On the Kadomtsev-Petviashvili Equation and Associated Constraints

The initial-boundary-value problem for the Kadomtsev-Petviashvili equation in infinite space is considered. When formulated as an evolution equation, found that a symmetric integral is the appropriate choice in the nonlocal term; namely, . If one simply chooses , then an infinite number of constraints on the initial data in physical space are required, the first being . The conserved quantities are calculated, and it is shown that they must be suitably regularized from those that have been used when the constraints are imposed.     

Unified and generalized Fresnel numbers

The concept of Fresnel number is discussed and expressions are derived for misaligned optical systems. For the case of perfectly aligned optical elements, the usual number,N, based on a Fresnel zone concept is found to be given byN = (a ²/)(D ₁/B ₁ +A ₂/B ₂), whereB ₁,D ₁ andB ₂,A ₂ are the transfer matrix elements of the optical systems before and after a circular aperture of radiusa respectively. A modified definition of the Fresnel number is proposed for Gaussian beam propagation. This parameterN _G, is related to the complex beam parameter and may be represented by the angle = tan^–1 N _G, found in the familiar Collins chart and its dual representation. A general relation for the transformation of this Fresnel number is found. The expressions for Gaussian beam transformation are thus simplified, since the waist-waist transform is given byN _G1 =N _G2 = 0. Finally, these two kinds of Fresnel numbers are written as tensors when applied to cases involving elliptical apertures, astigmatic beams and nonsymmetrical systems.     

New oxamidato-bridged Cu(II)-Ni(II) complexes: supramolecular structures with thiocyanate ligands and hydrogen bonds. Magnetostructural studies: DFT calculations

Four new supramolecular compounds of Cu(II)-Ni(II) have been synthesized and characterized: [Cu(Me(2)oxpn)Ni(mu-NCS)(H(2)O)(tmen)](2)(ClO(4))(2) (1), [Cu(Me(2)oxpn)Ni(mu-NCS)(H(2)O)(tmen)](2)(PF(6))(2) (2), [Cu(oxpn)Ni(mu-NCS)(NCS) (tmen)](n) (3), and [Cu(Me(2)oxpn)Ni(mu-NCS)(NCS)(tmen)](n) (4), where oxpn = N,N'-bis(3-aminopropyl)oxamidate, Me(2)oxpn = N,N'-bis(3-amino-2,2'-dimethylpropyl)oxamidate, and tmen = N,N,N',N'-tetramethylethylenediamine. Their crystal structures were solved. Complexes 1 and 2 have the same tetranuclear cationic part but a different counteranion. The cationic part consists of two [Cu(Me(2)oxpn)Ni] moieties linked by SCN(-) bridged ligands and intra-tetranuclear hydrogen bonds. In the case of complex 3, a two-dimensional system was built, the thiocyanate ligand linking the dinuclear units gives a chain, and the chains are linked together by hydrogen bonds; intrachain hydrogen bonds are also present. For complex 4, the thiocyanate ligands produce intermolecular linkages between the dinuclear entities, giving a one-dimensional system; intrachain hydrogen bonds are also present. The magnetic properties of the four complexes were studied by susceptibility measurements vs temperature. DFT calculations were made to study the contribution of the SCN(-) and hydrogen bond bridges in the magnetic coupling.     

Pressurized liquid extracts from Spirulina platensis microalga. Determination of their antioxidant activity and preliminary analysis by micellar electrokinetic chromatography

In this work, different extracts from the microalga Spirulina platensis are obtained using pressurized liquid extraction (PLE) and four different solvents (hexane, light petroleum, ethanol and water). Different extraction temperatures (115 and 170 degrees C) were tested using extraction times ranging from 9 to 15 min. The antioxidant activity of the different extracts is determined by means of an in vitro assay using a free radical method. Moreover, a new and fast method is developed using micellar electrokinetic chromatography with diode array detection (MEKC-DAD) to provide a preliminary analysis on the composition of the extracts. This combined application (i.e., in vitro assays plus MEKC-DAD) allowed the fast characterization of the extracts based on their antioxidant activity and the UV-vis spectra of the different compounds found in the extracts. To our knowledge, this work shows for the first time the great possibilities of the combined use of PLE-in vitro assay-MEKC-DAD to investigate natural sources of antioxidants.     

Two problematic human polymorphic Alu insertions

Analysis of two previously described polymorphic Alu insertions (Sb19.3 and NBC3) in world-wide human populations generated genotypic frequencies grossly in violation of Hardy-Weinberg equilibrium expectations. GenBank searches at the National Center for Biotechnology Information (NCBI) and sequencing analyses revealed that samples homozygous for the Sb19.3 Alu insertion amplify a band indistinguishable in size to the lack of insertion amplicon, corresponding to a paralogous locus on chromosome 4. This locus displays a very similar sequence (84%) to that flanking the Sb19.3 Alu insertion located at chromosome 19. Moreover, we have determined that NBC3, a different Alu insertion, is not located in the pseudoautosomal region of the Y-chromosome, as previously reported, but in position Yq11.2. Also, the band that mimics the lack of insertion amplicon corresponds to a paralogous locus located at chromosome X with a similarity of 92% to the sequence flanking the NBC3 Alu insertion. Finally, the utilization of newly designed primers avoided amplification from the paralogous loci and allowed a reliable assignation of genotypes for both loci. Unlike previously reported, using our new primers the Y-specific locus NBC3 was found not to be polymorphic in the populations analyzed.     

Fluorometric sensors based on chemically modified enzymes Glucose determination in drinks

In this paper an enzymatic fluorometric sensor for glucose determination in drinks is presented. The sensor film was obtained by immobilisation of glucose oxidase chemically modified with a fluorescein derivative (GOx-FS) in a polyacrylamide polymer. During the enzymatic reaction the changes in the fluorescence intensity of the GOx-FS are related to the glucose concentration. Working in FIA mode, the optimum conditions found were: 0.7 ml min(-1) flow rate, 300 mul sample injection and pH 6.5. The sensor responds to glucose concentrations ranging from 400 to 2000 mg l(-1), the reproducibility is around 3% and the life-time is at least 3 months (more than 350 measurements). The sensor was applied to direct glucose determination in drinks with good accuracy; interference caused by the filter effect was avoided by the kinetics of the reaction.     

Interaction and adhesion properties of polyelectrolyte multilayers

The growth, morphology, and interaction/adhesion properties of supported poly(sodium 4-styrenesulfonate)/poly(allylamine hydrochloride) (PSS/PAH) and DNA/PAH multilayers were investigated by means of surface plasmon resonance spectroscopy, atomic force microscope (AFM) imaging, and AFM-related force measurements. Multilayers were assembled on a prelayer of poly(ethylenimine) (PEI) both with and without drying. SPR results showed a linear growth of the assembly in the case of PSS/PAH multilayers and nonlinear growth for DNA/PAH multilayers. Measurements of forces acting between a bare glass sphere and a multilayer-coated surface indicated repulsive or attractive forces, depending on surface charge, which suggests that, on approach, electrostatic forces dominate. On separation, we observed large pull-off forces in the case of positively charged multilayers and weak pull-off forces in the case negatively charged multilayers. Multiple adhesions and plateau regions observed on separation were interpreted in terms of a bridging of multiple polymer chains between the glass particle and the multilayer and a stretching of the polyelectrolyte loops. The dependence of the pull-off force on the number of deposited layers shows regular oscillations.