Preparation and characterization of ZrO2:Sm amorphous thin films by solid state photochemical deposition method

Thin films of ZrO₂ loaded with 10, 30 and 50 mol% Sm were prepared by a photochemical method using thin films of metal acetylacetonate complexes as precursors. The photolysis of these films induces the fragmentation of the acetylacetonate ligand and the partial reduction of metal ion together with volatile organic compounds. When the metallic complex is exposed to air, the product of the reaction is metal oxide. The photoreactivity of these films was monitored by FT-IR spectroscopy, followed by a post-annealing treatment process. The obtained films were characterized by X-ray photoelectron spectroscopy and atomic force microscopy.Photoluminescense studies of the films employed 400 nm radiation for excitation of the Sm ions present. The emission spectra showed signals arising from the ⁴G_5/2→⁶H_J (J=3/2, 7/2, 9/2) transitions, where the ⁴G_5/2→⁶H_3/2 transition has the highest intensity. The concentration dependence of the PL intensity was also studied. A maximum PL intensity was observed with 10 mol% Sm content but then diminished with higher Sm concentrations.     

An improved upper bound on the maximum degree of terminal-pairable complete graphs

A graph $G$ is terminal-pairable with respect to a demand (loopless) multigraph $D$ on the same vertex set as $G$, if there exist edge-disjoint paths joining the end vertices of every demand edge of $D$. In this short note, we improve the upper bound on the largest $\Delta \left(n\right)$ with the property that the complete graph on $n$ vertices is terminal-pairable with respect to any demand multigraph of maximum degree at most $\Delta \left(n\right)$. This disproves a conjecture originally stated by Csaba, Faudree, Gyárfás, Lehel and Schelp.     

Flat surfaces,Bratteli diagrams and unique ergodicity à la Masur

Recalling the construction of a flat surface from a Bratteli diagram, this paper considers the dynamics of the shift map on the space of all bi-infinite Bratteli diagrams as the renormalizing dynamics on a moduli space of flat surfaces of finite area. A criterion of unique ergodicity similar to that of Masur’s for flat surface holds: if there is a subsequence of the renormalizing dynamical system which has a good accumulation point, the translation flow or Bratteli–Vershik transformation is uniquely ergodic. Related questions are explored.     

Proximal Point Methods for Lipschitz Functions on Hadamard Manifolds: Scalar and Vectorial Cases

In the second part of our study, we introduce the concept of global extended exactness of penalty and augmented Lagrangian functions, and derive the localization principle in the extended form. The main idea behind the extended exactness consists in an extension of the original constrained optimization problem by adding some extra variables, and then construction of a penalty/augmented Lagrangian function for the extended problem. This approach allows one to design extended penalty/augmented Lagrangian functions having some useful properties (such as smoothness), which their counterparts for the original problem might not possess. In turn, the global exactness of such extended merit functions can be easily proved with the use of the localization principle presented in this paper, which reduces the study of global exactness to a local analysis of a merit function based on sufficient optimality conditions and constraint qualifications. We utilize the localization principle in order to obtain simple necessary and sufficient conditions for the global exactness of the extended penalty function introduced by Huyer and Neumaier, and in order to construct a globally exact continuously differentiable augmented Lagrangian function for nonlinear semidefinite programming problems.     

On the derived category of quasi-coherent sheaves on an Adams geometric stack

Let $\mathsf{X}$ be an Adams geometric stack. We show that $\mathsf{D}({\mathsf{A}}_{\mathsf{qc}}(\mathsf{X}))$, its derived category of quasi-coherent sheaves, satisfies the axioms of a stable homotopy category defined by Hovey, Palmieri and Strickland in [13]. Moreover we show how this structure relates to the derived category of comodules over a Hopf algebroid that determines $\mathsf{X}$.     

Knot exteriors with all possible meridional essential surfaces

We show the existence of infinitely many knots where each exterior contains meridional essential surfaces of independently unbounded genus and number of boundary components. In particular, we construct examples of knot exteriors each of which has all possible compact orientable surfaces embedded as meridional essential surfaces. From these results, we also prove the existence of a hyperbolic knot exterior, not necessarily of a knot in the 3-sphere, for which there are meridional essential surfaces of simultaneously unbounded genus and number of boundary components.     

Energy decay and control for a system of strings elastically connected in parallel

In the present paper, we study energy decay and exact boundary controllability for a system of n one-dimensional linear wave equations coupled in parallel. The control obtained is a square integrable of the Neuman type for initial data with finite energy. The controllability time is near optimal value. We treat the case of control in the whole boundary and also in part of it.     

Rigidity of Free Boundary Surfaces in Compact 3-Manifolds with Strictly Convex Boundary

In this paper, we obtain an analogue of Toponogov theorem in dimension 3 for compact manifolds \(M^3\) with nonnegative Ricci curvature and strictly convex boundary \(\partial M\). Here we obtain a sharp upper bound for the length \(L(\partial \Sigma )\) of the boundary \(\partial \Sigma \) of a free boundary minimal surface \(\Sigma ^2\) in \(M^3\) in terms of the genus of \(\Sigma \) and the number of connected components of \(\partial \Sigma \), assuming \(\Sigma \) has index one. After, under a natural hypothesis on the geometry of M along \(\partial M\), we prove that if \(L(\partial \Sigma )\) saturates the respective upper bound, then \(M^3\) is isometric to the Euclidean 3-ball and \(\Sigma ^2\) is isometric to the Euclidean disk. In particular, we get a sharp upper bound for the area of \(\Sigma \), when \(M^3\) is a strictly convex body in \(\mathbb {R}^3\), which is saturated only on the Euclidean 3-balls (by the Euclidean disks). We also consider similar results for free boundary stable CMC surfaces.