Some global results for eigenvalue problems governed by a variational inequality

In this paper, we use the Leray-Schauder degree theory to obtain some information about the structure of the solution set of a large class of eigenvalue problems governed by a variational inequality. Applications are given to the unilateral postbuckling of a thin elastic plate.     

H‐self‐adjoint matrices. Application to radiosity

In computer graphics, in the radiosity context, a linear system Φx=b must be solved and there exists a diagonal positive matrix H such that H Φ is symmetric. In this article, we extend this property to complex matrices: we are interested in matrices which lead to Hermitian matrices under premultiplication by a Hermitian positive‐definite matrix H. We shall prove that these matrices are self‐adjoint with respect to a particular innerproduct defined on ?ⁿ. As a result, like Hermitian matrices, they have real eigenvalues and they are diagonalizable. We shall also show how to extend the Courant–Fisher theorem to this class of matrices. Finally, we shall give a new preconditioning matrix which really improves the convergence speed of the conjugate gradient method used for solving the radiosity problem. Copyright © 2002 John Wiley & Sons, Ltd.     

Universal ZN-graded differential calculus

We investigate the propeties of differential algebras generated by an operator d satisfying the property d^N = 0 instead of d² = 0 as in the usual case. Several examples of realizations of such differential algebras are given, either in the context of Z_N-graded N × N matrix algebras, or as a generalized differential calculus on manifolds.     

Synthesis of new 7-aminosterol squalamine analogues with high antimicrobial activities through a stereoselective titanium reductive amination reaction

A series of 7-amino- and polyaminosterol analogues of squalamine and trodusquemine were synthesized involving a new stereoselective titanium reductive amination reaction in high chemical yields of up to 95% in numerous cases. These derivatives were evaluated for their in vitro antimicrobial properties against human pathogens. All the compounds present excellent activities against Gram-positive bacteria exhibiting similar results against Staphylococcus aureus and Streptococcus faecalis with minimum inhibitory concentrations (MICs) varying from 2.5 to 10 μg/mL. Numerous derivatives possess also MICs against Gram-negative Escherichia coli bacteria (MICs varying from 2.5 to 10 μg/mL) suggesting that nature of the amino group attached to the sterol moiety plays an important role on the activities of such products.     

Discontinuity in decision-making when objectives conflict: a military command decision case study

In previous work, we considered the representation of human decision-making processes in closed-form simulation models of conflict. An important element of this representation is the rapid planning process that embodies the processing of information for situation assessment to support a course of action decision (eg in a military headquarters). The application of this work is in support of operational analysis models for defence procurement and balance of investment. This paper describes the application of non-linear multi-attribute utility theory in conflict scenarios in order to extend the representation of the rapid planning process to account for a wider set of subjective attributes of the decision-maker. The results show, through examination of experimental data, that decision-making can be modelled through a particular class of utility functions. These utilities embody a geometry which allows us to classify the types of decision being made when there are conflicting objectives and when decision-makers adopt very different and subjective appraisals of constraints and beliefs in outcome. The experimental results help to demonstrate that the subjective nature of the situation assessment, and the personality, training, experience and history of the decision-maker are central to the functional representations. This paper presents a way to capture this deeper representation of human decision-making in a way that is potentially useful for quantitative modelling using the rapid planning process as a basis.     

Towards a fully optimised organic LED device: Analysis of surface synthesis using coupling reactions by ToF-SIMS

Time-of-flight secondary ion mass spectrometry (ToF-SIMS) and polarisation-modulation reflection-absorption infrared spectroscopy (PM-RAIRS) have been used to monitor the surface synthesis of self-assembled aromatic π-conjugated molecular wires on gold substrates as a step towards a novel structure for organic electroluminescent devices (OLEDs). The wires have been synthesised using a series of Schiff's base coupling reactions in solution on a self-assembled monolayer of an aromatic thiolate anchor. ToF-SIMS and PM-RAIRS measurements have demonstrated that: (i) the anchor molecules self-assemble at the gold surface, (ii) the anchor molecules selectively react through imino coupling reactions with additional wire units with high efficiency and (iii) the wire-like structure is predominantly orientated normal to the surface.     

ARXPS-analysis and morphology of sputtered nanocrystalline TiC/SiC coatings

ARXPS (angle resolved X-ray photoelectron spectroscopy) measurements are used to obtain informations about surfaces and grain boundaries. Data acquired from nanocrystalline carbidic hard coatings have been employed to establish structural models. Magnetron-sputtered coatings of TiC, SiC and TiC/SiC were examined. In such coatings, partly defective TiC nanocrystallites are surrounded by interfacial carbide. This excess carbon shows a binding state similar to that of doped graphite or fullerenes. X-ray amorphous SiC is found in the residue. On top of sputtered SiC coatings, less oxide and graphite is found as compared to TiC/SiC or TiC coatings.