Time operator for diffusion

Volume: 11 Issue: 4 Pages: 465-477 Published: MAR 2000 Times Cited: 9 References: 15 Citation MapCitation Map beta Abstract: We extend the concept of time operator for general semigroups and construct a non-self-adjoint time operator for the diffusion equation which is intertwined with the unilateral shift. We obtain the spectral resolution, the age eigenstates and a new shift representation of the solution of the diffusion equation. Based on previous work we obtain similarly a self-adjoint time operator for Relativistic Diffusion. (C) 2000 Elsevier Science Ltd. All rights reserved.

The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.

System oriented neural networks - Problem formulation, methodology and application

A novel methodology is proposed for the development of neural network models for complex engineering systems exhibiting nonlinearity. This method performs neural network modeling by first establishing some fundamental nonlinear functions from a priori engineering knowledge, which are then constructed and coded into appropriate chromosome representations. Given a suitable fitness function, using evolutionary approaches such as genetic algorithms, a population of chromosomes evolves for a certain number of generations to finally produce a neural network model best fitting the system data. The objective is to improve the transparency of the neural networks, i.e. to produce physically meaningful

Influence of Formulation Factors on PpIX Production and Photodynamic Action of Novel ALA-loaded Microparticles

A novel 5-aminolevulinic acid (ALA)-containing microparticulate system was produced recently, based on incorporation of ALA into particles prepared from a suppository base that maintains drug stability during storage and melts at skin temperature to release its drug payload. The novel particulate system was applied to the skin of living animals, followed by study of protoporphyrin IX (PpIX) production. The effect of formulating the microparticles in different vehicles was investigated and also the phototoxicity of the PpIX produced using a model tumour. Particles formulated in propylene glycol gels (10% w/w ALA loading) generated the highest peak PpIX fluorescence levels in normal mouse skin. Peak PpIX levels induced in skin overlying subcutaneously implanted WiDr tumours were significantly lower than in normal skin for both the 10% w/w ALA microparticles alone and the 10% w/w ALA microparticles in propylene glycol gels during continuous 12 h applications. Tumours not treated with photodynamic therapy continued to grow over the 17 days of the anti-tumour study. However, those treated with 12 h applications of either the 10% w/w ALA microparticles alone or the 10% w/w ALA microparticles in propylene glycol gel followed by a single laser irradiation showed no growth. The gel formulation performed slightly better once again, reducing the tumour growth rate by approximately 105%, compared with the 89% reduction achieved using particles alone. Following the promising results obtained in this study, work is now going on to prepare particle-loaded gels under GMP conditions with the aim of initiating an exploratory clinical trial.

Development of operator independent bone cement vacuum mixing system for joint replacement surgery,

(2006) Vol. 35 No. 8 317

Genetic programming based formulation for fresh and hardened properties of self-compacting concrete containing pulverised fuel ash

Self-compacting concrete (SCC) flows into place and around obstructions under its own weight to fill the formwork completely and self-compact without any segregation and blocking. Elimination of the need for compaction leads to better quality concrete and substantial improvement of working conditions. This investigation aimed to show possible applicability of genetic programming (GP) to model and formulate the fresh and hardened properties of self-compacting concrete (SCC) containing pulverised fuel ash (PFA) based on experimental data. Twenty-six mixes were made with 0.38 to 0.72 water-to-binder ratio (W/B), 183–317 kg/m³ of cement content, 29–261 kg/m³ of PFA, and 0 to 1% of superplasticizer, by mass of powder. Parameters of SCC mixes modelled by genetic programming were the slump flow, JRing combined to the Orimet, JRing combined to cone, and the compressive strength at 7, 28 and 90 days. GP is constructed of training and testing data using the experimental results obtained in this study. The results of genetic programming models are compared with experimental results and are found to be quite accurate. GP has showed a strong potential as a feasible tool for modelling the fresh properties and the compressive strength of SCC containing PFA and produced analytical prediction of these properties as a function as the mix ingredients. Results showed that the GP model thus developed is not only capable of accurately predicting the slump flow, JRing combined to the Orimet, JRing combined to cone, and the compressive strength used in the training process, but it can also effectively predict the above properties for new mixes designed within the practical range with the variation of mix ingredients.

The maximal C*-algebra of quotients as an operator bimodule

We establish a description of the maximal C*-algebra of quotients of a unital C*-algebra A as a direct limit of spaces of completely bounded bimodule homomorphisms from certain operator submodules of the Haagerup tensor product of A with itself labelled by the essential closed right ideals of A into A. In addition the invariance of the construction of the maximal C*-algebra of quotients under strong Morita equivalence is proved.

Multidimensional operator multipliers

We introduce multidimensional Schur multipliers and characterise them, generalising well-known results by Grothendieck and Peller. We define a multidimensional version of the two-dimensional operator multipliers studied recently by Kissin and Shulman. The multidimensional operator multipliers are defined as elements of the minimal tensor product of several C *-algebras satisfying certain boundedness conditions. In the case of commutative C*-algebras, the multidimensional operator multipliersreduce to continuousmul-tidimensional Schur multipliers. We show that the multiplierswith respect to some given representations of the corresponding C*-algebrasdo not change if the representations are replaced by approximately equivalent ones. We establish a non-commutative and multidimensional version of the characterisations by Grothendieck and Peller which shows that universal operator multipliers can be obtained ascertain weak limits of elements of the algebraic tensor product of the corresponding C *-algebras.

Compactness properties of operator multipliers

We continue the study of multidimensional operator multipliers initiated in~cite{jtt}. We introduce the notion of the symbol of an operator multiplier. We characterise completely compact operator multipliers in terms of their symbol as well as in terms of approximation by finite rank multipliers. We give sufficient conditions for the sets of compact and completely compact multipliers to coincide and characterise the cases where an operator multiplier in the minimal tensor product of two C*-algebras is automatically compact. We give a description of multilinear modular completely compact completely bounded maps defined on the direct product of finitely many copies of the C*-algebra of compact operators in terms of tensor products, generalising results of Saar