Transience and recurrence of quantum Markov semigroups

 This article introduces a concept of transience and recurrence for a Quantum Markov Semigroup and explores its main properties via the associated potential. We show that an irreducible semigroup is either recurrent or transient and characterize transient semigroups by means of the existence of non trivial superharmonic operators. Received: 27 January 2003 / Revised version: 19 February 2003 / Published online: 12 May 2003 This research has been partially supported by the ``Cátedra Presidencial en Análisis Cualitativo de Sistemas Dinámicos Cuánticos', DIPUC, FONDECYT project 1030552, MIUR program ``Probabilità Quantistica e Applicazioni', 2003-2004 and MECESUP PUC 0103. Mathematics Subject Classification (2000): 60J45, 81S25, 60J99, 37A50, 47A40 Key words or phrases: Quantum Markov semigroups – Potential theory – Markov processes     

The uniqueness of Hering's translation plane of order 27

It is shown that the following conjecture of Kallaher and Ostrom [2] is correct: Hering's translation plane of order 27 is the only translation plane of odd dimension over its kernel which has a collineation group isomorphic to SL(2, w) with w prime to 5 and to the characteristic, and having no affine perspectivity.     

Possible origin of isotopic spin from extended conformal symmetry

In conformally covariant lagrangian density for conformal spinors interacting with tensor fields, the terms with Lorentz scalar-pseudoscalar bosons have a maximal internal symmetry su(2)_L⊕ su(2)_R⊕ u(1)_L⊕ u(1)_R and this internal algebra is Poincaré invariant; pion-nucleon Yukawa interaction is a particular case.     

Fundamental groupoids of digraphs and graphs

We introduce the notion of fundamental groupoid of a digraph and prove its basic properties. In particular, we obtain a product theorem and an analogue of the Van Kampen theorem. Considering the category of (undirected) graphs as the full subcategory of digraphs, we transfer the results to the category of graphs. As a corollary we obtain the corresponding results for the fundamental groups of digraphs and graphs. We give an application to graph coloring.     

Microwave-assisted regioselective cycloaddition reactions between 9-substituted anthracenes and levoglucosenone

The cycloaddition reactions of 9-substituted anthracenes and levoglucosenone were investigated under microwave irradiation and conventional heating conditions. Considering time, yields, and regioselectivity, microwave technology has proven to be an ideal tool to achieve this chemical transformation. [reaction: see text].     

Light-Based 3D Printing of Gelatin-Based Biomaterial Inks to Create a Physiologically Relevant In Vitro Fish Intestinal Model

To provide prominent accessibility of fishmeal to the European population, the currently available, time- and cost-extensive feeding trials, which evaluate fish feed, should be replaced. The current paper reports on the development of a novel 3D culture platform, mimicking the microenvironment of the intestinal mucosa in vitro. The key requirements of the model include sufficient permeability for nutrients and medium-size marker molecules (equilibrium within 24 h), suitable mechanical properties (G' < 10 kPa), and close morphological similarity to the intestinal architecture. To enable processability with light-based 3D printing, a gelatin-methacryloyl-aminoethyl-methacrylate-based biomaterial ink is developed and combined with Tween 20 as porogen to ensure sufficient permeability. To assess the permeability properties of the hydrogels, a static diffusion setup is utilized, indicating that the hydrogel constructs are permeable for a medium size marker molecule (FITC-dextran 4 kg mol⁻¹). Moreover, the mechanical evaluation through rheology evidence a physiologically relevant scaffold stiffness (G' = 4.83 ± 0.78 kPa). Digital light processing-based 3D printing of porogen-containing hydrogels results in the creation of constructs exhibiting a physiologically relevant microarchitecture as evidenced through cryo-scanning electron microscopy. Finally, the combination of the scaffolds with a novel rainbow trout (Oncorhynchus mykiss) intestinal epithelial cell line (RTdi-MI) evidence scaffold biocompatibility.     

Branching and Crosslinking in Coordination Terpolymerizations

A general kinetic method, based upon population balances of generating functions, is applied to the prediction of the microstructure and molecular size of non‐linear terpolymers obtained through the coordination polymerization of two monovinyl monomers and a non‐conjugated diene. A rather complex kinetic scheme involving crosslinking and long‐chain branching is considered. It is shown that even in these conditions it is possible to carry out the prediction of molecular size and mass distributions, sequence size distributions, and z‐average mean‐square radius of gyration of the polymers. The influence of some kinetic parameters on the properties of the products is studied, considering a homogeneous operation in a semi‐batch reactor. The used simulation method is able to predict these properties before and after gelation whenever it occurs.

     

Generalized non-Markovian optical Bloch equations

By considering single chromophore systems whose radiative decay can be written in terms of a nonlocal Lindblad-type evolution, the authors extend the formalism of generalized optical Bloch equations [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] to non-Markovian dynamics. They demonstrate that photon statistical properties such as bunching and antibunching, as well as sub- and super-Poissonian photon statistics can be fitted in the context of non-Markovian dynamics. The nonlocal effects may arise due to the interaction with a complex structured environment. In this case, the photon statistics can be related with the parameters that define the microscopic system-environment interaction. Alternatively, the authors demonstrate that effective dynamics such as triplet blinking, where the system is coupled via incoherent transitions to an extra dark state, can also be worked out in terms of generalized non-Markovian optical Bloch equations. The corresponding memory contributions are mapped with those that arise from the microscopic approach.