An apparatus for studying momentum-resolved electron-impact dissociative and non-dissociative ionisation

A spectrometer for recoil ion momentum measurements has been built for studying electron impact ionisation and dissociation of molecules. The apparatus is described in detail, highlighting its capabilities, as well as differences in design from the ones already in use elsewhere. Momentum spectra of ions resulting from 1300 eV electron impact on CO₂ are presented. We observe a broad momentum distribution for the dissociative ionisation reaction leading to the formation of C⁺, and two momentum groups in the CO⁺ and O⁺ channel. By recording multiple ions arising from the same dissociative ionisation event, we also demonstrate the formation of fragment pairs O⁺:CO⁺, C⁺:O⁺, and O⁺:O⁺.     

Perturbation of eigenvalues of matrix pencils and the optimal assignment problem

We extend the perturbation theory of Vi?ik, Ljusternik and Lidski?? to the case of eigenvalues of matrix pencils. This extension allows us to solve certain degenerate cases of this theory. We show that the first order asymptotics of the eigenvalues of a perturbed matrix pencil can be computed generically by methods of min-plus algebra and optimal assignment algorithms. We illustrate this result by discussing a singular perturbation problem considered by Najman. To cite this article: M. Akian et al., C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Self-Assembled Amino Acid Microstructures as Biocompatible Physically Unclonable Functions (BPUFs) for Authentication of Therapeutically Relevant Hydrogels

Counterfeited biomedical products result in significant economic losses and pose a public health hazard for over a million people yearly. Hydrogels, a class of biomedical products, are being investigated as alternatives to conventional biomedical products and are equally susceptible to counterfeiting. Here, a biocompatible, physically unclonable function (BPUF) to verify the authenticity of therapeutically relevant hydrogels are developed. The principle of BPUF relies on the self-assembly of tyrosine into fibril-like structures which are incorporated into therapeutically relevant hydrogels resulting in their random dispersion. This unclonable arrangement leads to distinctive optical micrographs captured using an optical microscope. These optical micrographs are transformed into a unique security code through cryptographic techniques which are then used to authenticate the hydrogel. The temporal stability of the BPUFs are demonstrated and additionally, exploit the dissolution propensity of the structures upon exposure to an adulterant to identify the tampering of the hydrogel. Finally, a platform to demonstrate the translational potential of this technology in validating and detecting tampering of therapeutically relevant hydrogels is developed. The potential of BPUFs to combat hydrogel counterfeiting is exemplified by its simplicity in production, ease of use, biocompatibility, and cost-effectiveness.     

Research problem

This section appears from time to time. Contributions are invited, and should be submitted to R C. Thompson, Mathematics Department. University of California, Santa Barbara, CA93106-3080, USA.     

Effect of high pressure on the nematic–isotropic transition in aerosil–liquid crystal composites

We report the first high pressure investigations of the nematic–isotropic transition in the composites of a liquid crystal compound with hydrophilic aerosil particles. The low concentrations of the aerosil particles used create soft gels of the composites. As expected T_N–Iso, the nematic–isotropic transition at room pressure exhibits a non-monotonic variation with increasing aerosil concentration. This non-monotonic behaviour is seen in the isobaric scans over the wide range of pressures studied, and its “magnitude” is dependent on the pressure applied. The surprising result of the present investigations on these nanocolloidal systems is that the slope of the pressure–temperature boundary also exhibits a non-monotonic dependence with the aerosil concentration, which qualitatively is similar to that of the transition temperature variation. Employing the transition enthalpy values determined at room pressure using differential scanning calorimetric scans collected at low heating rates, we calculate the transition volume dependence on the aerosil concentration. The study adds a new dimension, namely, the influence of pressure on liquid crystalline transitions in restricted geometries.     

Rank preservers of matrices over max algebra

The max algebra consists of the nonnegative real numbers equipped with two binary operations, maximization and multiplication. We consider the semimodules over max algebra and study the properties of the weak basis and weak dimension of the semi-modules. Moreover, we obtain the characterizations of those linear operators that preserve rank of matrices over max-algebra.     

On functions that preserve M-matrices and inverse M-matrices

In earlier works, authors such as Varga, Micchelli and Willoughby, Ando, and Fiedler and Schneider have studied and characterized functions which preserve the M-matrices or some subclasses of the M-matrices, such as the Stieltjes matrices. Here we characterize functions which either preserve the inverse M-matrices or map the inverse M-matrices to the M-matrices. In one of our results we employ the theory of Pick functions to show that if A and B are inverse M-matrices such that B ^?1 ≤ A ^?1, then (B+tI)?1 ≤ (A+tI)?1, for all t?≥?0.     

Purely sequential bounded-risk point estimation of the negative binomial mean under various loss functions: one-sample problem

A negative binomial (NB) distribution is useful to model over-dispersed count data arising from agriculture, health, and pest control. We design purely sequential bounded-risk methodologies to estimate an unknown NB mean \(\mu (>0)\) under different forms of loss functions including customary and modified Linex loss as well as squared error loss. We handle situations when the thatch parameter \(\tau (>0)\) may be assumed known or unknown. Our proposed methodologies are shown to satisfy properties including first-order asymptotic efficiency and first-order asymptotic risk efficiency. Summaries are provided from extensive sets of simulations showing encouraging performances of the proposed methodologies for small and moderate sample sizes. We follow with illustrations obtained by implementing estimation strategies using real data from statistical ecology: (1) weed count data of different species from a field in Netherlands and (2) count data of migrating woodlarks at the Hanko bird sanctuary in Finland.     

Studies on Morphology and Conductivity of Poly (N-methyl aniline) Nanoparticles Prepared in Nonstirred Reaction Medium

Summary: Polyaniline has elicited the most interest due to its wide range of applications in many fields. However insolubility and infusibility are the main factors that affect the application of polyaniline. We have studied and worked on the synthesis of dispersible polyaniline and the results are described here. Poly (N-methyl aniline) PNMANI nanoparticles with controllable morphology and sizes were prepared by removing a routine operation stirring from the conventional method of synthesis and using acrylic acid as a soft template. It is found that polymer formed in the non-stirring experiment predominantly produces highly dispersible, smooth nanoparticles with controllable morphology and sizes. These nanoparticles have large surface area and thereby high conductivity. Mechanism for generation of well dispersed and smooth nanoparticles is supported by homogeneous nucleation of polymer nanoparticles in non stirred experiments and the use of acrylic acid as a soft template. In the case of the experiment where the reaction mixture was stirred at 1000 RPM comparatively coral-like, granular and uncontrolled polymer particles were formed. These coral like granular particles were having comparatively small surface area and less conductivity. Conductivity measurements, UV- visible, XRD, FTIR spectroscopy and SEM were performed to characterize the product. This method can be used to synthesize highly conductive polymers in minimum time and bulk quantity.