Lump solitons in a higher-order nonlinear equation in 2+1 dimensions

We propose and examine an integrable system of nonlinear equations that generalizes the nonlinear Schrodinger equation to 2 + 1 dimensions. This integrable system of equations is a promising starting point to elaborate more accurate models in nonlinear optics and molecular systems within the continuum limit. The Lax pair for the system is derived after applying the singular manifold method. We also present an iterative procedure to construct the solutions from a seed solution. Solutions with one-, two-, and three-lump solitons are thoroughly discussed.

Dual self-image technique for beam collimation

We propose an accurate technique for obtaining highly collimated beams, which also allows testing the collimation degree of a beam. It is based on comparing the period of two different self-images produced by a single diffraction grating. In this way, variations in the period of the diffraction grating do not affect to the measuring procedure. Self-images are acquired by two CMOS cameras and their periods are determined by fitting the variogram function of the self-images to a cosine function with polynomial envelopes. This way, loss of accuracy caused by imperfections of the measured self-images is avoided. As usual, collimation is obtained by displacing the collimation element with respect to the source along the optical axis. When the period of both self-images coincides, collimation is achieved. With this method neither a strict control of the period of the diffraction grating nor a transverse displacement, required in other techniques, are necessary. As an example, a LED considering paraxial approximation and point source illumination is collimated resulting a resolution in the divergence of the beam of σ φ = ± μrad.

Unfolding Operator Method for Thin Domains with a Locally Periodic Highly Oscillatory Boundary

We analyze the behavior of solutions of the Poisson equation with homogeneous Neumann boundary conditions in a two-dimensional thin domain which presents locally periodic oscillations at the boundary. The oscillations are such that both the amplitude and period of the oscillations may vary in space. We obtain the homogenized limit problem and a corrector result by extending the unfolding operator method to the case of locally periodic media.

Do 5-Year-Old Children Perform Dual-Task Coordination Better Than AD Patients?

A cross-sectional study was carried out to examine the pattern of changes in the capacity to coordinate attention between two simultaneously performed tasks in a group of 570 volunteers, from 5 to 17 years old. Method: The results revealed that the ability to coordinate attention increases with age, reaching adult values by age 15 years. Also, these results were compared with the performance in the same dual task of healthy elderly and Alzheimer disease (AD) patients found in a previous study. Results: The analysis indicated that AD patients showed a lower dual-tasking capacity than 5-year-old children, whereas the elderly presented a significantly higher ability than 5-year-old children and no significant differences with respect to young adults. Conclusion: These findings may suggest the presence of a working memory system’s mechanism that enables the division of attention, which is strengthened by the maturation of prefrontal cortex, and impaired in AD. (J. of Att. Dis. 2016; 20(2) 87-95)

Dual Roles of Diadenosine Polyphosphates in Corneal Epithelial Cell Migration

Purpose. To investigate the influence of diadenosine polyphosphates on the rate of corneal epithelial cell migration. Methods. Primary corneal epithelial cell cultures were obtained from New Zealand White rabbits. Immunocytochemical experiments were performed by fixing the cells with 4% paraformaldehyde (PFA) and incubated with cytokeratin 3 primary antibody, which was subsequently incubated with a secondary IgG mouse labeled with FITC, and the cells were observed under confocal microscopy. Migration studies were performed by taking confluent monolayers that were wounded with a pipette tip and challenged with different di- and mononucleotides with or without P2 antagonist (n = 8 each treatment). For concentration–response analysis, compounds were tested in doses ranging from 10−8 to 10−3 M (n = 8). The stability of the dinucleotides was assayed by HPLC, with an isocratic method (n = 4). Results. Cells under study were verified as corneal epithelial cells via the immunocytochemical analysis. Cell migration experiments showed that Ap4A, UTP, and ATP accelerated the rate of healing (5, 2.75, and 3 hours, respectively; P < 0.05; P < 0.001), whereas Ap3A, Ap5A, and UDP delayed it (6.5, 10, and 2 hours, respectively; P < 0.05). ADP did not modify the rate of migration. Antagonists demonstrated that Ap4A and Ap3A did activate different P2Y receptors mediating corneal wound-healing acceleration and delay. Concerning the possible degradation of the dinucleotides, it was almost impossible to detect any products resulting from their cleavage. Conclusions. Based on the pharmacological profile of all the compounds tested, the two main P2Y receptors that exist in these corneal cells are a P2Y2 receptor accelerating the rate of healing and a P2Y6 receptor that delays this process.