Quasilinear -equation on bordered Riemann surfaces

We consider the existence of solutions of a nonlinear Riemann-Hilbert problem for a quasilinear -equation on a bordered Riemann surface. The first author was supported in part by a grant ``Analiza in geometrija' P1-0291 from the Ministry of Higher Education, Science and Technology of the Republic of Slovenia. The second author was supported in part by grants from FEDER y Ministerio de Ciencia y Tecnología numbers BFM2001-3894 MTM 2004-05878 and Consejería de Educacion Cultura y Deportes del Gobierno de Canarias, PI 2001/091.     

Protein-cofactor interactions in bacterial reaction centers from Rhodobacter sphaeroides R-26: effect of hydrogen bonding on the electronic and geometric structure of the primary quinone. A density functional theory study

The effect of hydrogen bonding to the primary quinone (Q(A) and Q(*)(-)(A)) in bacterial reaction centers was studied using density functional theory (DFT) calculations. The charge neutral state Q(A) was investigated by optimizing the hydrogen atom positions of model systems extracted from 15 different X-ray structures. From this analysis, mean values of the H-bond lengths and directions were derived. It was found that the N(delta)-H of His M219 forms a shorter H-bond to Q(A) than the N-H of Ala M260. The H-bond of His M219 is linear and more twisted out of the quinone plane. The radical anion Q(*)(-)(A) in the protein environment was investigated by using a mixed quantum mechanics/molecular mechanics (QM/MM) approach. Two geometry optimizations with a different number of flexible atoms were performed. H-bond lengths were obtained and spectroscopic parameters calculated, i.e. the hyperfine and nuclear quadrupole couplings of magnetic nuclei coupled to the radical. Good agreement was found with the results provided by EPR/ENDOR spectroscopy. This implies that the calculated lengths and directions of the H-bonds to Q(*)(-)(A) are reliable values. From a comparison of the neutral and reduced state of Q(A) it was concluded that the H-bond distances are shortened by approximately 0.17 Angstroms (His M219) and approximately 0.13 Angstroms (Ala M260) upon single reduction of the quinone. It is shown that the point-dipole approximation can not be used for an estimation of H-bond lengths from measured hyperfine couplings in a system with out-of-plane H-bonding. In contrast, the evaluation of the nuclear quadrupole couplings of (2)H nuclei substituted in the hydrogen bonds yields H-bond lengths close to the values that were deduced from DFT geometry optimizations. The significance of hydrogen bonding to the quinone cofactors in biological systems is discussed.     

Directional edge enhancement using a liquid-crystal display

We present a method for orientation-selective enhancement of the first derivatives of an image. The proposed method is based on the polarization properties of the twisted-nematic liquid-crystal displays (LCDs). LCDs are manufactured to work between a polarizer-analyzer pair, and for a given incident polarization direction, the image contrast will depend on the analyzer orientation. In particular, two analyzer orientations of interest could be identified for the proposed experiments: one that reproduces the image displayed on the LCD, and the other one (orthogonal to the former) that gives a negative (contrast reversed) replica of the original image. By placing a beamsplitter after the LCD, two images are spatially separated, analyzed by linear polarizers in perpendicular directions, and then slightly displaced. When the original image and its displaced (contrast reverted) replica are imagined together across a plane, one obtains a resultant image with enhanced first derivatives along a specific direction. Unlike the usual Fourier (coherent) image processing, the technique proposed here works with incoherent illumination. Validation experiments are presented.     

A simple osmotic stress test to predict boar sperm cryosurvival

This work was carried out to test whether viability of pig spermatozoa subjected to an osmotic test is correlated to sperm cryosurvival. Spermatozoa were cooled from 22 degrees C to -5 degrees C, aliquots were exposed to a series of hyperosmotic solutions (300-2100 mOsm/kg) for 15 min, immediately spermatozoa were re-warmed to 37 degrees C and isosmolarity was restored. Spermatozoa were cooled from 22 degrees C to -5 degrees C and one aliquot was exposed to the osmotic test while diluted spermatozoa were frozen-thawed. Plasma membrane-intact spermatozoa decreased as osmolarity increased (P < 0.0001), a further decreased (P < 0.0001) was observed when isotonicity was restored. Proportions of plasma membrane-intact and acrosome-intact cells from the osmotic test were no different from those after freeze-thawing: 36% vs. 35%, 80% vs. 80%, respectively. A significant correlation was found between the proportion of acrosome-intact cells after freeze-thawing and that from the osmotic test (r = 0.81, P <0.01). This test provides a useful and economical mean to predict in vitro boar sperm cryosurvival.     

Conceptualizations of slope in Mexican intended curriculum

Slope is a fundamental mathematics concept in middle and high school that transcends to the university level. An understanding of slope is needed at the university level since slope plays an important role in understanding problems involving variation and change. In this study Mexican curricula documents were examined to determine which conceptualizations of slope are addressed in the intended mathematics curriculum. To explain the results, we use conceptualizations of slope identified in previous research. Our findings reveal that, to a certain extent, the conceptualizations proposed in the Mexican intended mathematics curriculum differ slightly in terms of the emphasis and timing of instruction from what others have identified in the U.S., with slope as a geometric ratio receiving less emphasis in the Mexican curriculum. There was also noted discontinuity within the Mexican curriculum in introducing slope in grade 9 and subsequently introducing of linear functions in grade 10 without explicit mention of slope. Suggestions are made for future studies, both to consider the conceptualizations of slope promoted in the Mexican textbooks and the impact they have in classroom instruction and student learning of slope.     

Mean value formulas for Ornstein–Uhlenbeck and Hermite temperatures

Positivity - We obtain explicit mean value formulas for the solutions of the diffusion equations associated with the Ornstein–Uhlenbeck and Hermite operators. From these, we derive various...     

Pattern formation and morphology evolution in Langmuir monolayers

We present a study of how patterns formed by Langmuir monolayer domains of a stable phase, usually solid or liquid condensed, propagate into a metastable one, usually liquid expanded. During this propagation, the interface between the two phases moves as the metastable phase is transformed into the more stable one. The interface becomes unstable and forms patterns as a result of the competition between a chemical potential gradient that destabilizes the interface on one hand and line tension that stabilizes the interface on the other. During domain growth, we found a morphology transition from tip splitting to side branching; doublons were also found. These morphological features were observed with Brewster angle microscopy in three different monolayers at the water/air interface: dioctadecylamine, ethyl palmitate, and ethyl stearate. In addition, we observed the onset of the instability in round domains when an abrupt lateral pressure jump is made on the monolayer. Frequency histograms of unstable wavelengths are consistent with the linear-instability dispersion relation of classical free-boundary models. For the case of dendritic morphologies, we measured the radius of the dendrite tip as a function of the dendrite length as well as the spacing of the side branches along a dendrite. Finally, a possible explanation of why Langmuir monolayers present this kind of nonequilibrium growth patterns is presented. In the steady state, the growth behavior is determined by Laplace's equation in the particle density with specific boundary conditions. These equations are equivalent to those used in the theory of morphology diagrams for two-dimensional diffusional growth, where morphological transitions of the kind observed here have been predicted.     

Thermodynamic study of complexation of Zn(II)/L (L− = acetate,indomethacin and diclofenac anions) by isothermal titration calorimetry

Journal of Thermal Analysis and Calorimetry - In this work, a thermodynamic study of the Zn(II)/L systems (L??=?acetate, AcO? or indomethacin anion, Indo? or...