Asymptotic stability criteria for linear systems of difference-differential equations of neutral type and their discrete analogues

Electrical networks containing lossless transmission lines are often modeled by difference-differential equations of neutral type. This paper finds sufficient conditions for asymptotic stability for linear systems of these equations. Also given is a modification of the direct method of Liapunov for difference equations. This method is applied to finding asymptotic stability criteria for the discrete analogs of the linear system of difference-differential equations.     

A Liapunov functional for a matrix difference-differential equation

A quadratic positive definite functional that yields necessary and sufficient conditions for the asymptotic stability of the solutions of the matrix difference-differential equation $\text{x}\text{?}\text{(t) = Ax(t) + Bx(t ? τ)}$ is constructed and its structure is analyzed. This functional, a Liapunov functional, provides the best possible estimate for the rates of growth or decay of the solutions of this equation. The functional obtained, and its method of construction, are natural generalizations of the same problem for ordinary differential equations, and this relationship is emphasized. An example illustrates the applicability of the results obtained.     

A multicommuted flow system with solenoid micro-pumps for paraquat determination in natural waters

A flow system designed with solenoid micro-pumps is proposed for the determination of paraquat in natural waters. The procedure involves the reaction of paraquat with dehydroascorbic acid followed by spectrophotometric measurements. The proposed procedure minimizes the main drawbacks related to the standard chromatographic procedure and to flow analysis and manual methods with spectrophotometric detection based on the reaction with sodium dithionite, i.e. high solvent consumption and waste generation and low sampling rate for chromatography and high instability of the reagent in the spectrophotometric procedures. A home-made 10-cm optical-path flow cell was employed for improving sensitivity and detection limit. Linear response was observed for paraquat concentrations in the range 0.10–5.0 mg L⁻¹. The detection limit (99.7% confidence level), sampling rate and coefficient of variation (n = 10) were estimated as 22 μg L⁻¹, 63 measurements per hour and 1.0%, respectively. Results of determination of paraquat in natural water samples were in agreement with those achieved by the chromatographic reference procedure at the 95% confidence level.     

Infrared spectra of the WH4(H2)4 complex in solid hydrogen

The codeposition of laser-ablated tungsten atoms with neat hydrogen at 4 K forms a single major product with a broad 2500 cm(-1) and sharp 1860, 1830, 1782, 1008, 551, and 437 cm(-1) absorptions, which are assigned to the WH4(H2)4 complex on the basis of isotopic shifts and agreement with isotopic frequencies calculated by density functional theory. This D2d structured complex was computed earlier to form exothermically from W atoms and hydrogen molecules. Annealing the matrix allows hydrogen to evaporate and the complex to aggregate and ultimately to decompose. Comparison of the H-H stretching mode at 2500 cm(-1) and the W-H2 stretching mode at 1782 cm(-1) with 2690 and 1570 cm(-1) values for the Kubas complex W(CO)3(PR3)2(H2) suggests that the present physically stable WH4(H2)4 complex has more strongly bound dihydrogen ligands. Our CASPT2 calculations suggest a 15 kcal/mol average binding energy per dihydrogen molecule in the WH4(H2)4 complex.     

Isotope dilution quantification of ultratrace gamma-glutamyl-Se-methylselenocysteine species using HPLC with enhanced ICP–MS detection by ultrasonic nebulisation or carbon-loaded plasma

A method for the accurate determination of ultratrace selenium species of relevance to cancer research, such as gamma-glutamyl-Se-methylselenocysteine (γ-glutamyl-SeMC), using species-specific double isotope dilution analysis (IDA) with HPLC–ICP–MS is reported for the first time. The ⁷⁷Se-enriched γ-glutamyl-SeMC spike was produced in-house by collecting the fraction at the retention time of the γ-glutamyl-SeMC peak from a chromatographed aqueous extract of ⁷⁷Se-enriched yeast, pooling the collected fractions and freeze-drying the homogenate. The Se content of this spike was characterised using reverse isotope dilution mass spectrometry (IDMS) and the isotopic composition of this spike was checked prior to quantification of the natural abundance dipeptide species in garlic using speciated IDA. The extraction of the γ-glutamyl-SeMC species in water was performed in a sonication bath for 2 h after adding an appropriate quantity of ⁷⁷Se-enriched γ-glutamyl-SeMC to 50 mg of garlic to give optimal ⁷⁸Se/⁷⁷Se and ⁸²Se/⁷⁷Se ratios of 1.5 and 0.6, respectively. The effect of ultrasonic nebulisation, in comparison with the loading of the ICP with carbon (through the addition of methane gas on-line), on the detection of Se associated with γ-glutamyl-SeMC using collision/reaction cell ICP–MS with hydrogen as collision gas was investigated. Sensitivity enhancements of approximately fourfold and twofold were achieved using USN and methane mixed plasma, respectively, in comparison with conventional nebulisation and conventional Ar ICP–MS. However, an approximately twofold improvement in the detection limit was achieved using both approaches (42 ng kg⁻¹ for ⁷⁸Se using peak height measurements). The use of species-specific IDMS enabled quantification of the dipeptide species at ng g⁻¹ levels (603 ng g⁻¹ Se) in the complex food matrix with a relative standard deviation (RSD, n = 4) of 4.5%, which was approximately half that obtained using standard addition as a confirmatory technique. Furthermore, good agreement was found between the γ-glutamyl-SeMC species concentrations obtained using both calibration methods.     

Application of a Reflectance Confocal Microscopy Imaging Analysis Score for the Evaluation of Non-Melanogenic Changes in Male Photoaged Skin

The photoaging process is characterized by skin changes due to ultraviolet radiation exposure and is the principal environmental factor affecting skin aging. Reflectance confocal microscopy permits noninvasive skin imaging to understand how the photoaging process may change skin. Since men do not habitually use sunscreen, the application of skin imaging techniques is important to understand the influence of sunlight on their skin health. The aim of this study was to develop a score based on RCM imaging analyses to evaluate the morphological and structural changes in the photoaged skin according to literature data. The score was applied in order to determine possible correlations between chronological aging and sunscreen use behavior among men. Thus, 40 men aged 18 to 50 years were recruited, images from the frontal region of their skin were obtained and the score was applied. It was observed that habits are more important than age for the skin photoaging process. Men with photoprotection habits showed overall better skin morphological and structural characteristics regardless of age, demonstrating that sun protection behavior is a major key factor in the understanding of photoaging, so that men should be encouraged to start the use of cosmetic products and perform self-care.     

The Electronic Structure of the Al3− Anion: Is it Aromatic?

Multiconfigurational high‐level electronic structure calculations show that the ${{\rm Al}{{- \hfill \atop 3\hfill}}}$ ring‐like cluster anion has three close low‐lying electronic states of different spin, all of them having strong multiconfigurational character. The aromaticity of the cluster has, therefore, been studied by means of total electron delocalization and normalized multicenter electron delocalization indices evaluated from the multiconfigurational wave functions of each state. The lowest‐lying singlet and triplet states are found to be highly aromatic, whereas the next lowest‐lying state, the quintet state, has much less, though non‐negligible, aromatic character.