The non-self-adjointness of the radial momentum operator in n dimensions

The non self-adjointness of the radial momentum operator has been noted before by several authors, but the various proofs are incorrect. We give a rigorous proof that the $n$-dimensional radial momentum operator is not self- adjoint and has no self-adjoint extensions. The main idea of the proof is to show that this operator is unitarily equivalent to the momentum operator on $L^{2}[(0,\infty),dr]$ which is not self-adjoint and has no self-adjoint extensions.Comment: Some text and a reference adde

Dimension minimization of a quantum automaton

A new model of a Quantum Automaton (QA), working with qubits is proposed. The quantum states of the automaton can be pure or mixed and are represented by density operators. This is the appropriated approach to deal with measurements and dechorence. The linearity of a QA and of the partial trace super-operator, combined with the properties of invariant subspaces under unitary transformations, are used to minimize the dimension of the automaton and, consequently, the number of its working qubits. The results here developed are valid wether the state set of the QA is finite or not. There are two main results in this paper: 1) We show that the dimension reduction is possible whenever the unitary transformations, associated to each letter of the input alphabet, obey a set of conditions. 2) We develop an algorithm to find out the equivalent minimal QA and prove that its complexity is polynomial in its dimension and in the size of the input alphabet.Comment: 26 page

Elaboración del manual de sistema de gestión ambiental ISO 14001:2004 para una fábrica de etiquetas autoadhesivas

The current thesis talks about of the elaboration of a Manual for the implementation of the Environmental Management System (EMS) ISO 14001:2004, which was born from the necessity of the factory of SELF-ADHESIVE ETIQUETTES of a environmentally responsible production, so there is a process in order to implement in the company the necessary procedures for in the future, if the factory believes that is convenient, to reach the ISO 14001:2004 certification. For this, we drafted an environmental policy and objectives and goals and procedures and environmental management programs to be followed in this type of company, for its further development and implementation. This work presents the development of each step that need to be followed to develop a manual that allows the factory to control all the activities, through established procedures, to minimize the impacts that they have on the environment, supporting environmental protection and prevention of pollution in balance with the needs of the factory and its surroundings

Improvement on binding of chondroitin sulfate derivatives to midkine by increasing hydrophobicity

The interactions between chondroitin sulfate (CS) and a wide number of proteins modulate important biological processes. Here, the binding properties to midkine and pleiotrophin of sulfated, fully protected intermediates, typically obtained in the chemical synthesis of CS oligosaccharides, were tested for the first time. Using a fluorescence polarization competition experiment, we discovered that these synthetic precursors strongly bound these two closely related cytokines involved in cancer and inflammation. The relative binding affinities of these intermediates were significantly higher than those displayed by the corresponding fully deprotected oligosaccharides, indicating that the presence of hydrophobic protecting groups strongly enhanced the binding of CS-like derivatives to midkine. These compounds offer novel opportunities for the development of potent inhibitors/activators of CS-protein interactions with potential therapeutic applications.Ministerio de Economía y Competitividad CTQ2012-3260