and optical properties of porphyrin/Au and Au/porphyrin/Au systems

Porphyrin/Au and Au/porphyrin/Au systems were prepared by vacuum evaporation and vacuum sputtering onto glass substrate. The surface morphology of as-prepared systems and those subjected to annealing at 160°C was studied by optical microscopy, atomic force microscopy, and scanning electron microscopy techniques. Absorption and luminescence spectra of as-prepared and annealed samples were measured. Annealing leads to disintegration of the initially continuous gold layer and formation of gold nanoclusters. An amplification of Soret band magnitude was observed on the Au/meso-tetraphenyl porphyrin (TPP) system in comparison with mere TPP. Additional enhancement of luminescence was observed after the sample annealing. In the case of sandwich Au/porphyrin/Au structure, suppression of one of the two porphyrins’ luminescence maxima and sufficient enhancement of the second one were observed.     

Compositional and Structural Modifications by Ion Beam in Graphene Oxide for Radiation Detection Studies

In the present study, graphene oxide foils 10 μm thick have been irradiated in vacuum using same charge state (one charge state) ions, such as protons, helium and oxygen ions, at the same energies (3 MeV) and fluences (from 5 × 10¹¹ ion/cm² to 5 × 10¹⁴ ion/cm²). The structural changes generated by the ion energy deposition and investigated by X-ray diffraction have suggested the generation of new phases, as reduced GO, GO quantum dots and graphitic nanofibers, carbon nanotubes, amorphous carbon and stacked-cup carbon nanofibers. Further analyses, based on Rutherford Backscattering Spectrometry and Elastic Recoil Detection Analysis, have indicated a reduction of GO connected to the atomic number of implanted ions. The morphological changes in the ion irradiated GO foils have been monitored by Transmission Electron, Atomic Force and Scanning Electron microscopies. The present study aims to better structurally, compositionally and morphologically characterize the GO foils irradiated by different ions at the same conditions and at very low ion fluencies to validate the use of GO for radiation detection and propose it as a promising dosimeter. It has been observed that GO quantum dots are produced on the GO foil when it is irradiated by proton, helium and oxygen ions and their number increases with the atomic number of beam gaseous ion.     

Surface reconstruction with higher-order smoothness

This work proposes a method to reconstruct surfaces with higher-order smoothness from noisy 3D measurements. The reconstructed surface is implicitly represented by the zero-level set of a continuous valued embedding function. The key idea is to find a function whose higher-order derivatives are regularized and whose gradient is best aligned with a vector field defined by the input point set. In contrast to methods based on the first-order variation of the function that are biased toward the constant functions and treat the extraction of the isosurface without aliasing artifacts as an afterthought, we impose a higher-order smoothness directly on the embedding function. After solving a convex optimization problem with a multiscale iterative scheme, a triangulated surface can be extracted using the marching cubes algorithm. We demonstrated the proposed method on several data sets obtained from raw laser-scanners and multiview stereo approaches. Experimental results confirm that our approach allows us to reconstruct smooth surfaces from points in the presence of noise, outliers, large missing parts, and very coarse orientation information.     

Continuous global optimization in surface reconstruction from an oriented point cloud

We introduce a continuous global optimization method to the field of surface reconstruction from discrete noisy cloud of points with weak information on orientation. The proposed method uses an energy functional combining flux-based data-fit measures and a regularization term. A continuous convex relaxation scheme assures the global minima of the geometric surface functional. The reconstructed surface is implicitly represented by the binary segmentation of vertices of a 3D uniform grid and a triangulated surface can be obtained by extracting an appropriate isosurface. Unlike the discrete graph-cut solution, the continuous global optimization entails advantages like memory requirements, reduction of metrication errors for geometric quantities, and allowing globally optimal surface reconstruction at higher grid resolutions. We demonstrate the performance of the proposed method on several oriented point clouds captured by laser scanners. Experimental results confirm that our approach is robust to noise, large holes and non-uniform sampling density under the condition of very coarse orientation information.     

Preparation of bulk‐nanostructured UO2 pellets using high‐pressure spark plasma sintering for LWR fuel safety assessment

Nuclear fuel undergoes a significant restructuration during its lifetime in the nuclear reactor. Especially at the rim of the pellet, large UO₂ grains disintegrate into a nanosized material. In this paper, we focus on the preparation of bulk UO₂ with grain sizes below 100 nm to investigate the physico‐chemical properties of this so‐called “high burn up structure” (HBS). Preparation of bulk nanocrystalline materials is a challenge that can be overcome using the high‐pressure spark plasma sintering (HP SPS) technique. In‐house developed HP SPS with 500 MPa applied pressure was used for compaction of 11 nm UO₂ powder obtained by oxalate conversion. The procedure yielded dense (>90%) compacts with grain size as low as 34 nm for samples sintered at 800°C.     

The invertibility of operators and contraction mappings

Necessary and sufficient conditions for the invertibility of a (not necessarily linear) operatorN between normed linear spaces are given. It is shown thatN is invertible precisely if a certain operator associated withN is a contraction.