Complexation of Secondary Amides to Chromium(III): the X-Ray Structure of a Molecule with Two Modes of Monodentate Organic Amide Co-ordination

The X-ray crystal structure of the dimer [Cr{H(chba-Et)}(py)_2]_(2)·2py [H_(4)(chba-Et)= 1,2-bis(3,5-dichloro-2-hydroxybenzamido) ethane, py = pyridine] establishes, for the first time, the existence of N-co-ordination of an organic amide to Cr^III, the N-atom and carbonyl O-atom of two separate amide groups being co-ordinated to each Cr^III centre [Cr–N 2.030(6) and Cr–O 1.976(5)Å]; the potentially tetra-anionic chelating ligand leads to a variety of co-ordination modes

Mixed spatially varying L2L^2-BV regularization of inverse ill-posed problems

Several generalizations of the traditional Tikhonov-Phillips regularization method have been proposed during the last two decades. Many of these generalizations are based upon inducing stability throughout the use of different penalizers which allow the capturing of diverse properties of the exact solution (e.g. edges, discontinuities, borders, etc.). However, in some problems in which it is known that the regularity of the exact solution is heterogeneous and/or anisotropic, it is reasonable to think that a much better option could be the simultaneous use of two or more penalizers of different nature. Such is the case, for instance, in some image restoration problems in which preservation of edges, borders or discontinuities is an important matter. In this work we present some results on the simultaneous use of penalizers of $L^2$ and of bounded variation (BV) type. For particular cases, existence and uniqueness results are proved. Open problems are discussed and results to signal restoration problems are presented.Comment: 18 pages, 12 figure

Global Saturation of Regularization Methods for Inverse Ill-Posed Problems

In this article the concept of saturation of an arbitrary regularization method is formalized based upon the original idea of saturation for spectral regularization methods introduced by A. Neubauer in 1994. Necessary and sufficient conditions for a regularization method to have global saturation are provided. It is shown that for a method to have global saturation the total error must be optimal in two senses, namely as optimal order of convergence over a certain set which at the same time, must be optimal (in a very precise sense) with respect to the error. Finally, two converse results are proved and the theory is applied to find sufficient conditions which ensure the existence of global saturation for spectral methods with classical qualification of finite positive order and for methods with maximal qualification. Finally, several examples of regularization methods possessing global saturation are shown.Comment: 29 page

Generalized Qualification and Qualification Levels for Spectral Regularization Methods

The concept of qualification for spectral regularization methods for inverse ill-posed problems is strongly associated to the optimal order of convergence of the regularization error. In this article, the definition of qualification is extended and three different levels are introduced: weak, strong and optimal. It is shown that the weak qualification extends the definition introduced by Mathe and Pereverzev in 2003, mainly in the sense that the functions associated to orders of convergence and source sets need not be the same. It is shown that certain methods possessing infinite classical qualification, e.g. truncated singular value decomposition (TSVD), Landweber's method and Showalter's method, also have generalized qualification leading to an optimal order of convergence of the regularization error. Sufficient conditions for a SRM to have weak qualification are provided and necessary and sufficient conditions for a given order of convergence to be strong or optimal qualification are found. Examples of all three qualification levels are provided and the relationships between them as well as with the classical concept of qualification and the qualification introduced by Mathe and Perevezev are shown. In particular, spectral regularization methods having extended qualification in each one of the three levels and having zero or infinite classical qualification are presented. Finally several implications of this theory in the context of orders of convergence, converse results and maximal source sets for inverse ill-posed problems, are shown.Comment: 20 pages, 1 figur

Program Evaluation of Clark County Department of Family Services, Parenting Project

The Clark County Department of Family Services, Parenting Project, hereinafter referred to as Parenting Project, partnered with the University of Nevada, Las Vegas, School of Environmental and Public Affairs to participate in a program evaluation. The evaluation will serve as a tool to determine the effectiveness of the services delivered to the community by Parenting Project and to aid them in overall program improvement and implementation. This Program Evaluation focuses on two of the six core parenting classes that are currently offered free to the public, more specifically the Nurturing Parents and Families program and the ABC’s of Parenting. The identified programs utilize a pre-posttest inventory known as the Adult / Adolescent Parenting Inventory (AAPI-2). The AAPI-2 measures the risk of abusive parenting behaviors and is collected from each program participant. Data collected from the years 2005 - 2014 were used in the evaluation of the two programs