Hawking radiation by Kerr black holes and conformal symmetry

The exponential blueshift associated with the event horizon of a black hole makes conformal symmetry play a fundamental role in accounting for its thermal properties. Using a derivation based on two-point functions, we show that the full spectrum of thermal radiation of scalar particles by Kerr black holes can be explicitly derived on the basis of a conformal symmetry arising in the wave equation near the horizon. The simplicity of our approach emphasizes the depth of the connection between conformal symmetry and black hole radiance.     

Null decomposition of trees

Let $T$ be a tree. We show that the null space of the adjacency matrix of $T$ has relevant information about the structure of $T$. We introduce the Null Decomposition of trees, which is a decomposition into two different types of trees: N-trees and S-trees. N-trees are the trees that have a unique maximum (perfect) matching. S-trees are the trees with a unique maximum independent set. We obtain formulas for the independence number and the matching number of a tree using this decomposition. We also show how the number of maximum matchings and the number of maximum independent sets in a tree are related to its null decomposition.     

Linear attraction in quasi-linear difference systems

The equivalence and asymptotic equivalence between the solutions of a linear difference system and some families of quasi-linear ones are studied by using a Lipschitz component-wise condition combined with a spectrally small dichotomy, which is introduced. The equivalence is described by a homeomorphism and the results also include unbounded solutions. The results show the vectorial attractivity of the solutions of the linear part.     

Two hyperfinite constructions of the brownian bridge

Infinitesimal Analysis is used to give two constructions of the brownian bridge process. In the first construction a hyperfinite tied down random walk is used and a brownian bridge is obtained via the standard part map. As a consequence it is shown that the brownian bridge is the weak limit of a sequence of normalized tied down random walks. The second construction is based on a hyperfinite uniform empirical process. This construction gives an almost trivial proof of Donsker's Invariance Principle for the uniform empirical process     

Macro-Hybrid Variational Formulations of Constrained Boundary Value Problems

In the context of convex analysis, macro-hybrid variational formulations of constrained boundary value problems are presented. Monotone mixed variational inclusions are macro-hybridized on the basis of nonoverlapping domain decompositions, and corresponding three-field versions are derived. Then, for regularization purposes, augmented formulations are established via preconditioned exact penalizations and expressed in terms of proximation operators. Optimization interpretations are given for potential problems, recovering the classic two- and three-field augmented Lagrangian formulations. Furthermore, associated parallel two- and three-field proximal-point algorithms are discussed for numerical resolution of finite element discretizations. Applications to dual mixed variational formulations of problems from mechanics illustrate the theory.     

Molecular Scaffolds as Double‐Targeting Agents For the Diagnosis and Treatment of Neuroblastoma

The selective delivery of therapeutic and imaging agents to tumoral cells has been postulated as one of the most important challenges in the nanomedicine field. Meta‐iodobenzilguanidine (MIBG) is widely used for the diagnosis of neuroblastoma (NB) due to its strong affinity for the norepinephrine transporter (NET), usually overexpressed on the membrane of malignant cells. Herein, a family of novel Y‐shaped scaffolds has been synthesized, which have structural analogues of MIBG covalently attached at each end of the Y‐structure. The cellular uptake capacity of these double‐targeting ligands has been evaluated in vitro and in vivo, yielding one specific Y‐shaped structure that is able to be engulfed by the malignant cells, and accumulates in the tumoral tissue, at significantly higher levels than the structure containing only one single targeting agent. This Y‐shaped ligand can provide a powerful tool for the current treatment and diagnosis of this disease.     

Quantum parallelism as a tool for ensemble spin dynamics calculations

Efficient simulations of quantum evolutions of spin-1/2 systems are relevant for ensemble quantum computation as well as in typical NMR experiments. We propose an efficient method to calculate the dynamics of an observable provided that the initial excitation is "local." It resorts to a single entangled pure initial state built as a superposition, with random phases, of the pure elements that compose the mixture. This ensures self-averaging of any observable, drastically reducing the calculation time. The procedure is tested for two representative systems: a spin star (cluster with random long range interactions) and a spin ladder.     

New palladium (II) complexes containing phosphine‐nitrogen ligands and their use as catalysts in aminocarbonylation reaction

Aminocarbonylation of aryl halides, homogeneously catalysed by palladium, is an efficient method that can be employed for obtaining amides for pharmaceutical and synthetic applications. In this work, palladium (II) complexes containing P^N ligands were studied as catalysts in the aminocarbonylation of iodobenzene in the presence of diethylamine. Two types of systems were used: a palladium (II) complex formed in situ; and one prepared prior to the catalytic reaction. In general, the palladium complexes studied achieved high conversions in an average reaction time of less than 2 hr, which is less than that for the standard system (Pd (II)/PPh₃) used. The pre‐synthesized complexes were faster than their in situ counterparts, as the latter require an induction time to form the Pd/P^N species. The structure and electronic properties of the ligand P^N can influence both the activity and the selectivity of the reaction, stabilizing the acyl‐palladium intermediates formed in a better manner.