Stability and periodicity in discrete delay equations

In this research we study the stability of the zero solution of delay difference equations and the existence of unique periodic solution by utilizing fixed point theory. Mainly, we are interested in the qualitative analysis of the complete delay difference equation

Δx(t)=−a(t)x(t−τ).     

Capillary zone electrophoresis of linear and branched oligosaccharides

The electrophoretic behavior of derivatized linear and branched oligosaccharides from various sources was examined in capillary zone electrophoresis with polyether-coated fused-silica capillaries. Two UV-absorbing (also fluorescent) derivatizing agents (2-amino-pyridine and 6-aminoquinoline) were utilized for the electrophoresis and sensitive dtection of neutral oligosaccharides, e.g., N-acetylchitooligosaccharides, high-mannose glycans and xyloglucan oligosaccharides. The oligosaccharides labelled with 6-aminoquinoline yielded eight times higher signal than those tagged with 2-aminopyridine. Plots of logarithmic electrophoretic mobilities of labelled N-acetylchitooligosaccharides with 6-aminoquinoline or 2-aminopyridine versus the number of sugar residues in the homologous series yielded straight lines in the size range studied, the slopes of which were independent of the tagging functions. The slopes of these lines are referred to as the N-acetylglucosaminyl group mobility decrement. The oligosaccharides were better resolved in the presence of tetrabutylammonium bromide in the running electrolyte. Furthermore, the electrophoretic mobilities of branched oligosaccharides were indexed with respect to linear homooligosaccharides, an approach that may prove valuable in correlating and predicting the mobilities of complex oligosaccharides.     

Structural and photophysical properties of adducts of [Ru(bipy)(CN)4]2- with different metal cations: metallochromism and its use in switching photoinduced energy transfer

We show in this paper how the 3MLCT luminescence of [Ru(bipy)(CN)4]2-, which is known to be highly solvent-dependent, may be varied over a much wider range than can be achieved by solvent effects, by interaction of the externally directed cyanide ligands with additional metal cations both in the solid state and in solution. A series of crystallographic studies of [Ru(bipy)(CN)4]2- salts with different metal cations Mn+ (Li+, Na+, K+, mixed Li+/K+, Cs+, and Ba2+) shows how the cyanide/Mn+ interaction varies from the conventional "end-on" with the more Lewis-acidic cations (Li+, Ba2+) to the more unusual "side-on" interaction with the softer metal cations (K+, Cs+). The solid-state luminescence intensity and lifetime of these salts is highly dependent on the nature of the cation, with Cs+ affording the weakest luminescence and Ba2+ the strongest. A series of titrations of the more soluble derivative [Ru(tBu2bipy)(CN)4]2- in MeCN with a range of metal salts showed how the cyanide/Mn+ association results in a substantial blue-shift of the 1MLCT absorptions, and 3MLCT energies, intensities, and lifetimes, with the complex varying from essentially non-luminescent in the absence of metal cation to showing strong (phi = 0.07), long-lived (1.4 micros), and high-energy (583 nm) luminescence in the presence of Ba2+. This modulation of the 3MLCT energy, over a range of about 6000 cm-1 depending on the added cation, could be used to reverse the direction of photoinduced energy transfer in a dyad containing covalently linked [Ru(bipy)3]2+ and [Ru(bipy)(CN)4]2- termini. In the absence of a metal cation, the [Ru(bipy)(CN)4]2- terminus has the lower 3MLCT energy and thereby quenches the [Ru(bipy)3]2+-based luminescence; in the presence of Ba2+ ions, the 3MLCT energy of the [Ru(bipy)(CN)4]2- terminus is raised above that of the [Ru(bipy)3]2+ terminus, resulting in energy transfer to and sensitized emission from the latter.     

Probing the solvent dependent photophysics of fac-[Re(CO)3(dppz-X2)Cl] (dppz-X2 = 11,12-X2-dipyrido[3,2-a:2',3'-c]phenazine); X = CH3, H, F, Cl, CF3)

The results of electrochemical measurements, density-functional theory calculations, emission and time-resolved IR (TRIR) spectroscopic studies for fac-[ReCl(CO)3(dppz-X2)], (dppz = dipyrido[3,2-a:2',3'-c]phenazine; X = CH3, H, F, Cl, CF3) are reported. For all complexes the calculations show that the lowest unoccupied molecular orbital (LUMO) is a phenazine based orbital localized on the dppz ligand. We observe that three different excited states, IL pi pi*, metal-to-ligand charge-transfer (MLCT) (phen), and MLCT (phz), are formed depending upon the substituent on the dppz ligand and on the nature of the solvent. This means that both the energy and the nature of the photophysically active state(s) can be tuned by both chemical modification of dppz ligand and solvent properties. The excited-state dynamics in these systems is directly related to the mechanism of the "light switch effect", and ps-TRIR has allowed a deeper insight into this mechanism by being able to directly monitor the change in the population of the higher lying emissive phen-type (3)MLCT and IL pi pi* states and the dark (3)MLCT (phz) state depending on the different environmental factors.     

Une caractérisation de l'algèbre de Fourier pour certains groupes localement compacts

Let G be a separable locally compact group with type-I left regular representation, $\stackrel{?}{G}$ its dual and $A(G)$ its Fourier algebra. We prove an analogue of Parseval's theorem and that the mapping

$T?u(x):=\underset{\stackrel{?}{G}}{\int }Tr[T(\pi )\pi {(x)}^{?1}]{\mathrm{d}}_{\mu }(\pi )$

is an isometric isomorphism of Banach spaces from $L^1(\stackrel{?}{G})$ onto $A(G)$.     

Numerical investigations of cooling holes system role in the protection of the walls of a gas turbine combustion chamber

Numerical simulations in a gas turbine Swirl stabilized combustor were conducted to investigate the effectiveness of a cooling system in the protection of combustor walls. The studied combustion chamber has a high degree of geometrical complexity related to the injection system as well as the cooling system based on a big distribution of small holes (about 3,390 holes) bored on the flame tube walls. Two cases were considered respectively the flame tube without and with its cooling system. The calculations were carried out using the industrial CFD code FLUENT 6.2. The various simulations made it possible to highlight the role of cooling holes in the protection of the flame tube walls against the high temperatures of the combustion products. In fact, the comparison between the results of the two studied cases demonstrated that the walls temperature can be reduced by about 800°C by the mean of cooling holes technique.     

CFD investigation on mixing in a rapidly mixed tubular flame burner

Computational fluid dynamics is used to simulate a mixing process in a rapidly mixed tubular flame burner (RTFB). The effect of several parameters such as the swirl number (S), the velocity ratio (α) and the injector arrangements (N₁ and N₂) is investigated. The mixing process is identified for a variation of the swirl number (from 0.23 to 5.44) via the Lagrangian discrete phase model. The validation of the numerical results is performed by confronting the predicted particle trajectory, the tangential velocity and the mixing layer thickness results to the experimental data. By means of the validated model, a mathematical correlation between the mixing coefficient and the different geometric parameters characterizing the RTFB is established, enabling the prediction of the mixing time for any RTFB design.     

Strengthening Anti-Glioblastoma Effect by Multi-Branched Dendrimers Design of a Scorpion Venom Tetrapeptide

Glioblastoma is the most aggressive and invasive form of central nervous system tumors due to the complexity of the intracellular mechanisms and molecular alterations involved in its progression. Unfortunately, current therapies are unable to stop its neoplastic development. In this context, we previously identified and characterized AaTs-1, a tetrapeptide (IWKS) from Androctonus autralis scorpion venom, which displayed an anti-proliferative effect against U87 cells with an IC₅₀ value of 0.57 mM. This peptide affects the MAPK pathway, enhancing the expression of p53 and altering the cytosolic calcium concentration balance, likely via FPRL-1 receptor modulation. In this work, we designed and synthesized new dendrimers multi-branched molecules based on the sequence of AaTs-1 and showed that the di-branched (AaTs-1-2B), tetra-branched (AaTs-1-4B) and octo-branched (AaTs-1-8B) dendrimers displayed 10- to 25-fold higher effects on the proliferation of U87 cells than AaTs-1. We also found that the effects of the newly designed molecules are mediated by the enhancement of the ERK1/2 and AKT phosphorylated forms and by the increase in p53 expression. Unlike AaTs-1, AaTs-1-8B and especially AaTs-1-4B affected the migration of the U87 cells. Thus, the multi-branched peptide synthesis strategy allowed us to make molecules more active than the linear peptide against the proliferation of U87 glioblastoma cells.     

Synthesis,characterization, antifungal and antibacterial activities evaluation of copper (II), zinc (II) and cadmium (II) chloride and bromide complexes with new (E)-1-(3,4-dimethoxybenzylidene)-4-methylthiosemicarbazone ligand

The reactions of Cu (II), Zn (II) and Cd (II) chloride or bromide with (E)-1-(3,4-dimethoxybenzylidene)-4-methylthiosemicarbazone (MTSVT) lead to the formation of new complexes. They were characterized by spectroscopic studies: IR, ¹H and ¹³C NMR. The crystal structures of the compounds [MTSVT] ( L ), [ZnBr₂(MTSVT)₂] ( 2 ), [CdCl₂(MTSVT)₂] ( 3 ) and [CdBr₂(MTSVT)₂^.H₂O] ( 4 ) were determined by X-ray diffraction. For complexes 2 – 4 , the ion is coordinated through the sulfur atom. All compounds were tested for their antifungal activity against human pathogenic fungi Candida albicans and Aspergillus fumigatus, and for their antibacterial activity against Gram (+) Bacillus subtilis and Enterococcus faecalis as well as against Gram (−) bacteria such as Paracoccus yeei and Acinetobacter baumanii. The results indicated that the metal complexes exhibited a marked enhancement in antibacterial activity compared with the parent Schiff base.     

Synthesis and Characterization of Bis-1,2,3-Triazole Ligand and its Corresponding Copper Complex for the Development of Electrochemical Affinity Biosensors

The bis-triazole ligand and its corresponding copper complexes were synthesized and characterized for the first time and proposed as new labels for the development of electrochemical aptasensors. The bis-triazole ligand was prepared from methyl 1,6-heptadiyne-4-carboxylate and 2-(azidomethyl)phenol using classical CuAAC in presence of different copper salts. The X-ray structure of bis-triazole showed a symmetry center (C1). UV-Vis and X-band EPR spectra showed that the coordination capacity of the bis-triazole ligand was improved in the presence of triethylamine due to deprotonation of the triazole and phenolate moieties. After complexation with copper, the obtained complex was successfully attached to an anti-estradiol aptamer through thiol-maleimide coupling, and the resulting labelled aptamer was immobilized on a carbon screen-printed electrode by carbodiimide coupling. The electrochemical response of the resulting sensor was shown to decrease in the presence of estradiol, demonstrating that the developed complexes can be applied for the development of aptasensors.