Setting local rank constraints by orthogonal projections for image resolution analysis: Application to the determination of a low dose pharmaceutical compound

Raman chemical imaging provides chemical and spatial information about pharmaceutical drug product. By using resolution methods on acquired spectra, the objective is to calculate pure spectra and distribution maps of image compounds. With multivariate curve resolution-alternating least squares, constraints are used to improve the performance of the resolution and to decrease the ambiguity linked to the final solution. Non negativity and spatial local rank constraints have been identified as the most powerful constraints to be used.     

An approach to triquinane synthesis using the Pauson-Khand reaction

Tricyclic skeletons have been generated from acyclic enyne precursors by using an intramolecular Pauson-Khand reaction in combination with aldol, Michael and alkylation reactions.     

The Kissing Triangles: The Aesthetics of Mathematical Discovery

Papert's (1978) appeal to reconsider the power and possibilities of the aesthetic in mathematics learning is often ignored in mathematics education research. This paper begins with the premise, put forth by Dewey (1934), that the aesthetic structures many dimensions of inquiry and experience. In the same way that using particular paintings, musical compositions, or even everyday experiences has been instrumental to attempts by philosophers to understand the aesthetic dimensions of meaning and experience in artistic domains, I propose that analysing a particular encounter with mathematics may help reveal the nature and role of the often nebulous responses of elegance, beauty, and `fit' to which mathematicians lay claim in their mathematical activity. To achieve this, I draw on and adapt the defining features of the aesthetic character of experience set forth by the aesthetician Beardsley (1982). This, in turn, sheds light on the role thataesthetics can play in mathematical inquiry and experience, and provides initial categories and conjectures that can be used to investigate the potential roles of aesthetics in mathematics learning contexts.This revised version was published online in September 2005 with corrections to the Cover Date.     

Acetylene weak bands at 2.5 μm from intracavity Cr:ZnSe laser absorption observed with time-resolved Fourier transform spectroscopy

The spectral dynamics of a mid-infrared multimode Cr(2+):ZnSe laser located in a vacuum sealed chamber containing acetylene at low pressure is analyzed by a stepping-mode high-resolution time-resolved Fourier transform interferometer. Doppler-limited absorption spectra of C(2)H(2) in natural isotopic abundance are recorded around 4000 cm(-1) with kilometric absorption path lengths and sensitivities better than 3 10(-8) cm(-1). Two cold bands are newly identified and assigned to the ν(1)+ν(4) (1) and ν(3)+ν(5) (1) transitions of (12)C(13)CH(2). The ν(1)+ν(5) (1) band of (12)C(2)HD and fourteen (12)C(2)H(2) bands are observed, among which for the first time ν(2)+2ν(4) (2)+ν(5) (-1).     

On‐line Determination of Particle Size Distributions in Flowing Dispersions

Emulsions are of great importance to industry. They are involved in many engineering operations, including chemical reactions, extraction, emulsification and suspension polymerization, etc. However, an important problem for these processes is how to control the size distribution of the dispersed phase. Indeed, off‐line analysis of the emulsion may generate uncertainties due to sampling and dilution of the product, which are likely to change the dispersion state and physico‐chemical properties. In this work, an on‐line optical method is proposed to characterize dispersed media in real flowing conditions. This method is based on the time‐analysis of back‐scattered light fluctuations. The present paper deals with the development of this method and its application to dispersions of alumina in water. The results obtained with the on‐line optical method are compared with those acquired by classical laser light scattering and microscopy.     

N. Charton,A. Feldermann,A. Theis,M. H. Stenzel,T. P. Davis,C. Barner‐Kowollik,Initiator efficiency of 2,2′‐azobis(isobutyronitrile) in bulk dodecyl acrylate free‐radical polymerizations over a wide conversion and molecular weight range (2004) 42(20) 5170–5179

The original article to which this Erratum refers was published in J Polym Sci Part A: Polym Chem (2004) 42(20) 5170–5179. No abstract.     

Multiscale variety in complex systems

The Law of Requisite Variety is a mathematical theorem relating the number of control states of a system to the number of variations in control that is necessary for effective response. The Law of Requisite Variety does not consider the components of a system and how they must act together to respond effectively. Here we consider the additional requirement of scale of response and the effect of coordinated versus uncoordinated response as a key attribute of complex systems. The components of a system perform a task, with a number of such components needed to act in concert to perform subtasks. We apply the resulting generalization—a Multiscale Law of Requisite Variety—to understanding effective function of complex biological and social systems. This allows us to formalize an understanding of the limitations of hierarchical control structures and the inadequacy of central control and planning in the solution of many complex social problems and the functioning of complex social organizations, e.g., the military, healthcare, and education systems. © 2004 Wiley Periodicals, Inc. Complexity 9: 37–45, 2004     

Existence results for some quasilinear parabolic problems

We first give an existence theorem, for some equations associated with Leray-Lions operators, assuming the existence of a subsolution smaller than a supersolution. Then we prove, with an additional hypothesis on the operator, that in the previous theorem, we can replace the subsolution by two subsolutions and the supersolution by two supersolutions. Finally, we deduce the existence of a smallest and a greatest solution.