Stability of the Minimizers of Least Squares with a Non-Convex Regularization. Part I: Local Behavior

Many estimation problems amount to minimizing a piecewise C^m objective function, with m ≥ 2, composed of a quadratic data-fidelity term and a general regularization term. It is widely accepted that the minimizers obtained using non-convex and possibly non-smooth regularization terms are frequently good estimates. However, few facts are known on the ways to control properties of these minimizers. This work is dedicated to the stability of the minimizers of such objective functions with respect to variations of the data. It consists of two parts: first we consider all local minimizers, whereas in a second part we derive results on global minimizers. In this part we focus on data points such that every local minimizer is isolated and results from a C^m-1 local minimizer function, defined on some neighborhood. We demonstrate that all data points for which this fails form a set whose closure is negligible.     

Synthesis,spectroscopic and thermal characterization of Co(II) tetrahydrogen hexaoxoiodate tetrahydrate

A new cobalt(II) tetrahydrogen hexaoxoiodate tetrahydrate Co(H₄IO₆)₂·4H₂O is prepared by crystallization from an acidic aqueous solution. This compound is identified by quantitative analysis, TG, DTA, DSC and IR spectra. A thermal decomposition scheme is proposed. Some phase transitions are identified and the corresponding enthalpy changes are determined.     

A two-level Kaluza-Klein theory

Let the Lie groups G and H act on the manifold P in such a way that P fibres as a principal G-bundle over P/G and as an H-bundle over P/H. We find that every pair (,) where is an H-invariant connection form in PP/G and is a G-invariant connection form in PP/H corresponds uniquely to a connection form in PP/(H×G) and a cross-section of a vector bundle with base P/(H×G).     

Surface interaction and self-assembly of cyclodextrins with organic dyes

The interaction of seven novel substituted merocyanine dyes, i.e. 1-methyl-4-[2-(3-methoxy-4-hydroxyphenyl)ethenyl)]pyridinium iodide, 1-methyl-4-[2-(3,5-dimethoxy-4-hydroxyphenyl)ethenyl)]pyridinium iodide, 1-methyl-4-[2-(4-dimethylaminophenyl)ethenyl)]pyridinium iodide, their quinoide forms as well as 1-methyl-4-[2-(3-methoxy-4-oxocyclohexadienilydene)ethylidene]-1,4-dihydropyridine, 1-methyl-4-[2-(3,5-dimethoxy-4-oxocyclohexadienilydene)ethylidene]-1,4-dihydropyridine, with α-CD, γ-CD as well as functionalized γ-cyclodextrin phosphate sodium salt is studied by the methods such as UV–Vis and fluorescence spectroscopy, linear-polarized infrared (IR-LD) spectroscopy of oriented colloids in nematic host, ¹H- and ¹³C-NMR spectroscopy, HPLC ESI tandem mass spectrometry, scanning electron and tunneling microscopy, powder X-ray diffraction as well as thermal methods. A formation of the 1D and 2D “supramolecular polymers” with nanosizes is found. The dyes are adsorbed on the CDs surface and form a hexagonal microcrystalline sub-structures. Remarkable fluorescence properties depending of the type of the substituent in the dyes, in solid-state are observed.     

1,10-Phenanthrolinium hydrogensquarate monohydrate—A non-centrosymmetric structure from two non-chiral agents

Four different dimethyltin(IV) complexes of Schiff bases derived from 2-amino-3-hydroxypyridine and different substituted salicylaldehydes have been synthesized. The compounds, with the general formula [Me₂Sn(2-OArCHNC₅H₃NO)], where Ar = –C₆H₃(5-CH₃) [Me₂SnL¹], –C₆H₃(5-NO₂) [Me₂SnL²], –C₆H₂(3,5-Cl₂) [Me₂SnL³], and –C₆H₂(3,5-I₂) [Me₂SnL⁴], were characterized by IR, NMR (¹H and ¹³C), mass spectroscopy and elemental analysis. Me₂SnL³ was also characterized by X-ray diffraction analysis and shows a fivefold C₂NO₂ coordination with distorted square pyramidal geometry. H₃C–Sn–CH₃ angles in the complexes were calculated using Lockhart's equations with the ¹J(^117/119Sn–¹³C) and ²J(^117/119Sn–¹H) values (from the ¹H-NMR and ¹³C-NMR spectra). The in vitro antibacterial and antifungal activities of dimethyltin(IV) complexes were also investigated.     

Chiral Aminoalcohols and Squaric Acid Amides as Ligands for Asymmetric Borane Reduction of Ketones: Insight to In Situ Formed Catalytic System by DOSY and Multinuclear NMR Experiments

A series of squaric acid amides (synthesized in 66–99% isolated yields) and a set of chiral aminoalcohols were comparatively studied as ligands in a model reaction of reduction of α-chloroacetophenone with BH₃•SMe₂. In all cases, the aminoalcohols demonstrated better efficiency (up to 94% ee), while only poor asymmetric induction was achieved with the corresponding squaramides. A mechanistic insight on the in situ formation and stability at room temperature of intermediates generated from ligands and borane as possible precursors of the oxazaborolidine-based catalytic system has been obtained by ¹H DOSY and multinuclear 1D and 2D (¹H, ^10/11B, ¹³C, ¹⁵N) NMR spectroscopy of equimolar mixtures of borane and selected ligands. These results contribute to better understanding the complexity of the processes occurring in the reaction mixture prior to the possible oxazaborolidine formation, which play a crucial role on the degree of enantioselectivity achieved in the borane reduction of α-chloroacetophenone.     

Bifocal-polarization holographic lens

We present a holographic lens with novel features recorded in an azopolymer film. Two holographic modulations, bulk birefringence and surface relief, are induced in the medium at the same time. The resultant holographic element has two focal planes, and the polarization of light in the focal points depends on the polarization of the incident light. Applications of this device for writing-reading information in two planes simultaneously or separately are described.     

Integrity of endothelium in cryopreserved human cornea

The aim of the present study was to elaborate an optimal method for cryopreservation of human donor cornea for transplantation and to follow the morphological changes in the structure of the endothelial cell layer using scanning electron microscopy (SEM). Sixteen groups, with four donor cornea each, were cryopreserved at cooling rates of 1 degree C per min and 5 degree C per min. Four cryoprotectants (glycerol, dimethyl sulfoxide, 1,2-propanediol, polyethylene glycol-400) in two concentrations (5% and 10% v/v) were prepared on the bases of medium Optisol GS supplied with 20% v/v human serum albumin. Four additional human cornea were used as controls. Endothelial cell recovery of the cornea after thawing and 24 hours culture, was calculated as a percent of the preserved recovered cells. Sufficient recovery of the endothelial cell layer, making the cornea suitable for transplantation was obtained using the cryoprotectants dimethyl sulfoxide and especially polyethylene glycol-400.     

Some examples on the use of atomic emission spectral analysis in analytical control of the preparation of oxide single crystals

The application of atomic emission spectrometric methods (AES) to the different stages of preparation of white sapphire and neodymium doped yttrium-aluminium garnet (Y₃Al₅O₁₂ : Nd³⁺) single crystals is discussed. Optimum conditions for d.c. arc analysis of NH₄Al(SO₄)₂·12H₂O and Al₂O₃ were established and the detection limits for impurities were determined. The applicability of laser spectral microanalysis for monitoring the distribution of neodymium in the single crystals is shown.