Algebraic perturbation methods for the solution of singular linear systems

A singular matrix A is perturbed algebraically to obtain a nonsingular matrix B. Particular solutions of Ax=b can be found as unique solutions of Bx=d, where d is an algebraic perturbation of b. More specially, null vectors and generalized null vectors of A can be found as unique solutions of linear systems. It is shown also that B^?1AB^?1 is a generalized inverse of A.     

Deformation of gradient shape as a result of preferential adsorption of solvents in mixed mobile phases

Gradient elution has been studied in typical normal and reversed-phase systems. Deformations of gradient profiles have been evidenced as a result of preferential adsorption of modifiers of the mobile phase. This phenomenon was pronounced in the normal-phase system, for which gradient profiles deviated significantly from those programmed. This influenced the retention and shapes of band profiles of the eluting solute. Hence, in order to predict gradient propagation correctly the adsorption equilibrium of modifiers has been quantified. Moreover, at low modifier content, deformations of band profiles of the solute has been registered as a result of the competitive adsorption in the system solute-modifier. This effect has been predicted by a competitive adsorption model. For the reversed-phase systems the influence of the modifier adsorption on gradient propagation was insignificant for typical mobile phases investigated. Therefore, the work has been focused on gradient predictions in the normal-phase system.     

Approximating eigenfunctions of Fredholm operators in Banach spaces

A singular Fredholm operator A is perturbed by an operator of finite rank to obtain an invertible operator B. Theory previously developed for A and B in Hilbert spaces is extended here to Banach spaces. The operator B^?1 is used to construct independent elements in the null spaces N(A), N(A²),…, N(A^k), for some positive integer k, and a basis for N(A) and N(A²). The theory is used to compute approximations to eigenfunctions and generalized eigenfunctions of integral operators.     

The onset of coulomb explosions in polyatomic molecules

With the development of high intensity femtosecond lasers, the ionisation and dissociation dynamics of molecules has become an area of considerable interest. Using the technique of femtosecond laser mass spectrometry (FLMS), the molecules carbon disulphide, pyrimidine, toluene, cyclohexanone and benzaldehyde are studied with pulse widths of 50 fs in the near infrared (IR) wavelength region (790 nm). Results are presented and contrasted for laser beam intensities around 10(15) and 10(16) W cm(-2). For the lower intensities, the mass spectra yield dominant singly charged parent ions. Additionally, the appearance of doubly charged parent ions is evident for carbon disulphide, toluene and benzaldehyde with envelopes of doubly charged satellite species existing in these local regions. Carbon disulphide also reveals a small triply charged component. Such atomic-like features are thought to be a strong fingerprint of FLMS at these intensities. However, upon increasing the laser intensity to approximately 10(16) W cm(-2), parent ion dominance decreases and the appearance of multiply charged atomic species occurs, particularly carbon. This phenomenon has been attributed to Coulomb explosions in which the fast absorption of many photons may produce transient highly ionised parent species which can subsequently blow apart. Copyright 1999 John Wiley & Sons, Ltd.     

Uniform molecular analysis using femtosecond laser mass spectrometry

The potential of femtosecond laser time-of-flight mass spectrometry (FLMS) for uniform quantitative analysis of molecules has been investigated. Various samples of molecular gases and vapours have been studied, using ultra-fast ( approximately 50 fs) laser pulses with very high intensity (up to 1.6 x 10(16) Wcm(-2)) for non-resonant multiphoton ionisation/tunnel ionisation. Some of these molecules have high ionisation potentials, requiring up to ten photons for non-resonant ionisation. The relative sensitivity factors (RSF) have been determined as a function of the laser intensity and it has been demonstrated that for molecules with very different masses and ionisation potentials, uniform ionisation has been achieved at the highest laser intensities. Quantitative laser mass spectrometry of molecules is therefore a distinct possibility. Copyright 1999 John Wiley & Sons, Ltd.     

Efficient Extraction of Fermentation Inhibitors by Means of Green Hydrophobic Deep Eutectic Solvents

The methods for hydrogen yield efficiency improvements, the gaseous stream purification in gaseous biofuels generation, and the biomass pretreatment are considered as the main trends in research devoted to gaseous biofuel production. The environmental aspect related to the liquid stream purification arises. Moreover, the management of post-fermentation broth with the application of various biorefining techniques gains importance. Chemical compounds occurring in the exhausted liquid phase after biomass pretreatment and subsequent dark and photo fermentation processes are considered as value-added by products. The most valuable are furfural (FF), 5-hydroxymethylfurfural (HMF), and levulinic acid (LA). Enriching their solutions can be carried with the application of liquid–liquid extraction with the use of a suitable solvent. In these studies, hydrophobic deep eutectic solvents (DESs) were tested as extractants. The screening of 56 DESs was carried out using the Conductor-like Screening Model for Real Solvents (COSMO-RS). DESs which exposed the highest inhibitory effect on fermentation and negligible water solubility were prepared. The LA, FF, and HMF were analyzed using FT-IR and NMR spectroscopy. In addition, the basic physicochemical properties of DES were carefully studied. In the second part of the paper, deep eutectic solvents were used for the extraction of FF, LA, and HMF from post-fermentation broth (PFB). The main extraction parameters, i.e., temperature, pH, and DES: PFB volume ratio (V_DES:V_PFB), were optimized by means of a Box–Behnken design model. Two approaches have been proposed for extraction process. In the first approach, DES was used as a solvent. In the second, one of the DES components was added to the sample, and DES was generated in situ. To enhance the post-fermentation broth management, optimization of the parameters promoting HMF, FF, and LA extraction was carried under real conditions. Moreover, the antimicrobial effect of the extraction of FF, HMF, and LA was investigated to define the possibility of simultaneous separation of microbial parts and denatured peptides via precipitation.